advances.in.microstrip & printed antennas-wiley1997.lee

Advances in Microstrip and Printed Antennas

I Edited by

I KAI FONG LEE WE1 CHEN

A WILEY-INTERSCIENCE PUBLICATION

JOHN WlLEY & SONS, INC. NEWYORK/CHICHESTER/WEINHEIM/BRISBANE/SINGAPORE/TORONTO

This text is printed on acid-free paper.

Copyright 0 1997 by John Wiley & Sons, Inc.

All rights reserved. Published simultaneously in Canada.

Reproduction or translation of any part of this work beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012.

Library of Congress Cataloging-in-Publication Data

Advances in microstrip and printed antennas / edited by Kai Fong Lee and Wei Chen.

p. an. - - (Wiley series in microwave and optical engineering) "A Wiley-Interscience publication." Includes bibliographical references (p. ). ISBN 0-471-04421-0 (alk. paper) 1. Microstrip antennas. 2. Printed circuits. I. Lee, Kai Fong.

11. Chen, Wei, 1959- . 111. Series. TK7871.6.A394 1997 621.381'331 -- dc20 96-39032

Printed in the United States of America

1 0 9 8 7 6 5 4 3

Contents

Contributors

Preface

1 Probe-Fed Microstrip Antennas K. F. Lee, W Chen, and R. Q. Lee

1.1 Introduction 1.2 Full-Wave Analysis of Multilayer Multipatch Microstrip

Antennas 1.2.1 Introductory Remarks 1.2.2 Conventions and Definitions 1.2.3 Basic Formulations 1.2.4 Green's Functions

1.3 Spectral Domain Full-Wave Analysis of Probe-Fed Rectangular Microstrip Antennas 1.3.1 Formulation 1.3.2 Basis Functions 1.3.3 Multiple Feeds and Shorting Pins 1.3.4 Attachment Modes

1.4 Representative Numerical and Experimental Results 1.4.1 Single Patch 1.4.2 Single Patch in Multidielectric Media 1.4.3 Coplanar Parasitic Subarray 1.4.4 Two-Layer Stacked Patches

1.5 Rectangular Patch with a U-Shaped Slot 1.6 Concluding Remarks References

xiii

xvii

vi CONTENTS CONTENTS

2 Aperture-Coupled Multilayer Microstrip Antennas K . M . Luk, T M . Au, K . F . Tong, and K . F. Lee

2.1 Introduction 2.2 Green's Function Formulation

2.2.1 Field Components 2.2.2 Boundary Conditions

2.3 Galerkin's Method 2.4 Illustrative Results

2.4.1 Microstrip Antenna with an Air Gap 2.4.2 Coplanar Microstrip Subarrays 2.4.3 Offset Dual-Patch Microstrip Antennas 2.4.4 Two-Layer Microstrip Antennas with Stacked

Parasitic Patches 2.5 Infinite Arrays of Aperture-Coupled Multilayer Microstrip

Antennas 2.5.1 Skewed Periodic Structure and Floquet Modes 2.5.2 Infinite Array of Microstrip Antennas with Air Gaps 2.5.3 Infinite Array of Dual-Patch Microstrip Antennas

2.6 Conclusions Appendix: Fourier Transforms of Expansion and Test Functions Acknowledgments References

3 Microstrip Arrays: Analysis, Design, and Applications John Huang and David M. Pozar

3.1 Introduction 3.2 Analysis Techniques for Microstrip Arrays

3.2.1 Review of Microstrip Antenna Analysis Techniques 3.2.2 Full-Wave Moment Method Analysis 3.2.3 Calculation of Mutual Coupling 3.2.4 Infinite Array Analysis 3.2.5 The Active Element Pattern 3.2.6 Waveguide Simulators

3.3 Design Methodology 3.3.1 Array Configuration Design 3.3.2 Patch Element Design 3.3.3 Power Division Transmission Line Design 3.3.4 Microstrip Reflectarray Design

3.4 Applications 3.4.1 Military Applications 3.4.2 Space Applications 3.4.3 Commercial Applications

3.5 Summary and Conclusion References

4 Dual and Circularly Polarized Microstrip Antennas P. S. Hall and J . S. Dahele

4.1 Introduction 4.2 Polarization in Antenna Systems 4.3 Generation of Orthogonal Polarizations 4.4 Circularly Polarized Patches

4.4.1 Orthogonal Patches 4.4.2 Multipoint Feeds 4.4.3 Single-Point Feeds .

4.5 Dual Polarized Patches 4.5.1 Triangular Patch with Right- and Left-Hand

Circular Polarization 4.6 Microstrip Spirals

4.6.1 Operation of the Spiral Antenna 4.7 Special Substrates and Active Antennas 4.8 Dual and Circularly Polarized Arrays

4.8.1 Patch Arrays 4.8.2 Microstrip Line Arrays 4.8.3 Sequentially Rotated Arrays

4.9 Conclusions References

5 Computer-Aided Design of Rectangular Microstrip Antennas David R. Jackson, Stuart A. Long, Jeffery T . Williams, and Vickie B. Davis

5.1 Introduction 5.2 CAD Model for Rectangular Patch Antenna 5.3 CAD Formulas for Resonance Frequency 5.4 CAD Formulas for the Q Factors

5.4.1 Dielectric and Conductor Q Factors 5.4.2 Relation Between Surface-Wave and Space-Wave

Q Factors 5.4.3 Space-Wave Quality Factor

5.5 CAD Formula for Bandwidth 5.5.1 CAD Formula 5.5.2 Results

5.6 CAD Formula for Radiation Efficiency

vii

159 159

163

163 164 165 167 169 170 177 183

184 184 185 186 188 188 188 190 217 217

223

223 224 231 234 234

235 237 242 243 243 246

viii CONTENTS CONTENTS ix

5.6.1 CAD Formula 5.6.2 Results

5.7 CAD Formula for Input Resistance 5.8 CAD Formula for Probe Reactance 5.9 Results for Input Impedance 5.10 Radiation Patterns

5.10.1 Infinite Substrate 5.10.2 Truncated Substrate

5.1 1 CAD Formula for Directivity 5.12 Conclusions Appendix A: Derivation of the p Factor Appendix B: Radiation Formulas for HED and HMD References

6 Multifunction Printed Antennas J. R. James and G. Andrasic

6.1 Introduction 6.2 Printed Antenna Design Freedom 6.3 Multifunction Antenna Design Opportunities and

Recent Advances 6.3.1 Choice of Substrate Materials and Their Design

Potential 6.3.2 Innovative Use of Superstrates 6.3.3 Printed Conductor Topology 6.3.4 Quest for Feeder Simplicity 6.3.5 Conformality 6.3.6 Integration of Antennas and Circuits

6.4 Possible Future Developments 6.4.1 Impact of New Materials 6.4.2 The Application Drivers

6.5 Conclusions References

7 Superconducting Microstrip Antennas Jeffery T. Williams, Jarrett D. Morrow, David R. Jackson, and Stuart A. Long

7.1 Introduction 7.2 Basics of Superconductivity

7.2.1 General Properties of Superconductors 7.2.2 High-Temperature Superconductors 7.2.3 Characteristics of High-Temperature Superconductors

7.3 HTS Microstrip Transmission Lines and Antennas 7.3.1 Superconducting Transmission Lines and

Feed Networks 7.3.2 Superconducting Microstrip Patch Antennas

7.4 Design Considerations 7.5 Experimental Results 7.6 Summary Appendix References

8 Active Microstrip Antennas Julio A. Navarro and Kai Chang

Introduction The Early History of Integrated Antennas Diode-Integrated Active Microwave Antennas Transistor-Integrated Active Microstrip Antennas Diode Arrays for Spatial Power Combining Transistor Arrays for Spatial Power Combining System Applications Conclusions and Future Trends

Acknowledgments References

9 Tapered Slot Antenna Richard Q. Lee and Rainee N . Simons

Introduction Basic Geometries Design Considerations Fundamentals Analytical Methods 9.5.1 Analysis of Uniform Slotline by the Spectral

Domain Approach 9.5.2 Far-Field Computation Feeding Techniques Characteristics of TSA 9.7.1 Radiation Characteristics 9.7.2 Impedance Characteristics 9.7.3 Bandwidth Characteristics 9.7.4 Field Distributions Tapered Slot Antenna Arrays Active Tapered Slot Antenna Array

x CONTENTS CONTENTS x i

9.10 Conclusion References

10 Efficient Modeling of Microstrip Antennas Using the Finite-Difference Time-Domain Method Siva Chebolu, Supriyo Dey, Raj Mittra, and John Svigelj

10.1 Introduction 10.2 A Comparison of Various CAD Approaches 10.3 The Basic FDTD Algorithm 10.4 Efficient FDTD Modeling of Microstrip Antennas

10.4.1 Spatial Discretization 10.4.2 Source Excitation 10.4.3 Phased Array Excitation 10.4.4 Extrapolation Techniques 10.4.5 Impedance 10.4.6 Absorbing ~oundaries' 10.4.7 Radiation Pattern 10.4.8 Distributed Computing 10.4.9 Dielectric Loss Tangent

10.5 Single Patch Modeling 10.5.1 Impedance of a Patch Antenna Mounted on a

Moderately Thick Substrate 10.5.2 Impedance of a Patch Antenna Mounted on a

Thick Substrate 10.5.3 Effect of a Finite Ground Plane on Impedance and

Radiation Pattern 10.6 Analysis of a Two-Layer Stacked Patch Antenna 10.7 Design of a Compact Broadband Antenna 10.8 Conclusions References

1 1 Analysis of Dielectric Resonator Antennas K . M. Luk, K . W hung, and S. M . Shum

11.1 Introduction 11.2 Analysis of Aperture-Coupled Hemispherical DR Antenna

11.2.1 Problem Formulation 11.2.2 Moment Method Solution 11.2.3 Derivation of DR Antenna Green's Function GZy 11.2.4 Evaluation of Yi,, 11.2.5 Single-Cavity-Mode Approximation 11.2.6 Single-Cavity-Mode Radiation Field of the DR

Antenna

11.2.7 Results and Discussions 11.2.8 Summary

11.3 FDTD Analysis of Probe-Fed Cylindrical DR Antenna 11.3.1 The FDTD Method 11.3.2 Antenna Feed Modeling 11.3.3 Absorbing Boundary Condition 11.3.4 Input Impedance Calculation 11.3.5 Far-Field Calculations 11.3.6 Results and Discussions 11.3.7 Summary

References

Index

Contributors

C. Andrasic j. S. Dahele School of Engineering and Applied School of Engineering and Applied

Science Science Royal Military College of Science Royal Military College of Science Cranfield University Shrivenham Shrivenham, Wilts SN6 8LA Wilts SN6 8LA England England

T. M. Au Vickie B. Davis Center of Wireless Communications D~~~~~~~~~ of ~ l ~ ~ ~ ~ i ~ ~ l and National University of Singapore Computer Engineering Singapore University of Houston

Houston, TX 77204 Kai Chang U.S.A. Department of Electrical Engineering Texas A&M University College Station, TX 77843 U.S.A.

Supriyo Dey Electromagnetic Communication

- - - -

Laboratory

Siva Chebolu University of Illinois, Urbana-

Celwave Champaign

Division of Radio Frequency Urbana, IL 61801

Systems, Inc. U.S.A. Phoenix, AZ 85034 U.S.A. P. S. Hall

School of Electronic and Electrical W. Chen Engineering Cooper Energy Services University of Birmingham Mount Verson, OH 43050 Edgbaston, Birmingham B15 2TT U.S.A. England

xiii

xiv CONTRIBUTORS CONTRIBUTORS XV

John Huang Jet Propulsion Laboratory California Institute of Technology Pasadena, CA 9 1109 U.S.A.

David R. Jackson Department of Electrical and

Computer Engineering University of Houston Houston, TX 77204 U.S.A.

J. R. James School of Engineering and Applied

Science Royal Military College of Science Cranfield University Shrivenham, Wilts SN6 8LA England

K. F. Lee Department of Electrical Engineering University of Missouri-Columbia Columbia, MO 6521 1 U.S.A.

Richard Q. Lee NASA Lewis Research Center 21000 Brookpark Road Cleveland, OH 44135 U.S.A.

K. W. Leung Department of Electronic Engineering City University of Hong Kong Kowloon Hong Kong

Stuart A. Long Department of Electrical and

Computer Engineering University of Houston Houston, TX 77204 USA.

K. M. Luk Department of Electronic Engineering City University of Hong Kong Kowloon Hong Kong

Raj Mittra Department of Electrical Engineering Pennsylvania State University University Park, PA 16802-2705 U.S.A.

Jarrett D. Morrow Department of Electrical and

Computer Engineering University of Houston Houston, TX 77204 U.S.A.

Julio A. Navarro Boeing Defense and Space Group Seattle, WA 98124 U.S.A.

David M. Pozar Department of Electrical and I

Computer Engineering University of Massachusetts, Amherst Amherst, MA 01003 I

U.S.A.

S. M. Shum Department of Electronic Engineering City University of Hong Kong Kowloon I

Hong Kong

Rainee N. Simons NASA Lewis Research Center 21000 Brookpark Road Cleveland, OH 441 35 U.S.A.

John Svigelj Texas Instruments, Inc. 2501 University Drive MS 8019 McKinney, TX 75070 U.S.A. I

K. F. Tong Jeffery T. Williams Department of Electronic Engineering Department of Electrical and City University of Hong Kong Computer Engineering

Kowloon University of Houston Hong Kong Houston, TX 77204

USA.

Preface

Since the late 1970s, the international antenna community has devoted much effort to the theoretical and experimental research on microstrip and printed antennas, which offer the advantages of low profile, compatibility with integrated circuit technology, and conformability to a shaped surface. The results of this research have contributed to the success of these antennas not only in military applications such as aircraft, missiles, and rockets but also in commercial areas such as mobile satellite communications, the direct broadcast satellite (DBS) system, global positioning system (GPS), remote sensing, and hyperthermia. While many of the results of the late 1970s and 1980s were summarized in the Handbook of Microstrip Antennas, edited by J. R. James and P. S. Hall in 1989, the research on microstrip and printed antennas has continued unabated in the 1990s. In addition to advances in conventional topics, there have been new research areas. The purpose of this book is to update and to present new information on microstrip and printed antennas since the two-volume handbook was published. The contributors are all active researchers and well known in the field.

Chapters 1-4 deal with recent advances in conventional topics. These include accounts on recent results on probe-fed microstrip antennas and aperture- coupled microstrip antennas; analysis, design, and applications of microstrip arrays including the recently developed configuration known as microstrip reflectarray; and dual and circularly polarized planar antennas. Most of the topics in Chapters 5-11 are relatively new. They were not covered in the 1989 Handbook. These include the development of computer-aided design (CAD) formulas for the rectangular patch; the concept, development, and future possibilities of multifunction printed antennas; microstrip antennas made of high- temperature superconducting materials; active microstrip antennas; and tapered slot minted antennas. C h a ~ t e r 10 discusses the finite-difference time-domain method of analysis which is becoming popular due to its ability to handle complex configurations and to generate the characteristics of the patch over a broad band of frequencies with a single simulation. The book ends with a chapter

xvii

xviii PREFACE

on dielectric resonator antennas. These antennas have potential advantages over microstrip antennas at extremely high frequencies because of reduced copper loss. Although different in physical appearance, dielectric resonator antennas and microstrip antennas have much in common in analysis methods and design concepts. Because of page limitation, it is not possible to include all topics which represent advances in this field in the 1990s. It is hoped, however, that antenna researchers and practicing engineers will find much useful information in the coverage of the topics selected.

CHAPTER ONE

Probe-Fed Microstrip Antennas

K. F. LEE, W. CHEN, and R. Q. LEE

1.1 INTRODUCTION

One of the common methods of feeding a microstrip antenna is by means of a coaxial probe. The basic configuration is shown in Figure 1.1, where a single metallic patch is printed on a grounded substrate. A number of designs have evolved from the basic configuration. Figure 1.2 shows a design in which a fed patch is surrounded by closely spaced parasitic patches, which can have the effect of improving the impedance bandwidth and the gain of the antenna. Such a configuration is referred to as a coplanar parasitic subarray. Figure 1.3 shows cases where the metallic patch is embedded in a multilayered dielectric media. In Figure 1.3a, a superstrate or dielectric cover is used to protect the patch against . environmental hazards. If a naturally occurring dielectric layer such as ice is formed on top of the cover, the three-layer configuration of Figure 1.3b results. Figure 1 . 3 ~ shows a one-superstrate two-substrate geometry, as, for example, when an air gap is introduced between the substrate and the ground plane to alter the resonant frequency of the antenna. Figure 1.4 shows the two-layer stacked geometry consisting of one fed patch and a parasitic patch on another layer. These stacked patches are popular for providing wide bandwidth characteristics. Another wideband microstrip antenna is the rectangular patch with a U-shaped slot (Figure 1.5). In recent years, the various linearly polarized probe-fed microstrip antennas depicted above have been extensively studied. It is the purpose of

Advances in Microstrip and Printed Antennas, Edited by Kai Fong Lee and Wei Chen ISBNO-471-04421-0 0 1997 John Wiley & Sons, Inc.

2 PROBE-FED MICROSTRIP ANTENNAS

l------

, Conducting patch

I 1 1 Ground plane Coax feed

(b)

FIGURE 1.1 Basic configuration of the probe-fed microstrip antenna. (a) Top view, (b) side view.

this chapter to give a coherent account of recent work in this area. The materials to be presented are based mainly on the authors'research. Related work by others will be referenced but not described in detail.

We shall be concerned with rectangular patches only. However, the methods of analysis can be extended to other geometrical shapes; and many qualitative features are not dependent on whether the patches are rectangular or circular, which are the two most commonly used shapes in practice.

In Section 1.2, a general full-wave analysis of multilayer multipatch microstrip antennas is presented. The application of the analysis to probe-fed rectangular microstrip antennas is described in Section 1.3. Representative numerical and experimental results for configurations 1.1-1.4 are given in Section 1.4. Experi- mental results of the U-slot patch are described in Section 1.5. The chapter ends with some concluding remarks.

(a)

Parasitic Fed Parasitic

Coax feed (b)

FIGURE 1.2 Geometry of coplanar parasitic subarray. (a) Top view, (b) side view.

Superstrate Patch Superstrate 1

Substrate Suwrstrate 2 T r Coax feed

(a) Coax feed

(b)

i r Superstrate .T Substrate

Coax feed (c)

FIGURE 1.3 Microstrip antenna in multidielectric media. (a) Patch with superstrate, (b) patch with two superstrates, (c) patch with one superstrate and two substrates.

4 PROBE-FED MICROSTRIP ANTENNAS MULTILAYER MULTIPATCH MICROSTRIP ANTENNAS 5

Superstrate Parasitic patch

Substrate /Fed patch

Substrate

Coax feed

FIGURE 1.4 Geometry of two-layer stacked patches.

Coax feed

I , wtcn

FIGURE 1.5 Rectangular patch with a U-shaped slot. (a) Top view of the patch, (b) side view.

Air or foam

1 1

1.2 FULL-WAVE ANALYSIS OF MULTILAYER MULTIPATCH MICROSTRIP ANTENNAS

\ Ground plane

1.2.1 introductory Remarks

Consider first the basic form of the microstrip antenna shown in Figure 1.1. Although the antenna appears simple and is easy to fabricate, obtaining electromagnetic fields which satisfy all the boundary conditions is a complicated task. For this reason, simplified approaches such as the transmission line model and

the cavity model have been developed. The cavity model is particularly popular and will be commented on briefly.

The basic idea of the cavity model [I, 23 is to treat the region between the patch and the ground plane as a resonant leaky cavity. If the fields in the cavity excited by the probe can be obtained, equivalent sources can then be put in the exit region of the cavity, from which the radiation fields can be calculated. An effective loss tangent is introduced to account for conductor loss, dielectric loss, and radiation loss. The effective loss tangent is used in the calculation of input impedance and impedance bandwidth. The resonant frequencies of the antenna are determined by the resonant frequencies of the cavity.

The basic assumption which renders the calculations of the cavity model simple is that the substrate thickness is assumed to be much smaller than wavelength so that the electric field has only a vertical (z) component which does not vary with z. From this it follows that:

1. The fields in the cavity are TM (transverse magnetic). 2. The cavity is bounded by magnetic walls (H ,,,,,,,,,, = 0) on the sides. 3. Surface wave excitation is negligible. 4. The current in the coaxial probe is independent of z.

The coaxial probe is modeled by a current ribbon of a certain width, which is a free parameter chosen to fit the experimental data.

The cavity model has the advantages of being simple and providing physical insight. Design information for rectangular, circular, annular, and triangular patches can be obtained with relative ease [3].

There are a number of limitations to the cavity model even if the thin substrate condition is satisfied. The magnetic wall boundary condition leads to resonant frequencies which do not agree well with experimental observations, and an ad hoc correction factor has to be introduced to account for the effect of fringing fields. The width of the current ribbon used to model the coaxial probe is another ad hoc parameter. The model cannot handle designs involving parasitic elements, either on the same layer or on another layer. It cannot analyze microstrip antennas with superstrates. When the thickness of the substrate exceeds about 2% of the free space wavelength, the cavity model results begin to become inaccurate, due to the breakdown of (1)-(4). For these reasons, more accurate analyses of the microstrip antenna based on solving Maxwell's equations subject to the boundary conditions are clearly of interest. These are known as full-wave models and they are the topics of many papers that appeared in the recent literature. In this section we present our version of full-wave analysis which can be applied to a variety of multilayer multipatch microstrip antennas.

1.2.2 Conventions and Definitions

(1) ej"' convention: Throughout this chapter, all fields are assumed to have eJw' time dependency.


Using this definition, we now introduce the following notations for the reaction: (2) Fourier transform: The Fourier transform pair is defined as

+ .... ( J , , M,) = - J B(;j;).G2dv (1.11)

where

1.2.3 Basic Formulations

Usually it is more convenient to first find the localized Fourier transform and then convert it to the standard form. We define the localized Fourier transform as

In this section, we shall set up the basic formulation for general layered structures based on the electric field integral equations (EFIE).

1.2.3.1 Simple Region. We define a simple region as a region consisting of layered materials bounded by free space or metallic conducting surface(s) (Figure 1.6). It also contains radiating elements and feeding elements which are assumed to be approximately represented by a set of current expansions; that is, the current on the radiating elements and feeding elements is expanded into a set of basis functions: where Eo is a local reference point. y(xs) is related toy1(<) by

- +

(3) Reaction: The reaction of source 1 (J,, MI) to source 2 (T2, G,) is defined where are the basis functions and Cj are the corresponding coefficients.

A simple region may connect to the outside through aperture coupling. For the aperture coupling case, the electrical field in the aperture(s) is expanded into basis functions,

- where (El, HI) are the @Ids produced by source 1, is the electric current density of source i, and Mi is the magnetic current density of source i.

In this chapter, we will assume all media to be homogeneous and isotropic. For these media, the Reciprocity Theorem holds, which states that

Thus, the magnetic current excitation over the aperture@) is expressed by


,Conducting plane

MULTILAYER MULTIPATCH MICROSTRIP ANTENNAS 9

.Conducting plane

.Conducting plane

FIGURE 1.6 Examples of simple regions. Conducting patches embedded in multilayer dielectric media bounded by (a) two conducting planes, (b) one conducting plane. In (c), there are no conducting boundaries other than the patches.

where Ga = Ea x i and li?, = Ek x 6. 6 in the inward normal. Note that this expansion represents the magnetic current over all the aperture(s).

If we assume all.the metal sheets to be perfect conducts, the electric integral equation is established by forcing the total tangential electric field to vanish on all the metallic surfaces inside the region:

This is basically an integral equation. We will convert it to a set of linear equations using the Method of Moments. Using the current expansions, we have

Testing the above equation using z, we obtain

This is one of the most important equations in our formulation. We call it fundamental equation one.

If the metal sheets are not perfect conducts, we have to apply the impedance boundary condition

where Z, is the surface impedance @/square meter). Equations (1.19)-(1.21) become

Equation (1.26) is the generalization of fundamental equation one to nonperfect conductors.

To define the problem completely, we also need the condition of continuity of tangential magnetic fields across the aperture. The total tangential magnetic field in the inner side of the aperture(s) is


Testing it using Gm, we get

We call this equation fundamental equation two. Note that to apply the fundamental equation two, we also need to know the total tangential magnetic field on the other side of the aperture which usually is done by applying the same equation to the region on the other side of the aperture.

The two fundamental equations can also be written in matrix form. Define:

and

The fundamental equation one becomes

and the fundamental equation two is

Combining the two equations, we have

1.2.3.2 Complex Region. A complex region is a region consisting of two or more simple regions coupled through apertures (Figure 1.7). Let us label the simple regions sequentially from top down starting with region 0. Region k is on the top of region k + 1 with a common boundary which we label as interface k. The electric field in the apertures on interface k can be expanded as

Conducting planes

FIGURE 1.7 Examples of complex regions.

On the side of region k, ii = 2, and the magnetic current over the apertures is

where GL1 = E, x h and Gj: = zk x 2.2 is the inward normal. On the side of region k + 1, h = - i, and the magnetic current over the

apertures is

where Go = Eo x h and @ = Ei x 2. ii is the inward normal.

12 PROBE-FED MICROSTRIP ANTENNAS MULTlLAYER MULTIPATCH MICROSTRIP ANTENNAS 13

1.2.3.4 Far Fields. For an open structure, once the currents are known, the far fields can be computed using the Green's functions, which are discussed in detail in Section 1.2.4. If the Fourier transforms of the currents are readily available, the far-field computation is very simple. Assume that region 0 is free space andthat the region interface 0 is at z = 0. Choose z = 0 as a reference point. A far field A (F) is related to its Fourier transform by

Now, we can still write fundamental equations for each simple region: For region k,

where

k,,, = k , sin 0 cos cp

k,,, = k , sin 0 sin cp

k,,, = ko ICOS el

For region k + 1,

Using Eqs. (1.81) and (1.83) of the next section, the above equation can be written as

Equating (1.41) with (1.43) we obtain

1.2.4 Green's Functions

1.2.4.1 Spatial Domain Green's Function. In the spatial domain, the electric and magnetic fields and their sources are related through the dyadic Green's functions according to

which can be called fundamental equation three.

1.2.3.3 Excitations. As part of the feed modeling, we usually can specify an electric current or a magnetic current as a known incident source. We will still include this incident current in our total electric or magnetic current expansion [Eq. (1.15) or (1.17)], but its corresponding coefficient is a known constant. So, in our fundamental equations, some terms can be evaluated to constants, and those terms can be moved to the right-hand side to form an excitation vector and all other terms with unknown coefficients will be moved to the left-Land side. The equations can then be solved for the unknown coefficients.

- H,,, = - jco dV1E,,,(7,F')e(7').T,,,(T') J (1.54)


Layer 0

lnterface 0

Let FE layer n and 7 ' ~ layer m. The spatial electric and magnetic Green's functions are given by [4]

Layer 1

lnterface 1

and

lnterface k-1

Layer k

lnterface k

Layer k+l

FIGURE 1.8 A planarly layered medium.

where 7 is the field point and 7 is the source point, 7 and 7, are the electric and the magneticcurrent densities, respectively (the symbol J, is tsed in this section rather than M to highlight the symmetry of the equations), G, and G , are the electric dyadic Green? function and the magnetic dyadic Green's function, respectively, E , and He are the electricjeld ancmagnetic field, respectively, produced by the electric current, and E m and H , are the electric field and magnetic field, respectively, produced by the magnetic current.

Consider the planarly layered geometry shown in Figure 1.8. We assume that there are N + 2 layers (including free space and/or boundary conductors) labeled layer 0 to layer N + 1 and the interface between layer k and layer k + 1 is labeled interfaces k.


where a = TM or TE, which stands for T M wave or TE wave, respectively. where

The coefficient A", (n < m) is defined recursively by the following equation: If

then

Because A:, is given in Eq. (1.66), starting from A:,, all the A:, can be computed. In the equations above, R", and R", are the so-called generalized reflection coefficients [4] at the upper and lower boundaries of layer 1, respectively. They are also defined by the following recursive relations:

1.2.4.2 Spectral Domain Green's Functions. Transforming Eqs. (1.51) to (1.54), we obtain the following equations relating the sources and fields in the spectral domain:

where Rf:*, and RTEl are the Fresnel reflection coefficients defined by

Sm = - j w E,G; 3 , dz' l,. - - For surface current independent of z, the above equations can be simplified:

If one layer, say layer N + 1, is a conductor, then E , should be replaced by ~ / j w . So,

The spectral domain electric and magnetic Green's functions can be obtained by applying the Fourier transform to Eqs. (1.55) and (1.56). After some

18 PROBE-FED MICROSTRIP ANTENNAS SPECTRAL DOMAIN FULL-WAVE ANALYSIS 19

manipulation, their components are obtained as follows:

1 -k: FTM - j w p m G ~ = --- 6(z - z') 'kmzw&n m e r n

2. Find all the generalized reflection coefficients iteratively for all the layers using Eqs. (1.70)-(1.73).

3. Find the necessary B: and BE using Eqs. (1.64) and (1.65). 4. Find the coefficients A:, iteratively using Eqs. (1.66) and (1.69). 5. Find the necessary scalar waves F",sing - Eq. (1.63) or (1.67). 6. Find the Green's functions of interest.

The above procedure can be used to find the dyadic Green's functions analytically. It can also be used to find the dyadic Green's functions numerically. When it is applied numerically, it can handle an arbitrary number of layers, so it is well suited to be used in a general-purpose program.

1.3 SPECTRAL D O M A I N FULL-WAVE ANALYSIS OF PROBE-FED RECTANGULAR MICROSTRIP ANTENNAS

In this section, we shall narrow our focus to the specific case of rectangular microstrip antennas with a coaxial feed.

1.3.1 Formulation

6, can be obtained by applying the following replacements to Eqs. (1.89)-(1.98) above

Ce + C m (1.99)

&-'P (1.100)

In summary, to obtain the dyadic Green's functions, follow these steps:

1. Find all the Fresnel reflection coefficients for all the interfaces using Eqs. (1.74)-(1.80).

The configuration of the antennais shown in Figure 1.9. We first consider the case when only one probe feed is used. The formulation will be extended to allow for multiple feeds later. Since the region above the ground plane is a simple region, the fundamental equation one and two-that is, Eqs. (1.22) and (1.30)-can be applied here.

The total current on the patch and probe is expanded into

where Zatd,, is the basis function on the patch, f,, is the basis function on the probe, and is the attachment mode, a special basis function used to ensure the continuity of current a t the patch-probe junction. This will be discussed in detail in Section 1.3.4. The field inside the coaxial cable can be expressed as

20 PROBE-FED MICROSTRIP ANTENNAS SPECTRAL D O M A I N FULL-WAVE ANALYSIS 21

Layer 0 Interface 1

Layer 1 l nterface 2

Layer 2

Layer N

Ground plane

Coax feed

FIGURE 1.9 Geometry of probe-fed rectangular microstrip antenna in planarly layered medium.

where

go and Go are the fields of the TEM mode, gl and GI (1 > 0) are the fields of the higher modes, and z, is the z-coordinate -of the ground plane which we take as a reference point. The fields at the aperture ( z = 2,) are

The magnetic current over the aperture is given by

where

G1=Z1 x 2

bo= 1 f r o

bl = r,, where 1 > 0

Equation (1.22) can be written as


Assuming Eo and go to be the known incident fields, we can solve the above equationsfor the unknown coefficients. The input impedance Z, of the antenna is


derived from the reflection coefficient To by the equation

where Zo is the characteristic impedance of the coaxial cable. If the dimension of the coaxial cable is much smaller than the dimension of the

patch, use of higher-order modes is generally not necessary. If only the TEM mode is used, Eqs. (1.1 14)-(1.118) become

And the fundamental equation two can be written as

From Eq. (1.127), the input impedance can be expressed as

which is the same as the reaction formula used in Chen et al. [ 5 ] .

FIGURE 1.10 Overlapping piecewise rooftop basis function for currents in (a) x- direction and (b) y-direction.

1.3.2 Basis Functions

The basis functions on the patches are taken to be overlapping piecewise rooftop functions as shown in Figure 1.10.

The basis functions on the probe are taken to be a set of overlapping triangular functions as shown in Figure 1.1 1.

To allow for azimuthal variation of the current on the probe, the basis functions on the probe are written as -

f b.s = ,;,) sin k q

{nk,j ices xr } - ra)

whose Fourier transform is


FIGURE 1.1 1 Overlapping triangular basis function.

where J,(k, r,) is the kth-order Bessei function of the first kind, and

cos a = kJk, sin a = kdk,

1.3.3 Multiple Feeds and Shorting Pins

1.3.3.1 Multiple Feeds. In this section we will extend our formulation to handle multiple feeds. It is assumed that only the TEM mode is required to model the fields inside the coaxial cables. Let the total number of probe feeds be P.

The fields inside the cables can be written as

where v; represents the intensity of the incident waves and v; represents the intensity of the reflected waves. The magnetic current over the apertures is given by

= C (up+ + vvp) Gp (1.135) p= 1

where

The total current can be expressed as

where ~p,t,h2 is the basis function on the patch, f,,,, is the basis function on the probe, and fat,,,, is the attachment mode, a special basis function used to ensure the continuity of current at the patch-probe junction.

Now, Eq. (1.22) can be written as



Solving Eqs. (1.138), (1.140), (1.143), and (1.145) for v; in terms of v; yields

where [s] is the s-matrix (scattering matrix). One way to obtain the s-matrix numerically is to let

then solve for v, for each set of v i , which will be the corresponding column of the s-matrix.

1.3.3.2 Shorting Pins. Shorting pins are sometimes used to modify the behavior of patch antennas. For example, it can be used to suppress some modes of the patch current. Shorting pins can be modeled much the same way as probes. Modeling shorting pins is actually simpler, because they do not couple to the outside directly. The same basis function used on a probe can be used on a pin. For a shorting pin connecting the ground plane and a patch, attachment modes need to be used on the pin-patch junction. For a shorting pin connecting two patches, attachment modes need to be used at both pin-patch junctions.

1.3.4 Attachment Modes

The "attachment modes" are special types of basis function used to model the current in the vicinity of the probe-patch junction and to ensure the continuity of the current at the probe-patch junction. Part of a n attachment mode will exist on the probe surface (see Figure 1.12) and part of it will be on the patch surface.

Let us first find the current existing on the top of a magnetic wall cavity [6] excited by a uniform filament of current at (xi, y;). This current will be used in our attachment mode definition later.

FIGURE function.

1.1 2 Attachment mode on the probe: half-triangular

The dimension of the patch that the probe attaches to is a x b. The fields inside the cavity are found to be

m n ( x + t ) cos m n ( i p + f ) cos nn(Y+t) cos nn(y;+t) ' COS

a b b (1.149)

a

and

where

1 p=O and p = m or n.

The patch current can be computed as


where

mx(. + 4) cos

b b

COS

..(xi +;) ,n ..(Y + f ) cos ..(. + f)} a b b

(1.152)

By expanding cos ax into a Fourier series, we have I

m 6 , cos mx l~ cos ax C -(-I)"=

m=O m -a - R l x < a

a sin ax ' (1.153)

Taking derivative at both sides of the above equation, we have

-5 Em sin mx sin ax

( - I ) " ' = - 7 ~ - - x 5 x < x (1.154) ,,,=,, m2-a2 sln ax '

Using these two equations, the sum with respect to m in Eq. (1.151) can be carried out to yields

where

sin Z ( x + x i ) + sin Z [a - ( x i - x)] , x < x ;

sin Za

sinZ(x+x;)-sinZ[a-(x-xi)], x,xi sin Za

cos Z ( x + xi) + cos Z(a - Ix - xkl) 5, = Z sin Za

The Fourier transform of 7, may be evaluated term by term. Here we use the localized Fourier transform, which is defined as

where (x,, y,) is some constant reference point that may be chosen arbitrarily. For now (x,, y,) is left to be ~ndefined~later on it will be defined as the center of the probe. The Fourier transform of JP is evaluated to be

k,a Z cos Zx' - jk, ejkxxb + j sin- -----I - COS- 2 sin Za/2

jkx,b k, cos Zxb k,a jk, sin Zx' sin - +

+ n b 2 [ + z sin ~ a / 2 2 z cos ~ a / ; cos Y ] }

However, the above series is very slowly convergent. To avoid computation problem due to slow convergence, we separate the_series into two components. One is a fast convergent regular series denoted by f ~ g u ' a r . The other is a slowly convergent series which contains the singular behavior of yp at (xi , yb) and denoted by 7$"9""'. We write

where

S,, = Z cos Zxbjsin Za/2 (1.163)

C,, = jZ sin Zxbjcos Za/2 (1.164)


If xb < a/2, S,, and C,, decay exponentially. When xb approaches a/2, these terms decay more slowly. However, unless the feed is at a corner of the patch, one can always avoid this problem by choosing the coordinates wisely.

The last step in Eq. (1.165) is obtained using partial fraction expansion. From Eq. (1.153), we have

Hence, A(u) can be summed up in closed form:

- j cos(uyb) . k b sin(uyb) k b - -- s m + + j u ub

COS -2

sin - ub 2 2

COS - 2

Note that

Hence

The slowly convergent series (1.165) has thus been summed in closed form. Note that the first term in Eq. (1.172) is the current induced on two infinite parallel conducting plates by a uniform filamentary current.

Now we can define our attachment mode. Let (xp, yp) to be the center of the probe. The probe parts of the attachment modes are chosen to be

sin k q

whose Fourier transform is

where f OF (2) is a half-triangular function shown in Figure 1.1 1. The patch parts of the attachment modes have to be chosen so that the total

currents are continuous at the junction; that is, the currents that flow out of the junction are equal to the currents that flow into the junction from the probe. Using the patch current of a magnetic cavity which is given by Eq. (1.161) above, we define our patch part attachment modes to be

where

x ~ = x p + r a c o s ( p

- z p i s the patch current of the cavity and (m,, n,) is theresonant mode of the cavity. We subtract the resonant mode from the current T p in our attachment mode definition because the resonant mode is large and is all over the patch but the unknown patch current can be modeled by other basis functions on the patch, and the attachment mode is only intended to be used to ensure the continuity of the total current so we do not want the resonant mode to be included in the attachment mode. Since the resonant mode is continuous all over the patch, subtracting it from the patch current will not affect the current continuity.


N o w we need t o carry out the integral i n Eq. (1.175). Let's define

From Eqs. (1.180) and (1.181), the following equations can be derived [they are merely linear combinations o f Eqs. (1.180) and (1.181)]:

C ~ C , ~ U X ~ cos vyb] = jk J , (ks r,) e"' cos vy, cos ky (1.184)

S k [ e j u x k o s vyb] = jk+ '3 , (ks r,) ePXp sin vy, sin ky (1.185)

Ck[ejuxb sin vyb] = jk Jk (k , r,) ejuxp sin vy, cos ky (1.186)

S, [ejux"in vyb] = - jk + Jk (k , r J ejUxp sin vy, sin ky (1.187)

Sk[sin(uxl, + 9,) cos(vy; + €J2)l = Jk(k,ra) sin ky cos

(1.191)

SPECTRAL DOMAIN FULL-WAVE ANALYSIS 33

N o w we can easily carry out the integral i n Eq. (1.175). After carrying out the integral i n Eq. (1.175), the attachment modes o n the patch are found t o be

ik+' 7;; = -T Jn(kpr,) cos kcc(fkx + jk,) k,,

- k,2 j k ~ k (Gr korJ cos ky , A1(kJ ( i k x k y + jk:)e- jkyyp

7;; = - ~ ~ + + ' k ~ ~ J ~ ( k , r , ) s i n k c c ( P k ~ + j k y )

- k i 2 j k + l Jk (A k o ra) sin ky , An(k,) (Pk,k, + jka)e-jkyyp


Z cos(ZXp + F) s;, =

sin Za/2

z sin (Zx, + F) S" - -

Zn - sin Za/2

z cos(Zxp + F) C" - ' 2" -I cos Za/2

sin (k, b/2) + j sin(kayp) cos(kyb/2)} (1.200) cos (k, b/2)

A"(ka) = - L { Jin(ka 'P) sin (k, b/2) - j cOs(knyp) COS(~ , b/2) k, sm(k, b/2) cos (k, b/2)

REPRESENTATIVE NUMERICAL AND EXPERIMENTAL RESULTS 35

(1.205)

cos a = kdk,

sin cc = ky/k,

For the simplified case in which azimuthal variation is not taken into account, the patch part attachment mode is given by

f"" = xe = - j k i 2 JO(kpro)(fkx + jk,)

- k i 2 J,(& k0rJ ~ ' ( k ~ ( i k , k , + jk;)e-jkyYp

Z cos Zx, sin kxa/2 Z sin Zx, cos kxa/2

' ( sin za/2 + j cos za /2

1.4 REPRESENTATIVE NUMERICAL A N D EXPERIMENTAL RESULTS

Based on the formulation of Sections 1.2. and 1.3, a computer code has been written for probe-fed multilayer multipatch rectangular microstrip antennas. Special attention was paid to branch cuts and poles of the Green's function, avoidance of redundant reaction computations, and the spectral integral.

In this section, representative numerical results are preiented for the single patch, single patch in multidielectric media, coplanar subarrays, and two-layer stacked patches. Experimental results are included to validate the numerical results.


s

Conducting patch

FIGURE 1.13 Probe-fed rectangular patch on a grounded substrate.

1.4.1 Single Patch [I 51

1.4.1.1 Introductory Remarks. Figure 1.13 shows a rectangular patch with dimensions a x b printed on a grounded substrate of thickness d and relative permittivity 8,. The patch is fed by a coaxial probe at (x,, y,) with inner radius r, and outer radius r,. The radiation patterns of the antenna obtained from full-wave analysis are basically the same as those obtained from the cavity model [3]. Here, we are interested in the input impedance of the antenna.

The input impedance of this antenna has been studied by many authors using full wave analysis [7-151. In reference [9], the driving source is taken to be the probe current, which is assumed to be a constant filament. No effort was made to ensure current continuity at the probe-patch junction, nor was the singular nature of the current at the junction modeled by the basis functions. In later papers by Aberle and Pozar [lo, 111, the driving source is taken to be a delta-gap voltage at the base of the probe. Current continuity at the probe-patch junction is ensured by the use of an attachment mode. However, the numerical results obtained by Aberle and Pozar are still based on the assumption that the probe current is uniform across the thickness of the substrate.

In this section, numerical results based on the theory presented in Sections 1.2 and 1.3 are presented. This theory differs from that of Aberle and Pozar [lo, 111 in


a number of ways. First, the driving source is taken to be the electric field in the coaxial aperture (magnetic frill model), which is more rigorous than the delta gap model. second, the slowly convergent part of the attachment mode is summed up analytically in closed form, which considerably facilitates the numerical computation. Third, multiple expansion functions are used for the probe current to allow for both axial and azimuthal variations. Since the probe current is not regarded as a constant, the formulation is valid for electrically thick substrates.

In our theory, as well as those of Pozar and of Aberle and Pozar, the incident and scattered fields are calculated using Green's functions in the spectral domain. These functions are expressible in closed form. Other authors have studied the probe-fed single patch using space domain Green's functions which involve Sommerfeld integrals. In particular, the studies of Hall and Mosig [8] and of Zheng and Michalski [I21 are valid for electrically thick substrates.

1.4.1.2 Comparison with ExperimentalResuIts. We first check the validity of our analysis and computer code by comparing our numerical results with the measured data given in Figure 8 of Hall and Mosig [8]. The feed is located at x, = 0 and y, = 0.5b - F (see Figure 1.13). The comparison is shown in Figurel.14. It is seen that the agreement is excellent, giving confidence to our theory. The agreement appeared to be comparable to the corresponding comparison between measured data and the theoretical results of Hall and Mosig [8] shown in their Figure 8. The difference between their approach and ours is that they worked in the spatial domain while we worked in the spectral domain.

Next, we compare theoretical results with the measurements given in Schaubert et al. [14]. One difficulty encounteredis that the value of the substrate loss tangent, tan 6, was not given in reference [14]. Using tan 6 = 0.0006 and 0.003, we obtained the results shown in Table 1.1 for their cases l b and 2b, the antenna parameters ofwhich are given in Table 1.2. As far as resonant frequencies are concerned, the calculated values are insensitive to tan6 and agree with experimental values to within 2.5%. As far as the resonant resistance is concerned, it is seen that as t a n s increases from 0.0006 to 0.003, the resonant resistance decreases by 17.9% and 12.7% for cases l b and 2b, respectively. This shows that when comparison with experiment is made, it is important to use the true value of tan 6, which, however, was not given in reference 1141. Table 1.1 also shows the moment method results of Schaubert et al. 1141, which were obtained assuming the probe current to be a constant and no mention was made of the value of tan 6 used in their computations. Our results are based on a model which uses multiple expansion functions to take into account both the axial and azimuthal variations of the probe surface current. It is found, however, that the results obtained with and without azimuthal variations are almost identical, provided that the diameter of the probe is much less than the patch dimensions.

1.4.1.3 Changes of Impedance as Substrate Thickness Increases. In this section we results-illustrating the change to the input impedance as the substrate thickness increases, keeping the feed location and the other parameters


FIGURE 1.14 Measured [8] and calculated input impedance data for an a = 39.22-mm by b = 46.30-mm rectangular patch with a coaxial feed at F = 15.43 rnm using the present formulation. d = 7.976 mm, E, = 2.484, tans = 0.0006, r, = 0.635 mm, r, = 2.1 mm. x x x Calculated data, A f = 0.04 GHz. mmm Measured data [a], A f = 0.04 GH..

TABLE 1.1 Comparison of Measured Data from Schaubert et al. [I41 and Calculated Results

Our Calculated Results

Measured R,(R) Calculated Results

tan6= t a n s = C141

Case f,(GHz) R,(R) f,(GHz) 0.0006 0.003 f, R m

TABLE 1.2 Parameters for Cases 1 b and 2b of Schaubert et al. [I 41


-Advanced model

70.0- R- X - - - - - Advanced model Af = 0.02 GHz

227.00 228.00 229.00\*\230.00 231.00~.'232.00 233.00 234.00 235.00

-lO.O1 x107

Frequency (Hz)

(a)

70.07 R- X----. Advanced model

f: 2.14-2.26 GH

Af = 0.03 GHz

50.0-

? 30.0- E

214.00 216.00 218.00 220.00 222.00 224.00 226.00

Frequency (Hz)

(b)

FIGURE 1.15 Input impedance for a fixed feed position computed using the simple model and the advanced model presented in rectangular coordinates and in Smith Charts. a=3.0cm, b=2.0cm, &,=10.2, tan6=0.001, F=0.75cm,r,=0.22mm, R,= 1.40mm. (a) d = 0.127 cm, (b) d = 0.254cm, (c) d = 0.381 cm, (d) d = 0.508 cm, (e) d = 0.635 cm. (continued)

40 PROBE-FED MICROSTRIP ANTENNAS REPRESENTATIVE NUMERICAL AND EXPERIMENTAL RESULTS 41

207.00 209.00 211.00 213.00 215.00 217.00 219.00 22i.00 Frequency (Hz) x107

(C)

1.86 GHz

tt. Advanced mode - Simple mod

f: 1.86-2.22 GHz

80.0 ' \

70.0

00-

_ / - 0.-

0 50.0 ___.--. K 40.0

30.0

20.0 - . \ . .

...... .+ - . . . . . . .__ . I I I I

186.00 190.00 194.00 198.00 202.00 206.00 210.00 214.00 218.00 222.00 Frequency (Hz) .lo7

(d)

1.82 GHz 0-0-0 Advanced model - Simple model

A- f: 1.82-2.02 GHz X----, Advanced model Af = 0.04 GHz

x -.-.- Simple model ------- _ / * \

\

\

\

80.0 1

0.0 I I 182.00 186.00 190.00 194.00 198.00 202.00

Frequency (Hz) xlo7 (el

FIGURE 1.15 (continued)

fixed. The calculations are for a patch with a = 3.0 cm, b = 2.0 cm, fabricated on a substrate with E, = 10.2 and tan 6 = 0.001. The input impedance is computed for five thicknesses, beginning with d = 0.127cm and increasing at multiples of 0.127cm. For the TM,, mode, these thicknesses correspond to approximately the range 0.011,-0.0411,. The probe inner and outer radii are r, = 0.43 mm and R, = 1.40 mm, respectively. The feed position is pegged at F = 0.75 cm, which yields an input resistance of about 50R for d = 0.127 cm. The computations are performed using both the model assuming a uniform probe current (simple model) and the model which uses multiple expansion functions for the probe current (advanced model). The results are shown in Figures 1.15a-e, in which the impedances are presented both in rectangular coordinates and in Smith Charts. The following features are noted:

The results for the simple model are reasonably accurate for case a only. Significant deviations from the advanced model begin to appear in case b. For case e the simple model is totally inaccurate. At the frequency where the input resistance is maximum, there is significant inductive reactance even for case a. The reactance curve increases as the substrate thickness increases, and it does not become negative for cases c, d, and e. For these cases, a resonant frequency cannot be defined in terms of FIGURE 1 .I5 (continued)


FIGURE 1.16 Impedance bandwidth (VSWR= 2) as a function of substrate thickness when the feed is located at the optimum position. a = 3.0cm, b = 2.0cm, e, = 10.2, tan S = 0.001, r, = 0.22mm, R, = 1.4mm.

zero input reactances and it is more meaningful to define it as the frequency at which the input resistance is maximum.

3. The computed impedance bandwidth (VSWR= 2) are 0.56%, 1.13%, 1.33%, and 0.59% for cases a, b, c, and d, respectively. For case e(d = 0.635 cm), the VSWR = 2 circle does not intersect the impedance loci. This shows that, if the feed position is fixed, the impedance bandwidth does not increase monotonically with substrate thickness.

1.4.1.4 Optimization of Feed Position for Maximum Bandwidth. The results presented in Section 1.4.1.3 are for a fixed feed position. If the feed position is allowed to be optimized for maximum bandwidth, we obtain, using the advanced model, the result of Figure 1.16, which shows that the bandwidth does increase as d increases. The optimal feed positions are F = 0.74,0.71,0.67,0.63, and 0.55 cm for the five values of d. The impedance loci for d = 0.635 cm ( E 0.041 1,) when F is at 0.55cm is shown in Figure 1.17, which is considerably changed from that of Figure 1.15e. Similar changes also occur for the other four thicknesses.

1 A.2 Single Patch in Multidielectric Media [la, 221

1.4.2.1 Introduction. Microstrip antennas with more than one dielectric layers are of theoretical and practical interest. Several configurations of such

FIGURE 1.1 7 Smith Chart display of the input impedance obtained using the advanced model for d = 0.635cm when the feed is placed at the optimum location (F = 0.55 cm). a=3.0cm, b=2.0cm,&,= 10.2, tan6=0.001,rp=0.22mm,Rp= 1.4mm.

antennas are shown in Figure 1.18. In Figure 1.18a, a superstrate or dielectric cover is used to protect the patch against environmental hazards. If a naturally occurring dielectric layer such as ice is formed on top of the superstrate cover, the three-layer configuration of Figure 1.18 b results. Figure 1.18 b can also represent the situation when an unwanted air space exists between the substrate and the superstrate(&,, = 1). If an air gap is deliberately introduced between the substrate and the ground plane to alter the resonant frequency of the antenna, we have the one-superstrate two-substrate geometry shown in Figure 1.18~. In this section the results of our study of these configurations using the formulation of Sections 1.2 and 1.3 are presented.

1.4.2.2 Rectangular Patch with Dielectric Cover (Superstrate). A number of authors have studied the effect of a protective dielectric cover on a probe-fed rectangular patch antenna [16-201.

Figure 1.19 shows calculated input impedance of a rectangular patch with ~ , ~ = ~ , ~ = 2 . 6 4 , tanb2=tan63=0.003, d3=0.159cm, a=7.62cm, b = 11.43cm, r,, = 0.0635 cm, x, = 1.52cm, and y, = 0.385 cm for different values of the dielectric cover thickness d,. The cased, = 0 corresponds to the uncovered antenna, for


sr4 = 1 (Air) d4

FIGURE 1.18 Microstrip antennas with multidielectric layers. (a) Rectangular patch with a superstrate. (b) Rectangular patch with two superstrates. (c) Rectangular patch with a superstrate and two substrates.

dl = 0.795 cm 0.159 cm dl=Ocm \ \- (NO cover)

V 1.13 1.15 1.17 1.19 1.21

Frequency (GHz)

FIGURE 1.1 9 Input impedance Z = R + j X versus frequency for three values of cover thickness d,. = E , ~ =2.64, tansl = tan~5~=0.0()3, d2=0.159cm, a=7.62cm, b= 11.43cm, r, = 0.0635 cm, x, = 1.52 cm, y, = 0.385 cm. Crosses indicate the experimental results for the case of no cover [3].

tan 61 = 0

0 1.13 1.15 1.17 1.19 1.21 Frequency (GHz)

FIGURE 1.20 Input impedance Z = R + j X versus frequency for three values of cover relative permittivity. dl =d2 =0.159cm, &,,=2.64, tanC52=0.003,a=7.62cm, b= 11.43 cm, r, =0.0635cm, x,= 1.52cm, y, =0.385cm.

which measured results are available in Richards et al. [2] . The measured data are indicated as crosses in Figure 1.19. It is seen that the dielectric cover decreases the resonant frequency. However, neither the resonant resistance nor the impedance bandwidth changes appreciably as dl varies from 0 to 0.795 cm.

Figure 1.20 shows the calculated input impedance for different dielectric cover relative permittivity E,,. As E,, increases from 1 (no cover) to 2.64 to 13.2, the resonant frequency de&eases,8ccompanied by a slight increase in the resonant resistance. There is again no significant change in the impedance bandwidth.

In Chen et al. [20], computer-aided design formulas based on curve-fitting a database of moment method results are presented for the resonant frequencies of the TM,, and TM,, modes of a rectangular patch with a superstrate. The formulas, in polynomial form, can be used for a wide range of substrate and superstrate thicknesses and permittivities.

1.4.2.3 Rectangular Patch with Two Superstrates. In this section we present numerical results for a rectangular patch with two superstrates. The first super-


TABLE 1.3 Rectangular Patch with Two Superstrates: Figure 1 .I 6b with a = 3.375 cm, b=2.25cm, xp=O, yp=0.35cm, +,=3.2 (ice), &,=2.32, d2=0.76mm, &,,=4.0, d, = 1.55 mm

dl (mm) f o I @Hz) BW(%) HPBW 0.0 3.150 1.4 141" x 78" 1 .O 3.100 1.4 132" x 78" 2.0 3.070 1.4 125" x 78" Bare patch (dl = d2 = 0) 3.205 1.4 148" x 78"

strate is a dielectric cover for environmental hazard protection. The second superstrate represents ice formed on top of the cover. The geometry is that shown in Figure 1.18 b with the following parameters: a = 3.375 cm, b = 2.25 cm, x, = 0, yP=0.35cm,~,, =3.2(ice),e,,=2.32,d,=0.76mm,~,,=4.0,d,= 1.55mm.The results for resonant frequency, bandwidth (VSWR = 2), and half-power beamwidths are shown in Table 1.3 for three values of dl and for the bare patch (dl = d, = 0). The impedance loci and the normalized patterns for the four cases are shown in Figures 1.21 and 1.22, respectively.

The following features are noted:

1. The dielectric cover lowers the resonant frequency of the antenna by about 1.7%.

2. A second superstrate lowers the resonant frequency further: by 1.6% for dl = 1.0 mm and 2.5% for dl = 2.0 mm. Aside from a shift in frequencies, the shapes of the impedance loci remain essentially the same.

3. The superstrates do not cause any noticeable change in impedance bandwidth,

4. The HPBW in the x-z plane decreases from 148" for the bare patch to 125' for the case with d, = 0.76mm and dl = 2.0mm. The HPBW in the y-z plane remains at 78'.

1.4.2.4 Rectangular Patch with Superstrate and an Unwanted Air Space. In this section we present results illustrating the effect of an unwanted air space whichexists between the substrate and the superstrate plane. The geometry is still given by Figure 1.18 b, and the antenna parameters are a = 3.375 cm, b = 2.25 cm, x,=O, yp=0.35cm, &,,=2.32, dl=0.76mm, &,,=4.0, d3=1.55mm, &,,=I. The resonant frequencies and bandwidths for two values of thickness of the air space d, are shown in Table 1.4. It is seen that there is a slight increase of the resonant frequency due to the presence of the air space. However, the increase is only about 0.3 % as d, varies f;om 0 to 0.2 mm. The bandwidth remains at 1.4%.

FIGURE 1.21 (a) Impedance loci for rectangular patch with two superstrates: a=3.375cm, b=2.25cm, xp=O, yp=0.35cm, ~ , ~ = 2 . 3 2 , E,, =4.0, d2 =0.76mm, d, = 1.55mm, E,, = 3.2, dl = 0. (b) Same as (a) except dl = 1.0mm. (c) Same as (a) except d, = 2.0 mm. (d) Bare patch (dl = d, = 0).

1.4.2.5 Rectangular Patch with a Superstrate and Two Substrates. In this section we present results for the case of a rectangular patch with one superstrate and two substrates. Of particular interest is when an air gap is deliberately introduced between the substrate and the ground plane. As in the case of no superstrate [21], it is expected that the resonant frequency of the antenna can be altered by changing the width of the air gap.

48 PROBE-FED MICROSTRIP ANTENNAS REPRESENTATIVE NUMERICAL AND EXPERIMENTAL RESULTS

The geometry is given in Figure 1 . 1 8 ~ with the following parameters: a=3.375cm,b=2.25cm,xp=O,yp=0.5cm,~,,=2.32,d,=0.76mm,~,,=4.0, d, = 1.55mm. The resonant frequencies and bandwidths for three values of the air gap width d, are shown in Table 1.5. It is seen that, as the airgap width increases from 0 to l.Omm, the resonant frequency increases from 3.205 GHz to 4.040GHz (28%), accompanied by more than twofold increase in bandwidth.

1.4.2.6 Comparison with Experiment. To verify our theory, we fabricated a rectangular patch with two superstrates (Figure 1.18b) with the following parameters: a = 2.0 cm, b = 1.446cm, xp = 0, yp = 2.35mm, E,, = 2.17, E,, = 6.0, d, = 0.8 mm, d, = 2.54mm. The measured and computed resonant frequencies

- Bare patch (dl = d2 = 0) - - - - - - - - dl= 0 .... ..*. . ... . . . . . dl = 1.0 rnm .-.--.-. dl = 2.0 mrn

FIGURE 1.22 (a) Normalized pattern in the x-z plane for rectangular patch with two superstrates. The antenna parameters are the same as in Figure 1.19. (b) Normalized pattern in y-z plane for rectangular patch with two superstrates. The antenna parameters are the same as in Figure 1.19.

and patch the (dl bare = dz = 0)

(b)


TABLE 1.4 Rectangular Patch with a Superstrate and an Unwanted Air Space: Figure 1.18b with a = 3.375~1~1, b= 2.25 crn, xp= 0, yp = 0.35 crn, E, = 2.32, d, =0.76rnrn,~,=l (air),&,=4.0,d3=1.55rnm

4 (mm) f o ~ (GH4 BW (%)

0 3.150 1.4 0.1 3.157 1.4 0.2 3.161 1.4


TABLE 1.5 Rectangular Patch with a Superstrate and Two Substrates: Figure 1 .l8c with a = 3.325cm, b=2.25cml xp=Ol yp=0.5cm, &,,=2.32, d2= 0.76mm,&,,=4.0,d3=1.55mm

TABLE 1.6 Rectangular Patch with Two Superstrates: Figure 1.18b with a = 2.0cm, b= 1.446 cm, xp = 0, yp=2.35mm, E,, =2.53, &,, =2.17, d, =0.8rnm, E.? = 6.0, d- = 2.54 mm

-

dl (mm) Theory Measurement 0.0 3.725 3.660 1.0 3.674 3.615 2.0 3.641 3.585

for three values of dl are shown in Table 1.6. The close agreement gives confidence to our theory. The discrepancy is most likely due to the tolerances associated with the values of the relative permittivities.

1.4.3 Coplanar Parasitic Subarray

1.4.3.1 Introductory Remarks. One way of increasing the bandwidth of the microstrip patch antenna is to introduce closely spaced parasitic patches on the- same layer as the fed patch. This has been a subject of considerable interest, both experimentally and theoretically. Wood [23] showed that the impedance bandwidth of a rectangular patch antenna can be enhanced by an adjacent patch. This was supported by the analysis of Mosig and Gardiol[24]. Aanandan et al. [25] studied a broadband design in which a rectangular patch was broken up into several gap-coupled rectangular strips. Another class of configurations consists of one fed rectangular patch and two or more parasitic patches placed symmetrically with respect to the fed element, forming a coplanar microstrip parasitic subarray. Figure 1.23 shows several configurations that have been studied: the radiating-edge (Figure 1.23 a) and nonradiating-edge (Figure 1.23 b) gap-coupled three-element subarrays and the five-patch cross (Figure 1.23~). Gupta [26] showed that the impedance bandwidth can be enhanced by using parasitic patches smaller than the fed patch. Lee et al. [27], MacKinchen et al. [28], and

Parasitic


FIGURE 1.23 Coplanar parasitic subarray configurations. (a) Radiating-edge-coupled three-element subarray, (b) nonradiating-edge-coupled three-element subarray, (c) five- patch cross.

Staker et al. [29] used parasitic patches of the same size as the fed patch and obtained improved gain characteristics. Planar arrays of five-patch crosses were also built and tested [30].

In this section the basic characteristics of the coplanar microstrip parasitic subarrays shown in Figure 1.23 are presented based on the spectral domain full-wave analysis of Sections 1.2 and 1.3 [31].

1.4.3.2 NumericalResults. The results for the input impedance of a radiating- edge-coupled three-element subarray for five gap widths are shown in Figure 1.24. The dimensions are given in the inset of Figure 1.24. As expected, the gap width is a sensitive parameter controlling the nature of the coupling. The results for case 5 (widest spacing) are basically those of the single patch without parasitics. As the gap width decreases, the curve for R broadens and becomes doubled humped for cases 1 and 2. Case 2 appears to be the one with the best bandwidth characteristics.

The results for a nonradiating-edge gap-coupled three-element subarray are shown in Figure 1.25. Here case 1 appears to yield the best impedance characteristics. The results for a five-patch cross are shown in Figure 1.26. For this configuration, case 2 again yields the best impedance characteristics.

In the above example, the impedance bandwidth obtainable is about 5-6%. By optimizing the various parameters, Gupta et al. [26] have reported that 10-20% bandwidths are obtainable. However, pattern degradation over the frequency band has been observed.

1.4.3.3 Comparison with Experiment. In Figure 1.27 we compare the theoretical input impedance results obtained from our analysis for a three-element linear array given in reference [26] and compared with his experimental data given in


2.605 crn 1.95 cm 2.605 crn

Frequency (GHz)

-100 l I I I I I I I 1 3.1 3.2 3.3 3.4 3.5

Frequency (GHz)

FIGURE 1.24 Input impedance Z = R +jX of a radiating-edge-coupled three-element subarray in which the parasitic patches are smaller than the fed patch, for five gap spacings. Substrate relative permittivity = 2.64, loss tangent = 0.001. Substrate thickness =

0.159cm. -.-.-, d = 0.0825 cm; ----, d = 0.165 cm; ---, d = 0.33 cm; --, d=0.66m;- , d = 1.32cm.

Figure 9.44 of Gupta [26]. It is seen that, aside from frequency shift of about 3%, the agreement between the computed and measured R and X is very reasonable. The shift in frequency may be due to the uncertainties in the values of substrate relative permittivity and substrate thickness.

Figure 1.28 shows the H-plane radiation patterns computed a t three frequencies for one of the three-element linear subarrays in reference 1291. The pattern a t 4.73 GHz compares well with the measured pattern given in Figure 2 of reference [29].


+ 3.9 crn + 3.9 crn 3.9 crn

[ p7npo5

3.1 3.2 3.3 3.4 3.5 Frequency (GHz)

0 l I I I I I I I I 3.1 3.2 3.3 3.4 3.5

Frequency (GHzI

FIGURE 1.25 Input impedance Z = R + j X of a nonradiating-edge-coupled three- element subarray in which the parasitic patches are smaller than the fed patch. Substrate loss tangent, permittivity, thickness, and the gap spacings are the same as in Figure 1.24. -.-.- . . , d = 0.0825cm; ----, d 0.165 cm; ---, d 0.33 cm; . . . a , d = 0.66cm; -, d = 1.32 cm.

1.4.4 Two-Layer Stacked Patches [38]

1.4.4.1 introductory Remarks. The stacked electromagnetically coupled patch (EMCP) antenna shown in Figure 1.29 has been shown experimentally to provide an impedance bandwidth which is significantly larger than that of a single patch [32]. A number of theoretical papers on the probe-fed E M C P


Frequency (GHz)

2.605

3.9 crn 2.605

cm I /0.45 ern

2.605 crn

2.605 crn

0

-50

1 I I I I I I I I 3.1 3.2 3.3 3.4 3.5

Frequency (GHz)

FIGURE 1.26 Input impedance Z = R + jX of a five-patch cross in which the parasitic patches are smaller than the fed patch. Substrate permittivity, loss tangent, thickness, and the gap spacings are the same as in Figure 1.24. -.-.-, d=0.0825cm; ---, d = O.165cm; ---, d = O.33cm; ....., d = O.66cm; - , d = 1.32cm.

antenna have also appeared in recent years [33-371. The theories in references [33-371 all assumed a uniform probe current. Also, except for reference [35], no attachment mode was used to ensure current continuity at the probe-patch junction. In this section we present some theoretical results obtained for the stacked EMCP using the formulation of Sections 1.2 and 1.3 [38].


2.605 crn 0.165 cm 2.605 cm

1.95 cm 0.45 crn - Present theory

0 l I I I I I I I I

3.1 3.2 3.3 3.4 3.5 Frequency (GHz)

\ - Present theory ------ Measurement [261

-50 1 I I I I I I I I

3.1 3.2 3.3 3.4 3.5 Frequency (GHz)

FIGURE 1.27 Comparison of the theoretical input impedance results obtained from our theory for a three-element linear array given in Gupta [26] with the experimental data given in Figure 9.44 of Gupta [26]. Substrate relative permittivity = 2.55; loss tangent = 0.001, substrate thickness = 0.159 cm.

To establish contact with measurement, we first compare the predictions of our model for the antenna depicted in Figure 8 a of Barlately et al. [33] with their experimental data. This is shown in Figure 1.30. The close agreement gives confidence to our theory. (A corresponding comparison between the theoretical predictions of Barlately et al. and experimental data was given in Figure 10 of Barlately et al. [33].)


Angle (Denreed

4.73 GHz

-- & I;: 1 .-.-.-.- - 4.43 4.53 GHz ,HZ

FIGURE 1.28 H-plane radiation patterns at three frequencies for a nonradiating- edge-coupled three-element linear subarray in which the parasitic patches are the same size as the fed patch. Substrate relative permittivity =2.2, loss tangent = 0.001, and thickness = 0.157cm. Crosses indicate the experimental data in Staker et al. WI.

Superstrate

Ground Plane

e

~oai ia l Probe r

FIGURE 1.29 Geometry of the stacked electromagnetically coupledmicrostnp antenna.

d

REPRESENTATIVE NUMERICAL AND EXPERIMENTAL RESULTS 57 - OurTheory

x x x Experiment

FIGURE 1.30 Comparison of our theoretical predictions and experimental data for the stacked antenna depicted in Figure 8a of Barlately et al. [33]: h, = 0, E,, = E,, = 2.33, h,=h,=0.51mm,F=4mm,a,=31.2mm,b,=18mm,al=28mm,bl=18mm.

1.4.4.2 Numerical Results. In this section we present numerical results obtained for a stacked antenna consisting of square patches and a stacked antenna consisting of rectangular patches. The antenna parameters are as follows:

Stacked square patches: a, = b, = 62.56mm, a , = b , = 67.84mm Stacked rectangular patches: a, = 62.56mm, b, = 41.71 mm

a , = 67.84mm, b, = 45.23 mm

Figure 1.31 shows the variation of input impedance with frequency for the stacked square patches for two feed positions: a feed near the center (F = 1.00 cm) and a feed near the edge (F = 2.90cm). The impedance loci exhibit a two loop characteristic. This is to be compared with the one loop characteristic of the single patch (when the parasitic patch is removed) shown in Figure 1.32. Note that, unlike the case of the single patch, the input resistances remain at relatively small


FIGURE 1.31 Impedance loci for a stacked square patch antenna with E,, =2.2, h 1 = 0 . 8 l m m , ~ , , = 1 . 2 , h2=11.2mm, ~ , , = 2 . 2 , h3=1.5mm. a ,=b2=62 .56mm, a , = bl = 67.84mm.

FIGURE 1.32 Impedance loci for the geometry of Figure 1.31 with the parasitic patch removed.

FIGURE 1.33 Impedance loci for a stacked rectangular patch antenna with a, = 62.56mm, b, = 41.71 mm, a , = 67.84mm, bl = 45.23 mm. The perrnittivities and thicknesses are the same as in Figure 1.31.

TABLE 1.7 Half-Power Beamwidths and Gains of Single and Stacked Patches

Patch HPBW (degrees) Gain (dB)

Single square patch Stacked square patch Single rectangular patch Stacked rectangular patch

values even when the feed is near the edge of the patch. Consequently, some external matching network needs to be introduced if wideband operation is to be realized.

The situation is somewhat different for the stacked rectangular patches. The impedance loci for this case are shown in Figure 1.33. It is seen that when the feed is near the edge (F = 2.90cm), the impedance bandwidth (as defined by VSWR c 2) attains the relatively large value of about 12% without the need of a matching network.

The half-power beamwidths and the gains of the single and stacked patches are given in Table 1.7, showing that the parasitic patch has the effect of enhancing the gain of the antenna.


(b) Smaller S l u hmaltk WCh

FIGURE 1.34 Impedance loci for stacked rectangular patches in which the parasitic patch is of the same size (case a) or smaller than the fed patch (case b). For case a, a,=al=62.56mm, b2=bl=41.71mm. For case b, a2=62.56mm, b2=41.71mrn, a, = 57.69mm, b, = 38.46mm. F = 2.90cm in both cases.

In the results presented above, the parasitic patch is larger than the fed patch. When the parasitic patch is made equal to or smaller than the fed patch, with other parameters remaining the same, the impedance locus no longer has the double-loop characteristic necessary for wideband operation. These are illustrated in Figure 1.34 for stacked rectangular patches fed at F = 2.90 cm. This illustration is intended to show the sensitivity of the impedance characteristics to patch dimensions. It does not preclude the possibility that suitable combination of spacings can yield a double-loop characteristic even if the parasitic patch is smaller than or of the same size as the fed patch.

1.4.4.3 The Need for Design Guides. The performance of the stacked EMCP antenna is sensitive to the various design parameters. For a designer who does not have a workable computer code, designing these antennas involves costly trial and error experimentation. For this reason it would b i helpful if we can extract from the computer code sets of antenna parameters (substrate and superstrate pennittivities and thicknesses, patch dimensions, feed position) which would yield a specified bandwidth at a given center frequency. As examples, three such sets are given in Table 1.8 for a stacked EMCP antenna operating at the center frequency of 5 GHz. Set 1 gives the parameters which will achieve


TABLE 1.8 Design Examples for Stacked Electromagnetically Coupled Patch Antennas at the Center Frequency of 5 GHz

BW (VSWR = 2)

12% 15%,

Parameter Set 1 Set 2 Set 3

E l 1.0 2.2 1.0 €2 1.2 1.2 1.2 83 2.2 2.2 2.2 h (mm) 0.0 0.26 0.0 h2 (mm) 3.580 3.630 3.500 h3 (mm) 0.493 0.486 1.200 a1 (cm) 2.296 2.198 2.300 b1 (cm) 1.275 1.465 1.278 a2 (cm) 2.000 2.027 2.000

FIGURE 1.35 Impedance loci for a stacked EMCP antenna with the parameters given by Set 1 of Table 1.8. Bandwidth = 12%.

a bandwidth of 12% for the case when there is no superstrate. The impedance locus is shown in Figure 1.35. When a superstrate of thickness 0.26 mm and relative permittivity of 2.2 is placed on top of the parasitic patch, the impedance locus becomes that shown in Figure 1.36 if the other parameters are the same as set 1. To achieve 12% bandwidth with the superstrate present, it is necessary to


FIGURE 1.36 Impedance loci when a superstrateof thickness h , = 0.26mm and relative permittivity E , ~ = 2.2 is added to the antenna of Figure 1.35.


RECTANGULAR PATCH WlTH A U-SHAPED SLOT 63

1.0


alter some of the parameters. The result is set 2, which differs from set 1 mainly in the patch dimensions. Set 3 gives the antenna parameters which will yield a bandwidth of 15% when no superstrate is present. The impedance loci of sets 2 and 3 are given in Figures 1.37 and 1.38, respectively. We have also verified from our computer code that if the center frequency is changed, it is only necessary to scale the length parameters accordingly (patch dimensions, substrate and superstrate thicknesses, feed location). Comprehensive design guides covering different combinations of commonly used substrate and superstrate materials are clearly of interest to antenna designers. Such design guides are not yet available in the literature.

1.5 RECTANGULAR PATCH WlTH A U-SHAPED SLOT

It was shown in Sections 1.4.3 and 1.4.4 that the bandwidth of the basic form of coaxially fed microstrip antenna can be enhanced to 10-20% by using parasitic patches either in another layer (stacked geometry) or in the same layer (coplanar geometry). Wider bandwidth, up to about 40%, can be obtained by feeding these antennas with a microstrip line through an aperture(see Chapter 2). However, the stacked geometry has the disadvantage of increasing the thickness of the antenna while the coplanar geometry has the disadvantage of increasing the lateral size of


Air or foam h

Ground plane I I Coax

FIGURE 1.39 Geometry of the coaxially fed rectangular patch with a U-shaped slot. (a) Top view of the patch. (b) Side view.

the antenna. It would therefore be of considerable interest if a single-layer single-patch wideband microstrip antenna could be developed. Such an antenna would better preserve the thin profile characteristics and would not introduce grating lobe problems when used in an array environment. Recently Huynh and Lee [39] reported measurements of a rectangular patch with a U-shaped slot which appears to have wide bandwidth characteristics.

The antenna used in the experiment of Huynh and Lee [39] is shown in Figure 1.39. Figure 1.40 a shows the impedance loci when the patch is 1.06 inches above the ground plane. This corresponds to h zz 0.08 1 at 900MHz. The impedance loci shows a double-looped characteristic, which is to be contrasted with the single-looped characteristic of the rectangular patch without the slot. The measured VSWR versus frequency is shown in Figure 1.40 b. The bandwidth (VSWR= 2) is about 40%. It is important to note that although this is an electrically thick probe-fed patch, there is no appreciable inductive component associated with the input impedance. This is vastly different from the case without

RECTANGULAR PATCH WITH A U-SHAPED SLOT 65

Frequency (GHz) (b)

FIGURE 1.40 (a) Measured impedance loci for h = 1.06 inches (~0.081 at 900MHz). (b) Measured VSWR versus frequency for h = 1.06 inches.

the slot, in which a large inductive reactance is present for substrate thicknesses exceeding 0.03 1 [15].

The radiation from the antenna is linearly polarized, with the E plane parallel to the vertical slots and the H plane parallel to the horizontal slot. The measured patterns in these planes at 900MHz are shown in Figures 1.41 a and 1.41 b. The patterns were found to be stable: The half-power beamwidths in the x-z (H) plane were 59" at 812 MHz and 57" at 1.1 GHz, whereas in the y-z (E) plane they were 65" at 812 MHz and 70" at 1.1 GHz. The beamwidths are narrower than those of the rectangular patch without the slot.


0'

FIGURE 1.41 (a) Measured pattern in the H (x-z) plane at 900 MHz for h = 1.06 inches. (b) Measured pattern in the E (y-z) plane at 900 MHz for h = 1.06 inches.

RECTANGULAR PATCH WITH A U-SHAPED SLOT 67

Huynh and Lee also measured the impedance loci when the patch is 0.53 inches above the ground plane, other parameters remaining the same. This corresponds to hx0.04412 at the new center frequency of 990MHz. The VSWR = 2 bandwidth for this case was found to be about 12.4%, which is still considerably larger than the patch without the slot. The input impedance again does not have an appreciable inductive component.

Following Huynh and Lee [39], Lee et al. [40] studied a variety of U-slot rectangular patches with center frequencies around 4.5 GHz. Their measurements included crosspolarization patterns and gain characteristics. They confirmed the wideband behavior of the structure and investigated the effects of - various parameters on the antenna performance. It was found that the antenna can be designed to have either wideband or dual-frequency characteristics. The gain of the U-slot patch is about 7dBi. Lee et al. [41] also studied a two-element array of U-slot patches. The array had an impedance bandwidth of 29.5%, centered around 4.5 Ghz, with good pattern characteristics.

The U-slot rectangular patch is an example of realizing wideband or dual- frequency behavior using a single patch on a single layer. It appears that the currents along the edges of the slot introduce an additional resonance, which, in conjunction with the resonance of the main patch, produce an overall broadband or dual-frequency response characteristic. The slot also appears to introduce a capacitive reactance which counteracts the inductive reactance of the probe. The moment method analysis described in this chapter and in the references, with

Frequency (GHz)

F IGURE 1.42 Theoretical VSWR versus frequency curve for the antenna of Figure 1.40 using the ENSEMBLE software developed by Boulder Microwave Technologies, Inc.


[28] J. C. MacKinchan, P. A. Miller, M. R. Staker, and J. S. Dahele, 'A Wide Bandwidth Microstrip Subarray for Array Antenna Applications Fed Using Aperture Coup- ling," IEEE AP-S Int. Symp. Dig., pp. 878-881, 1989. M. R. Staker, J. C. MacKinchan, and J. S. Dahele, "Synthesis ofIn-Line Parasitically Coupled Rectangular Microstrip Patch Antenna Subarrays," 18th Eur. Microwave Con$ Proc., Stockholm, Sweden, pp. 1069-1073,1988. P. A. Miller, J. C. MacKinchan, M. R. Staker, and J. S. Dahele, "A Wide Bandwidth, Low Sidelobe, Low Profile Microstrip Array Antenna for Communication Applica- tions," Proc. ISAP'89, pp. 525-528. W . Chen, K. F. Lee and R. Q. Lee, "Spectral-Domain Moment-Method Analysis of Coplanar Microstrip Parasitic Subarrays," Microwave Optical Technol. Lett., Vol. 6, NO. 3, pp. 157-163,1993. R. Q. Lee, K. F. Lee, and J. Bobinchak,"Characteristics of a Two-Layer Electromag- netically Coupled Rectangular Patch Antenna," Electron. Lett., Vol. 23, pp. 1070- 1072, 1987.. L. J. Barlately, J. R. Mosig, and T. Sphicopoulos, "Analysis of Stacked Microstrip Patches with a Mixed Potential Integral Equation," IEEE Trans. Antennas Propagat., Vol. AP-38, pp. 608-615, 1990.

[34] J. P. Daminano, J. Benneguouche, and A. Papiernik, "Study of Multilayered Microstrip Antennas with Radiating Elements of Various Geometry," Proc. IEE, Vol. 137, Pt. H, pp. 163-170,1990.

[35] A. N. Tulintseff, S. M. Ali, and J. A. Kong, "Input Impedance of a Probe-fed Stacked Circular Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. AP-39, Pp. 382-390,1991.

C361 T. M. Au and K. M. Luk, "Effect of Parasitic Elements on the Characteristics of Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. AP-39, pp. 1247- 1251,1991.

[37] Z. Fan and K. F. Lee, "Analysis of Electromagnetically Coupled Patch Antennas," Microwave Opt. Technol. Lett., Vol. 6, pp. 436-441,1994.

[38] K. F. Lee, W. Chen, and R. Q. Lee, "Studies of Stacked Electromagnetically Coupled Patch Antennas," Microwave Opt. Technol. Lett., Vol. 8, No. 4, pp. 212-215, 1995.

[39] T. Huynh and K. F. Lee, "Single-Layer Single-Patch Wideband Microstrip An- tenna," Electron. Lett., Vol. 31, No. 16, pp. 1310-1312, 1995.

[40] K. F. Lee, K. M. Luk, Y. L. Yung. K. F. Tong, and T. Huynh, "Experimental Study of the Rectangular Patch with a U-Shaped Slot," IEEE-APS Inter. Symp. Dig., pp. 10-13,1996.

[41] K. F. Lee, K. M. Luk,K. F. Tong, Y. L. Yung, and T. Huynh, "Experimental Study of aTwo-Element Array of U-Slot Patches," Electron. Lett., Vol. 32, No. 5, pp. 418-420, 1996.

[42] K. F. Lee, K. M. Luk,T. Huynh, K. F. Tong,andR. Q. Lee,"U-Slot Patch Wideband Microstrip Antenna," Proceedings of the 1996 WRI International Symposium, Plenum Press, New York, 1996.

CHAPTER TWO

Aperture-Coupled Muhilayer

K. M. LUK, T. M. AU, K. F. TONG, and K. F. LEE

2.1 INTRODUCTION

Microstrip antennas are commonly fed by one of three methods: (a) coaxial probe, (b) stripline connected directly to the edge of a patch, and (c) stripline coupled to the patch through an aperture. These are shown in Figure 2.1. Feeding by a coaxial probe has the advantages of ease in impedance matching and low spurious radiation and the disadvantage of having to physically connect the center conductor to the patch. In its basic form shown in Figure 2.la, the coaxially fed microstrip antenna has an impedance bandwidth of 2-3%. By using parasitic elements to create dual or multiple resonances, the bandwidth can be improved to 10-20% but seldom exceeds 20% [I-91. Coaxially fed microstrip antennas is the subject of Chapter 1.

The advantage of directly connecting a stripline to the edge of a patch is ease of fabrication. However, impedance matching is not as convenient as the probe feed case, and unwanted radiation from the feed line can be a problem. A method which has become very popular is to couple energy from the stripline through an aperture (slot) in the ground plane. This method, known as aperture coupling, was first proposed by Pozar [lo]. Some of its advantages are as follows: (a) The feed network is isolated from the radiating element by the ground plane which prevents spurious radiation; (b) active devices can be fabricated in a feed substrate with high dielectric constant for size reduction; (c) there are more degrees of freedom for the designer.

Advances in Microstrip and Printed Antennas, Edited by Kai Fong Lee and Wei Chen ISBN 0-471-04421-0 0 1997 John Wiley & Sons, Inc.

72 APERTURE-COUPLED MULTILAYER MICROSTRIP ANTENNAS

Conducting patch, , -.

Ground

Coaxial feed .-D/III

Conducting patch / \ A

Stripline (-&Ground

Conducting patch,

Apertu Ground

FIGURE 2.1 Exploded view of basic form of microstrip antenna. (a) Coaxial feed. (b) Direct stripline feed. (c) Stripline feed coupled through an aperture.

The slot that couples energy from the stripline to the patch can be either resonant or nonresonant. If it is resonant, it provides another resonance in addition to the patch resonance, resulting in an antenna with 10-15% impedance bandwidth. However, the resonant slot has a strong backlobe radiation which substantially reduce the gain ofthe antenna. For this reason, a nonresonant slot is usually used in aperture coupled microstrip antennas. The impedance bandwidth of the basic form of such antenna (Figure 2.1~) is typically 6-7%.

As with coaxially fed microstrip antennas, the impedance bandwidth of aperture coupled microstrip antennas can be enhanced by using stacked or coplanar parasitic elements. This chapter gives a coherent account of the authors' recent work in this area. The most significant result we have obtained is that

GREEN'S FUNCTION FORMULATION 73

aperture coupled multilayer microstrip antennas can attain bandwidths as large as 40%, which is greater than those of dipoles and slots and comparable to the horn antenna. Such bandwidths appear to be larger than those reported in references [I 11 and [12]. In reference [I 11, experimental results for the return loss and the radiation patterns of an aperture-coupled five-patch-cross coplanar subarray were reported. The 10-dB return-loss bandwidth of this subarray was found to be 10.5%. In reference [12], an aperture-coupled stacked microstrip antenna having a bandwidth of around 20% was obtained.

In Sections 2.2 and 2.3, a full-wave analysis of linearly polarized aperture coupled microstrip antennas is presented. In the analysis, the radiation from the coupling aperture in the ground plane is replaced by an equivalent surface magnetic current density on a ground plane without a slot. Spectral domain Green's functions of the multilayer structure are derived. Integral equations for the unknown current densities on the patches and the slot are formulated. Galerkin's procedure is employed to solve for the unknowns. The unknown reflection coefficient in the feedline is derived by using the reciprocity theorem. The formulation can be considered as generalization of the method by Pozar [13] for the single patch case. Illustrative results for input impedance, SWR bandwidth, operating frequency range, and far-field radiation patterns of a number of designs are given in Section 2.4. These include (a) a rectangular microstrip antenna with an air gap between the substrate and the ground plane, (b) coplanar parasitic subarrays, (c) an offset dual-patch antenna, (d) a symmetric two-layer five-patch microstrip antenna, and (e) a stacked parasitic-patch microstrip antenna. Experimental results are obtained to compare with theoretical predictions. Section 2.5 is concerned with the analysis and results of infinite arrays of aperture-coupled multilayer microstrip antennas using the Floquet theorem [14]. Scanning characteristics for arrays with rectangular and triangular grids are computed, and measured data from a waveguide simulator is included. The chapter ends with some concluding remarks.

2.2 GREEN'S FUNCTION FORMULATION

The geometry of an offset dual-patch microstrip antenna fed by the aperture- coupling technique is shown in Figure2.2. It is assumed that the dielectric layers and conductors are losslss and the substrates are infinite in extent. The thicknesses of the conductors are negligible compared with wavelength. The structure can be divided into two regions. In the feed region (z < 0), an %directed infinitely long microstrip line is located at z = - d and y = 0. The dielectric constant and thickness of the feed substrate are E,/ and d, respectively. The center of the aperture is located at the origin. In the patch region (z 2 O), the lower patch on z = 1 and the upper patch on z = 1 + s + hare supported by dielectric layers of the same relative permittivity; that is, a,, = E,, = a,. An airgap of thickness s separates the two dielectric layers.

GREEN'S FUNCTION FORMULATION 75 74 APERTURE-COUPLED MULTILAYER MICROSTRIP ANTENNAS

is located at (x,,, yo, -d) while the horizontal magnetic current is located at the (0,0,0-1.

The electric and magnetic field intensities (E and H) are expressed in terms of electric and magnetic vector potentials ( F and A) . They are shown as follows:

In Cartesian coordinates,

which satisfy the wave equations

To determine the solutions of 2 and F, A,,,., and F,,,,, are transformed into the spectral domain. The following two-dimensional Fourier transform pair is employed:

Ground plane 1 - Aperture Microstrip feedline

=copper Wldielecuic substrate foam material

FIGURE 2.2 Geometry of an aperture-coupled offset dual-patch microstrip antenna with an air gap. (a) Top view. (b) Side view.

2.2.1 Field Components [I 51 The quantity in Eqs. (2.5) and (2.6) with the tilde (-) is the Fourier transform of the corresponding one without the tilde.

Tranforming Eq. (2.4) into the spectral domain, we obtain the following ordinary differential equations:

The electromagnetic fields in any region can be expressed in terms of suitable components of electric and magnetic vector potentials. In the formulation, the radiation from the coupling aperture in the ground plane is replaced by that from an equivalent surface magnetic current density on the ground plane without the slot. Continuity of tangential electric field through the aperture is enforced by making the magnetic current above the ground plane equal to the negative of that below.

The first step of the analysis is to derive the electromagnetic fields of point horizontal electric and magnetic currents for the region z 2 0. Specifically, electric currents located at ( x , , y i , I ) and (x,, y,, I + s + h) are considered. The magnetic current is located at (0, 0 , 0 + ) .

The second step of the analysis is to find the magnetic field expressions for the horizontal electric and magnetic currents in the region z < 0. The electric current

where

kZ = &pa2 - f l l , Im (k) < 0


Solving Eq. (2.7), we have

- The unknown c ~ e _ f f i c i e n t ~ ~ , , , ~ ~ ,,+ and F,,,,,,,, are determined by the boundary conditions. The and E can-then be determined from Eq. (2.1)-(2.2). In this a_nalysis, we set A,(k,,k,, z) = F,(k, k , , z ) ~ 0, and E_q. (2.3) can be simplified as A =A$ + A,? and F = F$ + Fg. The Ex,,,, and H,,,,, in a source-free region can be written in terms of A,., and F,,, as

2.2.2 Boundary Conditions

We need to derive the electromagnetic fields due to point horizontal current elements located at the ground plane and at the lower and upper substrate surfaces. Specifically, electric currents I,, I,, and I, located, respectively, at (xO, yo, - d), (x,, y,, I), and (x,, y,, 1 + s + h), are considered. Magnetic current elements f K are located at the origin (O,O,Ok). The fields produced by each current are considered separately and are obtained by considering the Fourier transforms of the field components in separate regions. The solutions of vector potentials are obtained by matching the tangential field components at the interfaces subject to the following boundary conditions.

I. Boundary conditions for the case with electric current densities:

(i) Tangential electric field is continuous at the interfaces z = zj, j = 0,1,2,3, zo= -d , z ,= l , z ,= l+sandz ,= l+s+h .

GREEN'S FUNCTION FORMULATION 77

(ii) Tangential magnetic field component in the x-direction is continuous at z=zpj=0,1,2,3.

(iii) Tangential magnetic field component in the y-direction is discontinuous at the surfaces z = z,, z = z, and z = z, due to the presence of surface electric current densities.

(iv) Tangential electric field components are zero at the ground plane. (v) All fields satisfy the radiation boundary condition as lzl tends to infinity.

In mathematical form, we have

(i) lim,!?,,,(k,, ky,zj - v) = limE,,, (k, ky,zj + v), j =0,1,2,3 (2.17) v-0 v-0

(ii) lim fi,(k,, k,, zj - v) = limfi,(k, k,zj + v), j = 0,1,2,3 (2.18) v-0 "-0

lim 2 x [l?,(k,, k,, z0 - V) - fi, (k,, ky, 20 + v)I = 10'- j(k~xo + ~ Y Y O 1

- - A,, = -A,-

(iv) { - - for - d < z < l A,+ = +A,-

- - for z < - d , I - - + -

A,-=A,-=O for z > l + s + h

11. Boundary conditions for the case with a magnetic current density:

(vi) Tangential electric field is continuous at the interfaces on z = zj,j = O,l,2,3.

(vii) Tangential magnetic field is continuous at the interfaces z = z j , j = 0,1,2,3.

(viii) Tangential electric field component in the x-direction is not zero at the ground plane due to the presence of surface magnetic current density.

(ix) Tangential electric field component in y-direction is zero at the ground plane.

(x) All fields satisfy the radiation boundary condition as lzl tends to infinity.

t 78 APERTURE-COUPLED MULTILAYER MICROSTRIP ANTENNAS i I GALERKIN'S METHOD 79

In mathematical form, we have

(vi) lim Ex, ( k , k, zj - v) = lim Ex,, (k,, k,, zJ + v), j = 0,1,2,3 v-0 "-0

(2.22)

(vii) lim fix., (k,, k,, zJ - v) = lim fix,, (k,, k,, zJ + v), j = 0,1,2,3 v-0 "-0

(2.23)

(viii) (2.24)

- - (ix) F,+ = - F,- for - d ,< z < 1 (2.25)

Fx+ =F,+ = O for z < - d F,-=F,-=O for z > l + s + h

The spectral domain vector potentials and the corresponding Green's functions are derived in references [23] and [24].

2.3 GALERKIN'S METHOD

The electric and magnetic field integral equations are formulated by enforcing appropriate boundary conditions at the interfaces. One of the boundary conditions is zero tangential electric field E on eackmetal patch. The electric field is contributed by the magnetic current density Ma on the ground plane at z = Oi, the surface electric current density J , , on the lower patch at z = I, and the surface ! electriccurrent density J , , on the upper patch at z = 1 +-s + h. Another boundary condition is the continuity of tansengal magnetic field H across the aperture; that is, the total magneti5field ofM,, J , , and J , , as z+0+ is equal to the total I

magnetic field of -Ma and J f on z = - d as z+0-. As a result, we have the following integral equations:

where p and x(yf) represent the reflection coefficient and the modal field of the feedline, respectively. The reflection coefficient in the feedline is introduced by

using the reciprocity theorem [13]. The reflection coefficient is obtained by

where sa is the aperture surface in the ground plane. For the narrow slot case, the cha_nge of progagation phase across the width of the aperture is negligible.

J,1,3, and M, are the unknowns to becJeteminedJy the method of moments. The unknown surface current densities (J ,,,, and Ma) are expanded into sets of basis functions:

Nt N1+2

Tsi = I , J,? + c I,, J,, 9 1 (lower patch) m= 1 n = l .i = { NS N6

(2.30)

@,= c v , M , ~ + c V"MJ 2 (upper patch) m=l n = 1

where I,,,, and Vm,, are unknown constants of the basic functions. The Fourier transform pairs of the basis functions are given in the Appendix. Equations (2.27)-(2.29) can be rewritten as follows:

For the x-direction:

For the y-direction:


To solve for the unknowns, it is necessary to have N t ( = N , ) linearly i = l

independent equations. Equations (2.3 1)-(2.34) are then weighted with testing functions. A symmetric product (z, s ) can be defined as

A particular choice of the testing functions is that identical to the basis functions, using the Galerkin procedure. Then the symmetric product of an Pdirected test function with an &component of an electromagnetic field is known as self- or mutual-impedance functions (Z, or T,$ or self- or mutual- admittance functions (Y, or C,$. The vector functions Av are obtained in reference [13].

The path of integration is selected to avoid the surface wave poles. The contour path C,j,,, for /3 goes up from the origin with a slope = 1 until at a height j [ above the Re[,!?] axis. It then proceeds parallel to the R e m axis until passing /3 = 2&k0 (for the feed region) or 2&k0 (for the patch region) and rolls off to the ReD] axis with a slope = - 1. Finally it goes along the Re[/3] axis to + co. This method works well for 4' of the order of O.O1ko. The Gaussian quadrature procedure is applied to evaluate the integrals and each integration is terminated at 150k0 (k, is free-space wavenumber). The basis functions are expressed in the form of separation variables (x, y). Each matrix element with different testing function and field component is formulated in references 113, 17,24, and 251.

The effective propagation constant /3, of a microstripline feed is determined by the following characteristic equation [16]:

Assuming the input current I i = lA, the characteristic impedance Zc of the microstrip feedline is determined by computing the voltage between the microstrip line and the ground plane [17] and is given by

Then we arrive at the following matrix equation:

where

ILLUSTRATIVE RESULTS 81

where the superscript T indicates the matrix transpose. When we substitute Eq. (2.47) into Eq. (2.39), the matrix equation becomes

The unknown amplitudes of the basis functions are solved by Gauss elimination with complete pivoting [18]. The unknown reflection coefficient p in the microstrip transmission line is estimated by Eq. (2.47). The input impedance Zin of the aperture-coupled microstrip antenna evaluated at the position x = 0 can be written as

where I , is the stub length from x = 0 to the open-end termination of the microstrip feedline with an equivalent conductor extension correction. Expres- sions for the far-field radiation patterns are also obtained using standard procedures [19]. The correctness of the computer code is confirmed by comparison with the results reported in reference [13].

2.4 ILLUSTRATIVE RESULTS

In this section the theory is employed to design several types of aperture-coupled multilayer microstrip antennas. Characteristics of input impedance, SWR bandwidth, resonant or midband operating frequency, and far-field radiation

82 APERTURE-COUPLED MULTILAYER MICROSTRIP ANTENNAS ILLUSTRATIVE RESULTS 83

patterns are presented. All computed results converge to steady solutions when N,,,,, 3 15, N,,, 2 5,and N, = 0. The $directed electric current elements have insignificant effect on the impedance behavior. In a number of cases, experimental data are obtained to compare with the theoretical predictions.

2.4.1 Microstrip Antenna with an Air Gap

A spectral domain moment method analysis of the coaxially fed rectangular microstrip antenna with an air gap has been presented by Fan et al. 1201. It is difficult in practice to tune the resonant frequency of this type of microstrip antenna by introducing an air gap as the length of probe from the ground to the patch element has to be adjusted. On the contrary, this tuning technique can be implemented for aperture-coupled patch antenna because there is no physical contact between the radiating element and the feeding network. The geometry of sn aperture-coupled rectangular microstrip antenna with an air gap is shown in Figure 2.3. The dimensions of the patch and the aperture are 20.0 x 20.0 mm2 and

Microstrip feedline

c o p p e r PEldielectric substrate 1 foam material

FIGURE 2.3 Geometry of an aperture-coupled rectangular microstrip antenna with an air gap. (a) Top view. (b) Side view.

0.5 x 10.Ommz, respectively. The identical substrates are used in

patch is centered above the aperture. Two this analysis; that is, d= h= 1.59mm and . -

= E , ~ = 2.32. The width of the open-circuited microstrip line of characteristic impedance Z, = 50Q is wJ = 4.6mm. The length of the stub is If = 10.0mm. Numerical results for SWR against frequency are obtained to compare with experimental data.

For this geometry, Eqs. (2.27H2.28) can be simplified as follows:

Figure2.4 shows the characteristics of the aperture-coupled rectangular microstrip antenna with different air-gap spacing s. It is found that the resonant frequency increases with the air-gap height, while the input resistance and reactance decrease. The SWR bandwidth is enhanced at suitable s. The tunable range of the aperture-coupled microstrip antenna with air-gap spans as large as 14% of the resonant frequency. The back lobe radiation reduces slightly with a wider air gap. The E-plane beamwidth decreases slightly as s increases. The H-plane pattern has no significant change for different air-gap spacing.

2.4.2 Coplanar Microstrip Subarrays

Four configurations of coplanar parasitic elements incorporated into the aperture-coupled microstrip antennas are investigated in this section. The geometries of the structures to be considered are shown in Figures 2.5 and 2.6. Additional patches are gap-coupled to the nonradiating edges of the fed rectangular patch. The sizes of the additional patches are identical for each configuration. The resonant lengths of the parasitic patches are the same as that of the fed patch; that is, a, = a,. The displacement in x-direction (Figure 2.6) between the centers of the fed patch and the parasitic elements is x,. In all cases, the gap between the two adjacent metal patches is 1.0mm in the y-direction. Subarray 1 and Subarray 2 have two and four parasitic elements, respectively. The individual centers of the parasitic elements are (x,, & y,, 1) for Subarray 1 and (x, + xd, + y,, I ) for Sub- array 2.

The parameters of the feed and antenna substrate are E,/ = E , ~ = 2.32, d = 1.6 mm, and 1 = 3.2mm. The center of the aperture is located a t the origin. The dimensions and the center of the fed patch are 19.3 mm(2a1) x 28.5 mm (2w1) and (x,, 0, I), respectively. For fixed sizes of aperture and fed patch, maximum SWR bandwidth is attained by varying x,, w, and x,. The dimensions of each configuration are shown in Table 2.1.

Equations (2.27) and (2.28) are modified as follows:


(c) E plane

0- 4.0 4.14.2 4.34.44.54.64.74.84.9 5.0

Frequency (GHz) (b)

(dl H plane

FIGURE 2.4 Characteristics of an aperture-coupled rectangular microstrip antenna with different air gap s. (a) Calculated input impedance loci. (b) SWR against frequency. (c,d) Calculated far-field radiation patterns.

Calculated Measured

s = 0.00mrn -- s = 0.lOmm eaee ---- s = 0.20 mm --------------- s=0.30mm oooo

s = 0.40mm

s = 0.50 mm

ILLUSTRATIVE RESULTS 8 5

- Aperture 1 ~ i c r o s t r i ~ feedline

Ground plane

Aperture dielectric substrate

Microstrip feedline c o p p e r

FIGURE 2.5 Geometry of an aperturezoupled microstrip antenna with two parasitic elements (Subarray 1). (a) Top view. (b) Side view.

(i) For the two parasitic elements case:


Ground plane 2 / 1 / MPdielectric substrate

Microstrip feedline c o p p e r

FIGURE 2.6 Geometry of an aperture-coupled microstrip antenna with four parasitic elements (Subarray 2). (a) Top view. (b) Side view.

(ii) For the four parasitic elements case:

TABLE 2.1

zb0 230

, (mm) 1, (mm) a, (mm) w, (mm) X I (mm) w2 (mm) x, (mm) y2 (mm)

Subarray 1L 4.6 16.0 0.75 15.0 9.0 7.125 0.00 22.375 Subarray 2L 4.6 16.0 0.75 15.0 9.0 7.125 + 11.65 22.375 Subarray 1S 4.8 14.0 0.25 12.5 7.5 8.550 0.00 23.800 Subarray 2s 4.8 14.0 0.25 12.5 7.5 8.550 + 12.65 23.800

Single-patch L 4.6 16.0 0.75 15.0 9.0 - - - Single-patch S 4.8 14.0 0.25 12.5 7.5 - - -

Note: L denotes a large aperture size, while S denotes a small one.

FIGURE 2.7 Characteristics of an aperture-coupled rectangular microstrip antenna (single-patch L). (a) Input impedance locus; frequency scan: 3.5-5.OGHz, in steps of 0.1 GHz. (b) Calculated far-field radiation patterns, f = 4.1 GHz. --- E plane; --- H plane.

Figures 2.7 and 2.8 show input impedance locus against frequency and far-field radiation patterns of an aperture-coupled rectangular microstrip antenna for different aperture sizes and stub lengths. It is observed that for a given metal patch, the back lobe radiation can be decreased by reducing the aperture dimensions. However, the SWR bandwidth is lessened as the aperture sizes become smaller. It is also found that the far-field radiation patterns show no significant variation with the aperture dimensions.

Figures2.9-2.12 show the characteristics of an aperture-coupled coplanar microstrip subarray for the four configurations. For the E-plane radiation pattern, it is observed that the strongest radiation direction shifts slightly from the broadside direction at higher operating frequency. The front-to-back ratio


FIGURE 2.8 Characteristics of an aperture-coupled rectangular microstrip antenna (Single-patch S). (a) Input impedance locus; frequency scan: 3.5-5.OGHz, in steps of 0.1 GHz. (b) Calculated far-field radiation patterns, f = 4.2GHz. --- E plane; ---- H plane.

and the cross-polarization are increased with operating frequency. The beamwidth is slightly reduced at higher operating frequency. The cross-polarized fields are below 40 dB over the passband and are too small to display in the figures.

With a smaller aperture, the SWR bandwidth of Subarray 1s is slightly greater than that of Subarray 1L. However, the SWR bandwidth reduces with increasing x,for the case of two parasitic patches. To conclude, the SWR bandwidth and the E- and H-plane beamwidths can be improved by changing the sizes and the locations of the parasitic patches.

The calculated 3-dB beamwidth, SWR bandwidth, %BW, midband operating frequencyf,, and lower and upper cutoff frequencies ( f,, f,) for the four configurations are listed in Table 2.2. It is found that the configuration Subarray 2L

TABLE 2.2

E x H Beamwidth

fL(GHz) f&GHz) f,(GHz) atf, BW(GHz) %BW

Subarray 1L 3.896 4.400 4.148 118" x 62" 0.504 12 Subarray 2L 3.812 4.530 4.171 94" x 52" 0.718 17 Subarray 1s 3.980 4.540 4.260 116" x 52" 0.560 13 Subarray 2s 3.935 4.534 4.235 92" x 50" 0.599 14


(b) f = 3.9 GHZ

(d) f = 4.4 GHz

FIGURE 2.9 Characteristics of an aperturesoupled coplanar microstrip subarray (Sub- array 1L). (a) Input impedance locus; frequency scan: 3.0-5.0GHz, in steps of 0.1 GHz. (b-d) Calculated far-field radiation patterns for different operating frequencies. --- Copolarized E plane; ---- copolarized H plane; - cross-polarized E plane.

attains the largest bandwidth and also has a smallest beamwidth. Comparison between theory and experiment is shown in Figures 2.10 and 2.11. Good agreement is observed.

Theoretically, the back lobe radiation can be made to vanish by using an infinite plane reflector sheet below the feed substrate. We are going to investigate this case and assume that the reflector is located at z = - d - t. Since the dominant radiation is contributed by the metal patches, the optimum spacing t between the feed substrate and the reflector should be smaller than one- quarter of a free-space wavelength. The characteristics of SWR bandwidth


d . . . . . . , . . . . . . . I 3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9

Frequency (GHz) ' (a)

(c) f = 4.2 GHz

(b) f = 3.8 GHz

FlGURE2.10 Charactehtics of an aperture-coupled coplanar microstrip subarray (Subarray 2L). (a) SWR against frequency. ooo Measured; -calculated. (b-d) Far-field radiation patterns for different operating frequencies.

Calculated Measured

--- Copolarized E plane A A A A - - - - - - - Copolarized H plane a • 0

Cross-polarized E plane

3.5 3.7 3.9 4.1 4.3 4.5 4.7 4.9 Frequency (GHz)

(a)

ILLUSTRATIVE RESULTS

(b) f = 4.0 GHz

(c) f = 4.2 GHz (d) f = 4.5 GHz

FIGURE 2.11 Characteristics of an aperture-coupled coplanar microstrip subarray (Subarray IS). (a) SWR against frequency. 0.0 Measured; - calculated. (b-d) Far-field radiation patterns for different operating frequencies.

Calculated Measured

--- Copolarized E plane A A A A

- - - - - - - Copolarized H plane noon Cross-polarized E plane


(dl f = 4.5 GHz

FIGURE 2.12 Characteristics of an aperturetoupled coplanar microstrip subarray (Subarray 2s). (a) Input impedancelocus; frequency scan: 3.5-5.0GHz, in steps of 10GHz. (b-d) Calculated far-field radiation patterns for different operating frequencies. --- Copolarized E plane; ---- ~~polarized H plane; - cross-polarized E plane.

and far-field radiation patterns of Subarray 1 s and Subarray 2L with different t are studied.

With the reflector present, one of the boundary conditions shown in Section 2.2 is modified: the tangential electric field components are zero at z = - d - t. Equations (2.69)-(2.76) are modified in the formulation of the matrix equation.

Figures 2.13a and 2.14a show, respectively, the Smith chart for the Subarray 1 s and SWR plot of the Subarray 2L for different t. Maximum bandwidth for the subarrays is attained at t = 1.5 mm. The E-plane and H-plane beamwidths are

(c) f = 4.1 GHZ

(b) f = 3.8 GHz

(d) f = 4.5 GHz

FIGURE 2.13 Characteristics of an aperturetoupled coplanar rnicrostrip subarray (Subarray IS with reflector). (a) Input impedance loci for different t; frequency scan. 3.5-5.0 GHz, in steps of 0.1 GHz. 0-0-0 Without reflector; o-0-0 t = 1.5 mm. , A-A-A t = 3.0mm. (b-d) Calculated far-field radiation patterns for different operating frequencies, t = 1.5 mm. --- Copolarized E plane; ---- copolarized H plane, - cross- polarized E plane.

changed only slightly across the passband. The calculated results of the Subarray 1 s and the Subarray 2L with reflectors are tabulated in Table 2.3.

2.4.3 Offset Dual-Patch Microstrip Antennas

An aperture-coupled offset dual-patch rnicrostrip antenna (Figure2.2) is examined here. Two sets of configurations are considered. The dielectric constant


0 . . 3.0 4.0 J 5.0

Frequency (GHz) (a) (b) f = 3.6 GHz

(dl f = 4.5 GHz

FIGURE 2.14 Characteristics of an aprtunooupled coplana microstrip submay (Subarray 2L with reflector). (a) SWR against frequency for different t. - Without reflector;---t = 1.0mm; ---- t = 1.5 mm; - - - t = 2.0- (b-d) Far-field radiation patterns for different operating frequencies, t = 1.5mm. Cdculatcd: --4opolakcd E plane; ---- Copolarized H plane; --- Cross-polarized E plane; ---- Cross- polarized H plane.

TABLE 2.3

E x H Beamwidth

With reflector fdGHz) ~H(GHz) j.(GHz) at& BW (GHz) %BW

Subarray 1s 3.717 4.544 4.131 120" x 60" 0.827 20 Subarray 2L 3.513 4.578 4.046 102. x 56' 1.065 26

TABLE 2.4

2 2 0 z < 0

b(mm) I ( = ) a, (-1 x1 (-1 s1 (-1 a, (mm) x, (mm)

Offset 1 16.0 1.6 9.45 - 8.4 6.0 11.8 - 1.0 Offset 2 13.0 3.2 9.65 - 6.0 4.0 11.6 0.0

and thickness of the feed substrate are 2.32 and 1.6 rnm, respectively. The width of the microstrip feedline is 4.6 mm. The dimensions of the aperture are 30.0mrn x 1.5 mm. The relative permitivity of patch substrates is 2.32. The width of the metal patches are identical, and w, = w, = 14.25 mm. The thickness of the upper dielectric layer is 1.6 mm. The dimensions of each configuration are shown in Table 2.4.

Figure2.15 shows the comparison of the theoretical results with measurements for the SWR against frequency. The theory uses both entire basis and piecewise sinusoidal functions. It is found that there is no significant difference in SWR behavior between the two functions. The edge condition is applied to the aperture field expansion and the microstrip feedline current expansion. The effect of the edge condition is not obvious.

Figures 2.16 and 2.17 show the far-field radiation patterns. It is observed that the beam squint occurred in the E plane at higher operating frequency. The agreement is reasonably good. It is found that when the lower substrate thickness increases, better front to back ratio is obtained.

The calculated and measured results for the two configurations are shown in Table 2.5. Reasonable agreement between theory and experiment is observed. The measured bandwidth is slightly larger than the theoretical one. The shift in resonant frequency may be caused by the finite ground plane and the tolerance in geometrical and physical parameters. It should be mentioned that larger SWR bandwidth is attained with the use of a thicker substrate for the fed patch. Moreover, the total thickness (d + 1 + s + h) for the offset 2 is less than that of offset 1.

For the dual-patch antenna with offset 2, the effect of the horizontal displacement of the lower patch on the SWR and radiation patterns is also investigated. Figure 2.18 shows the SWR against frequency for different x,. It is found that the bandwidth is enhanced with a suitable value of x,.

Figure 2.19 shows the calculated co- and cross-polarizations radiation patterns at the E plane and the H plane for the aperture-coupled dual-patch antenna offset 2 with different x, . It is found that the front to back ratio decreases as x, is increased. For the E-plane radiation pattern, the strongest radiation direction shifts alightly away from the broadside direction at higher operating frequency and at larger x,. The levels of crosspolarization at the E plane and the H plane increase with x,. The maximum value at the E plane and H plane are about - 40dB and - 50dB and across the passband, respectively.


0- 3 4 5 Frequency (GHz)


(a) f = 3.5 GHz

(a) Offset. 1

FIGURE 2.16 Far-field radiation patterns of an aperture-coupled offset dual-patch microstrip antenna for different operating frequencies (Offset 1).

ot . . . . . . . . , , , , , , 3 4 5

Frequency (GHz) (b) Offset.2

FIGURE 2.15 SWR against frequency for aperture-coupled offset d u a antenna. oooe Measured.

EB PWS

Without edge condition - - - -_ _ _ _ _ _ _ _ _ _ _ _ Aperture and feedline with edge condition ---- - _ -

(d) f = 4.7 GHz

Calculated Measured

--- E plane A A A A

- - - - - - - H plane onno

2.4.4 Two-Layer Microstrip Antennas with Stacked Parasitic Patches

In the previous two sections, bandwidth and gain enhancements of aperture- coupled patch antennas with the use of either stacked or coplanar parasitic elements have been studied. In this section, two microstrip antennas with stacked parasitic patches are presented.

(a) f = 3.5 GHZ


(b) f = 4.0 GHz

(c) f = 4.5 GHz (d) f = 4.9 GHz

FICURE2.17 Far-field radiation patterns of an aperture-coupled offset dual-patch microstrip antenna for different operating frequencies (Offset 2).

Calculated Measured

--- E plane A A A A - - - - - - - H plane 0000

2.4.4.1 Symmetric Two-Layer Five-Patch Microstrip Antenna. Figure 2.20 shows the geometry of a symmetric two-layer five-patch antenna, in which the fed patch is on the bottom layer and four parasitic patches are on the top layer. The lower patch is centered above the aperture. The dimensions of the parasitic patches are identical. The upper parasitic elements are located symmetrically


. . . . . . . . . I . . . . , , , ,

3 4 5 Frequency (GHz)

FIGURE 2.18 SWR against frequency of an aperture-coupled dual-patch microstrip antenna (Offset 2) for different x,.

with respect to the center of the fed patch. The characteristics of one such antenna are given in this section. The parameters of the feed substrate are erf = 2.32, d = 1.6mm, a, = 0.75mm, w, = 4.6mm, and I, = 13.0mm. The dielectric constant of patch substrates is 2.32. The thicknesses of the lower and the upper dielectric layers are 3.2 mm and 1.6 mm, respectively. The widths of the lower and upper patches are 2w1 = 28.5 mm and 2w2 = 1 . 8 ~ ~ = 25.65 mm. The resonant length of the upper patch is 212, = 23.2 mm. The dimensions of two antennas to be considered are shown in Table 2.6.

Equations (2.27)-(2.28) are modified as follows:

-180 -120 60 0 60 120 1 8 (Degree)

(a) Co-polarization, f = 3.7 GHz

(b ) Co-polarization, f = 4.1 GHz

-180 -120 -€a 0 €4 120 180 0 (Degree)

(c) Co-polarization. f = 4.5 GHz

0 (Degree)

(d) Cross-polarization, f = 3.7 GHz

-90 -60 -30 0 3 0 60 90 o (Degree)

(e) Cross-polarization, f = 4.1 GHz

0 (Degree)

(n Cross-polarization, f = 4.5 GHZ

FIGURE 2.19 Calculated co- and cross-polarized radiation patterns of an aperture- coupled dual-patch antenna (Offset 2) with different x, for different operating frequencies. E refers to E-plane pattern. (a-c) E-plane and H-plane copolarized fields. (d-f) E-plane and H-plane cross-polarized fields. - - - x, =O.OOmm; ---- x, = -2.00mm; --- X, = -4.00mm;----x, = -6.00mm. 101


TABLE 2.6

w~ (-1 a1 (mm) ~(mrn) x, (mm) y, (-1 Symmetry 1 15.0 12.2 2.0 + 15.6 f 16.825 Symmetry 2 13.0 11.8 3.0 f 12.6 f 13.325

-copper 48dielectric substrate foam material

FIGURE 2.20 Geometry of a symmetric two-layer five-patch microstrip antenna. (a) Top view. (b) Side view.

Figures 2.21 and 2.22 show, respectively, the characteristics of SWR bshavior and far-field radiation patterns of the antennas with Symmetv 1 and Symmetry 2. The E-plane and H-plane beamwidths decrease slightly at higher frequencies. It is observed that the beamwidth reduces and the cross-polariration increases when x, and y, increase. The calculated results are listed in Table 2.7. The bandwidth of Symmetry 2 appears to be larger than the values reported in reference [21] for a two-layer five-patch antenna fed by a stripline.


13 (Degree) (c) f = 3.8 GHz

8 (Degree) (d) f = 4.1 GHz

FIGURE 2.21 Characteristics of an aperturecoupled two-layer five-patch microstrip antenna (Symmetry 1). (a) SWR against frequency. (b-d) Calculated far-field radiation patterns for different operating frequencies. --- Copolarized E plane; --- copolarized H plane; --- cross-polarized E plane; ---- cross-polarized H plane.

2.4.4.2 Symmetric Two-Layer Thee-Patch Microstrip Antenna. Figure 2.23 shows the geometry of an aperture-coupled microstrip antenna with two stacked parasitic patches. In this section, a wideband design procedure is demonstrated for this antenna.

For all configurations to be considered below, the parameters of the feed substrate are trf =2.32, d = 1.6mm, a, = 0.75mm, wf =4.6mm, and 1, = 13.0mm. The dielectric constant of the feed substrate is E , ~ = 2.32 and its thickness is d = 1.6mm. The dielectric constant of patch substrates is e, = 2.32.


ot 2.5 3.0 3.5 4.0 4!5

Frequency (GHz)

O --.+ . .\

-10 - - -1

0 30 60 90 120 150 I 0 (Degree)

(c) f = 3.6 GHz

FIGURE 2.22 Characteristics of an aperture-coupled two-layer five-patch microstrip antenna (Symmetry 2). (a) SWR against frequency. (b-d) Calculated far-field radiation patterns for different operating frequencies. --- Copolarized E plane; - copoldzed H plane; --- cross-polarized E plane; ---- cross-polarized H plane.

TABLE 2.7

E x H Beamwidth

f, (GHz) f, (GHz) f, (GHz) a tL BW (GHz) %BW

Symmetry 1 3.369 4.135 3.752 72" x 56" 0.766 20 Symmetry 2 2.864 4.336 3.600 80" x 64" 1.472 41

c o p p e r .Ejdielectric substrate 0 foam material

FIGURE 2.23 Geometry of an aperturecoupled microstrip antenna with two parasitic elements. (a) Top view. (b) Side view.

The thicknesses of the lower and upper substrates are 1 = 3.2 mm and h = 1.6 mm, respectively. The width of the fed patch is 2w, = 30.0 mm and the resonant length of the parasitic patches is 2a2 = 20.0 mm.

Equations (2.56)-(2.57) are simplified as follows:


FIGURE 2.24 Smithchart plot of the calculated input impedance of an aperture-coupled microstrip antenna with x, = 13.0mm for different s.

Figure2.24 shows the calculated impedance loci of an aperture-coupled microstrip antenna for different s with a fixed value of x, = 13.0mm. The dimensions of all metal patches are equal; that is, a, = a 2 = 10.0mm and w, = w2 = 15.0mm. The width of the aperture is 15.0mm. The reference plane is established at the center of the aperture. The frequency range is from 3.0 GHz to 5.0GHz with a step of 0.1 GHz. It is observed that the "coupling loop" on the Smith chart becomes smaller as s is increasing. The calculated lower and upper cutoff frequencies (f,, f,), midband frequencyf,, SWR bandwidth, and percentage bandwidth (%BW) are shown in Table 2.8. It is found that the SWR bandwidth attains a maximum value when s = 3.0mm.

Figure2.25 shows the calculated impedance loci of the aperture-coupled microstrip antenna for different x,. The substrate spacing s between the two patch substrates is 3.0mm and other parameters are same as before. As x2 increases, the coupling loop also reduces. The calculated results are listed in


FIGURE 2.25 Smith chart plot of the calculated input impedance of an aperture-coupled microstrip antenna with s = 3.0mm for different x,.

TABLE 2.8

s (mm) fL (GHz) f,, (GHz) f, (GHz) BW (GHz) %BW

. .- . .

w,, = 15.0 mm, a, = 10.0 mm, w, = 15.0 mm, and w, = 13.0 mm.

Table 2.9. A maximum bandwidth is obtained when s=3.0mm and x, = 12.0 mm while all patches are identical. From the above results, it is seen that the bandwidth of the patch antenna can be enhanced with appropriate values of s and x,.

For the values of s and x, just determined, further increase in bandwidth is found if the resonant length of the lower patch (2a,) is reduced to 19.0 mm. The


TABLE 2.9

X2 (mm) f~ (GHz) f~ (GHz) j; @Hz) BW (GHz) %BW

11.0 3.324 4.575 3.950 12.0

1.251 3.396

32 4.7 13 4.055

13.0 1.317

3.438 33

4.743 4.091 1.305 32

w,= 15.0mm,a,=10.0mm,s,=3.0mm,andx2= 15.0mm.

'.-I--' - wr~ = 15.0 mm, wr = 15.0 mm

6 w t ~ = 14.0 mm, y = 15.0 mm

FIGURE 2.26 Smith chart plot of the calculatedinput impedance of an aperture-coupled microstrip antenna with s = 3.0mm and x2 = 12.0- for different w, or w,.

widths of the aperture w, and the parasitic patches w , are then adjusted. Figure 2.26 shows the input impedance loci of the aperture-coupled microstrip antenna with s = 3.0mm and x, = 12.0mm for different w, or w,. The calculated results are tabulated in Table 2.10. With a smaller aperture width, 2wo = 28.0mm, a bandwidth of 37% is obtained. It is also found that the bandwidth can be increased by increasing the width of the parasitic patches w, and/or by reducing the width of the aperture.

INFINITE ARRAYS 109

TABLE 2.1 0

w,(mm) w, (mm) ~ ( G H z ) fH(GHz) f,(GHz) BW (GHz) %BW

15.0 15.0 1.347 3.345 4.692 4.019 33

15.0 16.0 1.366 3.323 4.689 4.006 34

14.0 15.0 1.494 37 3.292 4.786 4.039

a, = 9.5 mm, s = 3.0 mm, and x, = 12.0 mm.

TABLE 2.1 1

w, (mm) w2 (-1 fL (GHz) fH (GHz) f,(GHz) BW (GHz) %BW

14.0 20.0 1.522 39 3.194 4.716 3.955 13.0 23.0 1.810 45 3.100 4.910 4.005

The characteristics of aperture-coupled microstrip antennas with smaller aperture width and larger parasitic patch width are shown in Figure2.27. Figure 2.27 a shows SWR against frequency for different w, and w,, and other parameters are the same as those shown in Figure 2.26. The calculated results are listed in Table 2.11. A 45% bandwidth is attained for w, = 13.0mm and w, = 23.0 mm. Experimental results are obtained to compare with the theory. The discrepancy between theory and experiment may be caused by the finite ground plane, the tolerance in geometrical and physical parameters, and the imperfection of the measurement environment. No significant improvement in bandwidth is found by changing s, x,, a,, w,, w,.

2.5 INFINITE ARRAYS OF APERTURE-COUPLED MULTILAYER MICROSTRIP ANTENNAS

In this section, a full-wave analysis of infite arrays of aperture-coupled microstrip antennas are described. The periodic spectral Green's functions are derived by the Floquet theorem. Reflection coefficient versus scan angle in an arbitrary scan plane is calculated. Measured data obtained from a waveguide simulator are used to compare with the theory.

2.5.1 Skewed Periodic Structure and Floquet Modes [22,23]

Figure 2.28 shows the geometry of an infinite array of aperture-coupled multilayer microstrip antenna. The dielectric layers are extended in the xy or x' y'

11 0 APERTURE-COUPLED MULTILAYER MICROSTRIP ANTENNAS INFINITE ARRAYS 111

Frequency (GHz) ............... a1 = 9.5 mm, I N ~ = 14.0 mm, IN, = 20.0 mm a, = 9.5 mm, wo = 13.0 mm, w 2 = 23.0 mm . . Measurement al=9.5mm, wo=13.0mm, w2=23.0mm

(a) (b) f = 3.1 GHz

(c) f = 4.0 GHz (d) f = 4.9 GHz

FIGURE 2.27 Characteristics of an aperture-coupled microstrip antenna, s = 3.0mm and x, = 12.0mm. (a) SWR against frequency for different w, and w,. (b-d) Far-field radiation patterns for different operating frequencies.

Calculated Measured

--- E plane A A A A - - - - - - - H plane O O O D

' 'Feedline Ground plane

FIGURE 2.28 Geometry of an infinite array of aperture-coupled multilayer rnicrostrip patches.

plane. The periodicity is along two oblique coordinates, x' and y'. A unit cell is a parallelogram with lengths U, and U, along the x' and y' coordinates, respectively, and 6 and 4 are scan angles. The shape angle of the parallelogram is r. Any one of the unit cells is specified by the indices (p, q) that determine the x' and y' coordinates of the cell center.

For the xy periodic structure, the electromagnetic fields in such a unit cell satisfy Maxwell's equation and are subject to Floquet boundary conditions. The Fourier integrals are replaced by an infinite summation of Floquet modes (space harmonics). Specifically the following changes are effected:

11 2 APERTURE-COUPLED MULTILAYER MICROSTRIP ANTENNAS

where

For skewed periodic structure, the patches and apertures are periodical in x' and y'. The coordinates (x', y') are related to the (x, y) coordinates by

x = x ' + y1c0sI; y = y' sin 5

The complete solutions of k, and ky are found as

The assumption of no mutual coupling between the feedlines is made [14]. The (p, q) modal magnetic field on the (p, q) feedline is only a function of the unknown magnetic current density on the ground plane at @, q). The active input impedance of an aperture-coupled microstrip antenna array is determined by any one of the feedline. The elements of the impedance and admittance matrices are modified as follows:

(i) I; = 90"

INFINITE ARRAYS 113

(ii) I; # 90"

The determination of the unknown input impedance of the aperture-coupled microstrip antenna array follows that described in Section 2.3 for the single element case. The definition of the active reflection coefficient T(B, @) for the scan angle 0 and 4 is

All computed results converge to steady solutions when the Floquet wavenumbers lpl and Iql2 60.

2.5.2 Infinite Array of Microstrip Antennas with Air Caps

An infinite array of aperture-coupled microstrip antennas with an air gap is examined. The calculated reflection coefficient versus scan angle is investigated for different scan planes.

The parameters of the feed and antenna substrates, as well as the dimensions of the aperture and the patch, are described in Section 2.4.1 and are repeated here for convenience:e,=2.32,d = h = 1.6mm,wf =4.6mm,lf = 10.0mm,ao=0.25mm, s = 0.5 mm, and a, = w, = 10.0mm. The element spacing is 25.0mm (z 0.351,,, lo, refers to the mid-band wavelength of an array). The width of the aperture 2w0 is modified to 14.0 mm for good matching to a 5 0 4 microstrip feedline at broadside scan.

Figure2.29 shows the scan characteristics of an infinite array of aperture- coupled microstrip antenna with an air-gap. It is found that the resonant frequency of an array with a rectangular or a triangular grid increases with air-gap spacing. Moreover, no significant difference in the scan characteristics is observed between the triangular array and the rectangular array.


0.9-

0.8-

0.7-

0.6-

0.5-

0.4- ,. 1 ; 0.3-

I , .

/. +-.-.:j 0.2- r--. 4 A-

~ . O M , , , , , a

0 10 20 30 40 50 60 70 80 90 . Scan Angle 0 (Degree)

(a) Rectangular grid, f = 4.25 GHz

0.4 ....... "-_._..__.-_(.._...I__._..__.I_.._...,_(.._...I__._..__.I_.._..,,

0.3

0.2

0.1

0.0

(b) Triangular grid, f = 4.25 GHz

. . . . . . 0.0 , , , ,

3.5 4.0 4.5 5 Frequency (GHZ)

(d) Triangular grid, 0 = ,$ = 0-

FIGURE 2.29 Scan characteristics of an inhite array of aperture-coupled Mcrostdp antennas with air gaps. (a, b) Calculated reflection coefficient magnitude versus senn ande 0 for E, D, and H planes, s = 0.5 mm. - - - E plane; ---- D plane; - -- H plane. (c, d) Calculated reflection coefficient magnitude against frequency in the broadside dir~tion. --- s = 0.3 nun; ---- s = 0.5mm; - - - s = 0.7mm.

2.5.3 Infinite Array of Dual-Patch Microstrip Antennas

Infinite arrays of probe-fed stacked microstrip patches were investigated by Lubin and Hessel [26] and by Aberle at al. [27] It was found that the scan-bandwidth was increased if the dielectric constant of the upper layer was smaller than that of the lower layer according to a relationship. Moreover,

. - . ~

Frequency (GHz)

Frequency (GHz) (b l0 = 50'

0.9

0.0 u 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Frequency (GHz) (c) 0 = 60'

Frequency (GHz) (dl 0 = 40'

2.0 2.5 3:0 3;5 4;0 4:5 5:0 Frequency (GHz)

(el 0 = 50' 1.0, I

0.oI.. . . . . . . . . . . . . . . . I 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Frequency (GHz) (f) 0 = 60'

FIGURE 2.30 Scan characteristics of an infinite array of dual-patch microstrip antenna with rectangular and triangular grids against frequency for different 0 scan volumes, x, = 0.0 mm. (a-c) Rectangular grid. (d-f) Triangular grid. - Broadside; --- E plane; ---- D plane; - a - H plane.

115

Frequency (GHz) (b) 0 = 50'

2.0 2.5 3.0 3.5 4.0 4.5 5.0 Frequency (GHz)

lc) 0 = 60"

Frequency (GHr)

2.0 2.5 3.0 3:5 4:0 . _._ Frequencv (GHz)

. . Frequency (GHz) (0 e = 60'

FIGURE 2.31 Scan characteristics of an infinite array of offset dual-patch microstrip antenna with rectangular and triangular grids against frequency for different 0 scan volumes, x, =: l.Omm. (a-c) Rectangular grid. (d-f) Triangular grid. - Broadside; --- E plane; ---- D plane; H plane. 116

INFINITE ARRAYS 117

TABLE 2.12 - - Scan-Bandwidth (%)

Rectangular Grid (r = 90") Triangular Grid (r = 60")

6 Without Offset With Offset Without Offset With Offset

frequency-independent matching networks were necessary to be inserted between the array elements and the feedlines. It is not easy to implement the desired dielectric constant of the upper layer, and frequency-independent matching networds are difficult to design over wide operating frequencies. It will be seen in the results that follow that the above disadvantages can be overcome by using an infinite array of dual-patch microstrip antennas with an air gap between the substrates supporting the patches.

After selecting a set of element spacings of U, and U, and the scan angle (0,4), the element parameters are adjusted until a maximum bandwidth is obtained. An array with a triangular grid and with a scan angle of 0 = 60" in the H plane is selected. The calculated reflection coefficient magnitude against frequency for different scan angles at different scan planes are reported. Numerical results for reflection coefficient magnitude against frequency are obtained to compare with measurements from a waveguide simulator.

The element spacings in two oblique directions are equal and are selected to be 30.0 mm. The parameters of the feed substrate are described in Section 2.4.3 and are repeated here: E , ~ = 2.32, d = 1.6mm, w =4.6mm, and If = 13.0mm The dimensions of the aperture are 1.0mm x 24.0mm. The thicknesses of the lower and upper dielectric layers are 3.2mm and 1.6mm, respectively. The relative permittivity of the patch substrates is 2.32. The air-gap spacing between two patch substrates are 4.5 mm. The resonant lengths of the lower and upper patches are 19.8 mm and 20.2 mm, respectively. The width of each metal patch is identical; that is, w, = w, = 12.5mm. The upper patch is centered above the aperture.

Figures 2.30 and 2.31 show, respectively, the scan characteristics of the infinite array with a rectangular and triangular grids for different scan angles (0,4). A larger scan-bandwidth is obtained at higher scan angle 0. For this configuration, the scan-bandwidth is increased slightly if the patches are offset.

The scan-bandwidths (%) of the configuration in different scan volumes 0 are tabulated in Table 2.12. We can conclude that the scan-bandwidth of an array can be optimized with appropriate a ,,,, s, x,, and U ,,,.

I CONCLUSIONS 11 9

11 8 APERTURE-COUPLED MULTILAYER MICROSTRIP ANTENNAS

Calculated

Measured

----- Scan angle FlGURE2.32 Reflection coefficient magnitude against frequency for m aperture- coupled dual-patch microstrip antenna, a, = 9.9mm, a, = 10.1 mm, w, = w, = 12.5mm, x, =O.Omm,s=4.5mm, U,= Uy=30.0mm, t=W.

Figure 2.32 shows the active reflection coefficient magnitude against frequency for the waveguide simulator of an aperture-coupled dual-patch microstrip antenna. The simulated array is arranged in a rectangular grid (5 = 90'). The lengths of unit cell in the x and y directions are equal; that is, U x = U,, = 29.0mm. The TE,, waveguide mode is used to simulate scanning of the array in the H plane from an angle of 51.6" at 3.3 GHz to an angle of 31.9" at 4.9 GHz. The reference plane is selected at the center of the aperture. Qualitative agreement between theory and measurement is obtained. A 40 O phase lag of the measured reflection coefficients is observed compared to that of the calculated result. The discrepancy between theory and measurement may be caused by the imperfect contact between the metal patches and the waveguide walls.

2.6 CONCLUSIONS

In this chapter, the method of moments has been employed to evaluate the characteristics of aperture-coupled multilayer rectangular microstrip antennas. The substrate effect has been taken into account with the use of spectral domain

Green's functions. Piecewise simusoidal modes have been chosen as expansion and testing functions. The unknown reflection coefficient in the microstrip feedline has been formulated by using the reciprocity theorem. Different special cases of multilayer patch antennas have been examined.

The tunable characteristic of an aperture-coupled patch antenna with an air gap between the antenna substrate and the ground plane has been investigated. The resonant frequency and the front-to-back ratio of this patch antenna increase, while the maximum input resistance and the E plane beamwidth decrease with increasing air gap width.

The SWR bandwidth and far-field radiation patterns of coplanar microstrip subarrays have been studied. The parasitic elements are gap-coupled to the nonradiating edges of the fed patch. The parasitic elements can improve the antenna bandwidth and directivity, but high backlobe and cross-polarization levels have been found. Nevertheless, the maximum level of E plane cross-polarization is below - 30 dB across the passband. A microstrip subarray with a planar reflector has also been examined. In addition to the reduction in backlobe level, the bandwidth is also enhanced with a suitable distance between the reflector and the feed substrate. The radiation patterns do not vary significantly.

The characteristics of an aperture-coupled dual-patch antenna have been evaluated. Maximum bandwidth is attained by choosing appropriate resonant lengths for the patches, substrate spacing, and offset displacement. The cross- polarization levels increase with offset displacements. The maximum level of cross-polarization at the E plane is about - 40dB. Beam squint has been observed in the E plane.

Two versions of aperture-coupled two-layer microstrip antenna with stacked parasitic patches have been presented. For the five-patch design, large SWR bandwidth and narrow beamwidth can be obtained by using relatively large values of x,, and y,; x, and y, are the displacements of the four parasitic patches. With the use of this kind of high gain microstrip antennas, the sizes of microstrip array may be reduced for a given gain. This advantage is very attractive for applications in satellite communications. For the three-patch design, the effects of the positions and dimensions of two stacked parasitic elements on the input impedance, SWR bandwidth, and radiation patterns have been examined. A wideband design procedure is demonstrated.

A full-wave analysis of infinite arrays of aperture-coupled patch antennas has been carried out. If a large scan volume is required, the element spacings in both oblique directions should be around 0.41,. It is also found that an array with a triangular grid has the wider scan angle in the E plane.

Computed results have been compared with experimental data for patch antennas with an air gap, a coplanar subarray, an offset dual-patch antenna, and an infinite array of dual-patch antennas. Reasonable agreement between theory and measurement has been obtained. The developed computer code can be used to generate design data for different structures at different operating frequency bands. Further work will be focused on the design of aperture-coupled multilayer CP microstrip antennas and arrays.

REFERENCES 121

A C K N O W L E D G M E N T S

The authors are especially grateful to Dr. C. S. Leung, Dr. P. C. Ng, and Mr. W. W. Luk for their coordination in the moment method computation a t the Chinese University of Hong Kong.

REFERENCES

[I] R. Q. Lee, K. F. Lee, and J. Bobinchak, "Characteristics of a Two-Layer Electromag- netically Coupled Rectangular Patch Antenna," Electron. Lett., Vol. 23, pp. 1070- 1073,1989; see also IEEE Trans. Antennas Propagat., Vol. AP-38, pp. 1298-1302, 1987.

[2] R. Q. Lee and K. F. Lee, "Gain Enhancement of Microstrip Antennas with Overlaying Parasitic Directors," Electron. Lett., Vol. 24, pp. 656-658, 1988.

[3] J. P. Darniano, J. Bennegueouche, and A. Papiernik, "Study of Multilayer Microstrip Antennas with Radiation Elements of Various Geometery," IEE Proc. Microwave Antennas Propagat., pp. 163-170,1990.

[4] L. Barlatey, J. R. Mosig and T. Sphicopoulos, "Analysis of Stacked Microstrip Patches with a Mixed Potential Integral Equation," IEEE Trans. Antennas Propagat., Vol. AP-38, pp. 608-615,1990.

[5] P. S. Bhatnagar, J. P. Daniel, K. Mandjoubi, and C. Terret, "Displaced Multilayer Triangular Elements Widen Antenna Bandwidth," Electron. Lett, Vol. 24, pp. 962-964,1988.

[6] G. Kumar and K. C. Gupta, "Nonradiating Edges and Four Edges Gap-Coupled Multiple Broad-Band Microstrip Antenna," IEEE Trans. Antennas Propagat., Vol. AP-33, pp. 173-178,1985.

[7] W. Chen, K. F. Lee, and R. Q. Lee, "Spectral Domain Moment-Method Analysis of Coplanar Microstrip Parasitic Subarrays," Microwave Opt. Technol. Lett., Vol. 6, No. 3, pp.157-163, 1993.

[8] K. F. Lee, W. Chen, and R. Q. Lee, "Studies of Stacked Electromagnetically Coupled Patch Antennas," Microwave Opt. Technology Lett., Vol. 8, No. 4, pp. 212-215,1995.

[9] A. N. Tulintsett, S. M. Ali, and J. A. Kong, "Input Impedance of a Probe-Fed Stacked Circular Microstrip Antenna," IEEE Trans. Antennas Propagat., AP-39, pp. 1247- 1251,1991.

[lo] D. M. Pozar, "Microstrip Antenna Aperture-Coupled to a Microstrip Line," Elec- tron. Lett., Vol. 21, pp. 49-50, 1985.

[l l] J. C. MacKinchan, P. A. Miller, M. R. Staker, and J. S. Dahele, " A Wide Bandwidth Microstrip Subarray for Array Antenna Applications Fed Using Aperture Coup- ling," IEEE AP-S Int. Symp. Dig., pp. 878-881,1989.

1121 F. Croq, and D. M. Pozar, "Millimeter-Wave Design of Wide-Band Aperture- Coupled Stacked Microstrip Antenna," IEEE Trans. Antennas Propagat., Vol. AP-39, pp. 1770-1776,1991.

[13] D. M. Pozar, "A Reciprocity Method of Analysis for Printed Slot and Slot-Coupled Microstrip Antennas," IEEE Trans. Antennas Propagat., AP-34, pp. 1439-1446, 1986.


[14] D. M. Pozar, "Analysis of an Infinite Phased array of Aperture-Coupled Microstrip Patches," IEEE Trans. Antennas Propagat., AP-37, pp. 418-425, 1989.

[I51 C. A. Balanis, Advanced Engineering Electromagnetic, John Wiley & Sons, New York, 1989.

[I61 R. W. Jackson and D. M. Pozar, "Full-Wave Analysis of Microstrip Open-End and Gap Discontinuities", IEEE Trans. Microwave Theory Techniques, Vol. MTT-33, pp. 1036-1042, 1985.

[lfl D. M. Pozar, "Input Impedance and Mutual Coupling of Rectangular Microstrip Antenna," IEEE Trans. Antennas Propagat., AP-30, pp. 1191-1196,1982.

[I81 K. E. Atkinson, An Introduction to Numerical Analysis, John Wiley & Sons, New York, 2"* edition, 1978.

[I91 R. E. Collin, Antennas and Radiowave Propagation, McGraw-Hill, New York, 1985. [20] Z. Fan and K. F. Lee, "Spectral Domain Analysis of Rectangular Microstrip

Antennas with an Air gap," Microwave Opt. Technol. Lett., Vol. 5, No. 7, pp. 315-318,1992.

[21] H. Legay and L. Shafai, "New Stacked Microstrip Antenna with Large Band- width and High Gain," IEE Proc. Microwave Antennas Propagat., Vol. 141, No. 3, pp. 199-204,1994.

[22] A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering, Prentice-Hall, New York, 1991.

[23] J. J. H. Wang, Generalized Moment Methods in Electromagnetics: Formulation and Computer Solution o f Integral Equations, John Wiley & Sons, New York, 1991.

[24] T. M. Au and K. M. Luk, "Effect of Parasitic Element on the Characteristics of Microstrip Antenna," IEEE Trans. Antennas Propagat. Vol. AP-39, pp. 1247-1251, 1991.

[25] T. M. Au, K. F. Tong, and K. M. Luk, "Analysis of Offset Dual-Patch Microstrip Antenna," IEE Proc. Microwave Antennas Propagat., Vol. 141, No. 6, pp. 523-526, 1994.

[26] Y. Lubin and A. Hessel, "Wide-Band, Wide-Angle Microstrip Stacked-Patch- Element Phased Arrays, IEEE Trans. Antennas Propagat., Vol. AP-39, pp. 1062- 1070,1991.

[27] J. T. Aberle, D. M. Pozar, and J. Manges, "Phased Arrays of Probe-Fed Stacked Microstrip Patches," IEEE Trans. Antennas Propagat., Vol. AP-42, pp. 920-927, 1994.

CHAPTER THREE

Microst rip Arrays: Analysis, Design, and Applications

JOHN HUANC and DAVID M. POZAR

3.1 INTRODUCTION

In many microstrip antenna applications, systems requirements can be met with a single patch element. In other cases, however, systems require higher antenna gains while maintaining a low-profile structure, which calls for the development of microstrip arrays. This chapter explores the analysis techniques, design methodology, and applications of microstrip array antennas for current and future advanced systems.

Microstrip arrays, due to their extremely thin profiles (0.01-0.05 free-space wavelength), offer three outstanding advantages relative to other types of antennas [I-31: low weight, low profile with conformability, and low manufacturing cost. Because of these attractive features, many military, space, and commercial applications are employing microstrip arrays instead of conventional high-gain antennas, such as arrays of horns, helices, slotted waveguides, or parabolic reflectors. However, advantages of the microstrip array can be offset by three inherent drawbacks: small bandwidth (generally less than 5%), relatively high feed line loss, and low power-handling capability. To minimize these effects, accurate analysis techniques, optimum design methods, and innovative array concepts are imperative to the successful development of a microstrip array antenna. For example, accurate analysis and a correct design approach can often overcome deficiencies in such performance factors as mutual coupling, beam

Advances in Microstrip and Printed Antennas, Edited by Kai Fong Lee and Wei Chen. ISBNO-471-04421-0 0 1997 John Wiley & Sons, Inc.

123

124 MICROSTRIP ARRAYS: ANALYSIS, DESIGN, AND APPLICATIONS

scanning effect, pattern shaping, power divider configuration, and impedance matching.

In this chapter, several different techniques for analyzing microstrip arrays are briefly reviewed. One technique-the full wave moment method-is presented in more detail because it is probably the most widely used technique due to its accuracy and reasonable computation time. In addition to analysis techniques, practical design approaches for microstrip arrays are presented, including patch elements and power division circuits. A recently developed array configuration, namely the microstrip reflectarray, is highlighted. Applications of microstrip arrays in the military, space, and commercial segments are also discussed.

3.2 ANALYSIS TECHNIQUES FOR MICROSTRIP ARRAYS

Accurate, flexible, and computationally efficient analysis techniques are important for antenna design primarily to reduce costly and time-consuming experimental cut-and-try design cycles. Analysis can also provide a more complete understanding of the operation of an antenna and can aid in optimizing its performance or determining limitations in its performance. As discussed in reference [4], microstrip elements can often be successfully designed with little or no computer-aided design (CAD) support, but the increased complexity of microstrip arrays is more often facilitated by the availability of robust CAD tools. Another factor in the evaluation of the current state of the art in microstrip antennas analysis and associated CAD software is that there is a very wide variety of element geometries, feeding methods, and substrate configurations for practical microstrip antennas and arrays. The majority of microstrip arrays are designed as fixed-beam broadside antennas, often with the feed network located coplanar with the array elements for purposes of simplicity and economics. In this case, the design procedure can be broken into the fairly disparate steps of element design, array layout and spacing, and feed design. The design of the radiating element involves considerations such as the bandwidth and polarization specifications. The grid layout, the number, and the spacing of the array elements are determined by the required principal plane beamwidths, or the gain, of the array. The feed network is a function of the amplitude tapers required for the sidelobe specification, impedance matching to the elements, and the array bandwidth and may take the form of a series feed or a corporate feed. Fortunately, mutual coupling can often be ignored for fixed- beam microstrip arrays, a fact which greatly simplifies the design procedure, since for purposes of design the elements and their excitations can be treated as if they were isolated. The feed network can then generally be simply designed with impedance matching networks and power divider circuits, possibly with the aid of a microwave circuit CAD tool.

The situation is more complicated for arrays with high gain (more than about 30dB) [5], very low sidelobes (less than about 30dB) [6], or arrays operating a t millimeter-wave frequencies (higher than about 20 GHz) [5]. In these cases, loss

ANALYSIS TECHNIQUES FOR MICROSTRIP ARRAYS 125

and tolerance effects may accumulate sufficiently to cause severe performance degradation, and it becomes critical to have CAD design tools based on solid analysis. Such tools are only partially available at the present time.

The design and analysis of scanning phased microstrip arrays is another situation that typically requires rigorous and versatile CAD software. The primary driver for this requirement is the fact that such antennas are very expensive because of the phase shifter or T/R module cost per element, so it is critical that antenna performance be analyzed and optimized accurately and thoroughly; Experimental trials using small arrays, active element patterns, and waveguide simulators can play an important role in the design process, but accurate CAD models can provide much more information about important effects such as scan blindness, impedance mismatch, losses, random errors, sidelobe levels, and cross-polarization as a function of any design parameter. Unlike the case for fixed beam arrays, scanning arrays usually do require the inclusion of mutual coupling effects, as well as the effect of the feed network, for a complete characterization of the array. This is a very difficult problem in general, especially for arrays that have more than a few elements (so that coupling effects are important) but are too small to apply the infinite array approximation.

In the following sections we will present a brief review of several analysis techniques for microstrip arrays and then concentrate on full-wave moment method techniques for single elements, mutual coupling between elements, and infinite array analysis. We will also discuss the use of the active element pattern and waveguide simulators in array design.

3.2.1 Review of Microstrip Antenna Analysis Techniques

Compared to other types of antennas, microstrip antenna analysis is complicated by the presence of a dielectric inhomogeneity, a narrow-band impedance characteristic, and a wide variety of patch, feed, and substrate configuration. Present microstrip antenna models invariably compromise their treatment of one or more of these features. Most theories to date can be categorized as either (a) simplified (or reduced) analyses that maintain simplicity at the expense of accuracy or versatility or (b) full-wave models that maintain accuracy and rigor at the expense of computational efficiency. There is no model or CAD package that can provide accurate results for a significant fraction of the microstrip antenna and array geometries that are of practical interest a t this time.

Reduced analyses refer to microstrip antenna models that introduce one or more simplifying assumptions to the problem. These thus include (a) the cavity model [3,7, 8, 111, which uses a magnetic wall boundary condition around the periphery of the patch to form a closed resonant cavity, (b) the transmission line model [3,9, 111, which models the element as a section of transmission line with load admittances to model the radiating edges of the antenna, and the multipart segmentation model [3, 10, 111, which generalizes the cavity model to treat arbitrarily shaped elements. These models were the first to be developed for microstrip antennas and have proven to be very useful for practical design as well

126 MlCROSTRlP ARRAYS: ANALYSIS, DESIGN, AND APPLICATIONS

as providing an intuitive explanation for the operation of the microstrip element. Generally they give good results for antennas on thin, low-dielectric constant substrates. While originally developed for probe-fed and line-fed elements, models of this type have also been proposed for more complicated structures such as the aperture coupled patch element 1121 and proximity coupled element [ll], as well as for elements covered with radome layers [3,11]. Generally, however, the inclusion of multilayer substrates requires more rigorous modeling techniques.

In recent years, because of the vast increase in computer power, finite element and finite difference time domain (FDTD) methods have begun to be applied to microstrip and other planar antenna problems [13]. Such methods offer what are probably the most versatile computational techniques presently available and are beginning to become available as commercial CAD packages. These methods are relatively "brute force" in nature, however, requiring considerable computational resources and offering little physical insight into the operation of the antenna. Such numerical models are already reducing the need for electromagnetic analysts, but it remains true that more analytically based solutions for particular geometries, such as cavity models or moment method solutions, can give more accurate results with less computational effort.

3.2.2 Full-Wave Moment Method Analysis

Microstrip antenna models that account for the dielectric substrate in a rigorous manner are referred to as full-wave solutions. Thus "full-wave" may be used to describe FDTD or finite element solutions, but most of the full-wave analyses of microstrip antennas have been moment method solutions using the exact Green's function for the dielectric substrate. This techniques enforces the boundary conditions at the air-dielectric interface and treats the contributions of space waves, surface waves, dielectric loss, and coupling to external structures in an accuratemanner. It is also possible to apply the method to a wide variety of patch and substrate geometries, including arrays, mutual coupling effects, multiple layers, stacked elements, and various feeding methods, and it can be easily extended to infinite arrays of microstrip antennas [3,11]. It is probably the most popular analysis technique for microstrip antennas and arrays.

While the reader is referred to the literature for details on the analysis of particular microstrip antenna geometries [3,11], we can summarize some of the key features of the full-wave moment method procedure here. The equivalence theorem is used to replace conducting patch elements with equivalent electric surface currents, and slot elements are replaced with equivalent magnetic currents. A moment method solution is then derived from the enforcement of the continuity of electric or magnetic fields at the patch or slot elements. The fields from these current elements are found using the exact Green's function for the substrate geometry, which can be derived in closed form for a wide variety of multilayer substrates consisting of isotropic, anisotropic, ferrite, or chiral materials [3,11]. The key calculation in this procedure then becomes the evaluation


of impedance matrix elements having the general form I

where Ji and Jj are the expansion and test mode currents, and G is the dyadic Green's function for the substrate geometry. This sixfold integration involves surface wave poles, a slowly converging integrand, and singularities associated with the source point. The evaluation of this expression therefore requires considerable care and attention to details.

The order of integration in Eq. (3.1) can be chosen in at least two ways, leading to solutions with somewhat different characteristics. In the full-wave spectral domain approach [3,11,15], the space integrations over the expansion and test mode coordinates x, y, x,, yo are done in closed form, which amounts to taking the Fourier transform of the expansion and test modes. Then the rectangular spectral variables k, and ky are transformed to polar coordinates, f l and a, where k, = f l cos a, k y = f l sin a. Then Eq. (3.1) reduces to

which is in a convenient form for numerical evaluation. The source singularity that occurs in Eq. (3.1) when x = x, and y = yo is eliminated in Eq. (3.2) by the smoothing process of integrating over the expansion mode to form the Fourier transform Fj. This is a convenient feature of the spectral domain method, especially for the evaluation of self-impedance terms because it eliminates the need for special treatment of the source singularity. There is still a surface wave pole associated with the TM, surface wave, but this can be treated fairly easily 1141. It is also convenient to use the residue of the surface wave pole to evaluate the surface wave power generated by the antenna, in contrast to the more cumbersome method of using a volume integral of the surface wave fields [15].

Alternatively, the spectral variables in Eq. (3.1) can be transformed to polar form, and the a integration done in closed form, to yield

which is generally referred to as the space domain approach because of the remaining integrations over the space coordinates. The source singularity that remains in this formulation requires special consideration, but can be treated in a manner very similar to the treatment of the source singularity for wire antennas. The integration over f l must be performed numerically, but there are several techniques for doing this efficiently [3, 161. Recent work in this area has focused

128 MICROSTRIP ARRAYS: ANALYSIS, DESIGN, AND APPLICATIONS i ANALYSIS TECHNIQUES FOR MlcRosTRlP ARRAYS 129

FIGURE3.1 Measured and calculated input impedance of an aperture-coupled stacked microstrip antenna. Substrate thickness (bottom layer) = 0.508mm, (top layer) = 0.7874m~ (feed layer) = 0.508. Dielectric constant (bottom layer) = 2.2, (top layer) = 2.33, (feed layer) = 2.2. Bottom patch length and width = 3.5mm. Top patch length and width = 3.8 mm. Slot length = 3.2mm, slot width = 0.4mm. (From reference 18,0 1991 IEEE.)

on the mixed potential approach [17], which expresses the Green's function in a form that facilitates the evaluation of the source singularity terms.

There have been literally dozens of microstrip geometries analyzed using full-wave techniques, and we refer the interested reader to the literature for examples [3, 111. Here we provide only one result to demonstrate the type of problem that can be efficiently and accurately treated using full-wave moment method procedures. Figure 3.1 shows the measured and calculated input impedance of an aperture-coupled stacked microstrip antenna element operating at K band [18]. The analysis of this antenna involves the treatment of three dielectric layers, a ground plane, two rectangular patches, and a coupling slot. The calculated impedance locus is in good agreement with measured data, and it demonstrates an impedance bandwidth of approximately 25% at 20GHz.

3.2.3 Calculation of Mutual Coupling

As mentioned above, many cases of practical microstrip array design do not require consideration of mutual coupling 119, 201. Mutual coupling effects are

often negligible for microstrip arrays because of the presence of the electrically thin grounded substrate (this is also the primary cause of their narrow impedance bandwidth). But there are cases where mutual coupling effects are not negligible and must be included; examples are scanning phased arrays, arrays on electrically thick substrates, and arrays with main beams far off broadside. This can be done by measuring coupling coefficients in a small array 1213, but calculation of S-parameters or impedance parameters is preferable for design and optimization. The full-wave moment method discussed in the preceding section is perfectly suited to this task, because it includes all surface wave, space wave, and dielectric loss effects. Such solutions for mutual coupling have thus been camed out for a wide variety of patches, including rectangular, circular, probe-fed, aperture-fed, stacked, and covered elements [3, 111.

As an example, we present in Figure 3.2-the measured and calculated coupling (S,,) versus separation for two probe-fed circular microstrip elements, for both E-plane and H-plane configurations. Very good agreement is obtained between theory and experiment. Similar results are obtained for rectangular patches and for patches with different feeding methods. Generally, coupling increases with substrate thickness and dielectric constant. The effect of a cover layer is also to increase coupling levels. As in the results of Figure 3.2, mutual coupling usually decays monotonically with separation, but recent analytical work [22] has shown that nonmonotonic decay is possible for certain ranges of substrate

- E plane theory ----- H olane thew

-40.00 I I I I I 0.00 0.20 0.40 0.60 0.80 1

S (free space wavelengths)

FIGURE 3.2 Measured and calculated mutual coupling between two probe-fed circular microstrip antennas versus separation. Substrate thickness = 0.15cm, dielectric constant = 2.64, patch radius = 0.93 cm, radius to feed = 0.31 cm, frequency = 5.5 GHz.

130 MlCROSTRlP ARRAYS: ANALYSIS, DESIGN, A N D APPLICATIONS

thickness and dielectric constant. This type of anomaly is caused by the interference of space wave and strongly excited surface wave terms and can occur in both the E-plane and the H-plane.

The results of Haddad and Pozar [22] have also shown that there are ultimate decay rates for mutual coupling of printed antennas versus separation, and that these rates are dominated by the surface wave field for large separations. E-plane coupling has an asymptotic form of S12 - r-'I2, while H-plane coupling has an asymptotic form of S12 - r - 3 1 Z . This explains the observation from Figure 3.2 (and other results) that E-plane coupling decays more slowly than H-plane coupling.

While the moment method results of Eqs. (3.1)-(3.3) can be used in principle to compute mutual coupling between widely separated microstrip elements, the Fourier transforms become highly oscillatory for separations more than about a wavelength, resulting in slow convergence. In this case it is expedient to use an asymptotic approximation for the Green's function. This is usually developed from the space domain representation of Eq. (3.3) and leads to a result for the Green's function that is essentially in closed form [22]. If the asymptotic development is done carefully, accurate results can be obtained for spacings as close as 212. An example comparing mutual impedance computed numerically from Eq. (3.1) with that of the asymptotic expressions from reference [22J is shown in Figure 3.3, for E-plane and H-plane cases.

Once mutual coupling data have been obtained for a particular array, the problem remains of how to incorporate it into the design of the array. If the array is analyzed using a moment method, finite element, or finite difference procedure that models the entire array and feed network, then mutual coupling effects will be automatically included. This may be feasible for small arrays [23, 241, but computational effort increases drastically with array size, so large arrays can seldom be modeled in this manner. Infinite array models can treat large arrays with mutual coupling effects, but the infinite array approximation precludes treatment of a realistic (nonperiodic) feed network. A general method for including mutual coupling in array design is to treat the N-element array as an N-port network and use microwave network theory to find the element amplitudes, phases and the input reflection coefficients for various excitations. Thus, for an N-element array having N feed ports fed with matched voltage generators, Vi, the reflection coefficient at the jth port can be expressed as

where Sij is the scattering parameter between the ith and jth elements. This result assumes dominant mode operation of the patch, which is generally a good assumption for microstrip antennas. Observe that in the absence of mutual coupling, where Sij = 0 for i # j (a diagonal scattering matrix), Eq. (3.4) reduces to


.. . .. .... . . .. . . X, asymptotic X, MOM [lo]

30

FIGURE 3.3 (a) E-plane and (b) H-plane mutual impedance between two printed dipoles, computed using spectral domain numerical integration (moment method), and a closed- form asymptotic expression for the Green's function in the space domain. Substrate thickness = 0.11, dielectric constant = 3.26, dipole length = 0.372.

which is the expected result for isolated elements. When mutual coupling is nonzero, the matrix is no longer diagonal, and the reflection at the jth element is seen from Eq. (3.4) to depend on the relative excitations at all other elements.

132 MICROSTRIP ARRAYS: ANALYSIS, DESIGN, AND APPLICATIONS ANALYSIS TECHNIQUES FOR MICROSTRIP ARRAYS 133

One final point to consider in regard to mutual coupling analysis is that a distinction must usually be made between a moment method mutual coupling term, like Zij of Eqs. (3.1)-(3.3), and a port mutual coupling term, such as Sv The former case represents field coupling between two expansion modes as part of the moment method solution and does not directly relate to voltage, current, or impedance that would be measured at the terminals of an antenna element. The latter quantity is based on the voltage and current relationship at the terminals of the antenna. In the case of a printed dipole having an idealized gap feed, these quantitiesmay beequivalent, but for other feeds a transformation must be used to convert the results of the moment method solution to port quantities [23].

3.2.4 Infinite Array Analysis

An infinite array antenna is a periodic structure of a linear or planar array of identical radiating elements with uniform spacing, and is excited with uniform amplitude generators having a progressive phase shift to steer the main beam. An infinite array can provide a very good approximation to a finite linear or planar array that is too large to be efficiently modeled on an element-by-element basis. The impedance seen at an element in an infinite array is dependent on the scan angle of the array (the slope of the linear phase taper across the array), but is the same for all elements. This model thus compares well with the impedance seen by the central elements of a large array, but less so for the elements near the edges of the array. The main advantage of the infinite array model is the high degree of analytical simplicity introduced by the uniform periodic nature of the problem. In fact, the numerical solution of an infinite array of elements is typically faster than the corresponding analysis of an isolated elements of the same type.

Analysis of an infinite planr array begins by deriving the Green's function for an infinite array of infinitesimal dipole sources on the substrate geometry of interest. If we assume a uniform rectangular grid of dipoles located at coordinates

where a, b are the spacings along the x, y directions, respectively, and m, n are the indices of a given dipole, with - co < m, n < co, then the total field due to the infinite array can be found by substituting Eqs. (3.6) into Eq. (3.1) for x,, yo and summing over m and n. We also phase the dipole sources with the progressive phase shift given by

e-jko(moain Bcoa ++nbs in Bs in+) (3.7)

which causes the main beam to be scanned to the direction 0, 4. The resulting sixfold integration and double infinite summations can fortunately be simplified using the Poisson summation formula [3], to yield

where

represent Floquet mode wavenumbers. Note that the form of Eq. (3.8a) is very similar to the spectral domain expression for a single element given in Eq. (3.2), if the integrations over the continuous spectral variables are replaced with summations over the Floquet modes (discrete spectral variables). Further analytical details depend on the type of element and feed being modeled, and they can be found in the literature for many practical configurations [3,11].

Because of the importance of modeling large phased arrays, along with the interest in planer construction for such arrays, there has been a wide variety of infinite array solutions for probe-fed patches 125,261, aperture-coupled patches [27], probe-fed stacked patches [28], arrays of subarrays [29], and a variety of arrays of related patch and substrate configurations [I 11. Microstrip reflectarrays have also been successfully modeled with the infinite array approach [30]. As a typical example of an infinite array analysis, we show in Figure 3.4 the

0.7 0.8 0.9 1 1.1 1.2 1.3 NORMALIZED FREQUENCY

FIGURE 3.4 Calculated normalized element gain for an infinite array of probe-fed circular stacked patches, compared with an array of unstacked elements. Parameters for stacked case: bottom substrate thickness = 0.031, bottom dielectric constant = 3.2, bottom patch radius = 0.1631, top substrate thickness = 0.035 top dielectric constant = 1.8, top patch radius = 0.1711. Parameters for unstacked case: substrate thickness = 0.06L, dielectric constant = 2.5, patch radius = 0.1671. a = b = 0.421 for both cases. (From reference 28,a 1994 IEEE.)


normalized element gain (see following section) versus frequency for an infinite array of probe-fed circular microstrip patches, compared with the result for a similar array of unstacked elements. Note the increase in bandwidth for the stacked configuration.

An important effect that can be predicted using infinite array analyses is scan blindness. This is a condition that can occur for large phased array whereby a guided mode of the array structure can trap all transmit (or receive) power for a particular scan angle, driving the effective gain of the array to zero. The array is thus said to be "blindn at that angle. These conditions have been found to occur in a variety of waveguide and dipole arrays, as well as in printed antenna arrays of various types [3, l l , 25-29]. In the case of printed dipole and patch arrays, scan blindness can be traced to the forced resonance of a surface wave on the dielectric substrate [3, 11, 271. If the surface wave propagation constant is &, where k, < j3, < & k,, scan blindness will occur at a scan angle 0, q5 such that

where m and n are Floquet mode indices. Scan blindness is generally not observable in small arrays (neigher experimentally nor numerically), so the availability of an infinite array solution during the early stages of phased array design can be very helpful.

3.2.5 The Active Element Pattern

The active element pattern of an array refers to the radiation pattern of an array having a single driven element, with all other elements terminated in matched loads. Such a pattern obviously will depend on the position of the driven element in the array, but in the limit of an infinite periodic array the active element pattern will be independent of position due to the homogeneity of the structure. In this case, some very useful relations exist between the active element pattern and the scanning properties of the same array when operated with all elements excited with a uniform amplitude and a progressive phase shift. Thus, if we define the active element pattern for a single element in an infinite array as G,(0,, m,), and the reflection coefficient at an element in the fully excited array as r(0,, m,), then it can be demonstrated 1311 that

where a and b are the element spacings of the planar array. This relation indicates that the scanning array impedance mismatch is related to the shape of the active element pattern. Thus, for example, when the scanning array has a scan blindness, where I rl= 1, the active element pattern will have a null. The importance of this relation is that the scanning properties of a large phased array can be predicted by


measuring the active element pattern of a single element in the array. All unused elements can simply be terminated with matched loads, instead of the expensive phase shifter and power divider network that would be required for the fully excited phased array.

Note that measurement of the active element pattern does not give complete information about the impedance mismatch of the element in the corresponding phased array environment, since only the magnitude of the reflection coefficient is determined by Eq. (3.10). Thus, it is not possible to obtain the complex active input impedance of an element in an infinite phased array environment using the active element pattern. While it is possible to calculate active element patterns using a full-wave moment method solution [23], such a solution also provides more complete information in the form of the active input impedance.

Finally, we note that the term "active" in this context is traditionally used to refer to the fact that the phased array corresponding to the right-hand side of Eq. (3.10) would have all elements actively excited with generators. This term can admittedly cause some confusion with modern array systems that use electronic devices such as MMICs and T/R modules, but tradition will probably prevail in its use.

3.2.6 Waveguide Simulators

A waveguide simulator offers another method for testing the performance of an element in a large array environment without building a large and costly array and associated feed network. The waveguide simulator was first proposed by Wheeler [32] and has proven to be very effective in predicting the scan performance of a wide variety of waveguide, dipole, slot, and printed antenna [25-271 elements. The basic principle of operation of a waveguide simulator is that the walls of a rectangular waveguide can be used to image the currents on an antenna element placed inside the waveguide to emulate an infinite array environment. Since the dominant TE,, waveguide mode can be decomposed into two oblique- ly propagating plane waves bouncing off the waveguide walls, the waveguide simulator models an infinite array radiating a plane wave at the angle 0, such that

sin 0 = 112 Nb (3.11)

where b is the H-plane dimension of the guide, and N is the number of elements used in the H plane of the simulator. In fact, the simulated phased array actually emulates the simultaneous generation of two main beams, at the angle 0 and - 0, corresponding to an array with superimposed phasings that are the conjugate of each other. The input impedance of an array scanned to angle 0 is identical to the impedance of the array scanned to angle -0, so the measured impedance of a waveguide simulator corresponds to the impedance of the same element in a fully excited phased array scanned to the angle given by Eq. (3.11). The main advantage of the simulator over the active element pattern technique is that the simulator can be used to find the complex active input impedance of an element in


an infinite phased array environment, while that active element pattern can only be used to find the magnitude of the reflection coefficient of that element.

Equation (3.1 1) shows that the equivalent scan angle 0 depends on frequency, and one of the main disadvantages of the simulator technique is that it can provide impedance information only for combinations of angle and frequency that satisfy Eq. (3.11). Added flexibility can be obtained by using different numbers of elements in the simulator, using different waveguide sizes, or using higher-order waveguide modes [32], but such tactics have limited practical utility. In practice, large-scale phased array design typically involves the use of active element pattern measurements to provide matching data over a continuous sweep of scan angles, with waveguide simulators to provide spot checks of the complex input impedance at specific values of frequency and angle.

As an example of the utility of the waveguide simulator technique, we show in Figure 3.5 the results of waveguide simulator measurements used to validate full-wave calculations of an infinite printed dipole array on an inhomogeneous dielectric substrate [33]. Both the magnitude and phase of the reflection coefficient versus frequency have been verified, but only the magnitude is shown here. Note that a scan blindness occurs at a frequency of approximately 5.6 GHz. Unity

IRI

i n , 0.9 - Hybrid MOM

0.8 - Waveguide Simulator

0.7

0.6

0.5 0.4 0.3 0.2 0.1 0.0

4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 6.0

Frequency (GHz)

FIGURE 3.5 Measurements from a waveguide simulator and moment method calculations for an infinite array of printed dipoles on an inhomogeneous substrate. Bottom substrate: thickness = l.Ocm, dielectric constant = 2.60. Support post: height = 0.86cm, width = 0.28cm, length = 4.0cm, dielectric constant = 2.60. Dipole: length = 3.7cm, width = 0.19 cm. a = 4.43 cm, b = 2.38 cm.

DESIGN METHODOLOGY 137

reflection magnitude at the scan blindness is not observed due to losses in the simulator.

3.3 DESIGN METHODOLOGY

The previous section presented techniques for analyzing a variety of microstrip array configurations with different types of patch elements. To ease the design process, these techniques have been developed into several user-friendly computer-aided-design (CAD) tools by several institutions. However, an analysis technique or a CAD tool cannot, by itself, generate an array design. It can only analyze the design's configuration and improve its accuracy. The basic design configuration has to originate from human experience, knowledge, and innovation, even though an optimum and accurate design often cannot be achieved without an analysis tool. Figure 3.6 depicts a typical microstrip array development process. The block labeled "Computer Analysis Software" represents the central processing unit into which a human must enter the proper design data to initiate the design process. The block labeled "Antenna Design Techniques" represents a tool for generating preliminary input design data, which is the main subject of this section. It includes techniques to design array configurations, patch elements, element feeds, and power division transmission lines. Since element feed designs, including probe-fed and aperture-coupled designs [12,27], have already been covered in Chapters 1 and 2, they are not repeated here. For patch element designs, the most popular rectangular and circular patches are emphasized. For power divider designs, simple but accurate closed-form equations are given for various networks. With this knowledge of how to generate the

FEEDBACK IDEAS FEEDBACK CORRECTIONS I I I 1

1 I FEEDBACK CORRECTIONS

t

FIGURE 3.6 Microstrip array antenna development block diagram.

INNOVATIVE DESIGN IDEAS

-) FABRICATION

7 _ HUMAN DESIGN * SOFTWARE MEASUREMENT

RESULT

ANALYSIS RESULTS

TECHNIQUES

FINAL DESIGN

7 I P


array configuration and design the element, the element feed, and the power division network, a person should be able to confidently design a single or multilayer microstrip array antenna.

3.3.1 Array Configuration Design

Before carrying out a detailed design, it is critically important to lay out the most suitable array configuration for a particular application. Viable array configurations include series-fed or parallel-fed, single layer versus multiple layer, with variables such as substrate thickness, dielectric constant, array size, patch element shape, element spacing, etc. The selection of the configuration depends upon many factors, such as antenna gain, bandwidth, insertion loss, beam angle, gratinglsidelobe level, polarization, power handling capability, and so on. Sev- eral important microstrip array configuration that often challenge the skills of antenna designers are discussed below.

Series Feed. In a series feed configuration [3,34], multiple elements are arranged linearly and fed serially by a single transmission line. Multiple linear arrays can then be fed either serially or in parallel to form a two-dimensional planar array. Figure 3.7 illustrates two different configurations of the series feed method: the in-line feed using two-port patches and the out-of-line feed using one-port patches. The in-line feed [35,36] has the feed transmission line and the radiating elements arranged in the same line, while the out-of-line feed [20] has the feed line arranged parallel to the elements. The in-line feed array occupies the smallest real estate with the lowest insertion loss, but generally has the least polarization control and the narrowest bandwidth. The in-line feed, shown in Figure 3.7, is generally more suitable for generating horizontal polarization than circular polarization. It has the narrowest bandwidth because the line goes through the patches. Thus, the phase between adjacent elements is not only a function of line length but also of the patches' input impedances. Since the patches are amplitude

in-line series feed

s out-of-line series feed

FIGURE 3.7 Series-feed microstrip arrays.


weighted differently with different input impedances, the phases will be different for different elements and will change more drastically as frequency changes due to the narrow-band characteristic of the patches.

The series-fed array can also be classified into two types: resonant and traveling-wave [3,34]. In a resonant array, the impedances at the transmission 1i11e junctions and the patch elements are not matched. The elements are spaced multiple integrals of one wavelength apart so that the multiply bounced waves, caused by mismatches, will radiate into space in phase coherence. Because of this single- or multiple-wavelength element spacing, the beam of the resonant array is always pointed broadside. For the same reason, the bandwidth of a resonant array is very narrow, generally less than 1%. With a slight change in frequency, the one-wavelength spacing no longer exists, thereby causing the multiply bounced waves not to radiate coherently but, instead, to travel back into the input port as mismatched energy. Both in-line and out-of-line feed arrays can be designed to be of resonant type.

For the traveling-wave array type, the impedances of the transmission lines and the patches are generally designed to be matched, and the element spacing can be one wavelength for broadside radiation, or less than one wavelength for off-broadside radiation. Because the wave is traveling toward the end of the array without multiple reflections and the array is designed with a certain amplitude distribution, there is generally a small amount of energy remaining at the array end. This remainingenergy can be either absorbed by a matched load or reflected back to be reradiated in phase for broadside radiation [20]. The array can also be designed such that the last element radiates all of the remaining energy [20]. The traveling-wave array has a wider impedance bandwidth, but its main beam will scan in direction as frequency changes. A general rule of thumb for the frequency- scanned beam of a traveling-wave array is one degree of beam tilt per 1% of frequency change. For an instantaneous wideband signal, a beam-broadening effect will occur for a traveling wave array. Both the in-line and out-of-line series-fed arrays of Figure 3.7 can be designed as the traveling-wave type. There are also other forms of series-fed microstrip arrays: chain, comb line, rampart line, Franklin, and coupled dipole [3,34]. These arrays operate similarly to the arrays shown in Figure 3.7, except that they use microstrip radiators with different radiating mechanisms.

Parallel Feed. The parallel feed, also called the corporate feed, is illustrated in Figure 3.8, which shows that the patch elements are fed in parallel by the power division transmission lines. The transmission line divides into two branches and each branch divides again until it reaches the patch elements. In a broadside- radiating array, all the divided lines are the same length. In a series-fed configuration, shown in Figure 3.7, the power is fed to the elements one after another. In other words, in a series feed, the remaining power from the first element is used to feed the second element, and so on. The first elements has the shortest transmission line. The insertion loss of a series-fed array is generally less than that of a parallel-fed array because most of the insertion loss occurs in the transmission


parallel feed I I

I I

serieslparallel feed 1

FIGURE 3.8 Configurations of parallel feed and hybrid series/parallel feed microstrip arrays.

line at the first few elements of the series-fed array and very little power remains toward the end of the array. Most of the power is radiated by the time the end elements are reached. Despite its relatively higher insertion loss, the parallel-fed array does have one significant advantage over the series-fed-wideband performance. Since all elements of a parallel-fed array are fed by equal-length transmission lines, when the frequency changes, the relative phases between all elements will remain the same and thus no beam squint will occur. The bandwidth of a parallel-fed microstrip array is limited by two factors: the bandwidth of the patch element and the impedance-matching circuit of the power-dividing transmission lines, such as the quarter-wave transformer. A series-fed array can achieve a bandwidth on the order of 1 % or less, while a parallel-fed microstrip array can achieve a bandwidth of 15% or more, depending on the design.

Hybrid Series/Parallel Feed. An example of a hybrid series/parallel-fed array is depicted in Figure 3.8, where a combination of series and parallel feed lines is used. In a hybrid array [20, 371, the smaller series-fed subarray will yield a broader beamwidth, which has a smaller gain degradation due to beam squint with frequency change. Hence, a hybrid-fed array will achieve a wider bandwidth than a purely series-fed array having the same aperture size. Of course, because of its partial parallel feed, the insertion loss of a hybrid array is higher than that of a purely series-fed array. This hybrid technique gives the designer an opportunity to make design trade-offs between bandwidth and insertion loss.

Regardless of whether the array is parallel or series fed, two recently developed powerful arraying techniques can be employed to significantly improve the array's performance. The first is to reduce cross-polarized (cross-pol) radiation in a planar array by oppositely exciting adjacent rows or columns of elements in phase and in orientation [20], as shown in Figure 3.9 a. Another technique is


FIGURE3.9 (a) Microstrip array elements with rows fed by opposite phases and orientations. (b) Sequentially arranged four-element subarray.

shown in Figure 3.9 b for a circularly polarized array, in which every adjacent four elements placed in a rectangular lattice can be sequentially arranged in both phase and orientation to achieve good circular polarization over a wide bandwidth [38,39].

Single-Layer or Multilayer Design. A microstrip array can be designed in either a single-layer or multilayer configuration. The factors that determine this choice are complexity and cost, sidelobe/cross-pol level, number of discrete components, polarization diversity, bandwidth, and so on. When the given electrical requirements are more relaxed, a single-layer design will generally suffice. Because all the transmission lines and patch elements are etched on the same layer, it has the advantage of lower manufacturing cost. However, when extremely low sidelobe or cross-pol radiation (e.g., less than - 30 dB) is required, the double-layer design seems to be the better choice. With all the transmission lines etched on the second layer behind the radiating patch layer, the double layer's ground plane will shield most of the leakage radiation of the lines from the patch radiation. This leakage radiation becomes more pronounced when discrete components, such as MMIC T/R modules and phase shifters, are placed in the transmission line circuits. Thus, it is more desirable to place all discrete components behind the radiating layer in a multilayer configuration. When dual-linear or dual-circular polarization is required with high polarization isolation, it is often more desirable to design the feed circuits of the two polarizations on two separate layers, as shown in Figure 3.10. When a radiating patch with a thick substrate is used to achieve wider bandwidth, it is best to design the transmission lines on a separate layer because

142 MICROSTRIP ARRAYS: ANALYSIS, DESIGN, AND APPLICATIONS DESIGN METHODOLOGY 143

, radiating

ground plane with crossed slots

microstrip transmission line

FIGURE 3.1 0 Multilayer dud-polarized microstrip patch element.

the transmission lines may become wider than is practical if designed on the same thick layer as the radiating patches. In other cases, when an extremely wide bandwidth requirement can be met only by using multiple stacked patches [18], the multilayer design becomes the obvious choice. With the advancement of the aperture-coupling technique that allows the transmission line to- feed the patch, the multilayer design becomes much more feasible than those that use feedthrough pins.

OtherArray Configuration. When designing a microstrip array, various antenna parameters, such as substrate thickness, dielectric constant, and element spacing, can all play important roles in determining an array's performance. Substrate thickness determines bandwidth, as well as the antenna's power-handling capability [40]. The thicker the substrate, the more power it can handle. For ground applications, a thicker microstrip array can generally handle several hundred to a few thousand watts of peak power. For space applications, due to the effect of multipacting breakdown [41], only tens of watts are attainable. The dielectric constant of the substrate material also affects the bandwidth. The higher the dielectric constant, the narrower the bandwidth 1401. Because of the loading effect, a higher dielectric constant reduces the patch resonant size and, hence, increases the element beamwidth. A wider element beamwidth is desirable for a large-angle-scanning phased array. Another important array design parameter is element spacing. It is often desirable to design a microstrip array with larger element spacing so that more real estate can be made available for transmission lines and discrete components. However, to avoid the formation of high grating lobes, element spacing is limited to less than one free-space wavelength for

broadside beam design and less than 0.6 free-space wavelength for a wide-angle scanned beam. In designing a wide-angle scanned microstrip phased array, substrate thickness, dielectric constant, and element spacing are all important parameters that need to be considered for reducing mutual coupling effects and avoiding scan blindness [29].

3.3.2 Patch Element Design

Patch elements come in various shapes, such as rectangular, square, circular, annular ring, triangular, pentagonal, and square or circular with perturbed truncations. These different shapes can often be used to meet various challenging requirements. For example, the rectangular patch, used for linearly polarized applications, can achieve slightly wider bandwidth than the square or circular patch. However, the square or circular patch, unlike the rectangular patch, can be excited orthgonally by two feeds to achieve circular polarization. In addition, the circular patch can be designed to excite higher-order modes for generating different-shaped patterns [42,43]. The pentagonal patch, as well as the square or circular patch with a small perturbation, can be used to generate circular polarization with only a single feed, which is often a desirable feature when simplicity and low insertion loss are required.

It should be noted that all of these patch shapes can be accurately analyzed and designed by the full-wave moment method discussed in Section 3.2.2. However, designing a patch using the moment method or any other rigorous technique requires a priori knowledge of the approximate size of the patch so that appropriate dimensions, rather than random numbers, can be input to the analysis computer code. With a few iterations of the computer code, the designer should be able to determine the precise dimensions of the patch at the required frequency. Once the dimensions are known, other parameters (e.g., input impedance, bandwidth, radiation patterns, etc.) can be accurately computed by the full-wave moment method. The patch element design process is very similar to that shown in Figure 3.6 for designing the complete array. The above-mentioned a priori knowledge of the approximate patch size (first-order design) can be acquired through experience, or derived by simple closed-form equations if available. Fortunately, the two most popular and often used patch shapes, rectangular (or square) and circular, do have simple closed-form equations available. These equations, in predicting the resonant frequency, can generally achieve an accuracy of within 2%. For the fundamental-mode rectangular patch, the first-order design equation [I] is given by

where

144 MICROSTRIP ARRAYS: ANALYSIS, DESIGN, A N D APPLICATIONS DESIGN METHODOLOGY 145

f is the resonant frequency, c is the speed of light, L is the patch resonant length, h is the substrate height, e, is the relative dielectric constant of the substrate, and w is the patch width.

For the circular patch with TM,, mode, the first-order design equation [I] is given by

where f, c, h, and E, are as defined for the rectangular patch design equation, a is the patch's physical radius, x,, is mth zero of the derivative of Bessel's function of order n, n represents the angular mode number, and m is the radial mode number.

There is no significant difference in performance between a fundamental-mode rectangular patch and a fundamental-mode circular patch. The circular patch does have the advantage of offering higher-order-mode performance with differently shaped radiation patterns [42,43]. These patterns can be either linearly or circularly polarized, depending on the configuration of the feed excitations.

3.3.3 Power Division Transmission Line Design

One of the principal shortcomings of a microstrip array with a coplanar feed network is its relatively large insertion loss, especially when the array is electrically large or when it is operating at higher frequencies. Most of the losses occur in the power division transmission lines' dielectric substrate at microwave frequencies. At millimeter frequencies, the loss in the copper lines becomes significant. It is thus crucially important to minimize insertion loss when designing the power division transmission lines. In order to minimize insertion loss, the following principles should be observed: The impedance of the power division circuit should be matched as much as possible; low-loss material should be used; at higher frequencies the roughness of the metal surface should be minimized; and the array configuration should be designed to minimize line length (as described in Section 3.3.1). This section discusses the impedance-matching techniques for power division circuits. Every designer has a somewhat different approach to design the microstrip circuit, but they all require a knowledge of the basic circuit components presented in the following subsections. In a good design with well-matched lines, the microstrip circuit will suffer less from mismatch losses and leakage radiation losses. Although most of the microstrip circuit components shown here are very fundamental and have been presented elsewhere in separate articles, they are discussed together here for convenient reference.

A very important circuit component in most microstrip array designs is the quarter-wave transformer (Figure 3.11), which transforms one impedance to another. The proper impedances for this transformation are given by the

FIGURE 3.1 1 Microstrip transmission line quarter-wave impedance transformer.

Coax Probe ,250 n (50 a)

FIGURE 3.1 2 Impedance-matchedmicrostripline feeding a patch element with quarter- wave sections.

following equation:

In Figure 3.1 1, the symbol Anis the effective wavelength in the microstrip line, and its equation is given in reference [44]. This quarter-wave transformer is not only used to transform between two different impedances, but also should be used where there is a possible impedance mismatch. For example, for the single-patch circuit shown in Figure 3.12, the quarter-wave section should be used at the coax input feed location and at the input to the patch. Both the coax input and the patch input locations may have some residual mismatches. For example, the 250-ohm input impedance of the patch may not be accurately predicted by CAD, due to inaccuracies in the model or inaccurate specification of the dielectric constant by the manufacturer, and the coax feed may not be perfectly matched to the microstrip line. The quarter-wave transformer can be used to minimize such mismatches. Because of the quarter-wave line's round-trip phase delay (180°), the reflected signal due to mismatch occurring at one location will cancel with that reflected from another location a quarter-wave distance away.

In a microstrip line with a given substrate height and dielectric constant, the width of line governs the characteristic impedance. To determine the microstrip


FIGURE 3.1 3 Microstrip two-way power divider.

line width with a specified line impedance, simple closed-form equations are given in reference [44]. These equations are generally accurate enough without resort- ing to the full-wave analysis or a CAD tool, unless there is a significant amount of mutual coupling between lines.

Another important microstrip circuit component that is used quite often is the two-way power divider, illustrated in Figure 3.13. In this figure, the input power P , with microstrip linewidth W , is split into powers P2 and P,, with linewidths W 2 and W , and impedances Z 2 and Z, . The fundamental design equations for this simple power divider are

angle A = arctan (W3/ W , )

Since there could be a small amount of impedance mismatch due to fabrication tolerance or other types of inaccuracies, it is more practical, as explained previously, to design the power divider with a quarter-wave transformer as shown in Figure 3.14.

A three-way power divider, illustrated in Figure 3.15, can also be designed based on the equations of the two-way divider. The design equations for this three-way divider are

z2 x z3 2, = ---- z, + Z,' ' 2 + ' 3 (3.16) z z z

p - - -1x P , , P -'x P , , P 2 = - - 1 x P , , -2 , -z , z2

With the above equations for the two-way and three-way power dividers, one


FIGURE 3.14 Microstrip two-way power divider with a quarter-wave transformer.

FIGURE 3.15 Microstnp three-way power divider.

should be able to derive the equations for any multiple power division with different combinations of power ratios.

In addition to the above reactive power dividers, two other types of power dividers are briefly presented here. One is the branch-line hybrid divider shown in Figure 3.16, and the other is the Wilkinson power divider shown in Figure 3.17. A reactive power divider does not provide isolation between the divided ports. Any mismatch at the end of a divided port will send the returned power into other ports, which can cause high sidelobe and cross-pol levels. Both the branch-line hybrid divider and the Wilkinson divider can generally provide more than 20 dB of isolation between the two divided ports. The branch-line hybrid, in addition to its capability of providing 90" phase differential between its two output ports, can also achieve different power divisions. In Figure 3.16, any mismatch-reflected power from port 2 and port 3 will go into the loaded port 4 and not into the input port 1. For the Wilkinson power divider depicted in Figure 3.17, mismatch- reflected power from the two divided ports will be mostly absorbed by the 100-ohm resistor.


'0-b '0 - a , -- impedances: - - Za Zb

b2 - a* = 1 .---..... matched condition

p 2 - 1 o r ratios: - ( ; 5 = (-$ "1

FIGURE 3.1 6 Microstrip hybrid branch-line power divider.

100 r2 resistor

I 1 = 0 ~ FIGURE 3.1 7 Microstrip Wilkinson power divider.

3.3.4 Microstrip Reflectarray Design

The microstrip reflectarray is a fairly new antenna concept 145-471. It consists of a very thin, flat reflecting surface and an illuminating feed, as shown in Figure 3.18. On the reflecting surface, there is an array of isolated microstrip patch

Feed Antenna


Rectangular Microstrip

Microstrip Transmission

Line

PG'PPPP PPPPffPP

PP5'pc'PG' Ground

Dielectric Substrate

FIGURE 3.18 Configuration of microstrip reflectarray.

elements (and no power division network). The feed antenna illuminates these patch elements, which are individually designed to scatter the incident field with the phase needed to form a constant aperture phase. This operation is similar in concept to the use of a parabolic reflector, which naturally forms a planar aperture phase when a feed is placed at its focus. Hence the term "flat reflector" is sometimes used to describe the microstrip reflectarray. This antenna concept combines some of the best features of the traditional parabolic teflector and the microstrip array technology. The main beam of the microstrip reflectarray can be designed to be fixed in direction, or actively scanned if phase shifters are used on the elements. Since the major portion of the antenna, the reflecting surface, is a flat structure with a low profile, the antenna can be either surface-mounted on an existing structure or easily deployed on a spacecraft to form a large aperture with a relatively small stowage volume. Without any power divider, the resistive insertion loss of this antenna, as a large array, is very small and is comparable to that of a parabolic reflector. For the same reason, no complex and costly beamformer is needed. The antenna, being in the form of a printed microstrip array, can be fabricated with a simple, low-cost etching process, especially when it is produced in large quantities.

To achieve the desired aperture, the backscattered field from each patch must have a reflection phase such that it compensates for the differences in path length from the feed to each patch in the array. There are presently three techniques used to compensate for the path-length differences. One is to attach variable-length open-circuit-terminated transmission line stubs to all identical-size patches


[45,46]. The lengths of these stubs, which can be less than a half-wavelength, are designed to compensate for the path-length differences. The second technique is to use patches of different sizes [47], since this changes the resonant frequency of the element, and hence its reflection phase. With this technique, no phase-delay transmission lines are needed. Patches with different sizes have different radiation impedances, which are complex numbers with different phase values and thus can be used to compensate for the path-length differences. The third technique, for circular polarization only, uses all identical elements. But the patches are designed with different angular rotations [48]. It is known that,for two circularly polarized identical elements having different angular rotations, the phases generated by these two elements will be different and will be proportional to the relative difference in rotation. Thus, the element angular rotations in a reflectarray can be designed to compensate for the path-length differences.

Microstrip reflectarrays, regardless of which phase-compensating technique is used, can all be designed by the procedures listed below:

1. Determine a preliminary reflectarray configuration-that is, aperture size, element spacing, and f / D ratio, based on the given requirements of gain, efficiency, beam angle and bandwidth [48].

2. Calculate the compensating phases needed for all the elements with an appropriate analysis technique, which can be either conventional array theory [46,49] or more accurate full-wave techniques [47, 501.

3. Design, fabricate, and test a single patch element to ensure that its resonant frequency meets the requirement. The f / D ratio and the element beamwidth should be correspondingly designed to ensure minimum loss of energy due to aperture mismatch. In the case where the reflectarray comprises variable-size patches, depending on the designer's experience level, several elements of different sizes may need to be calibrated analytically and experimentally to ensure that the needed different compensating phases can be achieved.

4. Design, fabricate, and test the feed horn. The horn should be designed to optimize the trade-off between taper loss and spillover loss, for the specified f / D ratio and array size.

5. Refine and finalize the reflectarray configuration with a detailed design. For example, the element spacing may need to be increased slightly to accommodate the patch and its phase-delay transmissionlines. The f / D ratio may need to be adjusted slightly to achieve the best illumination and spillover efficiencies based on the true measured feed horn pattern.

6. Fabricate and test the complete reflectarray. Efficiency is one of the most important parameters that needs to be measured. A successful and optimal- ly designed microstrip reflectarray should be able to achieve an efficiency of at least 55%.

An example of the result a microstrip reflectarray is shown in Figure 3.19. This design used a 15.24-cm square array of 784 elements with square microstrip


0

FIGURE 3.1 9 Measured and calculated patterns of a microstrip reflectarray operating at 28 GHz.

patches of variable size. The operating frequency was 28 GHz, and the array was designed to produce a main beam scanned 25" from broadside, with a circular corrugated horn feed antenna. The figure shows the measured and calculated E-plane patterns. The measured gain of this reflectarray was 31 dB, for an aperture efficiency of 54%.

Along with all the advantages of the reflectarray discussed above, there is one significant disadvantage associated with this antenna-that is, its narrow bandwidth, which is limited by four possible factors: (1) the patch element spacing, (2) the narrow bandwidth of the patch element, (3) the bandwidth of the feed horn, and (4) the differential spatial phase delay [48]. Among these four factors, the one that limits bandwidth the most is the differential spatial phase delay, which is basically the phase difference between the path from the feed to an arbitrary patch and the path from the feed to a reference patch. This differential spatial phase delay will change as frequency changes and will perturb the predesigned phases of all the elements and thus distort the radiation pattern characteristics. It has been determined that for a reflectarray with a n f/D ratio of 1.0, the largest bandwidth that can be achieved is about 10% [51]. It has also been determined that, for two reflectarrays having the same aperture size, the one with the larger f / D has

152 MICROSTRIP ARRAYS: ANALYSIS, DESIGN, AND APPLICATIONS APPLICATIONS 153

a wider bandwidth. Conversely, for two reflectarrays having the same f / D ratio, the one with the larger aperture size has a narrower bandwidth.

3.4 APPLICATIONS

Since the invention of the microstrip antenna several decades ago, the demand for its application has been increasing rapidly. Initial applications have been primarily in the defense sector. Because of their extremely thin profile and low weight, printed microstrip antennas have found many applications for conformal mounting on military aircraft, missiles, rockets, and satellites. In the commercial sector, the adoption of the microstrip antenna has not been as rapid during the past decade, primarily due to its relatively higher materials cost and the newness of the technology. During the earlier years, the costs of the microstrip antenna's substrate material, design effort, and manufacturing processes were considered noncompetitive when compared to monopole, helix, horn, or parabolic reflector antennas. In addition, the configuration and environment of most terrestrial communication systems did not warrant the use of microstrip antennas. For example, in a U H F cellular terrestrial communication system, with plenty of R F power and antenna real estate for its base stations, the mobile unit can perform adequately with a simple low-gain monopole antenna without any concern about its system gain margin being too small. During the past decade, however, the cost to develop and manufacture microstrip antennas has dropped significantly. This is because of the maturity of the microstrip antenna technology, the reduction in cost of the substrate material and manufacturing process, and the simplified design process using newly developed versatile CAD tools [4]. Furthermore, modem satellite communication applications benefit greatly from the small size and low profile features of the microstrip antenna. For example, in L-band mobile satellite communication systems 1521, because of the limited spacecraft solar-battery power and spacecraft antenna size, the mobile vehicle terminal requires a higher-gain antenna (on the order to 10dBi) in order to ensure an adequate system link margin. An antenna such as a horn, helix, or monopole array would be too bulky to be mounted on top of a passenger automobile. A low-profile printed microstrip array not only offers an aesthetically pleasing appearance, but also has a low manufacturing cost, especially when produced in large quantities.

The following subsections discuss some of the applications of microstrip arrays in the military, space and commercial sectors. The number of applications in these sectors is overwhelmingly large, and only a few representative examples are discussed here.

3.4.1 Military Applications

In the military sector, high-velocity aircraft, missiles, and rockets, as well as spacecraft, required low-profile and lightweight antennas, to be conformally

input

FIGURE 3.20 Series-fed microstrip array with variable element sizes for amplitude taper control and low-sidelobe performance. (From reference 5 3 , ~ 1990 IEEE.)

, : : : f l t r r 1 ~ k t ~ r 1 : : : feed radiating patches

side view

ground plane

FIGURE 3.21 Configuration of a log-periodic microstrip array. (From reference 54, printed with permission from IEE.)

mounted on their outside surfaces. The microstrip antenna is best suited for this requirement, since such an antenna would neither disturb the aerodynamic flow nor protrude inward to disrupt other already crowded space.

The applications of microstrip array antennas in the military sector have been numerous. They include functions such as guidance, fuzing, telemetry, command, communication, radar, ECM, ECCM, altimeters, beacons, GPS, and. so on. Three selected examples are presented here. One is a series-fed linear microstrip array [53] for a missile fuze application. It was designed by the University of Colorado for US. Navy air-to-air guided missiles. It was designed to have a forward-tilted beam with low sidelobes (z - 30 dB). The low-sidelobe requirement was set to minimize false alarms and for antijamming purposes. This antenna, sketched in Figure 3.20, is a traveling-wave array with accurately designed amplitude distribution for achieving the required low sidelobes. The second example, depicted in Figure 3.21, is a series-fed, electromagnetically coupled, log-period microstrip array [54]. It has an extremely wide bandwidth for meeting many of the military's multioctave requirements. The third example, shown in Figure 3.22, has a multilayer monolithic integrated phased-array architecture. This architecture has been under study in recent years by many researchers for the Air Force's "Smart Skin" program, where many intelligently controlled phased arrays are conformally mounted onto the aircraft outside surface. The antenna system is basically separated into three layers. The top layer is the radiating microstrip patches. The second layer consists of phase shifters, T/R modules, and intelligent command and control computer chips. This layer may be further subdivided into multiple layers, depending on the complexity

154 MICROSTRIP ARRAYS: ANALYSIS, DESIGN, AND APPLICATIONS APPLICATIONS 155

radiator layer

ground plane with aperture coupling slots

RF power distribution layer

FIGURE 3.22 Multilayer monolithic phased-array architecture.

and requirements. The bottom layer is the R F power distribution circuit. The connections between layers are implemented by a combination of aperture coupling slots and feedthrough pins.

In addition to the above examples and many other existing applications of the microstrip arrays for the military, it is expected that the microstrip array antenna will continue to play an important role in the arena of military operations.

3.4.2 Space Applications

In the space sector, numerous applications of microstrip arrays have been implemented. To name a few, the following space programs all have used or are using microstrip arrays: Earth Limb Measurement Satellite (ELMS), Interna- tional Sun Earth Explorer (ISEE), SEASAT, Shuttle Imaging Radar (SIR)-A, B, C series, Solar Mesospheric Explorer (SME), Cosmic Background Explorer, GEOSTAR, and Mars Pathfinder. Among these programs, the antennas for SEASAT and the SIR-A, B, C series are all large-panel microstrip arrays (s 10 m long) at L-band and/or C-band frequencies. These antennas are part of the synthetic-aperture radars used to perform Earth remote sensing functions. These large arrays, except the SIR-C, are all designed with fixed main beams. The SIR-C antenna, launched twice (1994 and 1995) on the space shuttle, has electronic beam-scanning capability with solid-state T/R modules and phase shifters. The antenna, shown in Figure 3.23 and 3.24, has separate L-band (12 m x 3 m) and C-band (12m x 0.75m) microstrip array panels developed by Ball Aerospace Corporation. An X-band fixed-beam slotted waveguide array (12m x 0.4m) developed in Germany is also part of the SIR-C antenna. Another antenna that is worthy of mention is a small (25-cm-diameter) X-band microstrip dipole array, shown in Figure 3.25. It was used as a telecommunication antenna on the Mars Pathfinder spacecraft launched in 1996 for Mars exploration. The antenna provides circular polarization with a peak gain of 25 dB. It is constructed with a corporate feed power divider and electromagnetically coupled dipoles. The

FIGURE 3.23 SIR-C antennas in laboratory configuration. The middle large panels are an L-band microstrip phased array with distributed T/R modules and phase shifters; the bottom small panels are a C-band microstrip array with distributed T/R modules and phase shifters: the top panels are an X-band slotted waveguide array.

divider and the dipoles are printed on multilayer honeycomb substrates which have open vented cells for space application. A polarizing cover sheet is used to achieve circular polarization.

In designing microstrip antennas for space applications, three critical areas need to be considered. One is that the antenna must be able to survive the violent vibration during launch from the Earth. Generally, a vibration shock on the order of lOGs or more must be tolerated. The soldering points of the coax connectors and the laminating epoxy material between different layers of the microstrip arrays all need to be made strong enough to survive the vibration, or noncontacting feeds (such as proximity or aperture coupling) must be used.

156 MICROSTRIP ARRAYS: ANALYSIS, DESIGN, A N D APPLICATIONS APPLICATIONS

FIGURE 3.24 SIR-C antennas in shuttle bay during flight.

The second area of concern is the extreme temperature variations that can occur in space. Depending on whether the antenna is facing the Sun or is in a shaded area, and depending on its distance from the Sun; the temperature, on average, can vary between 173 and 373 K (+ 100°C). The substrate material, as well as its laminating adhesive material, must survive physically and electrically throughout this temperature range over the lifetime of the spacecraft.

The third area of concern is the antenna's RF power-handling capability. The power-handling capability of the microstrip antenna is generally an order of magnitude less in space than in Earth's atmosphere. Due to the vacuum in space, a particular breakdown phenomenon known as multipacting [41] generally occurs at pressures lower than lo-' torr. At this low gas pressure, the electrons are more free to leave an electrode and move across to the opposite electrode. For a microstrip antenna, the two electrodes are the patch and its ground plane. Thus, in order to handle higher power in space, the microstrip antenna or microstrip transmission line must be designed with the proper thickness.

FIGURE 3.25 Mars Pathfinder microstrip dipole array for deep space telecommu tion application. (Courtesy of Ball Corporation.)

3.4.3 Commercial Applications

During the past decade, the demand for microstrip antennas for commercial applications [ 5 5 ] has increased rapidly. This trend is due not only to the antenna's low physical profile and small mass, but also to the maturity of the microstrip antenna technology, the cost reduction of the substrate material and manufacturing process, and the simplified design process facilitated by recently developed CAD tools. Several well-known areas in which the microstrip antenna is finding applications are mobile satellite and personal communications, direct broadcast satellite (DBS) services, global positioning system (GPS), aeronautical and marine radars, medical hyperthermia, and Earth remote sensing.


FIGURE 3.26 Microstrip array antenna for marine radar application. (courtesy of Furuno Corporation.)

Many examples of microstrip array antenna applications in the above areas are discussed and illustrated in reference C.551. Two additional examples are given here. One is the X-band marine weather radar antenna shown in Figure 3.26, in which 48 rectangular patches are series fed to generate a broadside fan-shaped beam. The simplicity of this microstrip array is obvious, in that only a single coax feed probe and a single array panel are assembled. Because of the antenna's light weight, a smaller and lower-cost drive motor is used. The second example is an antenna system that uses multiple microstrip phased arrays and is being implemented on the satellites of Motorola's Iridium program [56] for mobile satellite communications. The Iridium program will achieve worldwide hand-held cellular telephone service via a network of 66 satellites placed in low Earth orbit. Each satellite is equipped with three L-band phased-array panels, each of which generates 16 simulataneous beams. There are approximately 165 microstrip patches with GaAs T/R modules and phase shifters on each panel.

When developing antennas for commercial applications, the antenna designer must pay careful attention to one critical area: The antenna's manufacturing cost must be low enough to be affordable to its intended customers. This is especially

REFERENCES 159

true for large-quantity productions. The costs of the material, components, and manufacturing process are all important elements to be considered for achieving a price-competitive antenna system.

3.5 SUMMARY AND CONCLUSION

Analysis techniques and design methodologies for microstrip array antennas have been presented. In particular, the full-wave moment method and its applications for various microstrip arrays were presented in some detail. Practi- cal design techniques for the array configuration, radiating patch element, and power division transmission lines have also been thoroughly discussed. The design steps for the more recently developed microstrip reflectarrays were also outlined. Applications of microstrip arrays in the areas of military, space, and commerce were discussed. It is expected that, because of their small size and low mass, the demand for microstrip antennas in all three areas will continue to increase, especially in the commercial sector. On the other hand, there is also an unabated demand for improving the performance of microstrip array antennas,such as widening of the bandwidth and reduction of the antenna's insertion loss. By utilizing the analysis techniques and design methods presented in this chapter, in conjunction with innovative ideas, the performance of microstrip array antennas can be further enhanced to broaden their applications in the future.

REFERENCES

I. J. Bahl and P. Bhartia, Microstrip Antennas, Artech House, Dedham, MA, 1980. R. J. Mailloux, J. F. McIlvenna, and N. P. Kernweis, "Microstrip Array Technol- ogy," IEEE Trans. Antennas Propagat., Vol. AP-29, pp. 25-38,1981. J. R. James and P. S. Hall, Handbook of Microstrip Antennas, Peter Peregrinus, London, 1989. D. M. Pozar and J. R. James, "A Review of CAD for Microstrip Antennas and Arrays," in Microstrip Antennas: The Analysis and Design ofMicrostrip Antennas and Arrays, D. M. Pozar and D. H. Schaubert, eds., IEEE Press, New York, 1995. E. Levine, G. Malamud, S. Shtrikman, and D. Treves, "A Study of Microstrip Array Antennas with the Feed Network," IEEE Trans. Antennas Propagat., Vol. 37, pp. 426-434,1989. D. M. Pozar and B. Kaufman, "Design Consideration for Low Sidelobe Microstrip Arrays," IEEE Trans. Antennas Propagat., Vol. 38, pp. 1176-1185,1990. K. R. Carver and J. W. Mink, "Microstrip Antenna Technology," IEEE Trans. Antennas Propagat., Vol. AP-29, pp. 2-24,1981. D. Theroude, M. Himdi, and J. P. Daniel, "CAD-Oriented Cavity Model for Rectangular Patches," Electron. Lett., Vol. 26, pp. 842-844, 1990. H. Pues and A. Van de Capelle, "Accurate Transmission Line Model for the Rectangular Microstrip Antenna," IEE Proc., Vol. 131, pp. 334-340,1984.

160 MICROSTRIP ARRAYS: ANALYSIS, DESIGN, A N D APPLICATIONS REFERENCES 161

[lo] V. Palanisamy and R. Garg, "Analysis of Arbitrarily Shaped Microstrip Patch Antennas Using Segmentation Techniques," IEEE Trans. Antennas Propagat., Vol. AP-34, pp. 1208-1213,1986.

[ll] D. M. Pozar and D. H. Schaubert, eds., Microstrip Antennas: The Analysis and Design of Microstrip Antennas and Arrays, IEEE Press, New York, 1995.

[12] D. M. Pozar, "Microstrip Antenna Aperture Coupled to a Microstripline," Electron. Lett., Vol. 21, pp. 49-50, 1985.

1131 C. Wu, K.-L. Wu, Z.-Q. Bi, and Litva, "Accurate Characterization of Planar Printed Antennas Using Finite Difference Time Domain Method," IEEE Tmns. Antennas Propagat., Vol. 40, pp. 526-534,1992.

[14] D. M. Pozar, "Input Impedance and Mutual Coupling of Rectangular Micro- strip Antennas," IEEE Trans. Antennas Propagat., Vol. AP-30, pp. 1191-1196, 1982.

[15] D. M. Pozar, "Rigorous Closed-Form Expressions for the Surface Wave Loss of Printed Antennas," Electronics Lett., Vol. 26, pp. 954-956,1990.

[16] J. R. Mosig and F. E. Gardiol, "General Integral Equation Formulation for Microstrip Antennas and Scatterers," Proc. I E E , ~ V O ~ . 132, Part H, pp. 424-432, 1985.

[lq L. Barlatey, J. R. Mosig, and T. Sphicopoulos, "Analysis of Stacked Microstrip Patches with a Mixed Potential Integral Equation," IEEE Trans. Antennas Propagat., Vol. 38, pp. 608-615,1990.

1181 F. Croq and D. M. Pozar, "Millimeter Wave Design of Wideband Aperture Coupled Stacked Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. 39, pp. 1770-1776,1991.

[I91 D. M. Pozar and D. H. Schaubert, "Comparison of Three Series Fed Microstrip Array Geometries," 1993 IEEE International Symposium on Antennas and Propaga- tion, Ann Arbor, MI.

[20] J. Huang, "A Parallel-Series-Fed Microstrip Array with High Efficiency and Low Cross-Polarization;" Microwave Opt. Technol. Lett., V01.5, pp. 230-233,1992.

[21] K. Solbach, "Phased Array Simulation Using Circular Patch Radiators," IEEE Trans. Antennas Propagat., Vol. AP-34, pp. 1053-1058,1986.

[22] P. R. Haddad and D. M. Pozar, "Anomalous Mutual Coupling Between Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. 42, pp. 1545-1549,1994.

[23] D. M. Pozar, "Finite Phased Arrays of Rectangular Microstrip Patches," IEEE Trans: Antennas Propagat., Vol. AP-34, pp. 658-665,1986.

[24] Ensemble-Design and Review User's Guide, Boulder Microwave Technology, Boulder, CO.

[25] J. T. Aberle and D. M. Pozar, "Analysis of Infinite Arrays of Probe-Fed Rectangular Microstrip Patches Using a Rigorous Feed Model," IEE Proc., Vol. 136, Part H, pp. 110-119,1989.

[26] J. T. Aberle and D. M. Pozar, "Analysis of Infinite Arrays of One- and Two-Probe- Fed Circular Patches," IEEE Trans. Antennas Propagat., Vol. AP-38, pp. 421-432, 1990.

[27] D. M. Pozar, "Analysis of an Infinite Array of Aperture Coupled Microstrip Patches," IEEE Trans. Antennas Propagat., Vol. AP-37, pp. 418-425,1989.

[28] J. T. Aberle, D. M. Pozar, and J. Manges, "Phased Arrays of Probe-Fed Stacked Microstrip Patches," IEEE Trans. Antennas Propagat., Vol. 42, pp. 920-927,1994.

[29] D. M. Pozar, "Scanning Characteristics of Infinite Arrays of Printed Antenna Subarrays," IEEE Trans. Antennas Propagat., Vol. 40, pp. 666-674,1992.

[30] D. M. Pozar, S. D. Targonski, and H. D. Syrigos, "Design of Millimeter Wave Micro- strip Reflectarrays," IEEE Trans. Antennas Propagat., submitted for publication.

[31] D. M. Pozar, "The Active Element Pattern," IEEE Trans. Antennas Propagat., Vol. 42, pp. 1176-1 178,1994.

[32] H. A. Wheeler, "A Survey of the Simulator Technique for Designing a Radiating Element," in Phased Array Antennas, A. Oliner and G. Knittel, eds., Artech House, Dedham, MA, 1972.

[33] W. J. Tsay and D. M. Pozar, "Radiation and Scattering from Infinite Periodic Printed Antennas with Inhomogeneous Media," IEEE Trans. Antennas Propagat., submitted for publication.

[34] J. R. James, P. S. Hall, and C. Wood, Microstrip Antenna: Theory and Design, Peter Peregrinus, London, 1981.

[35] A. G. Derneyd, "Linearly Polarized Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. AP-24, pp. 846-851, 1976.

[36] T. Metzler, "Microstrip Series Arrays," IEEE Trans. Antennas Propagat., Vol. AP-29, pp. 174-178,1981.

[373 J. Huang, "A Ka-Band Circularly Polarized High-Gain Microstrip Array Antenna," IEEE Trans. Antennas Propagat., Vol. AP-43,113-117,1995.

[38] T. Teshirogi, M. Tanaka, and W. Chujo, "Wideband Circularly Polarized Array Antenna with Sequential Rotations and Phase Shift of Elements," Proc. ISAP, Japan, pp. ll7-120,1985.

[39] J. Huang, "A Technique for an Array to Generate Circular Polarization with Linearly Polarized Elements," IEEE Trans. Antennas Propagat., Vol. AP-34, pp. 1113-1123,1986.

[40] H. Howe, Jr., "Stripline Is Alive and Well," Microwave J., pp. 25-28,1971. [41] R. Woo, Final Report on RF Voltage Breakdown in Coaxial Transmission Lines, Jet

Propulsion Laboratory Technical Report TR32-1500, October 1970. [42] J. Huang, "Circularly Polarized Conical Patterns from Circular Microstrip An-

tennas," IEEE Tmns. Antennas Propagat., Vol. AP-32, pp. 991-994,1984. [43] G. Kumar and L. Shafai, "Generation of Conical Patterns from Circular Patch

Antennas and Their Performance," Canadian Elect. Eng. J., Vol. 10, pp. 108-112, 1985.

[44] I. J. Bahl and D. K. Trivedi, "A Designer's Guide to Microstrip Line," Microwaves, pp. 174-181,1977.

[45] R. E. Munson and H. Haddad, "Microstrip Reflectarray for Satellite Communica- tion and RCS Enhancement or Reduction," U.S. Patent 4,684,952,1987.

[46] J. Huang, "Microstrip Reflectarray," in IEEE AP-SIURSI Symposium, London, Ontario, Canada, pp. 612415,1991.

[47] S. D. Targonski and D. M. Pozar, "Analysis and Design of a Microstrip Reflectarray Using Patches of Variable Sizes," in IEEE AP-SIURSI Symposium, Seattle, WA, pp. 1820-1823,1994.

162 MICROSTRIP ARRAYS: ANALYSIS, DESIGN, A N D APPLICATIONS

[48] J. Huang, "Bandwidth Study of Microstrip Reflectarray and a Novel Phased Reflectarray Concept," in IEEE AP-SIURSI Symposium, Newport Beach, CA, pp. 582-585,1995.

[49] D. C. Chang and M. C. Huang, "Microstrip Reflectarray Antenna with Offset Feed," Electron. Lett., pp. 1489-1491. 1992. . .

[50] Y. Zhuang, K. Wu, C. Wu, and J. Litva, "Microstrip Reflectarray: Full-Wave Analysis and Design Scheme," in IEEE AP-SIURSI Symposium, Ann Arbor, MI, pp. 1386-1389,1993.

[51] J. Huang, Analysis of a Microstrip Rejectarray Antenna for Microspacecraft Applica- tion, Jet Propulsion Laboratory TDA Progress Report 42-120, pp. 153-172, 1995.

[52] W. Rafferty, K. Dessouky, and M. Sue, "NASA's Mobile Satellite Development Program," Proceedings of the International Mobile Satellite Conference, pp. 11-22, 1988.

[53] A. Benalla, K. C. Gupta, and R. Chew, "Computer Aided Design of Linear Series-Fed Microstrip Patch Arrays with a Dielectric Cover Layer," in IEEE AP-SLURSI Symposium, Dallas TX, pp. 1758-1761,1990.

[54] P. S. Hall, "Multioctave Bandwidth Log-Periodic Microstrip Antenna Array," Proc. IEE, Vol. 133, Part H, pp. 127-136, 1986.

[55] J. Huang, "Microstrip Antennas for Commercial Applications," in Microstrip Antennas: The Analysis and Design of Microstrip Antennas and Arrays, D. M . Pozar and D. H. Schaubert, eds., IEEE Press, New York, 1995.

[56] J. J. Schuss et al., "Design of the Iridium Phased Array Antennas," in IEEE AP-SIURSI Symposium, Ann Arbor, MI, pp. 218-221,1993.

CHAPTER FOUR

Dual and Circularly Polarized Microstrip Antennas

P. S. HALL and J. S. DAHELE

4.1 INTRODUCTION

Many current communication and sensor systems require a high degree of polarization control to optimize system performance. For microstrip antennas to be fully exploited in such systems, high polarization purity and isolation between orthogonal polarizations-be they linear or circular-are needed. This chapter will discuss the polarization capabilities of microstrip antennas and relate this to the current demand for circularly polarized and dual polarized planar antennas.

Historically, single linearly polarised microstrip patch antennas were the first to be developed. Soon after, techniques for circular polarization were demonstrated, but again involving only a single hand of polarization. It is well known that much physical insight can be gained from a model based on the modal view of patch operation, particularly so because of the relatively narrow bandwidths involved. Using this model, two orthogonal polarizations can be related to a pair of orthogonal modes on the patch. The quality of polarization and its control in either linear or circular systems is linked to how the two orthogonal modes in the antenna are excited and how well they can be controlled; this is, to some extent, related to the inherent isolation between them. This isolation is, in turn, dependent on the patch quality factor and the excitation geometry. Thus the likely cross-polarization or axial ratio is determined early on the design process and

Advances in Microstrip and Printed Antennas, Edited by Kai Fong Lee and Wei Chen. ISBN 0-471-04421-0 0 1997 John Wiley & Sons, Inc.

164 DUAL AND CIRCULARLY POLARIZED MICROSTRIP ANTENNAS

may in fact be determined by other parameters, such as bandwidth or the desired mechanical construction, unless specific measures are taken. The more recent desire for dual polarized antennas has put further emphasis on these difficult issues, and a new class of microstrip antennas known as sewdiplexing antennas have arisen, which aim to maximize the isolation between polarizations in such dual systems. This chapter will review the progress in the two areas of polarization control of circularly polarized and dual polarized microstrip antennas. In doing this, of course, the area of polarization control in linearly polarized antennas is also touched on. After specifying some of the parameters important when discussing polarization in antenna systems, we will examine the basic action of a patch antenna supporting two orthogonal modes in order to clarify the likely degree of polarization control that can be obtained from currently used microstrip antennas. Techniques are then reviewed in the following order: patches for circular and dual polarization, microstrip spirals and special types including those based on ferrite and chiral substrates, and finally circular and dual polarized array configurations.

4.2 POLARIZATION IN ANTENNA SYSTEMS

Several excellent references describe polarized electromagnetic waves [I, 23, and the interested reader is referred to these for details. For the purpose of this overview it is noted that, in general, waves are elliptically polarized and are defined by three variables, namely axial ratio, tilt angle, and sense. The IEEE standard definition 131 of sense states that for an approaching wave, counter- clockwise vector rotation corresponds to a right-handed wave and vice versa. For an infinite or zero axial ratio, linear polarization results and the tilt angle defines the orientation of the electric vector; sense is not applicable. For waves with close to linear polarization, axial ratio is not used but rather the level of cross- polarization in an orthogonal plane is quoted. Throughout this chapter, Ludwig's third definition of cross-polarization [4] is assumed. For near-linear polarization, sense is usually not quoted, although for calculation of coupling between slightly off linearly polarized antennas, whether similarly or orthogonally polarized, it is necessary to know all three parameters. For unity axial ratio, circular polarization results and the tilt angle is not applicable. The quality of slightly off circularly polarized waves is specified by the axial ratio; and again tilt angle is not usually quoted, although again for coupling between antennas all three parameters are needed.

For single polarization systems the antenna can be considered as a two-port device with port 1 comprising the interface with the transmitter or receiver and the other port as free space (Figure 4.1). The S parameters involve the usual antenna characteristics. For dual polarization a four-port representation must be used and additional parameters become evident. S, , is the isolation between the two input ports and represents that part of the signal to be transmitted on polarization 1-that is, coupled into port 2 assuming both polarizations are

GENERATION OF ORTHOGONAL POLARIZATIONS 165

, Polarization 1 1 I 1

. Polarization 2

FIGURE 4.1 S-parameter representation of antennas. (a) Single polarization. (b) Dual polarization. (8 1995 IEEE.)

being transmitted. S,, represents the amount of signal that was to be transmitted on polarization 1 but appears as polarization 2 and similarly for S,,. The isolation usually quoted for dual polarization antennas is S, , or S,,. S,, or S, , are usually specified by the cross-polarization or axial ratio of the radiated wave. S,,, S,,, S,, or S,, represents the wave scattered from the antenna when illuminated by an incoming wave and is important when considering antenna radar cross section.

4.3 GENERATION OF ORTHOGONAL POLARIZATIONS

Design of dual and circular polarization microstrip antennas demands precise control of the individual orthogonal radiated polarizations. In some microstrip antennas, the structure favorably supports a given polarization. For example, a high-aspect-ratio rectangular patch will give a relatively pure linearly polarized wave. Similarly the microstrip spiral or patch on a biased ferrite substrate readily gives circularly polarized waves. In general, however, the wanted polarizations are synthesized from a pair of orthogonal linear polarizations and the coupling, S,, in Figure 4.lb, is a critical guide to the quality of the antenna. Figure 4.2 a [5] illustrates the coupling between orthogonal ports in a dual linearly polarized circular microstrip patch. On resonance, the high Q patch with t = 3.2-mm substrate thickness has better than 50-dB isolation. For the low Q patch on a 12.3-mm substrate, higher-order modes are generated that degrade the isolation to about 28 dB. Feed geometry is also critical here since, in general, increasing feed port size increases coupling. This limits the upper frequency range of, for instance, probe feeds which mate to coaxial cable. However, isolation can be improved by optimizing the feed position [6]. Use of notched or slotted patches with two feeds to give dual circular polarization further increases this undesirable mode coupling. Figure 4.2 b [7] compares coupling in a dual linear and dual circular patch, with isolation degrading from about 20 dB for dual linear to less than 10 dB for dual circular.

The radiation pattern shape is also significant in this discussion of the fundamentals of polarization control. From the gross features of the pattern,


Frequency (MHz) (a)

Frequency (GHz) (b)

FIGURE 4.2 Coupling between orthogonal feed ports in circular microstrip patches. (a) Effect of patch Q [S]. (b) Comparison of dual linear and dual circular polarization [7]; patch diameter = 40 mm, substrate height = 0.79 mm, E, = 2.3. (Reprinted with permission from IEE.)

several important points emerge. The beamwidth in the two principal planes of a patch are unequal, which will give rise to unequal radiation amplitudes off broadside in dual linearly polarized antennas and will increase axial ratio off broadside in circularly polarized ones. In scanned arrays this means that polarization control degrades with scan angle until at very low angles only

CIRCULARLY POLARIZED PATCHES 167

vertical polarization with respect to the ground plane can be radiated. Further- more, it is obvious that in most patches some azimuthal variation of the polarization for dual linear or circular will take place. However, the circular symmetry of the circular patch radiating circular polarization gives no azimuthal variation [B] and is thus widely used in circularly polarized arrays.

4.4 CIRCULARLY POLARIZED PATCHES

Circularly polarized radiation can be generated by exciting two orthogonal patch modes in phase quadrature with the sign of the relative phase determining polarization hand. These modes may be excited in a number of ways, which are described below. Before reviewing the methods it is instructive to compare the relative performance of the feed arrangements. Figure 4.3 shows three methods of excitation applied to a square patch fed by microstrip lines. The comments that follow apply to all patch shapes and feed connection geometries. Figures 4.3 a and 4.3b show the two orthogonal modes excited by orthogonal feed lines. In Figure 4.3a the quadrature phasing is achieved by the difference in the line lengths to the patch feeds. In Figure 4.3b a hybrid is used to provide the phase offset and in addition gives isolation between the two feed points. Figure 4 . 3 ~ shows some typical hybrid coupler configurations. The branch line hybrid and rat race are characterized by a fourth port to which a matched load is connected. In the case of the Wikinson splitter the load is integrated. Such couplers are designed to isolate the two output ports so that power reflected from a mismatched antenna on these ports is transferred to the absorbing load. In the case of the patch fed by the T splitter, this reflected power is both reflected back to the antenna port from

I

FIGURE 4.3 Excitation methods for circular polarization. (a) Orthogonal feeds, reactive splitter. (b) Orthogonal feeds, isolating splitter. (c) Splitters: branch line, Wilkinson, hybrid ring. (d) Single-feed degenerate mode patch. (continued)


whichit came and transmitted onward to the other port. A significant redistribu- tion of the power supplied to the patch may result.

In both cases, that of isolated and nonisolated splitters, the patch input mismatch determines the overall frequency response of the antenna [9]. In the nonisolated case (Figure 4.3 a) the 90" phase shift between feeds means that the mismatch reflections tend to cancel at the input port, and the input match to the element remains acceptable over the bandwidth of a single mode. However, these element reflections coupled to the splitter output ports and result in radiation of the opposite hand of polarization. Calculations show that an element will have about 3-dB axial ratio when the VSWR is about 1.5. The isolated feed Figure 4.3b gives good axial ratio and input VSWR over the band as the reflected power is absorbed in the matched load on the fourth port of the hybrid coupler. This absorbed power is equal to the power radiated in the unwanted hand using a nonisolated feed, and thus in both cases the gains are identical. It is important to note, however, that an isolated feed geometry is preferable because it allows only the wanted hand of radiation.

The degenerate mode patch fed by a single line (Figure 4.3d) has been examined in the same way. The patch asymmetry excites the orthogonal mode. It is found that the performance is very similar to the reactive splitter fed patch (Figure 4.3a), with the axial ratio degrading rapidly with frequency away from


resonance while the input VSWR remains acceptable. Figure 4.3d is a more compact structure and is adopted in many practical antennas.

In many practical microstrip patch applications, the bandwidth of the patch will be narrower than that of the hybrid coupler described above. If this is the case, then the patch input mismatch will dominate the overall frequency characteristic. However, when the patch has been designed for wide bandwidth, errors in the 90" phase shift will occur at frequencies off resonance. Additionally, as noted in Section 4.3, undesirable mode coupling becomes significant in wideband patches, and this will perturb the polarization performance. The use of more than two feed points has been used to overcome these problems, and such methods are described in detail in Section 4.4.2. However, the results given there include two-point feeding, and readers interested in further information are directed to that section.

4.4.1 Orthogonal Patches

The two orthogonal modes needed to produce circular polarization may in fact be supported by orthogonal patches as shown in Figure 4.4a. The primary problem with this arrangement is that because the phase centers of the patches are displaced and because the E- and H-plane radiation patterns are dissimilar,

FIGURE 4.4 Generation of circular polarization using orthogonal linearly polarized patches. (a) Using two patches. (b) Using rotated quarter-wavelength shorted patches, closely spaced [lo, 111. (c) Using conventional

(4 square patches [12].


the axial ratio degrades away from broadside. This may be acceptable in an array designed for a broadside beam. However, in this case there are additional problems with the radiation pattern, and these are noted later. To form elements with good low-angle circular polarization, four quarter-wavelength shorted patches can be arranged as shown in Figure 4.4b [lo, 111. The patches radiate primarily from the edge opposite the short circuit and the four thus form what is essentially a crossed slot radiator. The patches can be fed from a small corporate feed network located behind the antenna. The technique of orthogonal patches has also been applied to arrays [12,13] as illustrated in Figure 4 .4~ . Discussion is left until Section 4.8.

4.4.2 Multipoint Feeds

The idea of using two feed points exciting the two orthogonal modes in a microstrip patch in phase quadrature is well known and has been used in many published antenna types. The method was first described two decades ago [14, 151 using through the substrate pin-type connections. Microstrip line excitation and aperture coupling are now also widely used [6,16]. However, such feeding is but a special case of a more general method based on sequential rotation. Originally applied to arrays, this technique is now seen to give valuable insights into the operation of two-port feeding and to explain why the use of more feed points gives improved performance. This section details the development of the design equations and outlines the conclusions derived from them.

In principle, circular polarisation can be generated by feeding a patch at M points such that the mth feed has a rotation I$,, from a fixed reference angle and an excitation phase of dm, given by

where p is a integer, M is the total number of feed points, and n represents the azimuthal mode number of the patch. Table 4.1 shows a variety of excitations, illustrated with circular discs and probe feeding. In Table 4.1 it is assumed that n = 1 is the wanted mode. It is also clearly seen than an excitation distributed evenly round 271. radians occurs for p = 2. It can be shown that this occurs in the general case when p = 2n. Figure 4.5 shows a circular patch for m = 3, p = 2.

Several effects are important in determining the overall performance.

1. Multiple reflections between the patch and power splitter as described for the M = 2, p = 2 case in Section 4.8.3.3.

2. Feeding phase errors due to creating the appropriate feeding phases, 4,,, by the use of excess line lengths. Off resonance there will be errors in 4,,.

3. Generation of higher-order modes within the patch. Each feed generates a spectrum of modes whose amplitudes depend on the excitation geometry


TABLE 4.1 Multiple Feed Point Disc Congurations with Performance Estimates

Sequential Rotation Cross-Polar Due Cross-Polar Due Cross-Polar Due Arrangement Feeding to Multiple to Feed Phase to Higher-Order M p Configuration Reflections Errors Modes . -

2 Moderate Moderate High

3 1 0 Zero Low High

3 Zero High Low

4 Zero Very low Very high

4 2 0 High Moderate Very low

and the patch Q. For instance in the patch of Figure 4.2a, thicker feed pins, thicker patch and lower dielectric constant will encourage generation of unwanted higher order modes in addition to the wanted mode. This issue is discussed in Section 3 and can be considered as an alternative way to view the coupling between the feed pins. As discussed there this coupling degrades polarisation control, and perturbs the radiation pattern shape.

Factors 1 and 2 are of fundamental importance to the performance of sequentially rotated arrays and are treated in Section 4.8.3. However, the results pertinent to multiple-point patch feeding are summarized here. Factor 3 is of primary importance for patches, and a full discussion is now given.

Isolating solitter

FIGURE 4.5 Circular patch with multiple point feeding (M = 3, p = 2, excess path lengths are 4, = 213 and 42 = 2213). (Reprinted with permission from IEE.)


It is assumed for simplicity that for a circular patch the radiated fields have a cos (s4) azimuthal dependence, where s is azimuthal index of the mode within the patch. If the mth excitation angle and phase is determined by Eq. (4.1), then the radiated field of the sth mode due to this excitation for a wanted mode n is given by

where a,, and b,, are functions of the relative excitation of the sth mode compared to that of the nth mode. In general, a and b are also functions of 0 and 4, the polar angles defined in Figure 4.5, and in this analysis this dependence is assumed throughout. If multiple reflections and feeding-phase errors are neglected, then the total radiated field for a patch with multiple feed points is

X sin

- 1)pn12) . exp { - j(rn - 1) (st - l)prr/2M) sin {(s' - 1) p42M)

where s' = s/n-The-first term in Eq. (4.3) represents the wanted hand of @rcul_ar polarization (8 + jd), and the second term represents the unwanted hand (8- jq5).

If modes other than the (say) wanted n = 1 mode are neglected, and M = 2 and p = 1, then the second term becomes zero and only the wanted hand is radiated. This corresponds to the two-point feeding described in Section 4.4. However, if higher-order modes are present, then cross-polarization will be radiated. If reference R,. and cross X,, polarization coefficients are defined by

Pn X,. = sin(sl + 1) - sin(sl + 1)- 2 "1 2M

then the polarization characteristics of the contribution from each mode can be examined. The overall polarization purity is then determined by R,. and X,, and the modal coefficients a,, and b,,. The latter depend on the patch geometry and substrate and can be obtained by mode-matching techniques for single-point excitation, although it is possible that slightly different mode excitations will occur in patches with multiple excitation. Table 4.2 gives R,, and X,. for the various source arrangements given in Table 4.1 for a wanted n = 1 mode. It can be seen that the conventional arrangement for circular polarization M = 2, p = 1 gives poor rejection of cross-polarization. Arrangements for circular symmetry- that is, p = 2n-give best rejection with performance improving with larger M.

DUAL AND CIRCULARLY POLARIZED MICROSTRIP ANTENNAS

I -30 -90 -60 -30 0 30 60 90

8, degrees (a)

8, degrees (b )

8, degrees (c)

FIGURE 4.6 Circularly polarized radiation patterns in 4 = 0 plane of multiple-feed- point microstrip discs. (a) M = 2, p = 1, (b) M = 3, p = 2, (c) M = 4, p = 2. Measured: - copolar, - - - cross-polar. Computed: --- copolar; -.- cross-polar (disc radius = 39 mm, feed pin radius = 21 mm, substrate e, = 1.06, thickness = 25mm, frequency = 1.85 GHz). (Reprinted with permission from IEE.)


The effect is illustrated in Figure 4.6 which shows measured and computed results for a thick patch on a low dielectric constant substrate fed at 2, 3, and 4 excitation points, respectively. The computed results are found using a cavity model with mode matching [17].

These results can also be understood intuitively by considering the multiple- feed-point excitation to be a "balanced" feeding of the wanted mode. For example, it is clear from Eq. (4.2) that the s = 0 mode has no azimuthal radiated field dependence, and this is also true of the fields within the patch. If, therefore, a pair of excitations on opposite sides of the patch are used with a 180' phase difference, then this mode will be suppressed. This balanced feeding using two and four excitation points has been described by several authors [14,15,18,20] and has also been found to give reduced scan blindness in phased arrays [21].

The effects of multiple reflections and feeding phase errors can be analyzed using similar methods, and these are described in Section 4.8.3. Table 4.1 sum- marizes the results together with those deduced from Table 4.2. Choice of an appropriate feeding codguration will depend on which of the three factors is most important. For narrow bandwidth patches, feed phase errors and higher-order modes will be less significant. M = 3, p = 1 or 2 and M = 4, p = 1 arrangements will give best performance. For wideband patches the choice is less clear cut, and detailed studies of the overall performance is necessary. However, Figure 4.7

Fractional frequency (f/fres)

FIGURE 4.7 Computed axial ratio of multiple-feed microstrip circular patches (disc radius 39 mm, feed pin radius = 21 mm, substrate e, = 1.06, h = 25 mm, - 2 feed, - 4 feed, - - - 3 feed, substrate e, = 2.32, h = 3.2mm, --- 2 feed). (0 1995 IEEE.)


shows axial ratio for thick circular patches [18]. In the thick patch, higher-order modes are excited and give rise to the coupling noted in Section 2. Use of more than two feeds [I91 will reduce this, as the figure shows, with both three and four-feed systems having beneficial effects. The three-feed patch has a lower axial ratio than the four feed type, as reflections from the nonisolating splitter radiate in the wanted polarization. In the thin patch, coupling is low and good axial ratio on resonance results. It is noted in reference [20] that the coupling between the orthogonal feed ports in a 0.05-wavelength-thick circular patch on E, = 1.21 material can be reduced from -28 dB on resonance for two probes to about -60dB for four probes. These values are close to those deduced from the computations used to produce Figure 4.7. The use of notches on dual-fed patches [22] has also been shown to reduce axial ratio by about 50%.

Axial ratio bandwidth can be increased in several ways. The use of parasitic elements [23] has been shown to achieve about 7% axial ratio bandwidth and 10-dBi gainwith two parasitic patches giving an overall element height of 0.56

Frequency

FIGURE 4.8 Amplitude and phase orthogonal modes in single-point feed circularly polarized microstrip patch [25]. (0 1969 IEEE.)


wavelength. A coplanar reactive splitter feed was used. A crossed slot [24] used to aperture couples series and parallel feeds to a square patch of approximate thickness 0.1 wavelength produced, for the series arrangement, 12% axial ratio bandwidth, and for the parallel feed using isolating splitters a 22% bandwidth. These configurations are similar in principle to the four-point feeding discussed above and give similar bandwidths.

4.4.3 Single-Point Feeds

Figure 4.3d shows a square patch with single-point feed where circular polarization is induced by a so-called perturbation segment, in this case a pair of truncated corners. Figure 4.8 [25] illustrates how such perturbation can generate circular polarization. Modes 1 and 2, in the diagonal planes, are of equal amplitude and in phase quadrature at f,. It is clear that off f,, phase and amplitude errors will rapidly degrade the axial ratio. Figure 4.9 [26] shows typical axial ratio and input VSWR which confirm the qualitative behavior noted earlier in this section. In addition, it is clear that axial ratio bandwidth is determined by the Q of the individual modes with a thicker, lower Q patch giving better axial ratio bandwidth. The shape of the perturbation segment or patch can vary widely; rectangular patch [27], patch with tabs [28], patch with notches [29], patch with center slot [30], patch with truncated corner [26], elliptical

1 I 1 1 2.51 1

3160 3170 3180 3190 Frequency (MHz)

FIGURE 4.9 Axial ratio and input VSWR of truncated-corner square microstrip antenna [26]. (0 1983 IEEE.)


patch [3 11, pentagonal patch [32], triangular patch [33], ring with notches [34], and loop [35] have been studied. There are some comparative studies available, although no exhausitive work appears to have been done. For instance, it is shown in reference [36] that significant differences in design procedure result for the feed point on the patch principle planes or on the diagonal, although for the two particular cases chosen (the truncated corner square patch and rectangular patch), almost identical axial ratio bandwidth is noted. Similarly, results given in reference [26] indicate that the square patch with diagonal slot has the largest axial ratio bandwidth, whereas minimum VSWR is obtained with the diagonal fed nearly square patch. The truncated corner patch has the best axial ratio, but least axial ratio bandwidth. It is clear the optimization of patch type will depend on system requirements. Aperture coupling is advantageous for many reasons, and patches fed from a single line using a cross-shaped slot [37] or single slot with a second parasitic slot [38] have been described. The latter is claimed to have higher isolation when used in simultaneous transmit and receive systems. Prox- imity coupling to afeed line with an overlaid patch [39] is also possible. Details of the square C P patch with perturbation segments are given in Section 4.4.3.1.

4.4.3.1 Analysis of the Square CP Patch. In the patch shown in Figure 4.10a,

AS = AS, +AS, = cz

S = a2

The feed can be located either on the x-axis or y-axis. Consider the electrically thin cavity under the patch with perfect magnetic walls at the patch periphery. The eigenfunctions excited in the cavity are given by 1251

1 N ; : l 4; - mode

FIGURE 4.10 (a) Equivalent circuit for rectangular patch CP antenna [29]. (b) Un- loaded Q and radiation efficiency of rectangular patch CP antenna. (c) Relationship between (As/s) and unload Q of rectangular patch CP antenna. (0 1982 IEEE.)

vf


g; - mode

60 ' 1 I I 1 1 I 1 1 lo

0 2 4 6 8

Substrate thickness (vh) (x 10-2) (b)

1-1 Yb Cii i,,

I I I I I

0 10 20 30 40 50 Unloaded Q (Qo)

(c)


4. = Vo sin kx 4b = Vo sin ky

(4.6)

where Vo = f i and k = n/a. The eigenfunction 4, relates to the TM,,, mode field distribution in the cavity, and 4, is related to the TMolo mode field. Thus by introducing perturbation in the form of truncated diagonal corners, two orthogonally polarized modes are excited in the cavity. With perturbation, the new eigenfunction 4' and the new eigenvalue K are given by

4' = P6, + Q 6 b

k'2 =

180 DUAL A N D CIRCULARLY POLARIZED MICROSTRIP ANTENNAS CIRCULARLY POLARIZED PATCHES 181

where P and Q are unknown expansion coefficients of &. The expressions for # and k' are variational; therefore the eigenvalue k' can be

derived from the general matrix

k2 + ql - r 2 ( 1 + p l ) 412 -kT2p12 det 1 (4.8) q I 2 - k'2p12 k2 + qz - k'2(1 + PJ

where

The new eigenvalues KO and kb corresponding to the new orthogonal eigenfunctions are given by

The resonant frequencies of the 4: and 4; modes are given by

fo = fo, + Af: = fo, (1 - 2Asls)

f b= for+* fb=fo , (4.10)

where fo, is the resonant frequency of the square patch without perturbation, and A f : and Af;I are frequency shifts off resonance for the 4: and 4; due to perturbation. The unknown expansion coefficients P and Q can now be determined by normalizing the new eigenfunctions for the and 4; modes; that is,

(4.11) Q,, = (- l / d ) (1 - 2As/s) z - 1 1 4

1 P b = Q b = -

Jz for 4; mode

The new eigenfunctions can now be evaluated as

4: = (4. - AM,^ = V, (sin kx - sin ky)@ (4.13)

9b = (4. + 4 b ) / f i = VO (sin kx + sin ky)@

where k: = & = k to first order of approximation. The energy distribution ratios after perturbations for the 4: and $; modes can be expressed as turns ratios

jV:, and N b given by

N: = (&a) (sin kx - sin ky)

Nb = (&a) (sin kx + sin ky)

The patch with perturbation can now be expressed as an equivalent circuit shown in Figure 4.10a. From the equivalent circuit, the complex induced voltages Vo and vb generated on the equivalent radiation conductances Gb and Gb can be assumed to correspond to the radiated fields caused by the orthogonal $: and 4; modes.

The complex amplitude ratio v0/ vb in the two orthogonal modes is obtained from the equivalent circuit as

where yo and % are input admittances for the orthogonally polarized 4: and gb modes, respectively. To first order of approximation, the unloaded Q factors Qoa and Q,, of the &a and #b modes are assumed to be equal; that is,

The condition for CP is that

vb/va = k j

that is,

For this condition to be met, we require

I Nb/N: 1 = 1 for x-axis feed point

and

I Nb/N: I = - 1 for y-axis feed point


Now for a feed on the x-axis or y-axis we have

By enforcing the condition I vb/va1 = 1 and arg(vb/va) = 90" for CP, we have

where

M = (1 + mAs/s)

N = (1 + nAs/s)

m, n are constants in

and for the square patch with perturbation being considered here, m = - 2, n = 0. Thus

The design of the patch with perturbation requires Q,, which depends on dimensions a, substrate thickness t , and the dielectric constant 6, for the substrate. For a patch with a = 9.14mm, t = 0.6 mm, and E, = 2.55, Q, and the radiation efficiency q% are shown as a function of t/A, in Figure 4.10b. The perturbation parameter (As/s)% is shown as a function of Q, in Figure 4.10~. The design procedure is as follows:

(i) From Figure 4.10b choose t/A, for q > 90% and find Q,. (ii) With the value of Q, from (i) determine the normalized perturbation

parameter (As/s) % required for C P from Figure 4.10~. (iii) Choose the feed on the x-axis for RHCP or y-axis for LHCP, with the

offset to match the antenna impedance, or alternatively use quarter-wave matching transformers.

The results for the patch dimensions considered here show that the axial ratio on boresight is less than 0.5 dB, while within $45" angular region its value remains less than 1.5dB.

DUAL POLARIZED PATCHES 183

4.5 DUAL POLARIZED PATCHES

There is currently much interest in patches that can produce either simultaneous orthogonal linear or circular polarisations at the same or at two close frequencies to reduce the size of equipment operating with diplexed signals. If two orthogonal linear polarizations at separate frequencies are required, then a rectangular patch with two feed points exciting the orthogonal modes [40] can be used. A multilayer construction with each pin feeding separate patches gives further flexibility. If the frequency separation is greater than the individual patch bandwidth, then isolation is primarily determined by frequency separation to patch bandwidth ratio. For closely spaced frequencies, such as those used at L band for satellite communication systems, square or circular patches can be used and isolation is dependent on geometry as noted in Section 4.2. Isolations greater than -35 dB for dual linear polarizations have been achieved [4] using optimized aperture coupling. The position and size of the orthogonal slot apertures is adjusted to minimize the higher-order mode excitation. Isolation of about - 40 dB has been achieved for an etched cross-patch [41] in which a gridded structure is used to polarize the surface currents in the direction of resonance. Dual circular polarization has been achieved in two ways. Analysis of the triangular patch 1331 reveals that there are a variety of feed points that will give either hand of circular polarization at different frequencies, as Figure 4.1 1 shows. The frequency spacing can be controlled to some degree by the aspect ratio alb. Operation of the triangular patch is discussed in Section 4.5.1. Similar characteristics can be obtained for a rectangular patch loaded with stubs [42]. Isolation between the

FIGURE 4.1 1 Feed location loci for circular polarization in equilateral triangle microstrip antenna [33]. - RHCP; --- LHCP. T,, and r, are contours for 1583.8-MHz operation and T, and T, for 1564.2-MHz operation; b/a = 0.98; a = 76 mm, substrate height = 3.2mm, E,, = 2.55. (Reprinted with permission from IEE.)

184 DUAL AND CIRCULARLY POLARIZED MlCROSTRlP ANTENNAS

FIGURE 4.12 ~ u a l circularly polarized ring and patch rnicrostrip antenna [43, 441. (0 1992 IEEE.)

dual polarizations is not reported in either case. Alternately, a multilayer structure using a short-circuited ring and patch (Figure 4.12) can be used [43,44]. By rotation of the patch with respect to the ring,isolation of about - 50dB can be achieved over a narrow range of frequencies.

4.5.1 Triangular Patch with Right- and Left-Hand Circular Polarization

The triangular microstrip patch is attractive for many applications due to its small size-that is, one-half to three-quarters that of a square patch antenna at the same frequency. The other advantage is that this patch can radiate CP at two frequencies [33].

In Figure 4.1 1 the loci of the feed location for each CP operating frequency are shown. For example, a patch with a = 76 mm, b/a = 0.98, and E, = 2.55 will produce CP at 1583.8 MHz when the feed is located on rl or r, loci, and at 1564.2MHz when the feed is on T, or T, loci. It can be shown that when the feed is located on loci Tl or T,, the antenna will produce RHCP radiation; with the feed on T, or T,, LHCP is produced. The CP operating frequencies can be adjusted by changing the ratio b/a. In the patch considered here, CP waves are always excited at two frequencies when b/a < 0.985 or when b/a > 1.015. The results show that, for the particular patch considered here, at each CP frequency the 3-dB axial ratio bandwidth is about 0.6%.

4.6 MlCROSTRlP SPIRALS

The application of the spiral concept to microstrip was first investigated by Wood 1451, who analyzed the radiation from curved microstrip lines and fabricated

MlCROSTRlP SPIRALS 185

a number of single-start spirals. He concluded that due to the tight wave trapping action of microstrip, the amount of power radiated per turn was significantly less than that from a conventional cavity-backed two-or-more-start spiral. This meant that radiation from the outer turns perturbed the pattern and led him to produce single-turn spirals having bandwidths up to 40% and radiation efficiencies of about 50% with well-behaved radiation patterns. Similar elements have been suggested recently for L-band land mobile communications applications [46]. One advantage of the one-start center-fed spiral is that a wideband balun feed is not needed. An alternative arrangement is to feed a one-start spiral with a small number of turns from the outside by a microstrip line, thus allowing use in corporately fed array. An optimized open-circuited spiral with 1.5 turns [47] gives less than 3-dB axial ratio over a 2.6% bandwidth on a 0.081-A-thick substrate; the measured gain of a four-element array is 13.7 dBi. Resistive loading [48] reduces the axial ratio to less than 1 dB and reduces the gain by about 0.7 dB.

Center-fed two-start rnicrostrip spirals [49] are now being examined as alternatives to the cavity-backed type where multioctave bandwidths are required. Wideband baluns are still required. By careful resistive loading at the outer edge, good performance over a 2 to 18-GHz range can be obtained, although the axial ratio is not as small as the best cavity-backed type [50]. Square-shaped spirals [51] and multimode types [52] with some beam scanning are also being investigated. Use of two dielectric layers has been shown to give a conical circularly polarized beam [53]. Operation of the two-wire spiral is discussed in Section 4.6.1.

4.6.1 Operation of the Spiral Antenna

The axial ratio bandwidth of the spiral antenna depends on its geometry such that the lower-frequency limit is controlled by the outer circumference of the spiral while the upper-frequency limit depends on the shape of the spiral near the feed point. In order to radiate a CP wave, the outer circumference must be greater than one wavelength. In a two-wire round spiral the axial ratio increases rapidly as the operating frequency is reduced because the reflected currents from the arm end are greater at lower frequency. Many of the developments in the design of CP spiral antennas are aimed at reduction of these currents either by using absorbers or by altering the geometry of the outer arms of the spiral. Absorption of currents is easier, but this reduces the overall efficiency of the antenna; therefore the alternative approach which produces good CP is the reduction of reflected currents by introducing small zigzag elements on the outermost arms of the spiral. The results show [54] that a spiral antenna with zigzag sections has a gain of about 4 dBi at 3 GHz and about 6 dBi at 6 GHz, while the axial ratio over this frequency range is better than 1 dB. As a comparison, the spiral without zigzag sections has similar gain, but the 1-dB axial ratio frequency range is only 5-6 GHz and at 3 GHz the axial ratio deteriorates to over 3 dB.


4.7 SPECIAL SUBSTRATES AND ACTIVE ANTENNAS

Both ferrite and chiral substrates have been examined recently in the search for improved polarization control of microstrip antennas. Das and Chowdhury [55] reported an early example of a patch on a ferrite substrate. The unique features of such an antenna [56] are as follows: First, a square patch with a single-feed probe will give (a) circular polarization switchable between right hand and left hand and (b) frequency tunable by adjusting the magnetic bias field [57]. Second, a phased array of such elements can be wide-angle impedance-matched, again by bias field control. Third, the radar cross section can be reduced in its "off' state by 20-40 dB [58]. For a patch on a 0.03-wavelength-thick (6, = 15) substrate, the impedance and axial ratio bandwidths are 1% and 13%, respectively. The wideband axial ratio behavior is attributed to the generation of an inherently circularly polarized mode within the ferrite and is seen to be an important and advantageous feature of such antennas.

Chiral substrates, although having an inherent handedness, have been found to possess some disadvantages [59] when used for microstrip patches. In particular, there are increased losses due to surface wave excitation and high cross-polarization. As yet, good system advantages have not been identified for the use of chiral substrates, although this may well happen in the future.

Little work appears to have been done on the circular polarization on conformably shaped substrates, although reference 60 derives the circular polarisation conditions for a rectangular patch on a cylinder.

Several active antennas with polarization control have been reported. Circular polarization has been generated using four quarter-wavelength active dielectric resonator antennas [61]. The use of external locking of two orthogonally polarized patch oscillators [62] has been shown to allow selectable polarization, both linear and circular. Selectable polarization has also been demonstrated with switched lines located beneath the ground plane 1631.

Two types of active patch antenna for simultaneous transmit and receive action using dual linear polarization have been reported. Figure 4.13a shows a circular patch antenna with integrated oscillator and receiving mixer [64]. The oscillator simultaneously operates as the transmit and local oscillator; thus different transmit and receive frequencies, separated by the intermediate frequency, must be used. This means essentially that no isolation between the transmit and receive frequencies by the two polarizations is needed but limits the use to channelized systems employing fixed spacing between transmit and receive frequencies. Identical or independently specifiable frequencies can be used in the antenna shown in Figure 4.13b [65]. Here isolation between the horizontally polarized transmit signal and vertically polarized receive signal is achieved using two-point feeding of square patches plus sequential rotation on the vertical polarization. Breakthrough of the transmit signal into the receive low-noise amplifiers is about -45 dB using this method.

Recently, a compact active polarization-angle antenna using a square patch has been demonstrated [66]. The circuit consists of a square patch with an

SPECIAL SUBSTRATES A N D ACTIVE ANTENNAS 187

Mixer

I

Substrate Substrate patch 1 patch 2 - \

Power co-r

Osc. FET rAmp. FET

Vda2 ,DC Block Vdo 1

I ' I

Variable phase shifter

FIGURE 4.1 3 Simultaneous transmit and receive dual polarized active patches. (a) tx/n frequencies offset by intermediate frequency. (b) Identical tx/n frequencies. (Reprinted with permission from IEE.)

overlay and incorporates two transistors in common base configuration. The transistors are connected on adjacent sides of the patch so as to excite orthogonal modes of oscillation. The antenna can be adjusted to produce radiation with (a) circular polarization of either sense and (b) linear polarization parallel to either patch side or diagonal. The antenna is constructed so that the transistor emitter

188 DUAL A N D CIRCULARLY POLARIZED MICROSTRIP ANTENNAS

terminals are both connected to a common potential, namely the patch. Since both transistors are operated in the common base configuration, both base terminals must be at earth potential at the frequency of oscillation. In order to bias the transistors correctly, the bases are decoupled from ground by suitable capacitors. The phase control which allows polarization agility is obtained by exploiting the variation in the transistor junction capacitance with the collector voltage. The antenna can be operated with or without injection locking. In the former case, the locking signal, typically about 10 dB below the radiated power, is applied via a capacitively coupled stub located near the comer of the patch. It is noted that with injection locking the antenna is more stable, easily controlled, and less influenced by spurious reflections.

The results show that when either one of the transistors is energized, a linearly polarized radiation in the 8= 0" or 90" planes is generated; the cross-polar radiation level is about 15 dB down. With both transistors energized, the power output is doubled and with appropriate collector bias adjustment, linear polarization in the 8 = 45" or 135" planes or circular polarization of either sense can be obtained. With the antenna adjusted for linear polarization, the cross-polar radiation is still about 15 dB down; in the circular polarization mode, the axial ratio is under 2 dB for the 6' = 30" range.

4.8 DUAL AND CIRCULARLY POLARIZED ARRAYS

In general, dual and circularly polarized arrays can be formed from the elements described in the preceding sections. This section reviews progress in array design or special array techniques that either simplify design or enhance performance of such arrays.

4.8.1 Patch Arrays

Improvements in the performance of two-dimensional patch arrays continue to be made. A four-element array of electromagnetically coupled patches with parasitic patches above [67l has been shown to have over a 85% efficiency and less than 3-dB axial ratio across a 13% bandwidth using honeycomb substrates. Dual linear polarization at 12.6GHz and 14.3 GHz, respectively, with about 35-dB isolation has been achieved with a multiple-layer 16-element array with two separate corporate feeds sandwiched between perforated ground planes [68].

4.8.2 Microstrip Line Arrays

The rampart line [69], chain antenna [70], square-loop line [71], crank line [72], herring-bone line [73], and strip/dipole array [74] are microstrip line arrays that give circular polarization (Figure 4.14). Many of these traveling wave arrays have similar characteristics. As an example, a rampart array having 10 periods [69] was found to give a peak axial ratio of less than 1 dB and an input return loss of

DUAL AND CIRCULARLY POLARIZED ARRAYS 189

Matched load Input 4

(b) %Capacitive ear

Matched load

FIGURE 4.14 Microstrip line, circularly polarized arrays. (a) Rampart line, (b) chain antenna, (c) square-loop line, (d) crank line, (e) herring bone, (f) slot-dipole array. (O 1995 IEEE.)

- 10dB. The beam direction and axial ratio are usually frequency-dependent. They should be operated with off broadside beam to ensure good input VSWR. Feeding at opposite ends will produce circular polarization of the opposite hand and although they can be considered dual polarization, the two hands will be radiated in beams oppositely displaced from broadside. Such arrays can be used to from simple two-dimensional arrays, but the frequency-dependent beam scan


FIGURE 4.15 Cross antenna for circular polarization [75] (single arm, two-turn cross with log periodic expansion). (0 1990 IEEE.)

renders them suitable only for narrow bandwidth applications. The beam scan problem is overcome by forming such line arrays into cross structures [75] (Figure 4.15). Here cross-polarization is achieved over more than 10% bandwidth with efficiencies greater than 80%.

4.8.3 Sequentially Rotated Arrays

4.8.3.1 Introduction. Sequential rotation [18, 76, 7fl is a technique that improves the axial ratio of circularly polarized arrays. Figure 4.16 shows the method, and Figure 4.17 shows two implementations. Each element in the subarray is rotated with respect to its neighbor, and the phase change generated by the rotation of the circularly polarized element is offset by an appropriate phase change in the excitation. This latter is usually created by a line-length change in the corporate feed. In Figure 4.17a, two pairs of elements having 0" and 90" rotations are shown; in Fig. 4.17b, 0°, 90°, 180°, and 270" rotations are used. The principle of the technique is that the cross-circularly polarized components of the elliptically polarized elements are canceled because the feeding phase changes are appropriate for the wanted hand of polarization only. These changes are calculated for the main beam peak only so that in some cases cross- polarization sidelobes may be higher than in a conventional array [18]. An additional benefit arises because reflections from mismatched elements cancel out in the feed. In the case of microstrip patches, axial ratio and input match both degrade off resonance and sequential rotation hence serves to widen the apparent bandwidth. Figure 4.18 [76] clearly shows the improvement in both axial ratio and input VSWR of eight-element arrays with sequential rotation applied to groups of four.

The advantages and limitations of the method can be deduced from the first-order analysis described in the next sections. The primary action, that of


M M - way splitter

FIGURE 4.1 6 Sequentially rotated feeding of circularly polarized array elements [76, 771. (Reprinted with permission from IEE.)

FIGURE 4.1 7 Sequentially rotated feeding of notched circular patches. (a) Pairs rotation. (b) Rotation of group of four. (Reprinted with permission from IEE.)

axial ratio and input VSWR improvement are explained in Sections 4.8.3.2 and 4.8.3.4. The secondary issue of unwanted grating lobes in the radiation pattern, which may ultimately limit the bandwidth improvements in some cases, is discussed in Section 4.8.3.5. Finally, the application of sequential rotation to dual polarized arrays is covered in Section 4.8.3.6.

4.8.3.2 First-Order Analysis. The rotation angles and feeding phases are determined by Eq. (4.1) of Section 4.4.2. The patch arrays of Figures 4.17a and


-, --.._- I'

Conventional ,' - Sequential

k f'

8.0

Frequency (GHz) (a)

--.-- Conventional - Sequential ?

Frequency (GHz) (b)

FIGURE 4.18 Measured bandwidth characteristics of sequentially rotated microstrip patch array [76]. (a) Axial ratio and. (b) VSWR (eight element arrays, substrate height = 4mm, c = 2.6).

4.1% are examples where M = 2 and p = 1 and M = 4 and p = 2, respectively. In fact, Figure 4.17a is a conventional arrangement of two pairs of sequentially rotated elements. An understanding of the technique can be gained by considering the radiated field E, from the first element of Figure4.16. If it is assumed to be elliptically polarized, then

E ~ ( o , ~ ) =a(O,+)B+jb(0,4)4 (4.21)

where Band 6 are polar unit vectors defined in the inset of Figure 4.16. For an element which is perfectly circularly polarized in the broadside direction,


0, degrees

FIGURE 4.1 9 Computed 4 = 0 circularly polarized radiation pattern of four-element linear microstrip disc arrays. (a) Conventionally fed. (b) Sequentially rotated feeding, M = 4, p = 2. - Copolar; ---cross-polar. (Both are arrays of notched patches; disc radius = 32 mm, d = 0.651,, substrate E, = 2.32, thickness = 1.59 mm, frequency = 1.65 GHz.) (Reprinted with permission from IEE.)

a(O,4) = b(O,4). The total field of the array is given by summing the M element fields. Figure 4.19 shows by way of example the result of this summation for a four-element linear array of circular microstrip patches. It is assumed for each element of this array that

Conventional feeding gives a main-beam cross-polarization level of about - 10dB. For the sequentially rotated array the cross-polarization in the main beam is canceled. Off the main beam the cross-polarization is, at some angles, greater than that in the conventional array case. It is clear that sequential rotation is, in general, just redistributing the cross-polarized power out into the radiation pattern away from the main beam. More consideration is given to the radiation pattern performance later.

194 DUAL A N D CIRCULARLY POLARIZED MICROSTRIP ANTENNAS

The total field on boresight (0 = 0, 4 = 0) is given by [76,78]

- - sinpx { .(M il)pn} +;(a1-b')(O-j4)-exp J (4.23)

P= sin - M

where a' = a (0,O) and b' = b (0,O). It is noted that ET is independent of element position. The first term represents the wanted polarization and the second the unwanted or cross-polarization. If each element is perfectly circularly polarized, then a = b and, as expected, the second term disappears. However, the second term also goes to zero when p Z iM, where i is an integer. This usually means that

In this case both components, a and b, are phased to produce the reference polarization. Thus even if the relative phase and amplitude of a and b change, which is the case in, for example, an off-resonant single-point-feed circularly polarized patch, then the polarization purity is maintained on boresight.

If it is further assumed that the radiating elements have an input reflection coefficient p, then the voltage V, incident on the feed splitter in a direction toward the input connector due to all the element mismatches is given by [76,78]

sin px v,= VOP

where Vo is the voltageincident on each radiating element and a constant current generator at each input is assumed. Equation (4.25) assumes that multiple reflections between the elements and the splitter are not set up. Provided that Eq. (4.24) is satisfied, then V, = 0 and a perfect input return loss will result.

4.8.3.3 Second-Order Effects. The second-order effects that occur is sequentially rotated arrays have been described in Section 4.4.2 and are as follows:

1. Multiple reflections between elements and feed splitter 2. Feeding phase errors 3. Higher-order mode generation within the elements

DUAL A N D CIRCULARLY POLARIZED ARRAYS 195

FIGURE 4.20 Multiple reflections in sequentially rotated patch array. - Input signal; -.- first reflection; first reflection passed to opposite patch; -- first reflection reflected to same patch.

Higher-order mode generation has been described in detail in Section 4.4.2, where it has a significant effect on the performance of patches with multiple feed points. However, the results there are general in that they apply to mays of elements that also generated unwanted modes that perturb the radiation pattern. The conclusions from that section are brought together with those deduced in this section. The first two issues are now considered.

(a) Multiple Reflections. Multiple reflections is one key process that determines the axial ratio bandwidth of the array. This point was made in Section 4.4 for patches fed at two points and is indeed applicable to both single patches and arrays. Figure 4.20 illustrates what is happening in a two-element array. The incident power illustrated by the solid lines is split to each element. The power reflected from the mismatched radiators (-.-), is then subsequently both reflected from the nonisolating splitter (- -), and transferred across to the other element (...) . This process then repeats until negligible power is involved. The phase and amplitude of the total reflected power that reaches the elements is determined by the sequential rotation arrangement.


If only the first reflection from the element is considered the total radiated field is obtained by adding the new contributions to Eq. (4.23) to give

M 1 - sinpx { (M E - - ( a + b ) ( 8 + j & + - ( a - b ) ( 8 - j 4 ) - e x p j T- 2 2 Px sin -

M

M-1 sin px . (M - 1)pn - P M (a + b)(a+j&-sm

Px sin - M M

The two new terms again represent the wanted and cross-polarizations and are both zero when the reflection coefficient p = 0. The first additional term is always zero when Eq. (4.24) is satisfied. The second additional term is also zero for this condition except when p = M/2-for example, for M = 2, p = 1 and M = 4, p = 2. The M = 2, p = 1 case (Figure 4.20) can be understood by considering the phase difference of the reflected signals shown. The reflected power from the element is 90" out of phase. The portion of this reflected by the splitter will experience a further 180" phase difference, and hence a total of 270", which will result in opposite-hand element excitation. The power transferred across the splitter experiences no extra phase shift because the two paths are equal. However, the two signals now excite the opposite patch, and this is also the condition for opposite-hand excitation. It is thus expected that p = M/2 arrangements will have a narrower axial ratio bandwidth than the others.

The second multiple reflections similarly modify the voltage incident on the input port. Equation (4.25) now becomes

which again is zero for 0 < p < M, except when p = M/2, in which case


Again p = M/2 arrangements are likely to have narrower input return loss bandwidths.

(b) Feed-Phase Errors. If the required phase shifts are created by extending the feeding line lengths, then errors will occur off the patch resonant frequency. At a fractional deviation 6 off the design frequency the phase shift, 4,,, of Eq. (4.1) be in error by a factor of (1 +a). The effect of this is quantified by defining a cross-polarization improvement factor F, [76], where

so that

where E, and Ex are the reference and cross-polarized radiated boresight electric fields, respectively, and matched elements are assumed. Figure 4.21 shows Fx6 for various sequential modes. For optimum improvement in the face of this factor, large M and small p are indicated.

0 1 2 3 4 5 6

Number of elements, M

FIGURE 4.21 Theoretical cross-polarization improvement factors F,6 due to cancellation of feeding phase deviations [Eq. (4.30)]. (Reprinted with permission from IEE.)

198 D U A L A N D CIRCULARLY POLARIZED MICROSTRIP ANTENNAS

TABLE 4.3 Deductions for Choice of Optimum Sequential Rotation Arrangement

Requirement Deductiona

Circular polarization Low cross-polarization from

(i) Multiple reflections (ii) Feeding-phase errors (iii) Higher-Order modes

P + MI2 large M , small p large M (> 2 4 , p = 2n

The parameters p, M, and n are defined in Eq. (4.1).

Table 4.3 shows the conclusions so far obtained for the best choice of rotation mode. To obtain circular polarization, the condition of Eq. (4.24) must be satisfied. In general terms, second-order effects are reduced for increasing M. However, this may lead to complexity in the feed design. In addition, increased radiation pattern perturbation off resonance due to large feeding-phase errors will cause frequency scanning effects in arrays unless small p is chosen. The best choice of M and p will depend on the specific application. For instance, in very narrow bandwidth antennas, feeding-phase errors and higher-order mode generation are likely to be small and multiple reflections will dominate the overall bandwidth performance. Similarly, if an isolated feed is used, then such reflections will be absent and the other effects must be examined. In most applications, all these effects will be present and more detailed analysis is necessary. Figure 4.22 shows computed and measured axial ratios of three typical circular patch sequential arrangements for both circularly polarized notched patch elements and linearly polarized circular patches. The elements were fed from power splitters located below the substrate. The computations were performed using the cavity model including higher-order mode excitation and a two-wire transmission line model of the feed network. Several points can be made:

1. Agreement between measurement and theory is acceptable for making deductions on the best configuration but show some differences.

2. The axial ratio bandwidth of the three-element array is significantly wider than the two- or four-element array in these relatively narrowband examples as indicated in Table 4.3.

3. The axial ratio bandwidth using linearly polarized elements is much less than that using circularly polarized elements.

The normalized gain of these three configurations is also shown in Figure 4.23. The gain of the three-element array is 1.8 dB less than that of the four-element array, but to allow comparison in this figure the difference has been removed. The gain bandwidth of the two-element array is identical to that of the four-element array. It is thus seen that the gain bandwidth of all configurations is similar. Gain


1.600 1.625 1.650 1.675 1.700 Frequency, GHz

(a)

Frequency. GHz

FIGURE 4.22 Sequentially rotated array boresight (0 = 0) axial ratio. (a) M = 2, p = l (b) M = 3 , p = 2 (c) M=4, p = 2 . Measured: - Notched CP patches; -- LP patches. Computed: - - - Notched CP patches; -.- LP patches. (Array details: disc radius = 32mm, feed pin radius = 9.5 mm, disc Q = 40.6, disc spacing = 120mm = 0.661, substrate height = 3.18 m m , E, = 2.32, patch group- ing shown inset.) (Reprinted with permission from IEE.)


loss off resonance is primarily due to the increase in the cross-polarization off boresight; losses due to feed dissipation and input mismatch are small. Although the axial ratio bandwidth is different, the cross-polarized power in the main beam is merely redistributed into the radiated field so that the overall gain performance is unchanged. This is an important point that is discussed later when radiation pattern effects are considered. Figure4.23 also shown that there is a considerable

Frequency, GHz 1.59 1.61 1.63 1.65 1.67 1.69 1.71

0 1

Frequency, GHz 1.59 1.61 1.63 1.65 1.67 1.69 1.71

FIGURE 4.23 Normalized gain of sequentially rotated arrays. (a) M = 4 , p=2 notched CP patches; Computed -, Measured 0. (b) Computed: - conventionally fed M = 4 notched CP patches; -- sequentially rotated M = 4 , p=2; --- sequentially rotated M = 3, p =2. Measured LP patches: 0 M = 4 p = 2; x M = 3, p = 2. (gain of M = 4 arrays normalized to peak of conventionally fed array; gain of M = 3 arrays normalized to peak of notched CP patch array; array details as in Figure 4.22.) (Reprinted with permission from IEE.)


loss in the arrays using linearly polarized elements due to the radiation of high cross-polarized lobes. This is also considered later.

4.8.3.4 Radiation Pattern Effeds. In this section the effects on the radiation pattern of an array when sequential rotation is applied are considered 179,801. Throughout the previous sections, these effects have been referred to and, in particular, the grating lobes that are set up. The effects can indeed be characterized in this way if errors distributions are estimated for the arrays. Because errors both in element polarization and excitation occur when the array is operated off resonance and these are then distributed in a systematic way across the array, grating lobes will be set up due to these errors. Such unwanted lobes may ultimately limit the bandwidth, particularly. in sidelobe-sensitive applications. Because they are grating lobes, array amplitude tapering will not significantly reduce them.

The grating lobe position, height, and polarization can be simply characterized by considering the array aperture distribution. Figure 4.24a shows a four- element array with sequential rotation. The mth element excitation can be

FIGURE 4.24 Sequential rotation in 2 x 2 element array. (a) Array configuration. (b) Excitation error distribution. (Reprinted with permission from IEE.)


written as

F, =A, (a cos +,, - jb sin 4,3 F,, = A,(a sin 4,, + jb cos 4,,) (4.3 1)

where A, is the element excitation and is ideally given by A, = expG+,,). a, b, and q5,, are as in Eqs. (4.5) and (4.1), respectively. F,, and F , are the element excitations in the x and y directions, respectively.

Considering the top two elements of Figure 4.24a (i.e., an M = 2, p = 1 array, 4p1 = 0,4,, = n/2), and writing F = (F,, Fy), we have

Now let

b/a=/l and AJA, = ja (4.33)

where /I and u are complex numbers which are ideally unity. The relative element excitations are then

The boresight polarization is

If either a = 1 (no feed errors) or = 1 (perfect circularly polarised elements), then Pb = j, which represents perfect circular polarization from the array. For the full array of Figure 4.24a, F, and F4 are identical to Eq. (4.34) as in the boresight polarization, Eq. (4.35).

fa) Grating Lobe Position. The excitation error distribution in the x or y components can now be found by normalizing the actual array distributions to arbitrary wanted distributions. For example, for the x components of Eq. (4.34) we have

where a unity wanted distribution is assumed. The error distributions is illustrated in Figure 4.24b. Similar distributions can be obtained for the y compo-


FIGURE 4.25 Sequential rotation in 2 x 2 element array. (a) Array configuration. (b) Excitation error distribution. (Reprinted with permission from IEE.)

nents. An alternative arrangement is given in Figure 4.25 with its error distribution. The two arrangements are both M = 4, p = 2 and will hence have similar boresight axial ratio and input return loss properties, but their patterns will be different. The grating lobe positions of the error excitations are illustrated in Figure 4.26, which is a polar plot of the radiation hemisphere; u and v are defined by

u = k,d, sin 0 v = k,d, sin 0

where k , is the free-space wavenumber and d, and d, represent spacings in the x and y directions, respectively. The array main lobes occur at u = v = 0 and u = f 271 and v = 4 2n. The error distribution lobes of the array of Figure 4.24 occur in the 4 = f 45" planes, and an element of d/L < 0.707 is required to just suppress them. Those of Figure 4.25 occur in the 4 = 0 plane and are just suppressed by a spacing of dl), = 0.5.

(b) Grating-Lobe Height and Polarization. The grating-lobe heights can be calculated from the array distributions. For the two-element array (M = 2, p = I),


FIGURE 4.26 Grating lobe diagram found from error distribution. x Main lobe of actual array; A grating lobes of Figure 4.24b; grating lobes of Figure 4.25 b. (Reprinted with permission from IEE.)

the grating-lobe level relative to the main lobe, G, and G,, are given by

where the factor & j is needed to refer the lobes to the subarray phase center. Combining Eqs. (4.38) and (4.34), we obtain

If u = 1 (i.e., no feed errors), then the first gating lobe is cross-polarized (G, = - G,). If B = 1 (i.e., circularly polarized elements), the first grating lobe is copolarized (G, = G,). In general, an elliptical polarization will occur.

If complex errors are defined as


then, if 6, E << 1, we obtain

As an example, let E = 6 = 0.3, which represents an element ellipticity of 1.3 (E 2.3 dB) and a feed imbalance of 2.3 dB, which are coincidentally in phase. Then, G, x 0.3, G, = 0, which indicates a linearly polarized grating lobe at a relative array factor level of about - 13 dB, or - lOdB relative to one linear component. The main-beam ellipticity has become P, % 1 + 6 ~ / 2 which is 1.05, or less than 0.5 dB. Thus sequential rotation has improved the main-lobe ellipticity from 2.3dB, but a grating lobe of - 13dB has been introduced at an angle 0 =sin-' ( 4 2 4 in the 4 = 0" plane.

For the M = 4, p = 2 case of Figure 4.24, the first grating lobes are in the 4 = f 45" planes at an angle 0 = sin-' [~~/f la. Calculations similar to those above indicate that grating-lobe heights are identical to the M = 2, p = 1 case. It should also be noted, of course, that these grating-lobe heights are array factor levels. Actual lobe heights are given by the product of the element factor and the array factor.

The grating lobes will result in reduced gain, and this is most noticeable when linearly polarized elements are used as in Figure 4.4~. Actual grating lobe height will reduce as the element spacing reduces due to the effect of the element pattern, and such arrays can be operated successfully with small element spacings. Figure 4.27 [I31 shows the normalized gain of arrays with different spacings. For

FIGURE 4.27 Computednormalizedgain of N x N element sequentially rotated arrays. Notched CP patches: - , d/L=0.45, 0.55, 0.65 and 0.75. LP patches: - - d/A = 0.45;- - - d / l = 0.55;--- d/A = 0.65;-.-d/L = 0.75. (Gain normalized to peak gain of conventionally fed array at 1.65GHz arrays are composed of groups of M = 4, p = 2 sequentially rotated subarrays; array details as in Figure 4.22.) (Reprinted with permission from IEE.)


FIGURE 4.28 Configuration of two-ring array antenna. (a 1995 IEEE.)

spacings less than about 0.65 gain loss is reduced with increasing array size. Figure 4.28 shows an alternative array arrangement [81] in which the gain of ring arrays is optimized by appropriate choice of the rotation of the starting element a, and a,. Gain within 1 dB of that for an array using circularly polarized elements is reported for this example operating at 1.636GHz with an element spacing of approximately 0.54 wavelengths. Gain improvement by optimization of a, and a, is about 1 dB.

(c) ReducedGrating-Lobe-Level Arrays. The subarrays of Figure 4.24 and 4.25 can be used in larger arrays in various different configurations. Figures 4.29 and

FIGURE 4.29 (A) Sequentially rotated array. (B) Equivalent error distribution (dashed line represents direction of significant grating lobes). (Reprinted with permission from IEE.)


FIGURE 4.30 (A) Sequentially rotated array. '(B) Equivalent error distribution. (Rep- rinted with permission from IEE.)

4.30 show two arrangements for 4 x 4 element arrays. It is clear from the error distributions that the grating lobes will be split and spread into a number of smaller lobes. Figure 4.31 shows the grating-lobe diagram. The nonuniformity of the subarrays in the larger arrays has increased the number of lobes from four in the case of Figure 4.24 to 16 for the arrangement of Figure 4.29 and 24 for Figure

FIGURE 4.31 Grating-lobe diagram found from error distribution. x Main lobes of actual array; 0 grating lobes of Figure 4.29B; A grating lobes of Figure 4.30B. (Lobe positions are symmetric about v axis; only half shown for clarity.) (Reprinted with permission from IEE.)


TABLE 4.4 Crating-Lobe Heights of Sequentially Rotated Arraysa

Array Factor Grating-Lobe Patch Element Patch Array Subarray Grating-Lobe Level Angle Factor Grating-Lobe Configuration (dB) (0) (dB) (dB)

Figure 4.24 - 12.9 41.8 - 3.0 - 15.9 Figure 4.25 - 12.9 70.5 - 7.5 - 20.4 Figure 4.29 - 18.9 28.0 - 1.5 - 20.4 Figure 4.30 -21.9 19.0 -0.5 - 22.4 Figure 4.32 - 22,31 - -29.5

" Results for Figure 4.32 are for 8 x 8 array. All other are for 2 x 2 array; lobe heights, when these are conventionally arrayed, will be identical.

4.30. Table 4.4 shows the main grating-lobe heights calculated using the analysis of Section b above.

The concept of reducing the regularity of the error distribution can be taken further in, for example, the array of Figure 4.32. Here an element-to-element rotation of 22.5" is used and the rotation follows a clockwise spiral around the subarray. The philosophy adopted here is to reduce the phase step per element by the application of rotation to larger groups and to use a configuration that reinforces the wanted hand of polarization. Table 4.4 shows that the lobe height is nearly - 30dB relative to the main beam. Figure 4.33 shows how the grating lobes are distributed in the radiation pattern.

In principle, a randomized sequential rotation configuration should represent the ultimate arrangement for grating-lobe suppression. As the grating lobes will

FIGURE 4.32 Sequentially rotated arrays using spiral configurations. (Reprinted with permission from IEE.)


FIGURE 4.33 Calculated radiation pattern of 16 x 16 element microstrip patch array of 8 x 8 element subarrays of form of Figure 4.32 conventionally arrayed (circular patches, axial ratio = 4dB, E, = 2.5, spacing = 0.751 frequency = 11.95 GHz, contours spaced by 5 dB, lowest contour = - 35 dB, contours show peak level whether wanted or cross-polar, shaded sidelobes are cross-polarized, pattern is plotted in polar coordinates with 0" < 0 < 90" running from centre to edge of plot). (Reprinted with permission from IEE.)

be scattered across the radiation pattern, a better measure of performance is to examine the average sidelobe increase. It is assumed that the average sidelobe increase, S, equals a2/G and that the directivity reduction, DL equals 1/(1 + a2), where a2 is the variance of the phase error and G is the array gain [82]. A 10% frequency shift gives a phase error variance of o2 = (1.1 ~ 1 2 ) ~ so that DL = 0.2dB and S, = 0.6 dB at - 20-dB sidelobe level for an 8 x 8 array. The 8 x 8 spiral array had SL E 3 dB, so it is clear that randomization will improve the pattern perturbations down to small levels.

Throughout this discussion, the effect of mutual coupling has been neglected. It has, however, been shown [83] that such coupling will result in significant additional errors to the aperture distribution. The errors are systematic and will give rise to further grating lobes in addition to those noted above. Similarly, the application of sequential rotation to phased arrays [84] emphasizes the import-


FIGURE 4.34 Silhouette of microstrip disc array with sequentially rotated feed network (array details: substrate 8, = 2.32, thickness = 1.59 mm = 0.06L0, frequency = 12.0 GHz, patch spacing = 0.71). (Reprinted with permission from IEE.)

ance of mutual coupling and the importance of grating lobes for wide-angle scanning.

Sequential rotation has also been shown to reduce the radiation pattern perturbations due to coplanar corporate feeds 1851. Figure 4.34 shows a sequential rotation array with M = 4, p = 2 subarrays and with subsequent rotation at the 2 x 2 subarray level. This has the effect of cophasing the radiation from pairs of T junctions which then radiate in the main beam direction with linear polarization, which in principle could be offset by appropriate modification of the element polarization. Figure 4.35 shows the radiation pattern improvement, computed using the equivalent magnetic source feed model [%6].

4.8.3.5 DualPolarizedArrays. Sequential rotation can be used to improve the performance of both dual linear and dual polarized arrays. If a dual feed element shown in Figure 4.36a is used, then the broadside radiated field of the mth element can be written as

Em = [ (a cos cbPm - bl cos $b, - j b2 sin $,,J 8 + (a sin $,, - b , sin $bm + jb, cos 4,,)4] ej9- (4.42)

where $,, and $,, are defined in Eq. (4.1), c#$, is the angle of the second feed, a and b, are a and b of Eq. (4.9, and b, represents the amplitude of the cross-

DUAL AND CIRCULARLY POLARIZED ARRAYS 21 1

FIGURE 4.35 Computed radiation pattern of 16 x 16 element arrays. (a) Sequentially rotated feed. (b) Conventional feed. (Array details are as in Fig. 4.34, patterns include feed and disc radiation.) (Reprinted with permission from IEE.)

polarized radiation due to the presence of the second feed. If the element is dual linearly polarized, then 4bm = $,, f 90°, b = 0, and a and b, represent the two linear polarizations. If the element is dual circularly polarized, with, for example, notches being used to generate the circularly polarized feeding, then a = f jb, and an inequality represents elliptical polarisations. Additional cross-polarization due to the presence of the other feed pin is represented by b,. An equation similar to Eq. (4.42) exists for excitation through feed 2.

Figure 4.36b illustrates how an array is fed with two corporate feeds and appropriate line lengths. Figure 4.37a shows an arrangement of elements for dual linear polarization with M = p = 2, M = p = 3, and M = p = 4, where as noted

21 2 DUAL AND CIRCULARLY POLARIZED MICROSTRIP ANTENNAS

splitter

FIGURE 4.36 Dual polarization. (a) Geometry of dual polarized disc element. (b) Sequentially rotated feeding applied to dual polarized arrays. (Reprinted with permission from IEE.)

previously the condition p = M gives linear polarization. The total horizontally polarized boresight field of such an array of M elements is given by

E,, = Ma 6- Mb, 4 (4.43)

and similarly for E,,. Here contributions from bl are not suppressed. If each element has an input reflection coefficient of p, then the total reflected voltage seen at the input to each corporate feed, ignoring multiple reflections, is given by

DUAL AND CIRCULARLY POLARIZED ARRAYS 21 3

FIGURE 4.37 Dual polarized sequentially arrays. (a) Conventional sequential rotation configurations. (b) Configuration for low cross-polarization. (Reprinted with permission from IEE.)

and no improvement to the input return loss results. Isolation between the two input ports is given in a similar way. The voltage appearing at the orthogonal polarisation port is given by

where z is the voltage coupling across each element and 4,,, and 4,, are 4,, for the horizontal and vertical feed networks, resvectivelv. Again no imvrovement to . * - - the isolation occurs due to the use of the sequential arrangement of Figure 4.37a.

By applying rotation to one polarization, the array of Figure 4.37b results. Here 4,,, = 4,,, = (m - 1)x and 4,,, = (6",,= 42 , and this arrangement is applicable to an array of any length M. Equation (4.43) now gives

where M' = 0 for M even and M' = f 1 for M odd. Cancellation of the cross- polarization is evident for both polarizations for M even. The input return loss is not improved, but perfect isolation is obtained for M even. Derivation of the

21 4 DUAL A N D CIRCULARLY POLARIZED MICROSTRIP ANTENNAS

FIGURE 4.38 Sequentially rotated dual linearly polarized arrays with improved isolation. (a) Four-patch array configuration. (b) Two-series array configuration.

improvements in the face of feeding-phase and higher-order modes are given in reference [7].

The api<cation of this principle is evident in the arrays of Figure 4.38. The 2 x 2 element array of Figure 4.38a [87] has an isolation of - 40 dB compared to similar, nonrotated types in reference 88 that have isolation of - 33 dB. The concept is also applied to the linear array shown in Figure 4.38b 1891.

The extension to dual circular polarization is more problematic. In such an array, either opposite polarity phasing or opposite sense feed rotation can be used. Figure 4.39a illustrates the first case. It can be seen that feed 1 has a positive feeding-phase progression while feed 2 is negative, with appropriate feed-point rotation to offset the phasing. In this case, for M = 4, p = 2 we have

= (m - 1 ) d M = - 42,,, where 4,, and 4,,, are the feeding phases for feeds 1 and 2, respectively. The broadside radiated field for polarization 1 is given by

M E,, =-(a+jb, +b2)(8+j$) 2

1 sin pn +-(a-jb,-b2)-exp{-j 2 Pn

sin - M

M

where 4bm = 4,,+ 90". A similar equation exists for polarization 2. For


FIGURE 4.39 Sequentially rotated dual circularly polarized patch array configurations. (a) Same-sense feed-point rotation. (b) Opposite-sense feed-point rotation. (c) Configur- ation based on dual linear concept of Figure 4.38. (Reprinted with permission from IEE.)

0 c p < m, Eq. (4.47) reduces to

M Mb E,, =i(a+ b2)(8+j$)--(8+j$) 2j (4.48)

and cross-polarization due to the presence of the orthogonal feed b, is canceled. Similarly, the voltage reflected off mismatched elements is zero for both polarizations and all sequential rotation arrangements. However, using Eq. (4.45) we obtain

and no improvement to the isolation occurs. Figure 4.39b shows an arrangement where opposite feed position rotation is used. It is clear that elements 1 and 2 are of a different form. In fact, the signal coupled from ports 1 to 2 in each type are 180' out of phase; this means that again no improvement to the isolation occurs, although cross-polar and mismatch cancellation is achieved as in the array of ~i~ure-4.39 b. -

A configuration based on that used for dual linear (Figure 4.38a) is shown in Figure 4.39~; but again due to the 180" inversions between the two types of elements, no improvement in isolation occurs. It is thus concluded that the


application of sequential rotation to dual circularly polarized arrays results in improved cross-polarization and input return loss, but no improvement in isolation occurs.

Good isolation can be achieved, however, if the main beam is squinted away from broadside. Assume that the feeding phase of polarization 1 in the array of Figure 4.39a is

where k, is the free-space wavenumber, d is the element spacing, and 9, is the squint angle, and similarly for polarization 2:

The feed rotation is as before. It can be shown that cross-polarization on the main beam peak is canceled as before. The coupled signals, using Eq. (4.45), is given by

Voz sin(Mk,d sin 0,) q=- M sin(k,d sin 0,) exp { - j(M - 1) k, d sin 0,) (4.52)

If Mk,d sin 0, = nn, where n is an integer, then Vi = 0 and good isolation will occur. Figure 4.40 shows the measured isolation of an array of the form of Figure 4.39~ with an appropriate squint, which for a 0.751, spacing on a four-element array is about 10". The one drawback with such an arrangement is that cross-polarized sidelobes are increased [7] which can be controlled to some extent by reducing the element spacing.

FIGURE 4.40 Measured isolation between polarizations of array of Figure 4.39~. - with squint --- without squint. Patch diameter= 11.9mm; patch spacing= 35.0mm; substrate thickness = 1.59mm; E, = 2.5. (Reprinted with permission from IEE.)

REFERENCES 21 7

4.9 CONCLUSIONS

The field of dual and circularly polarized microstrip antennas is a rich and diverse one with the freedom offered by the medium giving rise to many configurations. This chapter has attempted to give examples of the various types and to highlight some of the underlying principles and limitations. The concepts necessary for the generation of circular polarization have been known for some time and place constraints on the performance and in particular the bandwidth if simple nonisolating feeds or single-point feed patches are to be used. Reduction of the coupling between the required orthogonal modes is identified as important in obtaining both good-quality circular polarization and good isolation between dual polarizations, and this is related to patch Q and feeding geometry. Thick or multiple-layer parasitic patches help to increase circular polarization bandwidth as do& sequential rotation in arrays.

Dual polarization is an increasingly important requirement, and optimized patch and array geometry now allows isolation of the order of - 40 dB to be achieved for both linear and circular polarization. System requirements then dictate if further diplexing components are needed. Other types such as microstrip spirals, ferrite substrates, and active antennas are also noted as being significant and will no doubt have advantages in specific applications. In spite of the large number of types available, innovation and development continues apace in the quest for improved polarization control for current and future

REFERENCES

[I] W. L. Stutzman, Polarisation in Electromagnetic Systems, Artech House, Dedhan, MA, 1993.

[2] H. Mott, Polarisation in Antennas and Radar, John Wiley & Sons, New York, 1986.

[3] "IEEE Standard Definitions of Terms for Antennas," IEEE Trans. Antennas Propagat., Vol. AP-17, pp. 262-269,1969.

[4] A. C. Ludwig, "The Definition of Cross Polarisation," IEEE Trans. Antennas Propagat., Vol. AP-21, pp. 116-119,1973.

[5] J. R. James and P. S. Hall, Handbook of Microstrip Antennas, IEE Electromagnetic Wave Series 28, Peter Pengrinus, London, 1989, p. 260.

[6] Y. Murakami, W. Chujo, and M. Fujise, "Mutual Coupling Between Two Ports of Dual Slot Coupled Circular Patch Antennas," in IEEE International Antenna & Propagation Symposium, Michigan, 28 June 1993, pp. 1469-1472.

[7] P. S. Hall, "Dual Polarisation Antenna Arrays with Sequentially Rotated Feeding," IEE Proc., Vol. 139, Part H, No. 5, pp. 465-471,1992.

[8] J. R. James, P. S. Hall, and C. Wood, Microstrip Antenna Theory and Design, IEE Electromagnetic Wave Series 12, Peter Perigrinus, London, 1981, p. 87.

[9] Op. Cit., p. 176ff.

21 8 DUAL AND CIRCULARLY POLARIZED MICROSTRIP ANTENNAS

[lo] G. G. Sanford and L. Klein, "Recent Developments in the Design of Conformal Microstrip Phased Arrays," in IEE Conference on Maritime and Aeronautical Satellites for Communications and Navigation, London, 1978 IEE Conference Publi- cation No 160, pp. 105-108.

[ll] P. S. Hall, C. Wood, and J. R. James, "Recent Examples of Conformal Microstrip Antenna Arrays for Aerospace Applications," in 2nd ZEE Conference on Antennas & Propagation, York 1981, pp. 397-401.

[I21 J. Huang, "Technique for an Array to Generate Circular Polarisation with Linearly Polarised Elements," IEEE Trans. Antennas Propagat., Vol. AP-34, No. 9, pp. 1113-1123,1986.

[I31 P. S. Hall, J. Huang, E. Rammos, and A. Roederer, "Gain of Circularly Polarised Arrays with Linearly Polarised Elements," Electron. Lett., Vol. 25, pp. 124-125, 1989.

[14] D. J. Brain and J. R. Mark, "The Disc Antenna-A Possible L Band Aircraft Antenna," in Satellite Systems for Mobile Communications and Surveillance, London, IEE Conference Publication 95, pp. 14-16,1973.

[15] J. Q. Howell, "Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. AP-23, pp. 90-93,1975.

[16] A. Adrian and D. H. Schaubert, "Dual Aperture Coupled Microstrip Antenna for Dual or Circular Polarisation," Electron. Lett., Vol. 23, No. 23, pp. 1226-1228,1987.

C171 W. F. Richards, Y. T. Lo, and D. D. Harrison, "An Improved Theory for Microstrip Antennas and Applications," IEEE Trans., Vol. AP-29, pp. 38-46, 1981.

[I81 P. S. Hall, J. S. Dahele, and J. R. James, "Design Principles of Sequentially Fed, Wide Bandwidth, Circularly Polarised Microstrip Antennas," IEE Proc., Vol. 136, Part H, No. 5, pp. 381-389.1989. - -

[I91 T. Chiba, Y. Suzuki, N. Miyano, S. Muira, and S. Ohmori, "A Phased Array Antenna Using Microstrip Patch Antennas," in 12th European Microwave Conference, September 1982, pp. 472-477.

[20] T. Chiba, Y. Suzuki, and N. Miyano, "Suppression of Higher Modes and Cross Polarised Component for Microstrip Antennas," IEEE Antennas Propagation Symposium, pp. 285-288,1982.

[21] J. J. Shuss and J. D. Hanfling, "Nonreciprocity and Scan Blindness in Phased Arrays Using Balanced-Fed Radiators," IEEE Trans. Antennas Propagat., Vol. AP-35, No. 2, pp. 134-138,1992.

[22] T. Teshirogi and N. Goto, "Recent Phased Array Work in Japan," ESA/COST 204 Phased Array Antenna Workshop, 1983, pp. 37-44.

1231 E. Nishiyarna, S. Egashira, and A. Sakitani, "Stacked Circular Polarised Microstrip Antenna with Wideband and High Gain," IEEE Antennas & Propagation Sympo- sium, Chicago, 18 July 1992, pp. 1923-1926.

[24] S. D. Targonski, and D. M. Pozar, "Design of Wideband Circularly Polarised Aperture Coupled Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. AP-41, NO. 2, pp. 214-220,1993.

[25] Ref. 3, p. 222. [26] P. C. Sharmaand K. C. Gupta, "Analysis and Optimised Design of Single Point Feed

Circularly Polarised Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. AP-31, pp. 949-955,1983.

REFERENCES 219

[27] G. G. Sanford and R. E. Munson, "Conformal VHF Antenna for the Apollo-Soyuz Test Project," in IEE International Conference on Antennas for Aircraft and Space- craft, London, 1975, pp. 130-135.

[28] L. T. Ostwald and C. W. Garvin, "Microstrip Command and Telemetry Antennas for Communications and Technology Satellites," op. cit., pp. 217-222.

[29] M. Haneishi et al., "Broadband Microstrip Array Composed of Single Feed Type Circularly Polarised Microstrip Elements,' in IEEE Antennas & Propagation Sym- posium, May 1982, pp. 160-163.

1301 J. Kerr, Microstrip Antenna Developments, Workshop on Printed Antenna Technol- ogy, New Mexico State University, 1979, pp. 3.1-3.20.

[31] L. C. Shen, "Elliptical Microstrip Antenna with Circular Polarisation, "IEEE Trans. Antennas Propagat., Vol. AP-29, pp. 90-94,1981.

[32] H. D. Wienschel, "Cylindrical Array of Circularly Polarised Microstrip Antennas," in IEEE Antennas & Propagation Symposium, 1975, pp. 177-180.

[33] Y. Suzuki, N. Miyano, and T. Chiba, "Circularly Polarised Radiation from Singly Fed Equilateral-Triangular Microstrip Antenna," IEE Proc., Vol. 134, Part H, pp. 19&198,1987.

[34] T. Tsutsumi, S. Tsuda, A. Matsui, and M. Haneishi, "Radiation Properties of Circularly Polarised Microstrip Ring Antenna Excited by Dominant Mode," in International Svmposium on Antennas & Propagation, ISAP92, Sapporo, Japan, 1992, pp. 805-8081

[35] K. Hirose and H. Nakano, "Circularly Polarised Printed Loop Antenna Proximity Coupled to a Vertical Probe," in IEEE Antennas & Propagation Symposium, Chicago, 18 July 1992, pp. 1919-1922.

1361 M. Haneishi and S. Yoshida, "Design Method of Circularly Polarised Microstrip Antenna by One Point Feed," Electron. Commun., Vol. 64-B, No. 4, pp. 46-54,1981, (in Japanese).

[37] H. Inasaki and K. Kawabata, "Circular Microstrip Antenna with a Cross Slot for Circular Polarisation," IEICE Trans., Vol. E74, No. 10, pp. 3274-3279,1991.

[38] H. Shoki, K. Kawabata, and H. Iwasaki, "Circularly Polarised Slot Coupled Microstrip Antenna Using a Parasitically Excited Slot," IEICE Trans., Vol. E74, NO. 10, pp. 3268-3273,1991.

[39] H. Iwasaki, H. Sawada, and K. Kawabata, "Circularly Polarised Microstrip An- tenna Using Singly Fed Proximity Coupled Feed," in International Symposium on Antennas & Propagation, ISAP92, Sapporo, Japan, 1992, pp. 797-798.

[40] Ref. 3, pp. 318-320. Also seeY. Murakami, W. Chujo,I. Chiba, and M. Fujuse, "Dual Slot Coupled Microstrip Antenna for Dual Frequency Operation," Electron. Lett., Vol. 29, No. 22, pp. 1906-1907, 1993.

[41] L. Habib, G. Kossiavas, and A. Papiernik, "Cross Shaped Patch with Etched Bars for Dual Polarisation," Electron. Lett., Vol. 29, No. 10, pp. 916-918, 1993.

[42] Y. Murakami, K. Ieda, T. Yasuda, Y. Kawamura, and T. Nakamura, "Dual Band Circularly Polarised Stub Loaded Microstrip Antenna," in International Symposium on Antennas & Propagation ISAP92, Sapporo, Japan, 1992, pp. 793-796.

[43] M. Nakano, H. Arai, W. Chujo, M. Fujise, and N. Goto, "Feed circuits of double layered self diplexing antenna for mobile satellite communications," IEEE Trans. Antennas Propagat., Vol. 40, No. 10, pp. 1269-1271,1992.


[44] W. Chujo, M. Fujise, H. Arai, and N. Goto, "Improvement of the Isolation Charac- teristics of a Two Layer Self Diplexing Array Antenna Using a Circularly Polarised Ring Patch Antenna," IEICE Trans., Vol. E76-B, No. 7, pp. 755-758, 1993.

[45] C. Wood, ''curved Microstrip Line as Compact Wideband Circularly Polarised Antennas," IEE Proc. MOA, Vol. 3, pp. 5-13, 1979.

[46] A. Huhaneu, and S. Tallquist, "One Turn Antenna for L Band Land Mobile Communications," in Proceedings, Progress in Electromagnetics Research Sympo- sium, Pasadena, CA, 12 July 1993, p. 883.

[47] H. Nakano, G. Hirokawa, J. Yamauchi, and K. Hirosi, "Spiral Antenna with Coplanar Strip Line Feed," Electron. Lett., Vol28, No. 23, pp. 2130-2131,1992.

[48] H. Nakano, H. Mimaki, J. Yamauchi, and K. Hirose, "Numerical Analysis of a Low Profile Spiral Antenna," in X X I V URSI General Assembly, Kyoto, 1993, p. B3-10.

[49] J. J. H. Wang, and V. K. Tripp, "Design of Multioctave Spiral Mode Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. AP-39, pp. 332-335,1991.

[50] T. R. Holsheimer and J. C. Holloway, "Investigation of Spiral Performance Over Tightly Spaced Ground Planes," in IEEE Antennas & Propagation Symposium, Michigan, 28 June 1993, pp. 454-457.

[51] D. Shirley, "Spectral Domain Analysis of Square Spiral Microstrip Antennas," in IEEE Antennas & Propagation Symposium, Michigan, 28 June 1993, pp. 1466-1468.

[52] J. J. H. Wang, G. D. Hopkins, and V. K. Tripp, "Beam Switching and Steering of Spiral Mode Microstrip Antennas," in Proc ISAP92, Sapporo, Japan, 1992, pp. 789-792.

[53] I. G. Tiglis et al., "Radiation of a Planar Spiral Antenna Above a Double Dielectric Ground Plane," in IEEE, AP-S Symposium, Michigan, 28 June 1993, pp. 152-155.

[54] H. Nakano, Helical and Spiral Antennas, John Wiley & Sons, New York, 1987, Chapter 3.

[55] N. Das, S. K. Chowdhury, "Rectangular Microstrip Antenna on a Ferrite Substra- te," IEEE Trans. Antennas Propagat., Vol. AP-30, pp. 499-502.1982. - -

[56] D. M. Pozar, "Radiation and Scattering Characteristics of Microstrip Antennas on Normally Biased Ferrite Substrates," IEEE Trans. Antennas Propagat., Vol. AP-40, No. 9, pp. 1084-1092,1992.

[57] D. M. Pozar and V. Sanchez, "Magnetic Tuning of a Microstrip Antenna on a Ferrite Substrate," Electron. Lett., Vol. 24, pp. 729-731, 1988.

[58] D. M. Pozar, "Radar Cross Section of Microstrip Antenna on a Normally Biased Ferrite Substrate," Electron. Lett., Vol. 25, pp. 1079-1080, 1989.

[59] D. M. Pozar, "Microstrip Antennas and Arrays on Chiral Substrate," IEEE Trans. Antennas Propagat., Vol. AP-40, No. 10,1992, pp. 1260-1263.

[60] K. L. Wong and S. Y. Ke, "Cylindrical Rectangular Microstrip Patch Antenna for Circular Polarisation," IEEE Trans. Antennas Propagat., Vol. AP-41, No. 2, pp. 246-249,1993.

1611 T. B. Ng, Y. 0 . Yam, and L. M. Lam, "Active Quarter Wavelength Dielectric Radiator with Circularly Polarised Radiation Pattern, "Electron. Lett., Vol. 27, No. 19, pp. 1758-1759,1991.

1621 P. M. Haskins, P. S. Hall, and J. S. Dahele, "Polarisation-angle Active Patch Antenna," Electron. Lett., Vol. 30, pp. 98-99, 1994.

REFERENCES 221

[63] M. L. Charles, "Active Antennas with Polarisation Switching," C Onde Electrique, Vol. 73, No. 1, pp. 5-9, 1993.

[64] R. Flynt, L. Fan, J. Navarro, and K. Chang, "Low Cost and Compact Integrated Antenna Transceiver for System Applications," in IEEE MTT-S Symposium, Orlando, 15-19 May 1995, pp. 953-956.

[65] M. Cryan and P. S. Hall, "Integrated active antenna with simultaneous transmit receive operation," Electron. Lett., Vol. 32, No. 4, pp. 286-287, 1996.

[66] P. M. Haskins and J. S. Dahele, "Compact Active Polarisation-Angle Antenna Using Square Patch," Electron. Lett., Vol. 31, pp. 1305-1306, 1995.

[67] S. Borchi, P. Capece, M. Di Fausto, V. Mazzieri, and M. Votta, "Electrical Design of a Wideband, High Efficiency Circularly Polarised 4 Patch Subarray," in IEEE, AP-S Symposium, Chicago, 18 July 1992, pp. 1931-1934.

[68] T. Murata, M. Ohta, and H. Ishizaka, "Dual Frequency and Dual Polarisation Low Sidelobe Microstrip Arrays Antenna for Satellite Communications," in Proceedings ISAP Conference, Sapporo, Japan, 1992, pp. 1113-1 116.

[69] P. S. Hall, "Microstrip Linear Array with Polarisation Control," IEE Proc., Vol. 103H, pp. 215-224,1983.

[70] J. Henriksson, K. Markus, and M. Tiuri, "Circularly Polarised Travelling Wave Chain Antenna," in Proceedings, 9th European Microwave Conference, Brighton, 1979, pp. 174-178.

[71] T. Makimoto and S. Nishimura, "Circularly Polarised Microstrip Line Antenna," US Patent 4398 199,1983.

[72] S. Nishimura, Y. Sugio, and T. Makimoto, "Cranck Type Circularly Polarised Micro- strip Line Antenna," in IEEE Antennas & Propagation Symposium, 1983, pp. 162-165.

[73] R. P. Owens and J. Thraves, "Microstrip Antenna with Dual Polarisation Capabil- ity," in Proceedings, Military Microwaves Conference, October 1984, pp. 250-254.

[74] K. Ito, K. Itoh, and H. Kogo, "Improved Design of Series Fed Circularly Polarised Printed Linear Arrays," IEE Proc., Vol. 133H, pp. 462-466,1986.

[75] A. G. Roederer, "The Cross Antenna: A New Low Profile Circularly Polarised Radiator," IEEE Trans., Vol. AP-38,1990, pp. 704-710.

[76] T. Teshirogi, M. Tanaka, and W. Chujo, "Wideband Circularly Polarised Array Antenna with Sequential Rotations and Phase Shift of Elements," International Symposium on Antennas & Propagation, ISAP85, Tokyo, 1985, pp. 117-120.

[77] M. Haneishi, "Circularly Polarised SHF Planar Array Composed of Microstrip Pairs Element," in International Symposium on Antennas & Propagation, ISAP85, Tokyo, 1985.

[78] P. S. Hall, "Application of Sequential Feeding to Wide Bandwidth Circularly Polarised Microstrip Patch Arrays," IEE Proc., Vol. 136H, No. 5,1989, pp. 390-398.

[79] M. S. Smith and P. S. Hall, "Analysis of Radiation Pattern Effects in Sequentially Rotated Arrays," IEE Proc., Vol. 141, pp. 313-320,1994.

1801 P. S. Hall and M. S. Smith, "Sequentially Rotated Arrays with Reduced Sidelobe Levels," IEE Proc., Vol. 141, pp. 320-325, 1994.

[81] H. Iwasaki, T. Nakajima, and Y. Suzuki, "Gain Improvement of Circularly Polarised Array Antenna Using Linearly Polarised Elements," IEEE Trans. Antennas Propagat., Vol. 43, No. 6, pp. 604-608, 1995.


[82] J. Ruze, "Antenna Tolerance Theory: A Review," Proc. IEEE, Vol. 54, pp. 633-640, 1966.

[83] M. S. Smith, G. C. Sole, and B. N. Adarns, "Aperture Distribution Analysis of a Flat Plate Antenna from Short Range Pattern Measurements,"in IEE 8th International Conference on Antennas and Propagation, Edinburgh, pp. 182-185,1993.

[84] J. Notter and C. G. Parini, "Moments Method Analysis of a Finite Array of Arbitrary Shaped Microstrip Patch Radiating Elements," Int. J. Microwave and Millimetre Wave Computer Aided Design, Vol. 4, No. 1, pp. 18-30, 1994.

[85] P. S. Hall, "Feed Radiation Effects in Sequentially Rotated Microstrip Patch Arrays," Electron. Lett., Vol. 23, pp. 877-878, 1987.

[86] P. S. Hall and C. M. Hall, "Coplaner corporate feed effects in microstrip patch array Design," IEE Proc. Vol. 135, Part H, pp. 180-186,1988.

[87] J. Huang, "Dual Polarised Microstrip Array with High Isolation and Low Cross Polarisation," Microwave Opt. Technol., Lett., Vol. 41, No. 3, pp. 99-103,1991.

[88] E. Levine and S. Shtrikman, "Experimental Comparison Between Four Dual Polarised Microstrip Antennas," Microwave Opt. Technol. Lett., Vol. 3, pp. 17-18, 1990.

[89] A. Caille, 0. Mangenot, S. Remodiere, S. Bertrand, and A. Auriol, "Active Antenna for French X Band Spaceborne Radar," J . Int. Nice des Antennes, JINA 90, pp. 414-418,1990.

CHAPTER FIVE

Computer-Aided Design of Rectangular Microstrip Antennas

DAVID R. JACkiON, STUART A. LONG, JEFFERY T. WILLIAMS, and VlCKlE 8. DAVIS

5.1 INTRODUCTION

This chapter develops simple computer-aided design (CAD) formulas for the rectangular microstrip patch antenna. The CAD formulas are closed-form approximate expressions that describe the basic properties of the patch antenna. CAD formulas are presented for the resonance frequency, input resistance at resonance, radiation efficiency, bandwidth, and directivity. With the exception of the formulas for resonance frequency, all of the CAD formulas are derived from accurate analytical approximations of exact formulas and are therefore not simply empirical in nature. The CAD formulas account for radiation into space, surface-wave radiation, dielectric loss, and conductor loss. The formulas in all cases become more accurate as the substrate thickness decreases. With the exception of input resistance, the CAD formulas are independent of the specific feeding mechanism. The formula for resonant input resistance applies for the specific case of a probe feed. A CAD formula for the probe reactance is also given. Although derived for the rectangular patch, the CAD formulas for bandwidth, radiation efficiency, and directivity may be used in an approximate fashion for the circular patch as well, by applying the formulas to an equivalent square patch having the same area as the original circular patch.

Advances in Microstrip and Printed Antennas, Edited by Kai Fong Lee and Wei Chen. ISBN 0471-04421-0 0 1997 John Wiley & Sons, Inc.

224 COMPUTER-AIDED DESIGN OF RECTANGULAR MICROSTRIP ANTENNAS

In addition, a simple CAD model of the patch antenna is introduced for the calculation of input impedance. This model consists of a parallel RLC circuit (modeling the patch resonance) in series with a reactance (the probe reactance). This simple circuit, which follows directly from cavity model theory, can be used to calculate the input impedance at any frequency once the resonant input resistance, resonance frequency, and bandwidth of the patch are known. Hence, this simple circuit can be used directly with the above-mentioned CAD formulas. Alternatively, the CAD formulas for radiated and dissipated power can be used to calculate an effective loss tangent of the substrate, which can be used directly in a cavity-model analysis of the patch.

Results from the CAD formulas are compared with rigorous results from a spectral-domain analysis. Results show that the formulas for bandwidth, radiation efficiency, and directivity are very accurate, and even suffice for final design equations provided that the substrate thickness is small enough so that JE, h/Lo 10.10. The CAD formula for resonant input resistance loses accuracy sooner as the substrate thickness increases, but is accurate for substrate thickness in the range JE, h/Lo 50.03.

This chapter also discusses CAD formulas for the far-field radiation pattern of the rectangular patch on an infinite substrate. A comparison is made between formulas obtained from an electric current model and a magnetic current model. Both models are derived from different applications of the equivalence principle. In the electric current model the horizontal patch current is integrated to find the far-field pattern. In the magnetic current model the equivalent magnetic current at the boundary of the patch is used as the radiating source. It is demonstrated that both models yield the same result provided that the electric and magnetic currents in the two models correspond to the same cavity mode, and that the frequency of radiation is the resonance frequency of the cavity mode. Formulas obtained from both models are also presented for the far-field radiation pattern of a patch with a substrate that is truncated at the edges, and results are presented to show how these patterns differ from those for an infinite substrate.

5.2 CAD MODEL FOR RECTANGULAR PATCH ANTENNA

A probe-fed rectangular patch is shown in Figure 5.1. In the cavity model [ I , 21, a perfect magnetic-wall boundary is placed on the edges of the patch to form an ideal closed cavity. In order to account for fringing, the effective length of the patch is taken as L, = L + 2AL, where AL is an edge extension that is chosen to produce the correct resonance frequency for the dominant cavity mode of the patch. CAD formulas for AL are discussed in the next section. The resonance frequency of the dominant cavity mode, f ,, is related to the effective patch length by

CAD MODEL FOR RECTANGULAR PATCH ANTENNA 225

FIGURE 5.1 The probe-fed rectangular microstrip patch antenna. The feeding probe is a circular wire of radius a, located at (xo, yo).

where c is the speed of light, 2.99792458 x 10' m/s, and E, and y, are the relative permittivity and permeability of the substrate, respectively. The effective width of the patch, We, is chosen as We = W + 2AW, where the fringing width is chosen as PI

The fringing width is much less important than the fringing length, since it is the fringing length that determines the resonant frequency of the patch

The ideal magnetic wall allows for a simple modal expansion of the fields in terms of an eigenfunction expansion. The electric field E, inside the cavity, as well as the eigenfunctions, are independent of z, provided that the assumption is made that the probe current J, is constant (this is one restriction that limits the validity of the model to substrates that are thin compared to a wavelength). The eigenfunctions 4,, (x, y ) satisfy the eigenvalue equation

The eigenfunctions are cavity modes that can exist inside the magnetic-wall cavity, and the eigenvalues k,, are the corresponding wavenumbers of the resonant cavity modes. Because of the ideal cavity approximation, the eigenfunctions are complete and orthogonal, and the total field excited by the feed may be expanded in terms of these functions. Furthermore, the eigenvalues are all real numbers, independent of the substrate loss tangent (they are actually the cutoff wavenumbers of a corresponding rectangular waveguide with magnetic walls).


The eigenfunction expansion of the electric field inside the cavity is [I]

where

The inner product notation (f, g) denotes integration of the product f g over the area of the patch, and the effective complex wavenumber k, is defined by the relation kf = kl(1- jlJ, where k: = k : ~ , p, and I , is the effective loss tangent of the substrate. This effective loss tangent accounts for all loss mechanisms, including radiation into space, surfaces waves, dielectric loss, and conductor loss. Note that the wavenumber k, is real-valued even though the actual substrate may have a nonzero loss tangent; this loss is included in the effective loss tangent. For the rectangular patch, the eigenfunctions are

with eigenvalues

The effective loss tangent is related to the Q of the patch by the relation

The total quality factor Q may be expressed in terms of the Q factors associated with radiation into space (QSp), radiation into surface waves (Q,), dielectric loss (Qa), and conductor loss (QJ, through the relation

The dominant rectangular patch resonance occurs at the frequency for which k , z k,,. Assuming that the probe current I, is 1 A, Eq. (5.5) predicts that the dominant (1,O) cavity mode is excited at resonance with a maximum amplitude of

CAD MODEL FOR RECTANGULAR PATCH ANTENNA 227

This equation is used later to derive the CAD formula for input resistance at resonance.

The input impedance is calculated from an average voltage, obtained by integrating over the probe, as

which yields

For the rectangular patch, it is most convenient to model the cylindrical probe of radius a, centered at (x,, yo), as a flat strip of width w,, parallel to the y-z plane axis and centered at (x,, yo). One choice for the current distribution on the strip is a "Maxwell function" that includes the edge singularity. Assuming a probe current I,, the current density would be

For this choice, the strip width that best models the original probe would be [4]

Alternatively, a simpler choice for the probe current is a uniform current density,

For this choice, the correct strip width is [4]

The advantage of using the uniform current is that the formula for the reaction between the probe current and the eigenmodes [the numerator term in Eq. (5.1211 is simpler, involving only the sin (x) function instead of the J,(x) Bessel function. In particular, for the uniform probe current density, we obtain

228 COMPUTER-AIDED DESIGN OF RECTANGULAR MICROSTRIP ANTENNAS CAD MODEL FOR RECTANGULAR PATCH ANTENNA 229

where

sin (x) sinc (x) = -

X

For the rectangular patch, Eq. (5.12) then becomes

where the notation 6 , denotes the Kronecker delta (1 if m = 0, and 0 otherwise). From Eq. (5.12) it ~ollows that the input impedance may be written in the form

where

= -jw i k,2 - kL (5.21)

In this equation the amplitude terms

are frequency-independent. The Z i y terms in Eq. (5.20) represent impedances connected in series to yield the total input impedance. Taking the reciprocal of these impedance terms yields the admittance terms

Equation (5.23) provides the key for a physical interpretation of the result in Eq. (5.20). Each term Y l y ) has the form

FIGURE 5.2 Equivalent circuit of the probe-fed patch antenna.

which is the admittance for a parallal RLC circuit with a resonance frequency

Comparing Eqs. (5.23) and (5.24), it is seen that the two equations have the same mathemhL;cal form except for the fact that the constant 1/R term in Eq. (5.24) corresponds to a frequency-dependent term in Eq. (5.23). However, near the resonance frequency of the RLC circuit, w is approximately constant, and thus the first term in the last line of Eq. (5.23) is approximately constant. Hence, there is an approximate equivalence between the models. Therefore, the equivalent circuit shown in Figure 5.2 is an accurate model for the input impedance of the probe-fed patch. In this model the RLC circuit corresponding to the (0,O) mode is missing the inductance term. This mode corresponds to a uniform electric field in the patch cavity, with no magnetic field. The resonance frequency of this mode is zero, and it corresponds to a static eigenmode (which can exist independently, with no source, only at zero frequency). The resistance R in each of the circuits except the dominant (1,O) circuit can be neglected to a first approximation, because most of these modes modes radiate much less than the dominant mode and also because these resistances are effectively short-circuited by the inductors in the circuits [capacitor for the (0,O) mode]. If a narrow frequency region around o,,, the dominant rectangular patch mode resonance, is considered, the impedances for all other RLC circuits can be lumped into a single inductance, which models the stored energy in these other modes. The simple CAD model shown in Figure 5.3 is then obtained. The inductance L, is called the feed inductance, since most of the energy stored in the magnetic field of the higher-order modes exists near the feed (the total magnetic field inside the patch cavity is strongest at the surface of the probe, and it would be infinite on the axis of the probe if it were a filamentary wire).

The Q of the RLC circuit in Figure 5.3 is


FIGURE 5.3 CAD model of the probe-fed patch antenna, obtained from the circuit of Figure 5.2. This simple model is valid near the resonance frequency.

where the resonance frequency of the circuit is

A simple circuit analysis allows the input impedance of the CAD model in Figure 5.3 to be written near resonance as

Zill % jXf + R

1 +j2Q(f, - 1) (5.28)

where X f = wLf and the frequency ratio f, is defined as

The bandwidth (BW) of the patch may be calculated by assuming the patch is matched to an incoming transmission line with characteristic impedance Zo = R at the resonance frequency (neglecting the feed inductance), and calculating the lower- and upper-frequency limits f , and f, a t which the standing-wave ratio (SWR) is some specified value. The bandwidth is then defined as

(This bandwidth is unitless; it is multiplied by 100 to put the result in percent.) A simple calculation yields the result

CAD FORMULAS FOR RESONANCE FREQUENCY 231

In this chapter the specific choice SWR = 2.0 will be adopted, so that

The radiation efficiency, e, of the patch is defined as the power radiated into space divided by the total power, which includes the power radiated into space and surface waves, the power dissipated in the dielectric, and the power dissipated in the patch and ground plane. In terms of the Q factors, we have

The radiation efficiency and bandwidth of the patch are determined once the Q factors are known. In Section 5.3, CAD formulas will be presented for each of the Q factors in Eq. (5.9).

To determine input impedance from the CAD formula (5.28), three unknown parametars must be determined, in addition to the Q of the patch: the feed reactance (+), the input resistance at resonance (R), and the resonance frequency Cf,) (which is needed to determine f, for any given frequency). In the following sections, CAD formulas will be presented for each of these quantities. These CAD formulas are then used along with Eq. (5.28) to determine the input impedance.

5.3 C A D FORMULAS FOR RESONANCE FREQUENCY

Of primary concern in many applications is the value of the resonance frequency for a microstrip patch antenna. Since the bandwidth of these radiators is oftentimes quite small, the accurate prediction of their resonance frequency is most important. The simplest estimation is that the resonant dimension of the patch L is just equal to one-half wavelength in the dielectric material. This zero-order result (denoted as f :) is given by Eq. (5.1) with L, = L, so that

(In this formula, and all the following formulas in this section, the substrate is assumed to be nonmagnetic, so that p, = 1.) This approximation does not take into account the finite thickness of the substrate or the nonresonant width of the patch. Thus, it is only approximately correct for very thin substrates.

An equation for the fringing length proposed by Hammerstad [5] can be used to obtain a more accurate expression for the resonance frequency. Alternatively, a formula proposed by James, Hall, and Wood [6, pp. 99-1001 determines the resonance frequency directly, Both formulas are commonly used for more


accurate predictions for rectangular patches when the substrate is not necessarily extremely thin. Both equations share the concept of an effective dielectric constant, ceff, given by [fl

where is a dimension variable that can be either L or W in the formulas presented later.

Using the concept of fringing length, the resonance frequency is given by Eq. (5.1), with the effective length L, obtained by adding the fringing length AL to each end of the patch. The formula is

The Hammerstad formula for the fringing length [S] is

There is one important point that should be mentioned in connection with Eq. (5.36). This formula is often used in the literature with E,, instead of 8,. The original reference by Hammerstad [5] does not make it clear which is correct, since no formula for resonance frequency is actually given there. However, in our comparisons with measurements and the results from James (discussed below), we have obtained more accurate results by using e, when Eq. (5.37) is usedfor the fringing length. Therefore, Eq. (5.36) is used in the form shown for all of the results presented here.

James et al. [6] obtained a formula for the resonance frequency by directly modifying the zero-order result in Eq. (5.34). The formula is

where

CAD FORMULAS FOR RESONANCE FREQUENCY 233

FIGURE 5.4 Normalized resonance frequency versus the electrical thickness of the substrate, for a rectangular patch with W/L = 1.5. The normalized resonance frequency is the resonance frequency f divided by the zero-order value f :, which neglects fringing. 1, is the free-space wavelength at frequency f :. A comparison is shown between results from the CAD formula of Hammerstad, the CAD formula of James et al., and measured resonance frequencies. The solid dots denote the measured values. (a) E, = 2.2. (b) E, = 10.8.

Figure5.4 shows a comparison of CAD formulas (5.36) and (5.37) with formulas (5.38) and (5.39). The normalized resonance frequencies fo/ f predicted by the formulas are plotted versus the electrical thickness of the substrate in wavelengths (1,) for two different values of substrate relative permittivity.


Figure5.4a shows results for a low-permittivity substrate (E, = 2.2), while Figure5.4b shows results for a high-permittivity substrate (8, = 10.8). Measured results for the resonance frequency of a probe-fed rectangular patch are also included in the figures. The measured results were obtained by using a variety of different substrate thicknesses and patch sizes (with W/L= 1.5 for all patches). As can be seen, both CAD formulas predict a reduction of the resonance frequency as the substrate thickness increases. The Hammerstad formula agrees better with the measured results for the low-permittivity substrate, while the measured results are spread between the Hammerstad and James results for the high- permittivity substrates.

5.4 CAD FORMULAS FOR THE Q FACTORS

In this section, CAD formulas for the quality factors are presented. In the following sections these formulas are used together with the formulas introduced in Section 5.2 to obtain CAD formulas for bandwidth, radiation efficiency, and input resistance at resonance.

5.4.1 Dielectric and Conductor Q Factors

CAD formulas for Q, and Q, are well known [6, pp. 76-77]. Assuming the magnetic-wall approximation, a relatively straightforward analysis yields

and

where I, is the actual loss tangent of the substrate, p, is the relative permeability of the substrate, and R, is the surface resistance of the patch and ground plane metal. (If the patch and ground plane have different surface resistances, then R, is the average of the two resistances.) The surface resistance is calculated from the usual formula [8]

where w = 2n f and cis the effectivemetal conductivity. Due to surface roughness, the effective conductivity for copper patches and ground planes is usually taken to be approximately 3.0 x lo7 mhoslmeter rather than that of a pure bulk material (5.8 x lo7 mhoslmeter). Comparing Eqs. (5.40) and (5.41), it is seen that the dielectric loss Q is independent of substrate thickness, while the conductor

CAD FORMULAS FOR THE Q FACTORS 235

loss Q is proportional to the electrical thickness of the substrate (k,h). Hence, for thin substrates, the conductor loss (which is inversely related to Q,) will always dominate over the dielectric loss.

5.4.2 Relation Between Surface-Wave and Space-Wave Q Factors

The remaining two Q factors, Qsp and Q,, determine the amount of power radiated into space and surface waves. To relate these two Q factors, a radiation efficiency e: is defined, which is the radiation efficiency assuming no dielectric loss (I, = 0) and no conductor loss (a = a). This efficiency accounts only for power loss due to the excitation of surface waves. In terms of the Q factors, we obtain

where the radiation quality factor Qr is defined as

1 1 1 -=-+- Qr Qsp Qsw

To a good approximation, the efficiency e: may be approximated by the radiation efficiency erd of a horizontal electric dipole on top of the lossless substrate (the loss tangent I , of the substrate is set to zero). In general, the power radiated either into space or into surface waves is not approximated to a high degree of accuracy by the corresponding power radiated by a dipole, since the radiation from the patch comes from a distributed electric current and not a single point. There is, in effect, an array factor due to the distribution of the current over the surface of the patch. There are array-factor terms for both the power radiated into space and the power radiated into surface waves. It turns out that these two array factors are similar, so that the ratio of power radiated into space divided by power radiated into surface waves is very similar for both the patch and the dipole on the lossless substrate (the accuracy of this approximation will be demonstrated later when numerical results for the radiation efficiency are presented). A simple algebraic manipulation of Eqs. (5.43) and (5.44) yields

Hence, to a good approximation, we obtain

The surface-wave quality factor is thus known from the space-wave quality factor, provided that the radiation efficiency of the dipole is known.


The radiation efficiency for a horizontal electric dipole may be written as

where P Z d is the power radiated into space by a unit-strength horizontal electric dipole on the lossless substrate, and P:;d is the power radiated into surface waves by the dipole. In reference [9], a CAD formula for P g d is derived. The result is

where c, is a constant that depends only on the substrate material,

and n, is the index of refraction of the substrate,

Equation (5.48) is derived from an asymptotic approximation of the exact space-wave power formula, assuming that the substrate is thin, so that k,h << 1. This formula, therefore, becomes increasingly accurate as the substrate thickness decreases.

Two CAD formulas for the surface-wave power PEd have been previously derived. The first one, derived in reference [PI, is

This formula comes from an asymptotic approximation of the exact surface-wave power, assuming that the substrate is thin, so that k,h<< 1. For thin substrates, only the fundamental TM, surface wave mode is above cutoff, and Eq. (5.51) gives the power radiated into this surface wave.

An improved formula for P!id that is more accurate than Eq. (5.51) has been derived by Pozar [lo], by keeping higher-order terms in the asymptotic approximation. The result, derived in reference 10 for the case of a nonmagnetic substrate OL, = 1), is

where

phcd - vok; E,(x; - 1)3/2 SW (5.52)

8 &,[I + x1l + ( k o h ) m [ I + E;XJ

and

with


and

Although Eq. (5.52) is more accurate than Eq. (5.51), Eq. (5.51) has the advantage of providing more physical insight into the behavior of the surface-wave power. It is seen from Eq. (5.51) that the surface-wave power varies with substrate thickness as (k,h)" while the space-wave power varies as (koh)2, from Eq. (5.48). Hence, the radiation efficiency ep approaches 1.0 as the substrate becomes thinner. There- fore, for thin substrates, the surface-wave loss becomes negligible.

Figrq5.5 shows the accuracy of CAD formulas (5.51) and (5.52), for the radiation ehciency of a horizontal electric dipole on a lossless substrate (where 1, has been set to zero). In this figure, these two CAD formulas are compared with an exact result, obtained from a spectral-domain calculation [11] (where the dipole was approximated by a patch having dimensions much smaller than a wavelength). Results are shown for two different substrate permittivities, corresponding to a typical duroid substrate and a high-permittivity substrate, in Figures 5.5a and 5.5b, respectively. It is seen that both Eqs. (5.51) and (5.52) are fairly accurate up to approximately h/Ao z 0.10 for the low-permittivity substrate. For the high-permittivity substrate, Eq. (5.51) is accurate up to h/A, z 0.02 while Eq. (5.52) is accurate up to h/A, z 0.04. In Figure 5.5b, the results from Eq. (5.52) are plotted only up to h/A, z 0.078. At this point the equation breaks down since the argument of the square root in the calculation of the term x, becomes negative. The exact curve in Figure 5.5b exhibits a slope discontinuity at h/A, z 0.08, corresponding to the cutoff of the TE, surface-wave mode on the grounded dielectric slab.

5.4.3 Space-Wave Quality Factor

Equation (5.46) along with Eqs. (5.47), (5.48), and either (5.51) or (5.52), determine the surface-wave quality factor once the space-wave quality factor is known. To determine the space-wave quality factor, the power radiated by the patch antenna must be calculated, as well as the energy stored in the patch cavity. The space-wave Q factor is then determined from the standard formula for Q,


FIGURE 5.5 Radiation efficiency of a horizontal electric dipole on a lossless grounded substrate versus the electrical thickness of the substrate, for two different values of substrate permittivity. The CAD formulas are based on Eq. (5.47). One formula uses Eq. (5.51) to calculate the surface-wave power, while the other uses the improved formula (5.52). An exact result, obtained from a spectral-domain analysis, is also shown. (a) e, = 2.2. (b) 8, = 10.8.

where Us is the energy stored inside the cavity and P,, is the power radiated into space by the patch current. Both of these terms are calculated assuming a dominant mode current on the patch, corresponding to the (1,O) mode of the cavity.


The current density is taken as

where x' = x - Le/2 (the primed coordinate system (x', y') is measured from the center of the patch). This current density corresponds to a y -directed magnetic field inside the patch cavity, with H, = J,. The length of the patch in Eq. (5.54) has been taken as the effective length, even though the actual surface current exists only over the physical dimensions of the patch. The actual surface current J,, on the patch exhibits an edge effect, vanishing near the patch edges as Js, where s is the distance from the patch edge at x =O or x = L. The dominant cavity-mode current in Eq. (5.54) vanishes linearly (proportional to s) near the patch edges. The edge effect causes an additional amount of radiating current to be present on the patch, and this is approximately accounted for by choosing the patch length to be Le in Eq. (5.54). The effective length Le in this and all subsequent formulas is obtained from Le = L+ 2AL, where Eq. (5.37) is used for AL. For the same reasons, the effective width We = W + 2A W is used in all subs-went CAD formulas, with AWcalculated from Eq. (5.2).

To calculate the stored energy inside the cavity, it is noted that the energy stored in the electric and magnetic fields are equal at resonance (this is true for any cavity resonator), so that Uf = Uf. Hence, the total stored energy is given by

which results in

To calculate the power radiated into space, the patch is first replaced by an equivalent dipole that has the same dipole moment me,, defined from

A horizontal electric dipole of amplitude I1 = me, will radiate approximately the


same power into space as the patch (ignoring the array factor due to the distribution of the patch current over the surface of the patch). Therefore, to a first approximation, we obtain

where P;;* is given by Eq (5.48). Equation (5.57) becomes more accurate as the size of the patch decreases, since

this approximation ignores the patch array factor. It is possible to modify Eq. (5.57) to account for the array factor and thus improve the accuracy. To do this, a power ratio pis defined as the ratio of the actual power radiated into space by the patch, to the power radiated into space by the equivalent dipole with moment m,, ,

,2 p h c d eq sP

The factor p approaches 1.0 as the size of the patch becomes small compared to a wavelength (which in turn implies that the substrate permittivity becomes large). An approximate formula for the p factor may be obtained from some algebraic manipulations. Equation (5.58) is first written in terms of the far-field power patterns as

So2' S%' Sr(r, 0, &r2 sin 0 d0 d#J P = (5.59)

S,hcx(r, 0, #J)r2 sin 0 d0 d4

where S, is the power density (radial component of the Poynting vector) in the far-field from the patch current, and S F is the power density from an x-directed unit-strength dipole. To evaluate Eq. (5.59), the power density radiated by the patch is expressed as

where A(0, 4) is the patch array factor, defined as

where

k, = k, sin 0 cos #J

k, = k, sin 0 sin #J

CAD FORMULAS FOR THE Q FACTORS

Evaluating the integrals in Eq. (5.61) gives the result

and

Substituting Eqs. (5.63) and (5.64) into Eq. (5.62), and then inserting Eq. (5.62) into Eq. (5.60), allows the power density radiated by the patch to be written in terms of the -ver density radiated by the unit-strength dipole. Equation (5.60) is then used in Eq. (5.59) to evaluate the factor p. A closed-form approximate evaluation of Eq. (5.59)may be performed, if the assumption is made that the substrate is thin compared to a wavelength and that the patch dimensions are not too large compared to a wavelength [9]. This evaluation is performed in Appendix A. The result is

a p = 1 + 2 10 (k, We)' +(a: + 2a4)

where

It should be pointed out in reference [9] an error was made in the derivation of the factor p, so the above expression is different from the one in reference [9]. Figure5.6 shows a plot of the factor p versus the electrical patch length, for different aspect ratios We/Le. The results from Eq. (5.65) as compared with the exact p factor, calculated by numerically evaluating Eq. (5.59). Figure 5.6 shows that CAD formula (5.65) is quite accurate for resonant patches, since the maximum patch length (corresponding to a air substrate) would be LJL, x 0.5.


FIGURE 5.6 Plot of the factor p defined in Eq. (5.58). The results from CAD formula (5.65) are compared with an exact calculation, obtained by numerically evaluating Eq. (5.59).

Equation (5.58) allows the space-wave power radiated by the patch to be written as

Substituting Eqs. (5.48) and (5.56) into Eq. (5.66) yields the final CAD formula for the space-wave power radiated by the patch. Equations (5.66) and (5.55) may then be substituted into Eq. (5.53) to obtain a final CAD formula for the space-wave quality factor. After some simplifications, the final result is

From this expression it is seen that the space-wave quality factor varies inversely with the electrical thickness of the substrate (under the assumption that this thickness is small, which is one of the assumptions in the derivation).

5.5 CAD FORMULA FOR BANDWIDTH

Using the CAD formulas for the quality factors derived in Section 5.4, a final CAD formula for the bandwidth may be obtained, using the formulas presented in Section 5.2.

CAD FORMULA FOR BANDWIDTH 243

5.5.1 CAD Formula

The bandwidth of the rectangular patch antenna is found from Eq. (5.32), using Eq. (5.9) along with Eqs. (5.40), (5.41), (5.46), and (5.67). The result is

Equations (5.47) and (5.48) are used along with either Eq. (5.51) or (5.52) to calculate e r d in this equation [Eq. (5.52) will give more accurate results]. Equations (5.49) and (5.65) are used to calculate the terms c, andp, respectively.If dielectric and conductor losses are neglected (valid for substrates of moderate thickness), the bandwidth formula simplifies to

16 pc, h We BWO =+[(T)(&, )(&)(+)I

This CAD formula shows that the bandwidth is proportional to the electrical substrate thickness h/Ao (although the electrical substrate thickness must still be re la^ -1y small in order for this formula to be accurate). For thicker substrates, the radiation efficiency e,hcd begins to decrease due to surface-wave excitation, which causes the bandwidth to increase even faster than linearly. However, this is normally undesirable, since bandwidth is being increased at the expense of lost power. For thin substrates, the bandwidth will be determined by the dielectric and conductor Q factors, so that the first two terms inside the brackets of Eq. (5.68) dominate. Ultimately, for very thin substrates, it is the conductor Q that dominates. In this region the bandwidth increase is inversely proportional to the electrical substrate thickness. Here again, however, bandwidth is being increased at the expense of lost power, which is normally undesirable. It is also noted from Eq. (5.69) that the bandwidth is inversely proportional to the substrate permittivity. Hence, higher bandwidths are obtained by using thicker substrates with a low permittivity. The bandwidth is also increased by increasing the aspect ratio WIL. For very thin substrates, where dielectric and conductor losses dominate, the bandwidth is seen from Eq. (5.68) to be essentially independent of the patch dimensions (this is an undesirable region of operation).

5.5.2 Results

Figure 5.7a shows a comparison between CAD formula (5.68) (which includes the dielectric and conductor losses) and the exact bandwidth, obtained from the cavity model, for a patch with W/L= 1.5. The same effective width and length are used in the cavity-model calculation as in the CAD formula. Results are shown for a resonant patch on a low-permittivity substrate (6, =2.2) and a high- permittivity substrate (&, = 10.8). In these figures a loss tangent of 1, = 0.001 is assumed for both substrates, and a conductivity of a = 3.0 x lo7 mhoslmeter is


assumed for the patch and ground plane. A frequency of 5.0 GHz is assumed so that the factor Q, may be calculated. The results are then displayed versus electrical thickness h/A,. Equation (5.52) has been used to calculate e? in Eq. (5.68). In the cavity-model calculation, the frequencies for which SWR = 2.0 are determined numerically, assuming a perfect match at the center frequency. The feed position is at xo = L/4, yo = W / 2 for the cavity-model calculation (although bandwidth is not sensitive to feed location). When the electrical thickness of the substrate exceeds h/Ao c 0.05 for the low-permittivity substrate, the patch can no longer be made resonant by changing the length of the patch. In this region the

FIGURE 5.7 (a) The percent bandwidth of a rectangular patch versus the electrical thickness of the substrate, at a frequency of 5.0 GHz. The patch is resonant for all substrate thicknesses (input impedance is pure real), with W/L= 1.5. Results for two different substratepermittivities are shown, E, = 2.2 and 10.8. A loss tangent/, = 0.001 is assumed in both cases. The conductivity of the patch and ground plane are both taken as a= 3.0 x 107mhos/meter. The CAD formula is compared with results from a cavity- model calculation, which numerically finds the frequencies at which the SWR is 2.0 for a patch that is matched to the incoming feedline at the resonance frequency. The cavity-model calculation assumes that the feed is located at x, = L/4, yo = W/2 (the CAD formula does not account for the feed location). The results from the CAD formula are shown with solidlines. The results from thecavity-modelanalysis are shown with dots and squares, for the low- and high-permittivity substrates, respectively. The hollow dots indicate that no frequency can be found for which the input reactance is zero. In this case the resonance frequency is taken as the frequency for which the input reactance is a minimum. (b) The same CAD results in part (a) are compared with measured results. The dots and squares correspond to themeasured bandwidths for the low- and high-permittivity substrates, respectively.

CAD FORMULA FOR BANDWIDTH 245


probe inductance is sufficient to make the input impedance inductive for all patch lengths. The patch resonance is then defined from the patch length that minimizes the input reactance. The value of the reactance at the minimum point is subtracted from the input impedance at each frequency, and the SWR is then calculated by assuming a perfect match at resonance. The hollow dots for the low-permittivity case in Figure 5.7a indicate those points where this modified calculation has been used.

There is excellent agreement between the CAD formula and the "exact" cavity-model result for thin substrates. The CAD formula is accurate up to h/1, c 0.06 for the low-permittivity substrate, and up to h/Ao c 0.03 for the high-permittivity substrate. In both cases, the CAD formula is therefore accurate up to h/Ad = 0.1, where 1, is the wavelength in the dielectric. The results from the CAD formula are only plotted up to h/Ao =0.078 for the high-permittivity substrate, for the same reason discussed previously in connection with FigureSSb. Figure5.7a shows that the bandwidth increases almost monotonically with increasing substrate thickness. This is true until the substrate thickness becomes very small, a t which point the conductor loss begins to dominate.

Figure5.7b shows a comparison between the same CAD results shown in Figure 5.7a and recently obtained measured results. For the measured results, a slightly different definition of resonance frequency was used, namely the frequency for which the real part of the input impedance was maximum. However, this causes a negligible difference in the bandwidth calculation,


provided the electrical thickness of the substrate is relatively small. As for Figure 5.4, the measured results were obtained by using a variety of substrate thicknesses and patch sizes (with W/L = 1.5 for all patches). The agreement is seen to be quite good for both the low- and high-permittivity substrates, for the ranges plotted.

5.6 CAD FORMULA FOR RADIATION EFFICIENCY

Using the CAD formulas for the quality factors derived in Section 5.4, a h a 1 CAD formula for the radiation efficiency may be obtained, using the formulas presented in Section 5.2.

5.6.1 CAD Formula

Equation (5.33), along with Eqs. (5.9), (5.40), (5.41), (5.46), and (5.67), gives the final CAD formula for radiation efficiency. The result is

As for the bandwidth formula, Eqs. (5.47) and (5.48) are used along with either Eq. (5.51) or (5.52) to calculate ePd in this equation (Eq. (5.52) being more accurate). Equations (5.49) and (5.65) are used to calculate c, and p.

Equation (5.70) indicates that the radiation efficiency of the patch approaches the radiation efficiency of a horizontal electric dipole on a corresponding lossless substrate as the electrical thickness of the substrate increases. For thicker substrates the radiation efficiency will therefore decrease due to increased surface-wave excitation. For electrically thin substrates the dielectric and conductor losses dominate the surface-wave loss. In this region the efficiency increases as the substrate thickness increases. For very thin substrates the conductor loss is the dominant loss mechanism. In this region the radiation efficiency is proportional to (h/L,)2 and is very poor. Equation (5.70) predicts that the efficiency increases quadratically for very thin substrates, but eventually reaches a maximum for a particular substrate thickness. The efficiency then decreases as the substrate thickness is increased beyond this point, due to surface-wave loss. The optimum substrate thickness will depend on the permittivity of the substrate (it will increase as the permittivity decreases).

For thicker substrates the dimensions of the patch do not significantly affect the radiation efficiency, since the efficiency is essentially the same as that of the horizontal electric dipole. However, for thin substrates the efficiency is improved by making the aspect ratio W/L larger.

CAD FORMULA FOR RADIATION EFFICIENCY 247

5.6.2 Results

Figure5.8a shows a comparison between CAD formula (5.70) and the exact radiation efficiency obtained from a spectral-domain calculation [I l l , for a resonant patch on a low-permittivity substrate and a high-permittivity substrate, with W/L = 1.5. A loss tangent of I , = 0.001 is assumed for the substrate, and a conductivity of u = 3.0 x lo7 mhos/meter is assumed for the patch and ground plane. A frequency of 5.0 GHz is again assumed so that conductive losses may be calculated. Equation (5.52) has been used to calculate eyd in Eq. (5.70). The spectral-domain calculation does not directly account for conductor loss, since only space-wave and surface-wave powers are calculated. But conductor loss may be calculated separately by making use of the approximate formula (5.41) for Q,, along with Eq. (5.55) for the stored energy and the definition of Q, [6]. Because Eq. (5.41) is used in both the CAD and spectral-domain calculations, this comparison does not reflect the accuracy of Eq. (5.41). However, when the substrate is thin enough so that conductor loss is important in the calculation of efficiency, Eq. (5.41) is expected to be quite accurate.

Figure 5.8a shows that CAD formula (5.70) is accurate for substrate thick-

FIGURE 5.8 The radiation e5ciency of a rectangular patch versus the electrical thickness of the substrate, at a frequency of 5.0GI-Iz. The patch is resonant for all substrate thicknesses, with W/L= 1.5. Results for two different substrate permittivities are shown, E, = 2.2 and 10.8. The CAD formula is compared with results from a spectral-domain calculation. (a) A loss tangent /,, = 0.001 is assumed for both substrate permittivities. The conductivity of the patch and ground plane are both taken as u = 3.0 x lo7 mhosl meter. (b) The loss tangent is assumed to be zero, and the patch and ground plane are assumed to be perfectly conducting. (continued)



nesses up to h/A, x 0.1 for the low-permittivity substrate, and up to h/A, x 0.03 for the high-permittivity substrate. Figure 5.8a also shows that the efficiency is higher for the low-permittivity substrate, for the same electrical thickness h/A,. The optimum substrate thickness is h/A, z 0.02 for the low-permitivity substrate, and h/A, x 0.015 for the high-permittivity substrate. The CAD formula is accurate for predicting the optimum substrate thickness.

Figure 5.8b shows the radiation efficiency for the same patch and substrate as in Figure 5.8a, but with the dielectric and conductor losses neglected. That is, the loss tangent of the substrate has been set to zero, and the patch and ground plane are assumed to be perfectly conducting. The radiation efficiency therefore only accounts for surface-wave loss. In this case it is seen that the efficiency closely resembles that of a horizontal electric dipole on the same lossless substrate, shown in Figure 5.5. When conductor and dielectric losses are neglected, the efficiency decreases monotonically as the substrate thickness increases, at least until the substrate becomes quite thick.

5.7 CAD FORMULA FOR INPUT RESISTANCE

The input impedance of the patch may be calculated from the cavity model formula (5.19), using Eqs. (5.8) and (5.9) along with the CAD formulas for the Q factors that were given in Section 5.2. At resonance, the main contribution to the input impedance (which is purely resistive) comes from the dominant (1,O) mode. A simple CAD formula for the input resistance at resonance may be

CAD FORMULA FOR INPUT RESISTANCE 249

derived by including only the (1,O) contribution to the sum in Eq. (5.19). This contribution is the value of the resistor R that appears in the CAD circuit of Figure 5.3.

Assuming that only the dominant (1,O) mode is significant, the electric field inside the cavity is found from the (1,O) term of Eq. (5.4), with Alo given by Eq. (5.10). The input resistance is then determined from Eq. (5.11) as

Using the relation kloLe = a, valid at resonance, this simplifies to

tTqing Eqs. (5.8) and (5.9) along with (5.40), (5.41), (5.46), and (5.67) to evaluate the effective loss tangent I,, Eq. (5.72) becomes

If dielectric and conductor losses are neglected, Eq. (5.73) further simplifies to

Equation (5.74) indicates that the resonant input resistance is approximately independent of the substrate thickness, provided that the electrical substrate thickness is large enough so that dielectric and conductor losses may be neglected [the only term in Eq. (5.74) that varies with substrate thickness is erd, which is approximately equal to 1.0 for relatively thin substrates]. For thin substrates, Eq. (5.73) shows that the input resistance tends to zero as (h/Ao)2. The input resistance is independent of the probe position along the nonresonant dimension 01 axis), according to these formulas. These formulas predict that the resistance is maximum along the resonant edges of the patch (x, = 0, L) and is zero along the centerline (x, = L/2). Equation (5.74) also shows that the input resistance decreases as the aspect ratio W / L increases and that the input resistance increases as the substrate permittivity increases.


When implementing Eq. (5.73), x, is taken to be the x-axis distance from the probe to the effective edge of the patch, after the fringing length AL has been added to both edges of the patch. Therefore, the original distance x, (measured from the physical edge of the patch) is replaced by x, + AL in Eq. (5.73).

Figure 5.9a shows a plot of resonant input resistance versus electrical substrate thickness for a patch with W/L= 1.5, for both a low-permittivity and a high- permittivity substrate. Again, a frequency of 5.0 GHz is assumed so that conductive losses may be calculated. The feed position in this case is at a fixed position, halfway between the center of the patch and the edge at x, = L/4, yo = W/2, and the probe radius is 0.05 cm. The results from Eq. (5.73) are compared with results from the cavity model. This figure shows that the higher-order modes become more important as the substrate thickness increases, since there is more deviation between the results from Eq. (5.73) and the cavity model. The CAD formula is accurate for substrate thicknesses up to h/A, x 0.04 for the low-permittivity substrate and h/A, x 0.05 for the high-permittivity substrate. The dashed part of the CAD curves indicates that the patch reactance never went to zero. In this case, as in Figure 5.7a, the patch resonance was defined from the patch length that minimized the rectance. The hollow dots and squares for the low-permittivity and high-permittivity cavity-model curves in Figure 5.9a indicate that the patch was never resonant in this model, and resonance was therefore defined in the same way as for the CAD results. Both models predict that the patch ceases to become resonant at about the same substrate thickness, namely, h/A, c 0.04 for the low-permittivity substrate and h/A, % 0.05 for the high-permittivity substrate.

Figure5.9b shows a comparison between the same CAD results shown in Figure5.9a and the results from a spectral-domain calculation [12], which assumes a filamentary probe feed and one full-domain basis function in both the x and y directions. It should be commented that the filamentary probe model used to obtain the spectral-domain results is known to lose accuracy for thicker substrates; the accuracy is probably questionable for h/A, > 0.015. Because the probe inductance is not accounted for in the spectral-domain calculation, the resonance frequency will be shifted from that predicted by the CAD formula and the cavity model. This results in a significant difference in the predicted input resistance at resonance, since the input resistance is a function of frequency. Neglecting the probe inductance implies that the input resistance will be a maximum at the resonance frequency. With a nonzero probe inductance, the input resistance at resonance will be less than the maximum input resistance.

A more accurate calculation of input impedance can be obtained by using more basis functions together with an attachment mode on the patch [13].

Figure 5 . 9 ~ shows a comparison between the CAD results in Figure 5.9a with recently obtained measured results for the resonant input resistance. As mentioned previously in connection with Figure 5.7b, the definition of resonance frequency for the measurements was slightly different than the one used for the calculations. The measured results were obtained by using a variety of different substrate thicknesses and patch sizes, with all patches having an aspect ratio of W/L= 1.5. The agreement between the measured results and the CAD results is

CAD FORMULA FOR INPUT RESISTANCE 251

quite good, agreeing fairly well for substrate thickness in the range h/A, < 0.02 for the low-permittivity substrate, and h/A, < 0.015 for the high-permittivity substrate. The spectral-domain results shown in Figure 5.9b do not appear to agree as well with the measured results as do the CAD formula and cavity model. Due to the assumption of a filamentary probe feed and only one full-domain basis function in the x and y directions, the spectral-domain results are probably not very accurate beyond h/A, x 0.015.

FIGURE 5.9 (a) The resonant input resistance of a probe-fed rectangular patch versus the electrical thickness of the substrate, at a frequency of 5.0 GHz. Resonance is defined from the patch length that gives a pure real input impedance. The patch is resonant for all substrate thicknesses, with W/L= 1.5. The feed probe is located at xo = L/4, yo = W/2 and has a radius of 0.05 cm. Results for two different substrate permittivities are shown, E, = 2.2 and 10.8. A loss tangent d, = 0.001 is assumed for both substrate permittivities. The conductivity of the patch and ground plane are both taken as a = 3.0 x lo7 mhos/ meter. The CAD formula is compared with results from a cavity-model analysis, shown with dots and squares for the low- and high-permittivity substrates, respectively. The dashed part of the CAD curve indicates that no frequency can be found for which the input reactance is zero in the CAD model. Similarly, the hollow dots and squares indicate that no frequency can be found for which the input reactance is zero in the cavity model. In this case resonanceis defined from the patchlength for which the input reactance is amhimum. (b) The same CAD results for resonant input resistance shown in part (a), compared with the results from a spectral-domain calculation of resonant input resistance. The spectral- domain calculation assumes a filamentary probe feed, and thus neglects the probe reactance. (c) The same CAD for resonant input resistance shown in part (a), compared with measurements. The dots and squares correspond to the measured resonant input resistances for the low- and high-permittivity substrates, respectively. (continued)



5.8 CAD FORMULA FOR PROBE REACTANCE

The last remaining element of the CAD model in Figure5.3 that needs to be determined is the probe reactance X, = joLp All of the terms needed in Eq. (5.28) will then be known, and this equation may be used to calculate input impedance at any frequency. The probe is assumed to be a circular wire of radius a, centered at (xo, YO).

CAD FORMULA FOR PROBE REACTANCE 253

Comparing Figures 5.2 and 5.3, the probe reactance is the part of the input impedance due to all other modes except the dominant (1,O) mode. Therefore, from (5.12) we obtain

In the preceding equation the effective wavenumber k, has been taken as the real-valued wavenumber k: = k $ q ~ , , which is a sufficiently accurate approximation for all modes except the dominant (1,O) mode. Specializing to the case of the rectangular patch, using Eq. (5.19), the formula for probe reactance becomes

Zwation (5.76) represents the exact probe reactance, defined so as to be consistent with Figure 5.3. Although it is not difficult to numerically evaluate Eq. (5.76), it is convenient to approximate this equation with a simple CAD formula. It is especially useful to have such a simple CAD formula for patches on thin substrates, since the probe reactance will not be very large in this case, so that even a fairly approximate formula should s d c e .

One simple approximate formula for X, can be obtained by ignoring the cavity boundaries and calculating the reactance of the same probe in an infinite parallel-plate waveguide [14, p. 2281. The resulting expression for the probe reactance is

where y = 0.577216 is Euler's constant. This formula neglects the variation of the probe reactance with position and becomes more accurate as the probe radius becomes smaller. (As the probe radius becomes smaller, the energy stored in the magnetic field is concentrated more strongly near the probe, and thus the feed position or the shape of the patch becomes less important.) Because of the logarithm term, the probe reactance will increase very slowly as the probe radius decreases. If the probe radius is not too small and the substrate is electrically thin, the probe reactance will be small and can usually be neglected. However, for thicker substrates the probe reactance may be appreciable.

Figure5.10 shows a comparison between Eq. (5.77) and the exact probe reactance, Eq. (5.76). The probe reactance in Eq. (5.76) was actually calculated by finding the input reactance when the patch length is varied slightly to maximize


FIGURE 5.10 The probe reactance versus normalized feed position x, = 1-2xo/L. The substrate has a permittivity of s, = 2.2 and an electrical thickness h/A, = 0.02. The patch is resonant with W/L = 1.5. The radius of the cylindrical probe is 0.051,. The exact result is compared with the CAD formula based on a parallel-plate waveguide model.

the input resistance. At this point the RLC circuit in Figure 5.3 is resonant, so the input reactance is the probe reactance. This is equivalent to calculating the probe reactance with Eq. (5.76). The reactance is plotted versus feed position, for a probe radius of 0.05cm. The probe position is varied in the x direction, keeping yo = W/2. The patch is of resonant length on a low-permittivity substrate, with an aspect ratio W/L = 1.5. This figure shows that the CAD formula underestimates the probe reactance. The actual probe reactance is a function of feed position, increasing as the probe approaches the edge of the patch. Equation (5.77) is an asymptotic formula, becoming more accurate as the probe radius decreases. Equation (5.77) is seen to be fairly accurate when the probe is not too close to an edge of the patch.

5.9 RESULTS FOR INPUT IMPEDANCE

Equation (5.28) is the final CAD formula for input impedance. Equation (5.77) is used to determine X/. Equation (5.9), along with Eqs. (5.40), (5.41), (5.46)-(5.48) and (5.52), is used to determine Q. Equation (5.73) is used to determine R. Equation (5.36) is used to determine the resonance frequency fo, in order to calculate the frequency ratio f , in Eq. (5.29).

Figure 5.1 1 shows a comparison between input impedance (real and imaginary parts) calculated by Eq. (5.28) and by the cavity model [Eq. (5.19)]. The input

RESULTS FOR INPUT IMPEDANCE 255

I I 1

FREQUENCY (GHz) (a)

-20 -

-40 ' ' ' '

4 4.5 5 5.5 6 FREQUENCY (GHz)

(b)

FIGURE 5.1 1 Comparison of input impedance versus frequency for a rectangular patch with L= 2.0cm and W/L = 1.5. The feed probe is located at xo = L/4, yo = W/2 and has a radius of 0.05 cm. Results from the CAD model of Figure 5.3 are compared with results from the cavity model (labeled "exact"). The substrate has a permittivity of E, = 2.2 and a thickness of 0.1524cm. (a) Real part of input impedance, (b) Imaginary part of input impedance.

impedance is plotted versus frequency for a patch of dimensions L= 2.0cm and W = 3.0 cm on a low-permittivity substrate of moderate thickness (h = 0.1524 cm, corresponding to h/Ao = 0.0254 at S.OGHz), with an aspect ratio of W/L= 1.5. A loss tangent of I , = 0.001 is assumed for the substrate, and a conductivity of


a= 3.0 x lo7 mhoslmeter is assumed for the patch and ground plane. This comparison shows that the simple CAD model in Figure5.3 is an accurate representation of the complete circuit model in Fig. 5.2 over the bandwidth of the patch.

5.1 0 RADIATION PATTERNS

The calculation of far-field radiation patterns from patch antennas is well known. In this section the two basic models that are commonly used, the electric-current model and the magnetic-current model, are reviewed. To obtain simple formulas, the radiation patterns are based on the currents associated with the dominant cavity mode only. In this case it is shown that the two models give exactly the same results, provided that the patch is at resonance. Final formulas are first presented for the rectangular patch on a infinite substrate and ground plane (Figure5.1). Formulas are also presented for the radiation pattern of a patch antenna on a truncated substrate, where the substrate terminates at the edges of the patch (while the ground plane is still infinite). For this case both an electric- and a magnetic-current model may also be used, with both methods again agreeing at resonance. The presentation here follows that in reference 1151.

5.1 0.1 Infinite Substrate

5.10.1.1 Electric-CurrentMode!. The electric-current model for the rectangular patch antenna in Figure 5.1 uses the patch surface current in Eq. (5.54) to determine the far field. The radiation comes from the actual patch current on the substrate, as shown in Figure5.12a. The far-field components Ei (i = 0 or 4) are calculated from

where Ey is the corresponding far-field pattern of a unit-strength horizontal electric dipole in the x direction on top of the inbite substrate at x' = 0, y' = 0, and

k,= kosin0cos4

k, = k , sin 0 sin 4 The dipole pattern Ep is given in Appendix B. Performing the integration, the expression for the far-field pattern becomes

RADIATION PATTERNS 257

J s

FIGURE 5.12 Radiation models for a rectangular patch antenna. (a) Electriccurrent model for an infinite substrate. (b) Magnetic-current model for an infinite substrate. (c) Electric-current model for a truncated substrate. (d) Magnetic-current model for a truncated substrate.

5.10.1.2 Magnetic-Current Mode/. The magnetic-current model is based on applying the equivalence principle to the patch cavity to h d equivalent sources at the boundary [14, pp. 106-110J Assuming an idealized patch cavity with magnetic-wall boundary conditions, only equivalent magnetic currents will exist on the sides on the patch, since the tangential magnetic field is zero on the side walls. The electric field inside the cavity that is used to h d the equivalent magnetic currents is based on the assumption of a patch current given by Eq. (5.54). From Maxwell's equations, the corresponding electric field is

(The primed coordinate system is defined with the origin at the center of the patch surface, on top of the substrate.) The equivalent magnetic currents are found from M, = - A x E, with being the outword normal and E the electric field at the edges of the patch. The edges at x' = +_ L,/2 are termed the "radiating edges" (RE), while the edges at y' = We/2 are termed the "nonradiating edges" (NRE) [16, pp. 122-1231. The expressions for the equivalent magnetic currents at the


edges are M, = YMO, X' = + L,/2 (RE)

where

In the magnetic-current model, most of the radiation comes from the "radiating" edges, since the currents are uniform along these edges, and in the same direction on both edges. The magnetic currents are assumed to reside inside the substrate, as shown in Figure 5.12b. The radiation pattern is found from integrating over these currents. The total pattern comes from the RE and NRE contributions,

E k , 0,4) = EFE(r, 0,4) + EFE(r, 0,4) (5.84) where

EfE(r, 0,4) = 2 cos (k,L,/2) M,E?(~, 6,d; z')dkyy' dy' dzr (5.85)

and

Efm(r, 0,4; 2') d k x X ' dx' dy' (5.86)

In these equations E P ( r , 0,4; z') and E:my(r, 4 4 ; z') are the far-field components of a unit-strength horizontal magnetic dipole at x' = 0, y' = 0, and arbitrary z' (height h - lz'l above the ground plane), in the x or y direction, respectively. For completeness, formulas for these terms are given in Appendix B. Performing the integrations in Eqs. (5.85) and (5.86) yields,

E~(r,0,~)=(2hW.)MoE~(r,0,q5;O)cos - sinc *.W. tanc(kzlh) (";") ( 2 ) (5.87)

and

E Y ~ ~ ( ~ , 0,$) = (2L,h) M,E;""(~, 0,4 ;O) sin - (";")

where

kzl = k o $ m

RADIATION PATTERNS 259

and n, is the index of refraction of the substrate [Eq. (5.50)]. The sinc function appearing in Eq. (5.87) is defined in Eq. (5.18), while the tanc function is defined as

tan (x) tanc (x) = - (5.90)

X

It is proven in reference 15 that the electric-current model [Eq. (5.79)] gives the exact same result as the magnetic-current model [Eq. (5.84) with Eqs. (5.87) and (5.88)], provided that the dimensions of the patch are such that the dominant cavity mode is at resonance, so that k,L, = n. This ensures that the cavity field used to determine the patch surface current (electric-current model) and the magnetic currents at the edges (magnetic current model) is a valid field that satisfies Maxwell's equations.

Figure 5.13 shows the E- and H-plane radiation patterns for a typical patch on a low-permittivity substrate, where the patch length has been chosen to make the p-tch resonant. Only one pattern is shown in each plane, since both models give

- E PLANE --- H PLANE

FIGURE 5.1 3 Radiation patterns (E and H p1ane)for a rectangular patch antenna on an infinite substrate of permittivity E, = 2.2 and thickness h/A, = 0.02. The patch is resonant with WJL, = 1.5.


the same result. The E plane is broader than the H plane, and the pattern in both planes tends to zero at the horizon (0 = 90").

5.1 0.2 Truncated Substrate

The radiation pattern from a patch on a truncated substrate can also be obtained using either an electric-current model or a magnetic-current model. The geometry is the same as in Figure 5.1, except that the substrate terminates at the edges of the patch. The ground plane is assumed to remain infinite, however. In this case the derivations make use of the patterns of dipoles in free space over a ground plane, rather than dipoles.on top of an infinite substrate.

5.10.2.1 Electric-Current Model. The electric-current model uses the same patch current given in Eq. (5.54), but replaces the substrate with equivalent polarization currents Jd and Md. A z-directed electric polarization current exists in the substrate. A y-directed magnetic polarization current will also exist if the substrateis magnetic(p, # 1). Although this is not usually the case in practice, this possibility will be included for completeness. The radiation model is shown in Figure 5.12~. The far-field pattern is obtained from summing the contributions from the patch surface current, the electric polarization current, and themagnetic polarization current so that

where the superscripts s, e, and m denote patch surface current, electric polarization current, and magnetic polarization current, respectively. The contribution from the patch surface current is exactly the same as that in Eq. (5.79) for the in6nite substrate case, provided that E, = 1 and = 1 are used when calculating the dipole pattern E y (which will then be denoted EyO). Therefore, using Eq. (5.79), we obtain

sin (F) cos (F) E;(r, e, 4) = Epo(r, e, 4) (?) )i 1 1 (;y - (L+J

where

~,h '"O(r, e,4) = 2jE0 cos e cos 4 sin (koh cos 0)e-jw cw @

and

E?(r, 0,4) = - 2jE0 sin 4 sin(koh cos 0)e-Wc"*

with

RADIATION PAnERNS 261

The distance r in this last equation is measured from the origin of the primed coordinate system (at the middle of the patch surface) to the far-field observation point.

The far-field contribution from the electric polarization current

is polarized in the 0 direction only. This contribution is found from

where EPO(r, B,$; 0) is the far field of a unit-strength vertical electric dipole at x' = 0, y' = 0, z' = 0 (height h above the ground plane), given as

EPO(r, 8,d; 0) = - 2E0 sin Bcos (kohcos 0)e-jwcO" (5.98)

Substituting Eqs. (5.96) and (5.80) into Eq. (5.97) and performing the integrations, the result is

If the substrate is magnetic, a magnetic polarization current

will exist. The far-field contribution from this current will be

Ey(r, O,$) = ET"yO(r, 8,b; 0) sec (koh cos 8) 1" 1::, J - "" M;(& Y? - L.12

. cos (ko(h + z') cos e ) ~ ( ~ - = ' + kyy') dxl dyJ dzl (5.101)

where E:mYO(r, B,4; 0) are the far-field components from a unit-strength horizontal magnetic dipole in the y direction at x' = 0, y' = 0, z' = 0. These components are given by

2 E'fmO(r, 13~4; 0) = - Eo cos 4 cos (koh cos 0)e- jw case (5.102)

'lo

2 E!$'mO(r, 0, 4; 0) = - - Eo cos 4 sin 4 cos(koh cos 0)e-ikOhc0s8 (5.103)

'lo


Inserting Eqs. (5.100) and (5.54) into Eq. (5.101) and performing the integrations, the result is

5.10.2.2 Magnetic-CurrentModeI. The magnetic-current model for the patch on a truncated substrate is the same as for the magnetic-current model on the infinite substrate, with the substrate replaced by free space. The radiation model is shown i'n Figure 5.12d. The radiation pattern is given by Eq. (5.84) along with Eqs. (5.87) and (5.88), with the terms ETm" and EfmY calculated by assuming that E, = 1 and = 1. In this case (using a 0 superscript again to denote the absence of the substrate), the far-field components E P 0 are given by Eqs. (5.102) and

- E - PLANE --- H-PLANE

FIGURE 5.14 Radiation patterns (E and H plane) for a rectangular patch antenna on a truncated substrate of permittivity 6, = 2.2 and thickness h/& = 0.02. The patch is resonant with W,/L, = 1.5.

CAD FORMULA FOR DIRECTIVITY 263

(5.103). The far-field components EfmX0 are given by

L ~i"O(r, 0,+; 0) = - - 'lo Eo sin 4 cos (koh cos 0)e-~wc0s8 (5.105)

Z E y ( r , 0,+; 0) = - - Eo cos 0 cos 4 cos(koh cos 6)e-jwc"'e (5.106)

'lo

A proof in reference [I51 (similar to the one for the infinite substrate) shows that the electric- and magnetic-current models give the same result for the truncated patch, provided that the dominant cavity mode is resonant (k,L, = n).

Figure 5.14 shows the E- and H-plane patterns for the same resonant patch as in Figure5.13, but with a truncated substrate. In this figure, only one curve is shown for each plane as before, since the two models give the same result. The patterns of the truncated-substrate patch are very similar to those of the infinite substrate patch shown in Figure5.13. The main difference is near the horizon, where the E-plane pattern remains nonzero as 0 approaches 90" in the truncated case.

5.11 CAD FORMULA FOR DIRECTIVITY

In this section a CAD formula for the directivity of a rectangular patch antenna is derived, using the results of the previous section for the radiation pattern along with the results from Section 5.4 for the space-wave power radiated by the patch. The directivity is calculated at broadside, which will always be the maximum directivity (at least for reasonably thin substrates). The CAD formula is derived for the case of a patch on an infinite substrate, although the formula should be fairly accurate for the case of a truncated substrate as well, since the patterns are nearly the same for these two cases except near the horizon. Because the directivity formula is derived from the CAD formula for space-wave power, it has the same property of being more accurate for thinner substrates.

The directivity at 0 = 0, relative to an isotropic radiator, is defined as

where Sr(O,O) is the radial component of the Poynting vector S,(0, 4) in the far- field at broadside, and P,!, is the space-wave power, given by Eq. (5.66). The Poynting vector at broadside is calculated from

where the far-field component E, is related to the far-field of the unit-strength


horizontal electric dipole as

with the far-field component E j;'"(B, 4) given in Appendix B and the equivalent dipole moment me, given in Eq. (5.56). At broadside, we obtain

tan (kohnl) E:..io, 0 ) = 2Eo [ : J tan (kohnl) - j -

where Eo is defined by Eq. (5.95), and the substrate index of refraction is defined in Eq. (5.50). Substituting Eqs. (5.110) and (5.56) into Eq. (5.109) and then using Eqs. (5.108), (5.66), and (5.48) in Eq. (5.107) allows the final CAD formula to be obtained directly. The final result is

where the tanc(x) function appearing in the numerator is defined in Eq. (5.90), and the terms p and c, are defined in Eqs. (5.65) and (5.49), respectively. Equation (5.111) is the final CAD formula for directivity at broadside, relative to an isotropic radiator.

If the substrate is electrically thin, the term inside the square brackets in Eq. (5.111) is nearly unity and can be taken as such. In this case the CAD formula becomes even simpler,

A further simplification can be made if it is assumed that the patch is small enough so that the p factor can be taken to be unity, and if it is further assumed that the substrate index of refraction is large enough so that c, factor can be approximated as unity. In this case, Eq. (5.112) becomes

Equation (5.1 13) indicates that the directivity of a rectangular patch antenna on a thin substrate with a high permittivity will be close to the value of 3.0 (4.77dB) relative to an isotropic radiator. For a typical patch antenna on a low-permittivity duroid substrate, Eq. (5.112) is used with E, = 2.2, WJLe = 1.5, and k,Le = a. Evaluating the p and c, factors, the result for the directivity from Eq. (5.1 12) is D = 6.09 (7.85dB). The directivity thus decreases with increasing permittivity.

CONCLUSIONS 265

- exact ..---.-..--- CAD

FIGURE 5.15 Directivity of a rectangular patch on an infinite substrate versus the -1ectrical thickness of the substrate. The patch is resonant for all substrate thicknesses, WILL WJL, = 1.5. Results for two different substrate permittivities, e, = 2.2 and 10.8, are shown. The CAD formula is compared with results from an exact calculation.

Figure 5.15 shows a plot of directivity versus electrical substrate thickness for a resonant patch with an aspect ratio of We/Le= 1.5. Results are shown for a patch on a low-permittivity substrate and a high-permittivity substrate. The results from CAD formula (5.1 11) are compared with the ' exact directivity, obtained by numerically integrating the radiation power pattern to find the exact space-wave power. For thin substrates, the CAD formula is quite accurate for both the low- and high-permittivity substrates. The CAD formula is accurate for substrate thicknesses up to h/Lo z 0.07 for the low-permittivity substrate, and h/Lo z 0.03 for the high-permittivity substrate.

5.12 CONCLUSIONS

In this chapter, CAD formulas for a rectangular patch antenna have been presented. CAD formulas for the basic characteristics of the patch were presented, including resonance frequency, bandwidth, radiation efficiency, and directivity. These quantities are essentially independent of the specific type of feed. A CAD model for input impedance was also presented, for the specific case of a probe-fed patch. CAD formulas for the resonant input resistance of the probe-fed patch and the probe reactance were given. These formulas, along with


the CAD model, provide a simple means of calculating the input impedance at any frequency near the dominant-mode resonance.

With the exception of the CAD formulas for resonance frequency, the CAD formulas were derived from asymptotic approximations of the corresponding exact quantities, assuming that the substrate is thin compared to a wavelength. These approximations therefore become increasingly accurate as the substrate thickness decreases. Numerical results obtained from a spectral-domain method were presented for the various quantities, to determine the accuracy of the CAD formulas. In all cases, the accuracy improves as the substrate thickness decreases.

The CAD formulas for bandwidth, radiation efficiency, and directivity are the most accurate. They are sufficiently accurate that they may be used as final design equations for substrate thickness up to &h/lo x 0.10. The CAD formula for resonant input resistance loses accuracy sooner, being accurate only up to &h/lo x 0.03.

In additibn to the basic patch properties mentioned above, a comparison of CAD formulas for the radiation pattern of a rectangular patch was presented. Formulas for the radiation pattern based on two different models, the electric- current model and the magnetic-current model, were given. Formulas were given for a patch on an infinite substrate as well as for a patch on a truncated substrate, where the ground plane is infinite but the substrateexists only under the patch. In either case, the electric- and magnetic-current models give exactly the same results, provided that the patch dimensions are such that the dominant cavity mode of the patch is in resonance. The pattern for the truncated substrate case is very similar to that for the infinite substrate, except near the horizon.

APPENDIX A: 'DERIVATION OF THE p FACTOR

In this appendix the p factor in Eq. (5.65) is derived. From the far-field components for a horizontal electric dipole on top of a grounded substrate (see Appendix B), it follows that the far-field power pattern is of the form

where c, is a constant of proportionality. Using the identity

Eq. (5.65) becomes

p =: ~ o n ' 2 ~ ~ ' 2 ( s i n 2 4 cos2 0 + cos2 &Tt(O, 4) 7'; (8, $1 sin Od8d4 (5.116)

From reference [ l q , the following approximations are used for the trigonometric

APPENDIX A: DERIVATION OF THE p FACTOR 267

functions appearing in the functions TI and T,:

where

sin (x) - x 1 + a,x + a4x4 X

Using the above approximations, along with a power series expansion for (1 - x)-', the following approximation is obtained:

where

The term c, may be neglected. Using the above approximations, the expression for the p factor becomes

,, =: !:!:' (sin2 4 cos2 o + cos2 6) sin 6

The evaluation of the integrals in Eq. (5.120) is straightforward, but somewhat tedious. The following identities are used in the evaluation.


Using Eqs. (5.121)-(5.134), Eq. (5.120) reduces to the final result:

which is the same result shown in Eq. (5.65).

APPENDIX B: RADIATION FORMULAS FOR HED AND HMD 269

APPENDIX 8: RADIATION FORMULAS FOR HED AND H M D

In this appendix the final expressions for the far-field of horizontal electric dipole (HED) and a horizontal magnetic dipole (HMD) are given. The HED is assumed to be on the top of the grounded substrate. The H M D is assumed to be embedded at z', corresponding to a height h + z' above the ground plane (the origin is at the center of the patch, on top of the substrate). The HED is assumed to be x-directed, while formulas are given for both the x-directed and y-directed HMD. These formulas are needed in the electric and magnetic current radiation models.

A. x-Directed HED

For an x-directed horizontal electric dipole,

E v ( r , O,+) = E, cos &G(O)

E p ( r , 0 ,4) = - E, sin @(O)

where

2 tan (k,hN(O)) F (e ) =

N ( 4 tan (k,hN(O)) - j - sec 0 P,

2 tan(k,hN(e))cos 0 G(0) =

tan (k,hN(O)) - j L c o s 0 N ( @

and

B. y-Directed H M D

For a y-directed horizontal magnetic dipole, we obtain

E E p ( r , e, 4; z') = 2 cos e c(e) cos(k,(h + z') N ( @ )

' l o I E

E y ( r , 0,4; z') = - 2 cos 0 sin 4 D(0) cos (k,(h + z') N(0))

'lo [ COS (kohN(@) 1


where

- 2 j - L o s e C(6) = N(6)

(5.141) tan (kohN(6)) - j L c o s 6

N(6)

N(6) -2j-sec6 D(6) = K

N(0) (5.142)

tan (kohN(6)) - j -sec 6 P,

C. x-directed HMD

For an x-directed horizontal magnetic dipole, we obtain

REFERENCES

[I] Y. T. Lo, D. Solomon, and W. F. Richards. "Theory and Experiment on Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. AP-27, pp. 137-145,1979.

[2] W. F. Richards, Y. T. Lo, and D. Harrison, "An Improved Theory for Microstrip Antennas and Applications," IEEE Trans. Antennas Propagat., Vol. AP-29, pp. 38-46,1981.

[3] H. A. Wheeler, "Transmission-Line Properties of Parallel Strips Separated by a Dielectric Sheet," IEEE Trans. Microwave Theory Tech., Vol. MTT-13, pp. 172- 185,1965.

[4] D. M. Pozar, "Improved Computational Efficiency for the Moment Method Sol- ution of Printed Dipoles and Patches," Electromagnetics, Vol. 3, pp. 299-309,1983.

[5] E. 0. Hammerstad, "Equations for Microstrip Circuit Design," in Proceedings, 5th European Microwave Conference, pp. 268-272, Hamburg, 1975.

[6] J. R. James, P. S. Hall, and C. Wood, Microstrip Antennas-Theory and Design, Peter Peregrinus, Stevenage, U. K., 1981.

[7] M. V. Schneider, "Microstrip Dispersion," Proc. IEEE, pp. 144-146,1972. [8] S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication

Electronics, 3rd edition, p. 154, John Wiley & Sons, New York, 1993. [9] D. R. Jackson and N. G. Alexopoulos, "Simple Approximate Formulas for Input

Resistance, Bandwidth, and Efficiency of a Resonant Rectangular Patch," IEEE Trans. Antennas Propagat., Vol. AP-39, pp. 407-410,1991.

REFERENCES 271

[lo] D. M. Pozar, "Rigorous Closed-Form Expressions for the Surface-Wave Loss of Printed Antennas," Electron. Lett., Vol. 26, pp. 954-956, 1990.

[ll] D. M. Pozar, "Considerations for Millimeter Wave Printed Antennas," IEEE Trans. Antennas and Propagat., Vol. AP-31, pp. 740-747,1983.

[I21 D. M. Pozar, "Input Impedance and Mutual Coupling of Rectangular Microstrip Antennas," IEEE Trans. Antennas and Propagat., Vol. AP-30, pp. 1191-1196,1982.

(131 J. T. Aberle and D. M. Pozar, "Analysis of Infinite Arrays of One- and Two-Probe- Fed Circular Patches," IEEE Trans. Antennas Propagat., Vol. AP-38, pp. 421-432, 1990.

[14] R. F. Harrington, Time-Harmonic Electromagnetic Fields, McGraw-Hill, New York, 1961.

[15] D. R. Jackson and J. T. Williams, " A Comparison of CAD Models for Radiation from Rectangular Microstrip Patches," Int. J. Microwave Millimeter-Wave Com- puter-Aided Eng., Vol. 1, No. 2, pp. 236-248,1991.

[I61 K. F. Lee and J. S. Dahele, "Characteristics of Microstrip Patch Antennas and Some Methods of Improving Frequency Agility and Bandwidth," Chapter 3 in Handbook o f Microstrip Antennas, Vol. 1, IEE Electromagnetic Wave Series, Vol. 28, Peter Peregrinus, London, 1989.

[I71 M. Abramowitz and I. E. Stegun, Handbook of Mathematical Functions, National L. -eau of Standards AMS 55, Eqs. 4.3.96 and 4.3.98, p. 76, 1972.

CHAPTER SIX

Multifunction Printed Antennas

J. R. JAMES and G. ANDRASIC

6.1 INTRODUCTION

A multifunction antenna is one that is capable of fulfilling a performance specification that would conventionally require two or more separate antennas. The multifunction concept in itself is not new and is a somewhat obvious design aim when space, weight, and equipment costs need to be reduced. For instance, the early curtain wire antenna arrays used for radio broadcasting commonly incorporated several independent arrays that could be switched to operate over different frequency bands and propagation angles, thus economizing in the erection of large supporting towers. Prior to the inception of printed antennas, the benefits of combining two or more functions in one antenna were generally offset by a marked increase in constructional complexity and cost. The latter constructional complexity is evident in fairly recent developments of hybrid scanning antennas [I] and multibeam antennas [2] based on reflector, waveguide, and lens apertures. These antenna systems were evolved largely to satisfy the demands of the defense and satellite communication industries, in an era when cost factors were not critical parameters and commercial sector requirements were not a consideration.

The evolution of microstrip antennas, (or, more generally, printed antennas) [3-81 has brought about a remarkable change in antenna design and not the least in generating multifunction configurations where constructional simplicity and low manufacturing costs are retained. The multifunction antenna concept thus takes on a new prominence when realized in printed antenna technology,


274 MULTIFUNCTION PRINTED ANTENNAS

TABLE 6.1 Modern Systems That Will Benefit and in Some Cases Rely on the Creation of Low-Cost Multifunction Printed Antennas

0 Radar cross-section control of antenna elements and integral radomes. Communication antennas with facilities for multiple bands, polarization agility, interference suppression for EMC, diversity, personnel hazard reduction, etc.

0 Smart skin apertures offering multiple radar arrays, countermeasure facilities, adaptive beam scan, polarization agility, etc. Antennas integrated with sensors in security systems.

0 Antenna elements and arrays for automobile systems for tolling, anticollision radars, communication, etc.

0 Telemetry antenna systems for the utility industries for the direct monitoring of customer accounts and installations.

0 Antenna sensors for in-building wireless local area networks (LANS).

and there is no shortage of applications as outlined in Table 6.1. Defense multifunction system technology [9] and smart skin concepts [lo] provided much of the earlier impetus for aerospace antennas that share a common aperture, but more recently the commercial sector has been the driving force, notable in communications. For instance, a few examples of multifunction printed mobile antennas are:

0 Printed windscreen antennas [ I l l for the reception of multiple band radio and TV broadcast stations in road vehicles.

0 Credit card pager antenna [I23 with facility for switchable polarization control.

0 Adaptive printed antenna elements and arrays [13] mounted on land vehicles [14] and aircraft for reception of Global Positioning Satellites and Satellite communications.

The above examples also serve to emphasize how printed antenna technology has made possible [15] new types of electronic systems in communications, radar and navigation; these systems would not be otherwise feasible with conventional antennas. Furthermore, when the antenna can also perform more than one task, this added value often makes a cost critical commercial application viable.

In this chapter the aim is to focus on some of the more recent advances in multifunction printed antenna technology. The intrinsic printed antenna properties that are compatible with multifunction capabilities will be highlighted at the beginning in an attempt to unify some of the design concepts and also give a possible pointer to future multifunction opportunities and developments.

6.2 PRINTED ANTENNA DESIGN FREEDOM

Most printed antennas are constructed on planar microstrip substrates and are appropriately called microstrip antennas. This also includes the less

PRINTED ANTENNA DESIGN FREEDOM 275

common microstrip slot antennas and coplanar stripline radiators. Variations include multilayered printed conductors and substrates, as well as use of various substrate materials, and in some cases the substrate is replaced by an airspace. Sometimes the radiating elements are printed on thin dielectric films which can be deformed into various shapes to conform to nonplanar surfaces. 'Printed antennas' is a generic term that is understood to embrace the ever-increasing constructional variations that printed technology makes possible.

The advantages and disadvantages of printed antennas have been discussed [15] and are generally well known, although some misconceptions still exist regarding their relative simplistic construction and low cost of manufacture. The latter are only realizable for larger arrays of printed elements when the design parameters and tolerancing are under control; and although progress continues in computer-aided design (CAD) [16], further advances in this respect are

TABLE 6.2 Printed Antenna Intrinsic Design Features That Are Compatible with Multifunction Operation

Substrates . various materials such as dielectrics, ferrites, air, composite material rn Multilayered 0 Anisotropic rn Mechanically or electrically variable material parameters

Superstrates rn Weathershields, antistatic, RCS control 0 Similar design freedom as for substrates above

Printed Conductors 0 Continuous or grid, or strip conductor arrangements 0 Arbitrary conductor shapes rn Stacked proximity conductors 0 Planar proximity conductors 0 Multilayered conductor in multilayered substrate

Feeders 0 Multilayered planar structures rn Proximity coupling rn Back-fed arrangements 0 Arbitrary planar geometry

Conformal Geometry 0 Conductors, sub- and superstrates, and feed system conforming

to any planar or nonplanar surface 0 All structures remain relatively thin

Circuit Integration 0 Compatibility with printed and monolithic integrated circuits rn Active or passive implants readily incorporated 0 Active antenna concepts


required. Isolated printed antenna elements and small printed arrays continue to rely on experimental adjustments prior to manufacture. However, the design aspects of interest in this present chapter concern the intrinsic properties of printed antennas that specifically relate to achieving a multifunction performance and enable novel designs to be continually created. These properties, listed in Table 6.2, provide the designer with much additional design freedom not generally shared by conventional antennas such as reflector, wire, waveguide aperture antennas, and so on.

Most printed antennas embody a substrate in some form, and Table 6.2 notes the variety of options open to the designer regarding the type of material, the geometry, and in some cases the facility for varying the substrate properties by external electrical or mechanical control. When the antenna is to be fitted with superstrate, then similar options exist and the designer has even greater material design freedom. The printed conductors and feeders can be configured in numerous geometric forms with little or no additional manufacturing complexity while the entire antenna assemblies remain thin, with conformal freedom. Finally, the compatibility of printed antenna assemblies with printed and monolithic integrated circuit technology is an outstanding property.

There are numerous examples of multifunction printed antennas, and the most commonly occurring provide dual frequency operation, dual polarization, dual beams, and so on. As mentioned, our aim here is not to collate all these examples but rather attempt to relate and highlight multifunction design trends to intrinsic design parameters of printed antennas. As such we will examine each of the intrinsic design features of Table 6.2 and give illustrative examples, drawn from more recent innovation, where appropriate.

6.3 MULTIFUNCTION ANTENNA DESIGN OPPORTUNITIES AND RECENT ADVANCES

6.3.1 Choice of Substrate Materials and Their Design Potential

In printed antenna technology the substrate physically supports the printed elements and gives the thin planar structure its rigidity and mechanical strength. The substrate has the effect of concentrating the fields beneath the conductors and substrate resonator action is prominent in isolated elements while for feeder lines the substrate controls their electrical length. If the substrate dimensions and/or material properties can be made to be time varying in some way, then the designer has at hand a direct way of changing the printed antenna element resonant frequencies and also the phase distribution of a system of feeders which is the basic requirement for a phased array. The problem is how to bring about the control of substrate properties; in the majority of practical system requirements mechanical control is ruled out. The previous use of biased ferrite material to control antenna characteristics is well known [17-191, and ferrite appears to offer the best prospects for the control of printed antenna substrates. The use of

MULTIFUNCTION ANTENNA DESIGN OPPORTUNITIES AND RECENT ADVANCES 277

variable permittivity dielectric materials in antenna design has been constrained by the absence of suitable materials and particle impregnated materials have been considered [20]. However, there have been some recent developments including also chiral materials, that are described below.

6.3.1.1 Tuning and Polarization Agility. When a printed antenna is mounted on a ferrite substrate, one can expect some reduction in the overall antenna size and bandwidth together with a lowering of the radiation efficiency due to the additional magnetic substrate losses. However, excessive loss may cause the bandwidth to increase. Size reduction has been investigated for a rectangular printed element [21], and more recently the effect of subjecting the antenna to a plasma medium has been studied [22] to simulate the communication black- out phenomenon experienced by antennas mounted on space reentry vehicles. Apparently the presence of the ferrite substrate is desirable in such atmospheres.

When the ferrite substrate is magnetically biased, the resonant tuning characteristics of the printed antenna will be perturbed. Since printed antenna elements are generally weakly radiating printed resonators (i.e, high-Q, narrow bandwidth devices), the shift in resonant frequencies when bias is applied is similar to that for printed resonators; reference [23] presents an exact full-wave analysis for 11,. ?netic field bias directed normally to the plane of the ferrite substrate. Magnetic material loss and how it varies with applied magnetic field bias is clearly a parameter that can be significant. However, ferrite losses generally increase with frequency constraining the choice to commercially available higher-frequency materials. With such a choice of material, few references give details about losses which are presumed to be small. Experimental data on the effect of applying the magnetic field bias along an axis lying in the substrate plane along with the resulting tuning ranges are shown in Table 6.3 and have been measured [24] for a linearly polarized rectangular printed patch. Reasonable co- and cross-polarized radiation patterns were measured over the tuning ranges, but for certain magnetic field bias conditions the cross-polarization levels were high; this suggests interesting implications for circularly polarized patch elements 125,261. Subsequent experiments and computations confirm that several additional antenna functions can be incorporated in the design as follows. The experiments [27] on a square patch printed on a yttrium iron garnet (YIG) film which was

TABLE 6.3 Tuning Range and Magnetic Bias Direction for Rectangular Printed-Patch Antenna [241

Magnetic Bias Tuning Range Direction (GH4 Percentage


deposited on both sides of a gadolinium gallium garnet wafer confirmed that at 5.95 GHz the co- and cross-polarized radiation patterns were of comparable levels when the patch was edge excited by a single probe. Figure 6.1 gives the radiation patterns when the substrate is unbiased. When magnetic field bias is applied in a direction parallel to the plane of the substrate and orthogonal to the antenna E-plane radiation pattern, it was found that the copolarized radiation was not affected but the phase of the cross-polar radiation could be pulled to 90' with respect to the copolar radiation phase. The frequency shift of the cross- polarized radiation is relatively small and may make possible the choice of linear or circular polarization using magnetic field control. This is in contrast to the behavior of a printed antenna on a biased bulk ferrite substrate where the copolarized radiation is tuned by the bias action. Clearly the final design of the thin-film device involves many parameters.

Comprehensive computations [28-301 give a fuller picture of the degree of control of the radiation characteristics that are feasible for a bulk ferrite substrate biased normal to the substrate plane. The shift in the printed element resonant frequency is computed in Figure 6.2 for both right-hand and left-hand circular polarization by different methods. The latter curves track at different frequencies, the choice of which is determined by the polarity of the magnetic field bias. The computations include substrate surface waves which transport some of the available input power away from the printed element. The radiation efficiency due to the substrate waves is shown in comparison to the efficiency for a purely dielectric substrate as a function of bias field in Figure 6.3. If the ferrite substrate has a significant loss, then the radiation efficiency will be further reduced; this could be a disadvantage for some applications. Recent experiments 1311 on an annular ring element printed on YIG substrate demonstrate that good circular polarization is obtained for both the TM,, and TM,, modes with the magnetic field bias normal to the plane of the substrate. Figure 6.4 indicates how the tuning varied with bias and shows the circularly polarized radiation patterns for both modes. A bandwidth of about 1 % and return loss better than - 10 dB was maintained over the range of tuning, and the substrateloss was not significant. In these experiments a small magnet was placed beneath the substrate, but for in-plane bias the magnetic field can be a complete closed circuit and is easier to arrange. Despite the additional functions and agility that this bias-controlled ferrite technology offers, the requirement of a magnetic control circuit represents size, weight, and cost problems for some applications; the speed of switching and temperature sensitivity may also need consideration.

6.3.1.2 Beam Scanning of an Element and Arrays of Elements. The expectation that the beam shape and angular position of an antenna element printed on a biased ferrite substrate can be scanned simply by applying a magnetic field bias is based on earlier work [17-191 several decades ago. In recent experiments the ferrite material has also been deployed as both a substrate and a superstrate; but the latter topic will be nevertheless included in this section, which is predominantly about substrate techniques. Some interesting constraints are associated with


Bias field (Oe)

FIGURE 6.2 Resonant frequency for RHCP and LHCP modes for a square patch on a normally biased ferrite substrate, versus bias field. o FDTD (from reference 30, copyright 0 Annales des Telecommunications); --- cavity model (from reference 28, copyright 0 IEEE).

MULTIFUNCTION ANTENNA DESIGN OPPORTUNITIES AND RECENT ADVANCES

r

100 -

LHCP

9 - i RHcp

I

0 loo0 UXM

Bias field (G)

(a)

9 .g 50

0

1 1

-90 -45 0 45 90

Azimuth angle ( deg ) -

I

FIGURE 6.4 Annular ring patch antenna on normally biased ferrite substrate for two modes of operation. (a) Resonant frequencies versus bias field. (b) Circularly polarized radiation patterns. (From reference 31, copyright 0 IEE.)

0 200 400 600 800 loo0 1200

Bias field (Oe)

FIGURE 6.3 Efficiency versus bias field for RHCP and LHCP modes for a square patch on a normally biased ferrite substrate, versus bias field. Solid dots correspond to dielectric substrate of same geometry. (From reference 28, copyright 0 IEEE.)

the notion of beam scanning the radiation pattern of a printed element. For instance, from elementary physics it is known that plane-wave ray paths are refracted when passing from ferrite media to free space, and the angle of refraction can be controlled by the magnetic bias. In reality, the ferrite slab is not of infinite extent, and the beam emanating from a printed element will be an angular spectrum of plane waves. Even so, it might seem reasonable to expect some change of beam shape with magnetic bias. Against this expectation is the fact that


FIGURE 6.5 H-plane radiation patterns of patch antenna with ferrite superstrate of thickness h, at 8.6 GHz. i and ii are patterns of unmagnetized ferrite with h, = 1 mm and 3mm, respectively. iii is for magnetized ferrite with h, = 3mm. (From reference 33, copyright 0 IEE.)

printed elements have essentially the pattern characteristic of a magnetic dipole, and any significant departure from the latter characteristic will require either an increase in electrical size [32] or some sort of superdirective feed or aperture distribution. Evidence that size and aperture distributions are perturbed by the presence of the ferrite material is indicated in the following recent research on changing an element beam with magnetic field bias. A slab of magnesium-zinc spinel ferrite [33] was placed as a superstrate on a conventional circular patch printed on a thin alumina substrate. On applying in-plane magnetic bias the conventional dipole-like radiation pattern became much more directional as shown in Figure 6.5 and was beam scanned by 30". Some approximate calculations supported the observed effects, but the detailed behavior was considered to embrace leaky-wave and surface-wave action in the ferrite slab. As such the electrical size of the antenna now embraces the active region of the slab as well as the elements and has increased while the aperture distribution is contributed to by complex wave interaction effects. The presence of the ferrite slab increased the insertion loss and reduced the input bandwidth. An analysis of this finite ferrite slab structure, possibly using finite-difference time-domain (FDTD) methods, would no doubt show the extent to which the slab waves contribute to the radiation characteristics. Useful computed solutions for a Hertzian dipole sandwiched between an isotropic substrate and a ferrite superstate [34], both of infinite extent, show that a wide variety of radiation pattern shapes can be achieved depending on the direction of the magnetic bias relative to the superstrate plane. Some computed results for a microstrip dipole element on a ferrite substrate [35] are given in Figure 6.6 and further illustrate the sort of bias effects observed in Figure 6.5, but the latter patterns are clearly affected by the finite extent of the ferrite slab which is not allowed for in the above-mentioned mathematical models. It would appear that both substrates and superstrates


no

Bias field (G)

(b)

FIGURE 6.6 Radiation patterns of microstrip dipole antenna with biased ferrite 3-mrn- thick superstrate at 9 GHz. (a) H-plane patterns with bias field of (i) 600 G and (ii) LOW-G. (b) H-plane beam angle versus bias field. (From reference 35, copyright Elsevier

create similar beam disturbances when biased. Recent experiments [36] on a biased ferrite resonator emphasize the effect of the ferrite material boundary conditions; in this case, however, circular polarization control and not beam scan was reported.

The above scanned element radiation beams are very broad and the engineering challenge is to create a narrow beam printed array of elements on a ferrite structure that is scannable. Obviously the ferrite could be deployed in conventional isolated phase shifters, but the interest here is to integrate the scanning


TABLE 6.4 Performance of Two-Dimensional Traveling-Wave Ferrite-Loaded Millimeter of Printed Dipoles [39]

Wavelength 8 mm Number of elements 22 x 25 = 550 Gain 25 dB Beamwidth 4" to 5O Sidelobes - 13 dB (H plane), - 20dB (E plane) Scan in two-dimensions f 20" to + 30" Loss 3 to4dB VSWR c 1.5 Radiating power 10 kW pulse, mean 20 W Beam switching time 4~ Control circuit vower 8to12W

facility within the printed antenna structure itself. Several researchers have attempted to contribute innovations, and the wave interactions are clearly more complicated that those taking place in the isolated printed element case above. Experiments on 2 x 4 array of circular elements with feeds, printed on a YIG substrate [37], demonstrate beam scanning for different directions of in-plane magnetic bias. The problem with this constructionally simple arrangement is that the magnetic bias changes the element resonant frequency and the ferrite substrate is only effective directly beneath the feeder lines where it controls the feeder electrical length and hence the scan angle. A comprehensive computational investigation of an infinite array of dipole elements printed on a biased ferrite substrate [38] indicates that the degree of scan blindness is adjustable with the magnetic bias, as is the element resonant frequency. Strong substrate mode activity is evident in the numerical analysis, but practical ways of feeding the elements are not considered. A practically realizable array [39] uses the traveling-wave array principle to embrace both the array of printed elements and phase shift functions. A two-dimensional millimeter array demonstrated the scan performance given in Table 6.4 and is applicable to compact radar systems.

Types of ceramics such as barium strontium titanate (BST) can be created so that they have low losses and a relative permittivity that can lie in the range 15 to 10,000 [40-421. The relative permittivity is sensitive to an applied static bias voltage and can be changed by up to 30-54%. Ideas for designing beam scanned leaky wave antennas have been proposed [40] using the BST as a dielectric waveguide; but no details of the bias arrangement were given, other than mention of a bias voltage of 19 kV/cm, which may be incompatible with other voltage- sensitive components in some applications. It is considered 1401 that the bias control circuits would consume little power, unlike the ferrite bias circuits. The use of these dielectric materials is likely to be advantageous at higher frequencies where low loss ferrite is unavailable. A leaky-wave antenna at 40GHz using


Electrode phase shia

FIGURE 6.7 Leaky-wave antenna on BST film biased with electrodes operating at 40GHz (From reference 43, copyright 0 Microwaves & RF.)

a BST 6lm biased with interlaced electrodes 1431 is sketched in Figure 6.7. Unfortunately the change in the relative permittivity of the BST with bias is accompanied with increasing losses; proposals have been made [43] for combinations of BST and high-temperature superconducting electrodes to reduce the loss.

Optically active particles are a well-understood phenomenon in optical materials [44], and there are many examples in organic materials; for instance, a suger-water drop is an example of an isotropic optically active material. In such materials, plane harmonic waves can propagate without change in polarization only if they are circularly polarized, in which case the complex refractive index for left-hand circular polarization differs from that for right-hand circular polarization. In the mid-1980 there was a growing interest in the existence of materials with this activity at lower frequencies, such as in the microwave band; these are generally known as chiral material. Subsequently there has been an upsurge in analytical publications investigating the properties of chiral materials, assuming they can be practically realized, in various waveguide, propagation, and antenna applications, and so on. It was conjectured that chiral materials could be used as substrates for printed antennas [45]; the chiral property might well provide additional design freedom to control polarization, substrate surface waves, and possibly loss effects. Computations of patch antennas on chiral substrates did not indicate such benefits but in fact quantified several additional disadvantages [46]. Measurements on chiral substrates might well suggest other advantages, but the problem at present seems to be the practical realization of this new class of material [47]. Some further discussion of practicalities is given in the next section.


6.3.2 Innovative Use of Superstrates

In most applications, a printed antenna must be protected from the exterior environmental conditions, and some sort of weather shield or cover or aerodynamic radome is required. This leads to the concept of the electrically transparent superstrate in addition to the conventional substrate and the possible other advantages of this thicker radiating structure. Clearly the thickness, composition, and electrical parameters of the superstrate represent additional design freedom. In the extreme case the superstrate can be configured to create lens action [48] and a significant increase in gain; but even in planar superstrates, some degree of lens action is apparent [49]. Very high relative permittivity superstrates and substrates are used in microstrip hyperthermia applicators 1501 to match the device to the surface of the human body. The presence of a radome or indeed any periodic arrangement of material directly in front of large array of antenna elements generally exacerbates scan blindness problems. This has received much attention for dielectric material [51] and has already been mentioned above [38] in relation to ferrite substrates. Some of the more recent innovation features interesting techniques for controlling the radar cross section (RCS) of printed antenna elements and reducing interference effects as follows.

6.3.2.1 Radar Cross-Section (RSC) Control of Printed Antennas. In recent years there has been much effort expended in reducing the RCS of radiating apertures, elements, and arrays for defense applications. It was appreciated that any increase of dissipative loss associated with the antenna will damp down the reflected radar signal 1521, and hence it seemed feasible to use biased femte material as a switchable RCS control to bring about damping or detuning or both. When the antenna frequency and the radar frequency are widely separated as incommunication antennas, RCS control can be achieved by virtue of dispersive nature of the ferrite material itself [53] and no magnetic bias is required.

The switched RCS control of ferrite mounted printed antennas has been the subject of numerous computational studies during the past decade, including the use of both substrates and superstrates. For a substrate alone 1351 and a radome [54], a variety of magnetic field bias directions are dealth with, while reference [55] concentrates on the case of a normally biased substrate. The direction of the magnetic field bias determines the extent to which particular cavity modes of the printed patch antenna are perturbed. This is illustrated [56] in Figure 6.8a where the first resonance is hardly changed when y-direction bias is applied as opposed to the case for x-direction bias in Figure 6.8b where this resonance is shifted upward in frequency. Computed results for a normally biased ferrite substrate supporting a rectangular printed patch [55] illustrate (a) the RCS of cross- polarized scattering in Figure 6.9a and (b) the effect on the input impedance when the magnetic field bias is applied in Figure 6.9b. The application of these ferrite techniques seem reasonably evident whereby the direction of magnetic field bias is chosen to give maximum RCS reduction over the required bandwidth. The above-quoted results do not include a load on the patch antenna; and this will


r

FIGURE 6.8 Radar cross section (RCS) computations of rectangular patch antenna on a biased ferrite substrate lying in the x-y plane. (a) y-directed bias. (b) x-directed bias. - biased ferrite; --- unbiased femte. (From reference 56, copyright 0 IEEE.)

have some additional effect on the RCS. Less clear is the preferredlocation of the ferrite material in relation to the printed patch, and it seems likely that switchable RCS control can be achieved using biased ferrite material as a substrate or superstrate or as a combination of both. Unlike the beam scan control described


O I

FIGURE 6.9 Radar cross section (RCS) of square patch antenna on a normally biased femte substrate. The incident wave angles are 0, = 4; = 45". There is no load on patch antenna. (a) RCS for various conditions. (b) Corresponding patch antenna input impedance versus frequency. (From reference 55, copyright 0 IEEE.)

in Section 6.2.1.2, it would appear that the action is less sensitive to the lateral extent of the ferrite material boundaries. In practice the material dissipative loss in the "off state may not be negligible but is not generally considered to be a problem.


FIGURE 6.10 Radar cross section (RCS) of microstrip patch loaded with resistive skirt. Incident plane wave is at Oi = 70°, +i = 45'. (From reference 58, copyright 0 IEE.) - Unloadedpatch; --- with resistive skirt of resistivity = Zo/2, Z, = free-space impedance.

The direct attachment of either lumped loads or distributed skirt loads to the conducting surface of a patch antenna has been investigated [57, 581, and the concept here is to reduce the RCS at the expense of some loss in gain. This technique gives resonable RCS reduction outside of the resonant frequency of the patch antenna as shown in Figure 6.10; since the substrate is not involved, existing printed radiators can be readily modified. Presumably the loading material must be close to the patch-edge fringe fields for sufficient coupling to take place. It is a matter of interest to note that solar cells have been mounted in close proximity to the conducting surface of a patch antenna with apparently little degradation in the radiation action [59].

6.3.2.2 Interference Suppression for Printed Antennas. The use of lossy superstrates in RCS control can be carried out using various combinations of materials in layers [60]. The choice of materials can be increased by the use of thin resistive sheets [61], and surface waves can be supported by such arrangements [62]. In many communication applications the antenna is not required to embrace RCS control, but it will be an advantage sometimes to obtain some rejection of out of band signals from the antenna structure itself. With this in mind, a thin resistive sheet has been shown [63-651 to exhibit useful frequency selective properties by invoking the tuning behavior of a Salisbury screen absorber. The latter device has a thin conducting sheet positioned a quarter of a free-space wavelength above a ground plane. In practice, the sheet is held in


Thin carbon loaded sheets

Frequency (GHz)

FIGURE 6.1 1 Reflectivity R of thin carbon radome and patch antenna array. e, = 2.3, &,, = 1.05, d = 22.8mm, h = 1.58 mm. - Measured; --- calculated with y, = 0.9 - J.0.5. (From reference 63, copyright 0 IEE.)

position by a dielectric substrate and the spacing is thus reduced by (e,)", where e, is substrate relative permittivity. The conducting sheet plane-wave admittance y, = g + jb is chosen so that g = Y, = free-space admittance and the susceptance b tuned out by adjusting the spacing slightly, so a high degree of absorption is achieved over a narrow band. When the spacing is an integer multiple of half a wavelength, no absorption occurs and the structure should act as a transparent radome when superimposed on a planar printed antenna array as sketched inset in Figure 6.11 together with the computed and measured reflectivity R. The presence of the thin microstrip substrate of height h is seen to have negligible effect on R. The transparency of the structure is illustrated by the measurements in Figure 6.12b, confirming the anticipated behavior for normally incident plane waves. However, the angular spectrum of plane waves making up the broad beam of the printed patch antenna suffer some slight absorption/reflection as evidenced by the change in beam shape in Figure 6.12a. These effects were further investigated by the spectral analysis of a multilayered assembly of thin conducting sheets superimposed on a printed patch element represented by magnetic sources [64, 65) as sketched in Figure 6.13. Computations established that if a four- element printed array was scanned off-boresight by 30°, then the effect of a single-layer structure on the pattern shape is not significant, as shown in Figure 6.14. When two layers spaced a half-wavelength apart are used, a greater rejection of out-of-band signals can be achieved (Figure 6.15).

These rejection characteristics can be controlled in many ways, including (a) the use of multilayer dielectric spacers having different permittivities and (b) the


Elevation angle (deg) (a)

FIGURE 6.12 Characteristics of antenna and radome assembly of Figure 6.11 at 6GHz. (a) Computed E-plane patterns for y, = (l/Z,). -.-No radome; --- d = 25 mm; - d = 50 mm. (b) Loss of gain measured at boresight. (From references 63 and 64, copyright 0 IEE.)

superposition of circuit analogue sheets on the conducting layer [64]. A dual band antenna with interference suppression has been designed [6q that makes use of the periodic transparency of this conducting sheet technique.

Superstates having chiral properties offer additional design freedom that may assist in the above interference suppression technique, but the practical realization of such material has yet to be established, as noted in Section 6.3.1.2. Experiments were carried out [67] using a composite superstrate composed of minute helices packed in a host low-permittivity foam material. Measurements


Thin carbon sheet 2 \

Thin carbon sheet 1 \ Foam

Ground plane

FIGURE 6.1 3 Two-layer radome structure with E, = 2.3, E,~, = 8 , ~ ~ = 1.05, d = 22.8mm, h = 1.58mm; sheets 1 and 2 have y,, = (0.4/Zo) and y,, = (1.2/Zo), respectively.

-90 0 90

Elevation angle (deg)

FIGURE 6.14 Computed radiation patterns of an array of four patch antennas with the carbon radome as in Figwe 6.1 1, scanned off by 30". - No radome; --- d = A0/2 and ya = (l/Zo). (From reference 64, copyright 0 IEE.)

cast doubt on the degree of chirality obtained, and it is likely that the wideband reflectivity response given in Figure 6.16 is due to a combination of complex wave interactions between the helices. The interestingresult is that a window effect was achieved at 13.2 GHz, where the total structure thickness was about one wavelength. A radiating test indicated that the printed patch antenna pattern was largely preserved as before, but a transmission loss of 1.5 dB was experienced, presumably due to multiple scattering effects in the superstrate of helices.


Frequency (GHz)

FIGURE 6.1 5 Reflectivity of antenna and radome assembly of Figure 6.13.-Experi- mental; --- computed.

& - -30 -

-40- Patch antenna feed

FIGURE 6.16 Radome containing chiral material when placed above a patch antenna using the principles explained in relation to Figure 6.11. (From reference 67.)

In conclusion, the various experiments mentioned indicate that the thin conducting sheet interference suppression technique can be deployed in conjunction with a variety of composite superstrates to give additional freedom in the design of the suppression bandwidth. Only planar structures have been dealt with here, but it should be possible to create the same suppression mechanism in


TABLE 6.5 Variations in Printed Conductor Topology and Design Benefits

Variations Design Benefits

Printed conductor shape

Nonresonant conductors

Perturbing devices

Multiple coupled conductors

Circular, square, rectangular, triangular, pentagon, star, elliptic, annular rings, etc.

Wide curved elements for traveling wave action

Conductors with tabs, slots, shorting pins, sequential rotation, etc.

Vertical stacking and side-by-side in plane, in close proximity; parasitic element concepts

-

Trading bandwidth for size, choice of modes, and polarization

Very wideband circularly polarized

Control of bandwidth, beam shape, and polarization; size reduction

Bandwidth extension, dual band operation

a cylindrical structure having applications in omnidirectional base station antenna design.

6.3.3 Printed Conductor Topology

The printed conductor element of a printed antenna can have a wide variety of shapes and forms giving various benefits as outlined in Table 6.5. The most common shapes are rectangular and circular, sometimes possessing tabs, shorting pins, and slots for tuning and polarization control. It is also common practice to place several conducting elements in close proximity, either in stacked arrangement or lying side-by-side to achieve wider operating bandwidths, dual band operation, polarization control, and radiation pattern shaping. Resonant patch conductors can also be realized in coplanar waveguide technology, but applications so far have not been numerous. These design techniques offered by the printed conductor topology are well established and extensively catalogued [15]. There is also no shortage of papers dealing with the precise computation of the behavior of closely spaced printed conductors, and a typical recent example is reference [68].

Variations on these various techniques continue to be reported, and some recent innovation is as follows. Shorting pins can reduce the size of a resonant element and modify radiation characteristics, but recent experiments and theory [69, 701 claim significant dimensional reductions with bandwidth and gain reductions that are not excessive. Only one shorting pin is used on the circular patch as shown in Figure 6.17, and it is observed that a rectangular patch version could also no doubt be referred to as an inverted F antenna [71]. The use of shorting planes in a dual-frequency multilayered patch antenna with self-diplexing action (Figure 6.18) enables the annular ring element to be size reduced [72]. Thin slots in printed conductor elements have a variety of uses. For tuning


FIGURE 6.1 7 Patch antenna with shorting pin to reduce size. (From reference 70.)

I Ground plane

FICURE6.18 Dual-frequency multilayered diplexing patch antenna with shorting planes inserted in the annular ring antenna element. (From reference 72, copyright 0 IEE.)


Ground plane

FIGURE 6.1 9 Oversized slotted patch antenna having high directivity. (From reference 75, copyright o IEE.)

purposes the thin slots alter the length of the current paths in the conductor, thereby creating a tuning mechanism; recent examples of dual band [73,74] and wideband [I361 elements have been described. Wider slots can contribute to the radiation action as in the slotted oversize patch antenna [75] (Figure 6.19) whereby a higher directivity and good pattern control in achieved without a complicated feeder arrangement. The traveling-wave cavity action no doubt reduces the bandwidth, but no details are given in this respect. The concept of controlling the conductor current flow by a thin slot can be extended to create an anisotropic conducting surface. Such a surface composed of thin closely spaced conducting strips has been used with advantage on a printed vertical plate monopole [76], and similar surfaces have been used in microstrip patch elements to control the radiation pattern polarization and coupling [77].

Of the many above ways of configuring the conducting surface of a printed element, the concept of slot inclusions leads to the deployment of mesh-like resonating surfaces and considerable scope for multifunctional performance. These techniques are now presented as follows.

6.3.3.1 Dichroic Conductors. The use of dichroic or frequency-selective surfaces (FSS) in reflector antennas is well known and enables dual-band operation to


Substrate

Patch conductor

at f,

Dielectric spacer

Thii dielectricf ~ e s h ' ~ a t c h conductor film at f,

FIGURE 6.20 Exploded view of dual-band dichroic printed antenna array. The conventional patch array at frequency f,, is able to radiate through the lower-frequency mesh patch array at frequency fL. (From reference 78, copyright IEE.)

be achieved. Similar dual-band operation has been investigated for printed antennas 1781 and shown to be readily feasible. The remarkable thing about the use of the FSS principle in printed structures is the very close proximity of the various conductor surfaces compared to that found in dual-band reflector antenna design [79]. The new technique relies on the fact that a printed conducting element need not be a continuous surface and can in fact be a grid or mesh of conducting strips or wires. Clearly the modified surface influences current flow direction and hence the cross-polarization characteristics, but measurements [78] on several demonstrator arrays establish that this is not a problem. If the mesh conducting element resonates at a frequency f, and the periodic mesh structure has an FSS passband at f,,, then radiation at the latter frequency will pass through the mesh conductor from an adjacent printed antenna as sketched in Figure 6.20. Compact dual-band sandwiched arrays have been designed on this basis [78], and fH is typically 10 f,. A third radiating surface could be added at a still lower frequency of fJ10, and this might serve for low-directivity communication purposes in some applications. Applications for the dual-band dichroic technique include the provision of identification friend or


FIGURE 6.21 E-plane radiation patterns of mesh-type printed 2 x 2 array at 7GHz for two ground-plane constructions, - - , --- Mesh ground plane; - , --- Con- ventional continuous ground plane. (i) Copolar, (ii) Cross-polar. (From reference 80, copyright 0 IEE.)

foe (IFF) antennas on high-gain printed arrays. Another development of the dichroic concept is the use of mesh conducting surfaces for both the printed radiating elements and the printed antenna ground [80]. This structure is also optically transparent if narrow printed strips are used, and the antenna can be mounted in a glass window. Figure 6.21 gives the performance of a four-element mesh array for both a mesh and a continuous ground plane. Further examples have been given [81]. To some extents, this window antenna resembles printed on-glass antennas for automobile windscreens, but the difference is the presence of the mesh ground plane giving greatly reduced radiation in the backward direction. Another use of dichroic printed conductors is to increase the directivity of a primary antenna [82]. This surprising property is due to leaky wave action whereby the dichroic surface leaks out the radiation over a larger aperture area.


FIGURE 6.22 Measured H-plane radiation patterns at 8.26GHz of a microstrip patch element in close proximity to an inductive FSS, for three different spacings between the latter and patch. The spacing is a function of N defined in reference [82]. (From reference 82, copyright 0 IEE.)

An example is given in Figure 6.22 showing the effect of spacing between the primary patch antenna and the dichroic surface. The directivity increases somewhat with the number of superimposed dichroic surfaces used, and the latter can be inductive or capacitive. A conical horn composed of a printed dichroic surface [83] is seen in Figure 6.23 to behave the same as a conventional solid metal horn in the stopband of the conducting surface, but in the pass band of the latter, only the low-directivity waveguide aperture is radiating. Dichroic surface concepts are seen to be a fruitful concept to apply to printed antennas to achieve multifunction performance, and it is likely that much design novelty is yet to come. In particular, the recently introduced concept of "smart" FSS is an important multifunction development. An example using diode control of square loops is reference [102].


Azimuth (deg) ( b )

FIGURE 6.23 Frequency selective horn (FSH) antenna comprised of coaxial square printed elements. (a) Sketch of FSH elements. D = 5.5 mm, L, = 3.1 mm, L, = 5.2mm, u = 12.S0, L = 15.6cm. (b) H-plane radiation patterns at 14.5 GHz. - FSH copolar; --- FSH cross-polar; -0- solid horn; -0- open-ended waveguide. (From reference 83, copyright 0 IEE.)


I '' '1 q A, .-.-.-.- A . . . . . . , Substrate ..' - : .. . . .. .. .. .. ., .:.. . . . .. . . . . . . . - . . . . I f h . . .

\ Ground plane

FIGURE 6.24 Dual-band circular microstrip patch elements with large-frequency separation, typically 41. The design constraints on r,, r,, r,, and r, are described in reference [85] . (From reference 85, copyright IEE.)

6.3.3.2 Antenna Elements with IntegralArrays. The above examples showing that printed antennas comprised of grids behave in a manner similar to that of conventional patch elements suggests that smaller higher-frequency elements could be integrated into regions of the surface as sketched in Figure 6.24. Measurements and calculations [84-871 confirm that this is feasible and numerous practical examples are given. The higher-frequency printed elements in Figure 6.24 can be dimensioned so that their frequency of resonance is a t least four times that of the larger host-printed antenna. All elements can yield good circular polarization using conventional tab and excitation methods [85], but maintaining symmetry of the feeding arrangements underneath the host element is a design issue if the host element's axial ratio is to be controllable [86]. The dimensions of the higher-frequency elements, the annular slots, and element spacing are also constrained by mutual coupling and array grating lobe conditions. The radial passage of cylinderical waves within the host antenna is illustratedin Figure 6.25 and is an additional effect to consider [86] but is far less significant than the radiative coupling. Ways of obtaining a combined dual-


FIGURE 6.25 Sketch of section of dual-band elements of Figure 6.24 illustrating the additional coupling mechanism due to cylindrical waves. (From reference 85.)

frequency dual-beam array system have been proposed [85] and rely on the level of complexity of the supporting feeder arrangements that can be tolerated in any application. The dual-band operation of the host element and its four higher- frequency elements can be converted to a triple-band element by utilizing the separate resonant behavior of the slotted regions. An example of a triple-band cluster of such elements [87] is sketched in Figure 6.26, showing the provision of circular polarization in all bands by way of tabs and cutouts together with the position of the back-fed probes.

6.3.3.3 PrintedSuperconductors. The recent availability of high-temperature superconductors has encouraged research into the benefits of constructing antennas from superconducting material. It was conjectured that electrically small radiators could be designed having very low dissipative loss and hence a high efficiency, but feeder losses were expected to remain a problem unless the feeds themselves were of superconducting materials. These electrically small antennas would not in themselves be multifunctional but could be an integral part of a larger antenna system and are thus of interest here. However, recent research has confirmed the dominant influence of feeder systems on losses [88], that obstacles in the nearby environment can induce additional losses [89], and that superdirective arrays can in some circumstances be achieved without the need of superconductors [138]. Examples of superconducting printed patches with major size reduction [90] remain of interest for certain narrowband applications where the associated cryogenic accessories can be tolerated or are unnecessary as in some space equipment applications.

6.3.4 Quest for Feeder Simplicity

The design freedom associated with feeder configurations is immense, and the multitude of design options is well documented [91,92]. An outline summary of


High-frequency feed

\

/ Low frequency feed

FIGURE 6.26 Triple-band circular microstrip patch and slot elements having circularly polarized radiation patterns. The design constraints on r,, r,, r,, and r, are described in reference [87]. (From reference 87, copyright 0 IEEE.)

some of the salient features of feeder methods is given in Table 6.6 together with a note of problematical issues. It would seem that this magnitude of design freedom would make feeders a rich topic area for practical innovation, but this expectation is not realized in practice. Small two-dimensional arrays of printed conductors containing up to about 20 elements are amenable to experimental development without massive cost; also analytical methods [93,94] for multilayer substrates are becoming available, leading to computer-aided design (CAD) methodologies [95]. Larger two-dimensional arrays offer the greatest challenge for feeder innovation, but only a minority of the community of international printed antenna designers will have the opportunity of practical work experience of such large feeder systems. This and the inability of present CAD software [I61 to accurately model complex large-scale array and feeder systems clearly has a slowing-up effect on feeder innovation where the main thrust has to be reducing manufacturing costs through simpler feeding arrangements while maintaining array performance. Phased arrays of printed elements generally represent yet a further escalation in feeder complexity and hence manufacturing cost. Not surprisingly, recent literature contains little or no substantial advances on the


TABLE 6.6 Some Basic Feeder Methods and Associated Design Problems

Method of connection to a Direct connection or proximity coupled in the printed conductor element conductor plane

a Direct connection or proximity coupled from underneath conductor element

a Feeding from beneath is most suitable for conductor element within a multilayered substrate structure

Type of array feeder a Corporate feeders serve the array elements in a parallel splitting arrangement

a Series feeders excite the elements in line in a series arrangement

Feeds acting as radiators a So-called "chain" and "brick" arrays consisting of rectangular, triangular, and honeycomb-shaped feeder grids whereby the unwanted polarizations are self-canceling

Common feeder design a Dissipative losses, spurious radiation losses, problems achieving matched conditions over the operational

bandwidth, control of cross-polarization performance of array, suppression of unwanted waves in multilayered substrates and hence decreased interelement coupling, etc.

familiar feeder themes [91,92], but there appears to be realization that such feeder configurations and their problems will be best side-stepped using for instance quasi-optical and emerging optical technologies. Some information on these methods is as follows.

6.3.4.1 Quasi-Optical Methods. Zonal reflectors consisting of concentric ridges on a planar surface are well known, and it would appear that the use of printed zonal rings first attracted attention for millimeter-wave systems [96,97]. A completely planar millimeter-wave zonal plate antenna has been designed and evaluated [98], consisting of thin-film metal depositions on a planar dielectric substrate as sketched in Figure 6.27. The illumination at 230 GHz is provided by a resonant printed dipole on the outside surface of the substrate at the focus of the zonal printed ring plate. The investigation deals with the optirnizaton of various dimensions and recommends small adjustments to the geometry of the printed zonal rings to correct for the aberration of the illumination due to the susbstrate. Some illustrative measured and calculated radiation patterns are shown in Figure 6.28, and a performance summary is given in Table 6.7. This millimeter- wave array can be scaled down to lower frequencies and is viable at microwave bands. In the latter bands the gain and sidelobe levels are very competitive with that obtainable from a printed resonator array with a configuration of corporate feeders, but the zonal ring array may have a narrower bandwidth. A similar quasi-optical process is exploited in the reflectarray [139], where the scattering


Antenna and gold leads

Fused h reflector U F u s e d silica 'spacer substrate

FIGURE 6.27 Sketch showing construction of millimeter-wave integrated-circuit Fresnel zonal plate antenna. (a) Front view of zonal ring plates. (b) Sectional view showing printed conductors and substrates. (From reference 98, copyright 0 IEEE.)

FlGURE6.28 E- and H-plane radiation patterns of Fresnel zonal plate antenna at 230GHz corresponding to data in Table 6.7. Theoretical E- and H-plane gain = 24.8 dB. T h e o r y ; -a- measured. (From reference 98, copyright 0 IEEE.)

from printed dipole conductors on a ground-plane backed substrate is brought into focus by perturbing the radiation-phase conditions. This can be done by reactively loading each printed element. Measured and theoretical results for a low-cost array demonstration [99] are given in Table 6.8 and are compatible with a corporately fed array of printed elements. The possibility of electronically scanning the reflectarray using varactor diode reactive loading is discussed in


TABLE 6.7 Measured Performance of Zonal Ring Plate Array [98]"

Focal Length Diameter Gain Beamwidth (degree)

mrn fll mm dl2 N (dB) E plane H plane

2 3.01 20.87 31.46 26 16.5 14.9 23.2 4 6.03 21.13 31.85 22 21.3 7.1 7.1 6 9.04 20.72 31.28 18 25.2 4.5 4.0

10 15.07 21.40 32.26 14 23.3 4.2 3.0

"The parameters are as follows: f = focal length, d = plate diameter, L = wavelength, N =number of half-zones.

TABLE 6.8 Theoretical and Measured Performance of Reflectarray [99]

Measured

Parameter Theory 9.56 GHz 9.75 GHz 10.0 GHz Gain (dBi) 31.5 30.8 30.5 29.6 Beamwidth (degree)

E plane 3.8 4.0 3.8 3.8 H plane 5.0 5.1 5.0 5.2

Sidelobe level (dB) E plane - 24 - 22 -21.5 -20.5 H plane -21 - -17 - -17 - -17

Beam position level (degree) in E plane 25 24.8 24.5 23.6

Cross-polar level (dB) E plane - 26 - 23 - 22.5 H plane -21 -20 - 17

reference [99]. Two large back-to-back arrays [loo] of printed elements act as a lens when corresponding pairs of elements are reactively loaded. The assembly is thin and lightweight and can form part of a quasi-optical scanning system without the complexity of a corporate feeder.

6.3.4.2 Photonic Feedersystem Prospects. An obvious attraction to the use of fiber-optic feeders is their bandwidth and small size whereby conventional printed arrays can be placed in remote locations and fed with long lengths of fibers. The translation of microwave signals to lightwave bands and the reverse process can be effected with off-the-shelf modulators, laser sources, and photo detectors, but noise levels, linearity, and dynamic range need particular consideration for each application. Some generalities are discussed in reference [loll but there is a vibrant, expanding literature on the recent research thrust in this topic to which the reader seeking specific details is referred. Likely future developments include opto-electronic processing of microwave signals and direct physical


integration of opto-electronic assemblies with printed conductor radiators, in such a way as to avoid existing complex microwave feeder configurations.

6.3.5 Conformality

The conformality property of printed antennas whereby radiating elements can be made to fit flush with nonplanar surfaces is indeed an attractive design feature, particularly in mobile aerospace and land vehicle applications. There is of course a price to pay since the antenna array analysis, performance, and manufacture are greatly complicated by conformality. The extent of the complications depends on the surface geometry. For a high degree of surface curvature the conformal array can no longer be calculated in terms of element and array factors. Sidelobes and cross-polarization charactersitics are dominated by the surface geometry, as is mutual coupling, and all the design and manufacturing complexities of the associated feeder systems are compounded by the curvature of the structure. The effective aperture area is also reduced by conformality; and in an extreme case of, say, a convex-shaped body covered with printed elements, only a cluster of near-neighbor elements can be used to create a beam in a given direction. Clearly there must be obvious performance benefits arising from conformality to compensate for the added complexity, and the key here lies in the perceived applications. Our task in this section is more narrowly focused on recent advances, and we first recap typical previous conformal developments prior to asking what recent advances, if any, contribute to multifunction antenna behavior.

Antenna elements and arrays that are conformal with cylindrical surfaces are the most commonly encountered, probably for two reasons. First, a cylindrical conformal antenna is readily assembled in manufacture by rolling-up a sandwiched arrangement of dielectric spacer sheets and thin dielectric films upon which are printed the radiating elements and feeders. Second, the rotational symmetry is compatible with azimuthal omnidirectionality and there are numerous applications for such arrays in communication, radar, guided munitions [103,104], and, more rcently, mobile communications [105]. Examples of the use of other surfaces are not plentiful but include the conical nose cone of missiles [I061 and beam switched arrays on a hemispherical surface [107].

There are also some rather specialized applications in hyperthermia in cancer therapy [108]. It must be pointed out that the term conformal is now increasingly used to indicate that an element or array of elements is mounted on the body of a car or the fuselage of an aircraft, and so on, where the surface is essentially planar with little or no curvature within the confines of the antenna. Conformal- ity in this sense is thus understood to mean low profile or flush, and the array can be designed using planar geometry with appropriate geometrical diffraction theory (GTD) corrections, and so on.

As to recent advances on conformality using printed antennas on highly curved surfaces, we find little of significance and the references above perhaps represent the status quo. Of these, the concept of using the conformal printed radiator on an axially rotating bullet or shell as a spiral radar scan system is


a truly fascinating multifunction application. As regards the wide variety of so-called planar conformal antennas that are flush with equipment housings or vehicle surfaces, and so on, we find added-value diversity functions being incorporated; examples are most commonly found in mobile communication handsets and other portable communication equipment.

6.3.6 Integration of Antennas and Circuits

Microstrip and other printed technologies have been extensively developed for electronic circuits; hence it is no surprise to note the increasing trend towardsJhe integration of printed antennas and their associated circuits. The combining of semiconductor devices and printed antenna elements is likely to be instrumental in creating multifunction radiators because of the additional degrees of design freedom, but clearly the latter is related to how the integration is performed. There would appear to be two categories of integration. For instance, modern circuit technology enables circuits to be placed very close to the printed antenna element, and we refer to this here as a "compact package." In other forms of integration, semiconductors are implanted within the printed element itself; this concept is reminiscent of the so-called "active" wire antennas evolved several decades ago [log]. We note, however, that the term "active" seems to be associated with any type of printed element with compacted circuitry irrespective of whether or not the semiconductors are embedded in the radiator. We now consider the two categories of "active" printed antennas: compact packages and semiconductor loaded elements as follows.

6.3.6.1 Compact Packages. The size reduction of the circuit paths greatly reduces feeder line losses which are deterimental both to transmitting and receiving functions by way of loss of power and degradation of noise figure, respectively. Examples at microwave frequencies of transmitter and receiver broadband designs using a printed patch element have been described [110]. A circularly polarized transmitting printed element is also dealt with [ill]. At millimeter wavelengths (41-42 GHz), transmitting printed patch modules have been designed [l 123 using high electron mobility transistor (HEMT) amplifiers. Slot-coupled feeds tend to be commonly used as well as back-fed probes to bring the circuits in close proximity to the antenna assembly. Emphasis seems to be generally placed on the physical compactness and pattern characteristics maintained with less attention to nonlinear effects and signal integrity. Microwave oscillator integration has been copiously addressed, and there are several reports such as a slot-coupled patch antenna driven from a MESFET oscillator [I 131, various types of coplanar waveguide (CPW)-fed slot antennas [I141 with variable frequency FET oscillator, and so on. In some cases the patch antenna forms part of the planar printed oscillator feedback circuit [I 151, but radiation from the feeder lines is a consideration [I 161. From the multifunction antenna standpoint the most significant contribution is power-combining techniques which enable


large-power outputs to be radiated from an antenna array using several low- power semiconductor devices with innovative circuit interconnections. A four- element array fed with four Gunn diodes [I171 is shown in Figure 6.29a, and the oscillators are locked in the appropriate mode by the strong coupling provided by an interconnecting microstrip line containing chip resistors. Theory and measurement agree well as indicated in Figure 6.29b, which gives the radiation patterns of the four-printed-patch linear array. There are many ways of arranging these power-combining configurations, and oscillator locking can be achieved through the printed elements' mutual coupling mechanism [l 181. Furthermore, individual oscillator devices can be "phased pulled" when frequency-locked to facilitate a beam scan action without the need of separate phase-shifting components [119]. Just how these types of arrays are to be used is seldom elaborated upon, and there may be signal dynamic range and other limitations to consider. The concept of a beam scanned array with simple robust construction is particularly appealing for automobile anticollision systems and the like. Terahertz transmitting modules consisting of integrated configurations of monolithic nonlinear transmission lines and antennas printed on dielectric substrates have been reported [120].

6.3.6.2 Semiconductor Loaded Antennas. When semiconductor devices are loaded into the printed elements themselves, there is some economy in the circuit layout and the radiator is likely to be more versatile in its performance. This is generally the case; but as the following examples illustrate, the benefits in multifunction behavior are application-dependent and involve a variety of different ways of loading the semiconductors into the radiating element. A rectangular printed-patch element with an integral frequency-locked transistor oscillator can be phase-controlled with a varactor diode embedded in the patch [121], thus economizing on varactor bias circuitry. This single-element assembly can be arrayed with similar ones or utilized in orthogonal paired arrangements to form an adaptive polarization-agile radiator 11221. Another interesting use of printed- patch embedded varactors is to correct the element mismatch in a beam scanning array of elements [123]. Ingenious ways of connecting and embedding transistors into printed elements are numerous, with the aim of minimizing bias circuit connections and disturbance of the element geometry. An FET transistor oscillator has been fitted neatly into a slotline ring antenna [124]. A split rectangular-patch arrangement [I191 illustrated in Figure 6.30a allows economical embedding of an FET transistor, and a linear array of four such active elements also provides oscillator locking through mutual coupling, giving good agreement between theory and measurement (Figure 6.30b). A dual FET split- patch arrangement [I251 and the useof circular-patch split pairs [I261 have been described.

Semiconductor-loaded grid antenna arrays [I271 are innovative structures offering both high directivity and power combining. Low-power capability semiconductor devices are integrated into a periodic printed-grid structure whereby the radiating elements also provide the direct-current leads and feeders.


Patch antenna Junction

DC bias /

Gum diode

FIGURE 6.29 Quasi-optical four-element printed-patch array with four integral Gunn diode combining oscillators. (a) Sketch of array. (b) Radiation patterns at 12.45GHz. - Calculated; -- o-- measured. (From reference 117, copyright 0 IEEE.)

MULTIFUNCTION ANTENNA DESIGN OPPORTUNITIES AND RECENT ADVANCES 31 1

Patch antenna r FIGURE 6.30 Four-element locked FET oscillator printed-patch array at 10GH.z. (a) Sketch of layout. (b) H-plane radiation patterns for - 15" scan offset angle. ---Theory; -e- measured. (From reference 119, copyright 0 IEEE.)

31 2 MULTIFUNCTION PRINTED ANTENNAS

The grid itself can consist of printed dipoles or bow-tie dipoles or slots or any other form of element that serves as a multipurpose bias and feed network. Methods of modeling various grid configurations at microwave wavelengths have been presented 11281, and a sketch of a typical array arrangement is shown in Figure 6.31 where the inclusion of the mirror ground plane creates a Fabry- Perot cavity which facilitates oscillator locking. The radiation pattern for a MESFET grid oscillator system is shown in Figure 6.32, and the use of Gunn diodes has also been investigated [127]. Printed-grid oscillator arrays are particularly attractive at millimeter wavelengths 11291, and various types have been demonstrated at submillimeter wavelengths using ~ose~hson- junction oscillators 11301. Other design variations include the use of (a) orthogonal slot dipoles in a quasi-optical amplifier cell El311 to demonstrate a superior bandwidth compared with that obtained from grid arrays and (b) a MESFET transmission wave amplifier offering an independent choice of output polarization [132].

Two techniques using diodes in conventional arrays are described 11333. Varactor diodes loaded into the microstrip feeder of a proximity coupled patch traveling-wave linear array enable electronic beam scanning to be performed in a simple economical way. The physical layout is shown in Figures 6.33a and 6.33b, and a typical scanned radiation pattern is shown in Figure 6.33~. In another design a linear array of printed-patch elements with integral diodes enables the receiving mixer function to be embraced within each element together with beam-combining facilities. A superstrate polarizer blocks off radiation emergingfrom the presence of a local oscillator signal in each element as sketched in Figure 6.34, and an exploded view of the antenna under test is shown in Figure 6.35.

6.4 POSSIBLE FUTURE DEVELOPMENTS

6.4.1 Impact of New Materials

Of the intrinsic design features listed in Table 6.2, only substrates and superstrates are likely to be affected by the discovery of improved materials and composites. If substantial improvements occur, then the impact on multifunction printed antennas could be profound. For instance, both existing ferrite and ceramic materials incur dissipative losses and require problematical biasing arrangements for electronic control. A ferrite material operating at significantly higher frequencies, with a lower level of magnetic field control and less sensitivity to temperature changes, would be a breakthrough in many respects, but present material trends give no strong indication that such an advance is likely. For ceramic materials it is the high-voltage biasing field which limits its usage, and one might hope that in the future a few volts bias would suffice. Other material advances that would be welcomed include the realization of an effective chiral microwavematerial, new high-temperature superconductor materials that can be

POSSIBLE FUTURE DEVELOPMENTS 31 3

Substrate

Active grid Dielectric slab

FIGURE 6.31 Sketch of a quasi-optical power combining grid array configuration. (From reference 127, copyright IEEE.)

FIGURE 6.32 Radiation patterns for MESFET grid oscillator array at microwave frequencies. - E plane; --- H plane. (From reference 127, copyright 6 IEEE.)

31 4 MULTIFUNCTION PRINTED ANTENNAS

DC connection

(a)

FICURE6.33 Varactor-diode-controlled traveling-wave microstrip linear array. (a) Sketch of physical layout showing decoupling capacitor C,. (b) Photograph of 13-element varactor controlled array. (c) H-plane radiation patterns of 13-element array at 7.5 GHz for two values of varactor bias voltage VB - Measured;--- theory. (From reference 133, copyright IEE.)

POSSIBLE FUTURE DEVELOPMENTS 315


Local oscillator Polarizer \

, . Ground plane Substrate

FIGURE 6.34 Sketch of integral mixer antenna array showing superimposed polarizer. (From reference [133], copyright IEE.)

advantageously applied to large-array feeder systems and optical materials giving rise to higher-performance photonic devices for printed antenna array interconnections.

6.4.2 The Application Drivers

The intrinsic design features of Table 6.2 associated with conductors, feeders, conformal geometry, and circuit integration are far from exhausted; new ideas continue to give rise to innovation,initiated by fresh applications which are the drivingforces. It is difficult to predict new applications without an insight into the need, as is well appreciated, but it is instructive to look through the list of modern


FIGURE 6.35 Photograph of eight-element integral mixer antenna array with polarizer removed. (From reference 133, copyright G IEE.)

systems in Table 6.1 commenting on what else might develop from the present knowledge base.

To begin with, one might expect that applications from the civil sector will be more significant drivers than those from the defense sector, at least in the present era of leveling-out defense markets; lower cost antenna systems thus acquire added significance as does the concept of multifunctionality. The "smart skin" antenna concept [134,135] for defense aerospace systems involving multilayered electronically controlled materials will no doubt spin off in some way into commercial ventures or at least alter systems thinking; that is, designers will expect to allocate a region on an automobile or static equipment, and so on, that will accommodate all antenna requirements rather than bolt on radiators in any available space.

Mobile communications is an obvious growth area demanding numerous types of antennas with multiband, agile polarization, agile beam control, in-built diversity capabilities, and compatibility with EMC, yet static in-building wireless systems promise equal massive demands for "smart" user-friendly antennas in harmony with the furnishings. Optical sensors [I371 now compete with antennas for these wireless systems, and acoustic wave emitting devices are also useful for switching and relaying lower information. Whilst increasing use will be made of the whole of the natural spectrum of waves, RF and microwave radiation has advantageous floodlighting and penetration properties that will find increasing

REFERENCES 317

use in security, tolling, and telemetry systems, and this in turn is already heralding an unprecedented demand for all sorts of low-cost, robust antennas that can carry out many functions.

6.5 CONCLUSIONS

1. Printed antenna technology is seen to present designers with untold design freedom, enabling them to create antenna devices that can carry out more than one function. This, in turn, stimulates new system ideas, and there seems to be no end to the innovation being experienced with both the antennas themselves and the novel system applications.

2. Although defense requirements have provided the impetus in the past, it is the civil sector markets now that are also the drivers. Mobile and static communication systems are a massive growth area, but the growing attention to security and automatic remote monitoring systems is also impacting.

3. Printed antenna technology has a reliance on the availability of materials for substrates and superstrates, and photonic devices are becoming increasingly relevant in antenna feeder design. Any future advances in materials and photonics is likely to provide the multifunction printed antenna designer with even more design freedom.

REFERENCES

[I] R. J. Mailloux, Chapter 5, in Handbook of Antenna Design, A. W . Rudge, K. Milne, A. D. Olver and P. Knight, eds., IEE, Peter Peregrinus, London, 1982.

[2] L. J. Ricardi, Chapter 6, in Handbook of Antenna Design, A. W . Rudge, K. Milne, A. D. Olver, and P. Knight, eds., IEE, Peter Peregrinus, London, 1982.

[3] IEEE Trans Antennas Propagat., Special issue on microstrip antennas, Vol. AP-29, 1981.

[4] I. J. Bahl and P. Bhartia, Microstrip Antennas, Artech House, Dedham, MA, 1980. [5] J. R. James, P. S. Hall, and C. Wood, Microstrip Antenna Theory and Design, IEE,

Peter Peregrinus, London, 1981. [6] G. Dubost, Flat Radiating Dipoles and Applications to Arrays, Research Studies

Press, Letchworth England, 1981. [7] J. R. James and P. S. Hall, eds., Handbook of Microstrip Antennas, IEE, Peter

Peregrinus, London, 1989. [8] D. M. Pozar and D. H. Schaubert, eds., Microstrip Antennas, IEEE Reprint book,

IEEE, New Jersey, 1995. [9] R. Hallendorf, "Multifunction System Technology," J. Electron. Defense, 28-44,

1991. [lo] R. J. Mailloux, "Antennas and Radar," Microwave J., 28-33,1988.


[11] H. K. Lindenmeier, L. Reiter, J. Hopf, K. Fujimoto, and K. Hirasawa, Chapter 5, in Mobile Antenna Systems Handbook, K. Fujimoto and J. R. James, eds., Artech House, Dedham, MA, 1994.

[I21 R. Mumford, Q. Balzano, and T. Taga, Chapter 4, in Mobile Antenna Systems Handbook, K . Fujimoto and J. R. James, eds. Artech House, Dedham, MA, 1994.

[13] T. Shiokawa, S. Ohmori, and T. Teshirogi, Chapter 6, in Mobile Antenna Systems Handbook, K . Fujimoto and J. R. James, eds., Artech House, Dedham, MA, 1994.

[14] R. E. Munson, "Conformal Antennas for Smart Cars," in IEEE Aerospace Applica- tions Conference Proceedings, pp. 325-332,1994.

[I51 J. R. James and P. S. Hall, eds., Chapter 1, in Handbook of Microstrip Antennas, IEE, Peter Peregrinus, London, 1989.

[16] D. M. Pozar and J. R. James, "A Review of CAD for microstrip Antennas and Arrays, " in Microstrip Antennas, IEEE Reprint book, D. M. Pozar and D. H. Schaubert, eds., IEEE, New Jersey, 1995, pp. 51-56.

[I71 D. J. Angelakos and M. M. Korman, "Radiation from Ferrite-Filled Apertures, . Proc. IRE, Vol. 44, pp. 1463-1468,1956.

[I81 E. Stem and G. N. Tsandoulas, "Ferroscan: Toward Continuous-Aperture Scann- ing, "IEEE Trans. Antennas Propagat., Vol. AP-23, pp. 15-20,1975.

[19] N. Okamoto, "Electronic Lobe Switching by 90" Corner Reflector Antenna with Ferrite Cylinders," IEEE Trans. Antennas Propagat., Vol. AP-23, pp. 527-531, 1975.

[20] I. J. Bahl and P. Bhartia, "Leaky Wave Antennas Using Artificial Dielectric at Millimeter Wave Frequencies, "IEEE Trans. Microwave Theory Tech., Vol. MTT- 28, pp. 1205-1212,1980.

[21] N. Das and S. K. Chowdary, "Rectangular Microstrip Antenna on a Ferrite Substrate," IEEE Trans. Antennas Propagat., AP-30, pp. 499-502,1982.

[22] S. S. Pattnaik, R. K. Mishra, and N. Das, "Microstrip Antenna on a Ferrite Substrate in Plasma Medium, Indian J . Radio Space Phys., Vol. 20, pp. 417-419, 1991.

[23] K. Araki, D. I. Kim, and Y. Naito, "A Study on Circular Disk Resonators on a Ferrite Substrate, IEEE Tram. Microwave Theory Tech., Vol. MTT-30, pp. 147-154,1982.

[24] D. M. Pozar and V. Sanchez, "Magnetic Tuning of a Microstrip Antenna on a Ferrite Substrate," Electronics Lett., Vol. 24, pp. 729-730, 1988.

1251 H. How, P. Rainville, F. Harackiewicz, and C. Vittoria, "Radiation Frequencies for Magnetically Nonsaturated Ferrite Patch Antennas" [Abstract], J. Appl. Phys., Vol. 73, p. 6469,1993.

1261 J. S. Roy, P. Vaudon, A. Reineix, F. Jecko, and B. Jecko, "Circularly Polarised Far Fields of an Axially Magnetised Circular Ferrite Microstrip Antenna," Microwave Opt. Tech. Lett., Vol. 5, pp. 228-230, 1992.

[27] P. J. Rainville and F. J. Harackiewicz, "Magnetic Tuning of a Microstrip Patch Antenna Fabricated on a Ferrite Film,"IEEE Microwave Guided Wave Lett., Vol. 2, pp. 483485,1992.

1281 D. M. Pozar, "Radiation and Scattering Characteristics of Microstrip Antennas on Normally Biased Ferrite Substrates," IEEE Trans. Antennas Propagat., Vol. 40, pp. 1084-1092,1992.

REFERENCES 319

[29] D. M. Pozar and D. H.-Y. Yang, Correction to reference 28, IEEE Trans. Antennas Propagat. Vol. 42, pp. 122-123,1994.

[30] A. Reineix, C. Melon, T. Monediere, and F. Jecko, "The FDTD Method Applied to the Study of Microstrip Patch Antennas with a Biased Ferrite Substrate," Ann. Telecommun., Vol. 49, pp. 137-142, 1994.

[31] K. K. Tsang and R. J. Langley, "Annular Ring Microstrip Antennas on Biased Ferrite Substrates," Electron. Lett., Vol. 30, pp. 1257-1258, 1994.

[32] K. Fujimoto, A. Henderson, K. Hirasawa, and J. R. James, Small Antennas, Research Studies Press, 1987.

[33] A. Henderson and J. R. James, "Magnetised Microstrip Antenna with Pattern Control," Electron. Lett., Vol. 24, pp. 45-47, 1988.

[34] I. Y. Hsia and N. G. Alexopoulos, "Radiation Characteristics of Hertzian Dipole Antennas in a Nonreciprocal Superstate-Substrate Structure," IEEE Trans. An- tennas Propagat., Vol. 40, pp. 782-790,1992.

[35] H.-Y. Yang and N. G. Alexopoulos, "Printed-Circuit Antennae on Non-reciprocal Magnetic Thin Films," Thin Solid Films, Vol. 216, pp. 189-197,1992.

[36] A. Petosa, R. K. Mongia, A. Ittiboon, and J. S. Wight, "Switchable LP/CP Ferrite Disk Resonator Antenna," Electron. Lett., Vol. 31, pp. 148-189, 1995.

[37] H. How and T.-M. Fang, "Magnetic Steerable Ferrite Patch Antenna Array," IEEE Trans. Magn., Vol. 30, pp. 4551-4553, 1994.

[38] N. E. Buris, T. B. Funk, and R. S. Silverstein, "Dipole Arrays Printed on Ferrite Substrates," IEEE Trans. Antennas Propagat., Vol. 41, pp. 165-176, 1993.

[39] E. F. Zaitsev, Y. P. Yavon, Y. A. Komarov, A. B. Guskov, and A. Y. Kanivets, "MM-Wave Integrated Phased Arrays with Ferrite Control," IEEE Trans. An- tennas Propagat., Vol. 42, pp. 304-310,1994.

[40] V. K. Varadan, V. V. Varadan, and K. A. Jose, "Electronically Steerable Millimeter Wave Antennas, Proc. SPIE, Vol. 2189, pp. 184-192,1994.

[41] V. K. Varadan, D. K. Ghodgaonkar, V. V. Varadan, J. F. Kelly, and P. Glikerdas, "Ceramic Phase Shifters for Electronically Steerable Antenna Systems," Microwave J., pp. 116-127, 1992.

[42] R. W. Babbitt, T. E. Koscica, and W. C. Drach, "Planar Microwave Electro-optic Phase Shifters," Microwave J., pp. 63-79, 1992.

1431 0. Vendik and L. T. -Martirosyan, "Superconductors Spur Application of Fer- roelectric Films," Microwave & RF, pp. 67-70,1994.

[44] C. F. Bohren and D. R. Huffman, Absorption and Scattering of light by Small Particles, John Wiley & Sons, New York, 1983, Section 8.3, p. 185.

[45] N. Engheta, "Chiral Substrate in Microstrip Antennas: Chirostrip Antennas," in Proceedings, Progress in Electromagnetics Research Symposium (PIERS), Cambridge, MA, 1989.

[46] D. M. Pozar,"Microstrip Antennas and Arrays on Chiral Substrates," IEEE Trans. Antennas Propagat., Vol. 40,1260-1263,1992.

[47] S. Ougier, I. Chenerie, and S. Bolioli, "How to Tailor and Orientate Metallic Helices to get Microwave Chirality," in Proceedings of PIERS, 12-16 July, 1993, p. 625.

[48] J. R. James, C. M. Hall, and G. Andrasic, "Microstrip Elements and Arrays with Spherical Dielectric Overlays," IEE Proc., Vol. 133, Part H, pp. 474-482, 1986.

320 MULTIFUNCTION PRINTED ANTENNAS REFERENCES 321

[49] N. G. Alexopoulos and D. R. Jackson, "Fundamental Superstrate (cover) Effects on Printed Circuit Antennas," IEEE Trans. Antennas Propagat., Vol. AP-32, pp. 807- 816,1984.

[50] J. R. James, A. Henderson, and R. H. Johnson, Chapter 4, in Physical Techniques in Clinical Hyperthermia, J. W. Hand and J. R. James, eds., Research Studies Press, Letchworth England, pp. 149-209, 1986.

[51] J.-P. R. Bayard, Analysis of Infinite Arrays of Microstrip-Fed Dipoles Printed on Protruding Dielectric Substrates and Covered with a Dielectric Radome," IEEE Trans. Antennas Propagat., Vol. 42, pp. 82-89,1994.

[52] D. R. Jackson, "The RCS of a Rectangular Microstrip Patch in a Substrate- Superstrate Geometry," IEEE Trans. Antennas Propagat., Vol. 38, pp. 2-8, 1990.

[53] K. Fujimoto, A. Henderson, K. Hirasawa, and J. R. James, Small Antennas, Research Studies Press, Letchworth England, pp. 252-256,1987.

[54] D. M. Pozar, "A Magnetically Switchable Ferrite Radome for Printed Antennas," IEEE Microwave Guided wave Lett., Vol. 3, pp. 67-69 1993.

[55] D. M. Pozar, "RCS Reduction for a Microstrip Antenna Using a Normally Biased Ferrite Substrate," IEEE Microwave Guided Wave Lett, Vol. 2, pp. 196-198,1992.

[56] H.-Y. Yang, J. A. Casteneda, and N. G. Alexopoulos, The RCS of a Microstrip Patch on an Arbitrarily Biased Femte Substrate," IEEE Trans. Antennas Propagat., Vol. 41, pp. 1610-1614,1993.

[57] J. L. Volakis, A. Alexanian, J. M. Jin, and C. L. Yu, "Radar Cross Section Analysis and Control of Microstrip Patch Antennas," in Proceedings of the IEEE Antennas and Propagation Society International Symposium, 18-25 July 1992, pp. 2225-2228.

[58] J. L. Volakis, A. Alexanian, and J. M, Lin, "Broadband RCS Reduction of Rectangular Patch by Using Distributed Loading," Electron. Lett., Vol. 28, pp. 2322-2323,1992.

[59] M. Tanaka, Y. Suzuki, K. Araki, and R. Suzuki, "Microstrip Antenna with Solar Cells for Microsatellites," Electron. Lett., Vol. 31, pp. 5-6,1995.

[603 W. Gesang, E. Rothwell, K. M. Chen, K. Burket, W. P. Hansen, and J. L. Lin, "Receiving and Scattering Characteristics of an Imaged Monopole Beneath a Lossy Sheet," IEEE Trans. Antennas Propagat., Vol. 41, pp. 287-293,1993.

[61] T. B. A. Senior, "Combined Resistive and Conductive Sheets," IEEE Trans. Antennas Propagat., Vol. 33, pp. 577-579,1985.

[62] J. H. Richmond, "Propagation of Surface Waves on a Thin Resistive Sheet or a Coated Substrate," Radio Sci., Vol. 22, pp. 825-831,1987.

[63] A. Henderson, A. A. Abdelaziz, and J. R. James, "Microstrip Planar Array with Interference Suppression Radome," Electron. Lett., Vol. 28, pp. 1465-1466,1992.

1641 A. Henderson, A. A. Abdelaziz, and J. R. James, "Investigation of Interference Suppression Radome for Microstrip Arrays," Proceedings of the ICAP, Edinburgh, 1993, pp. 995-998,

[65] S. C. Griffiths, '"The Electromagnetic Analysis of a Two Layer Interference Suppression Radome Cover," unpublished student's report, 1993.

[66] A. A. Abdelaziz, A. Henderson, and J. R. James, "Dual Band Planar Antenna with Interference Suppression" IEE Colloq. Multi-band Antennas, Digest No. 19921181, 1992.

1671 A. Henderson, unpublished notes. [68] H. R. Hassani and D. M. Syakhal, "Study of Electromagnetically Coupled Stacked

Rectangular Patch Antennas," IEE Proc. Microwave Antenna Propagat., Vol. 142, pp. 7-13,1995.

[69] M. Sanad, "Effect of the Shorting Posts on Short Circuit Microstrip Antennas," in Proceedings of the IEEE Antenna Propagation Symposium, pp. 794-797,1994.

[70] R. Waterhouse, "Small Microstrip Patch Antenna," Electron. Lett., Vol. 31, pp. 604-605,1995.

[71] K. Fujimoto and J. R. James, eds., Mobile Antenna Systems Handbook, Artech House, Dedham, MA, 1994, Appendix, Glossary, p. 568.

[72] H. Iwasaki and Y. Suzuki, "Dual Frequency Multilayered Circular Patch Antenna with Self-Diplexing Function," Electron. Lett., Vol. 31, pp. 599-601, 1995.

[73] D. S. Hernandez and I. Robertson, "Duel Band Microstrip Rectangular Patch Antenna Using a Spur-Line Filter Technique," in 23rd European Microwave Conference Proceedings, Turnbridge Wells, UK, 1993, pp. 357-360.

[74] S. Maci, G. F. Avitabile, F. Bonifacio, and L. Borselli, "A Multiresonant Slotted Patch, in 23rd European Microwave Conference Proceedings, Turnbridge Wells, UK, 1993, pp. 341-344.

[75] H. Legay and L. Shafai, "Radiation Characteristics of Slotted Oversize Patch Antennas," Electron. Lett., Vol. 30, pp. 616-617, 1994.

[76] G. Andrasic, R. Drewett, I. Morrow, and J. R. James, "New Anisotropic Mono- pole Bandwidth Extension Concept, Electron. Lett., Vol. 30, pp. 1998-2000, 1994.

[77] J. M. Baracco, A. Roederer, and P. Brachat, "Dual-Polarisation Gridded Micro- strip Radiating Element," Electron. Lett., Vol. 31, pp. 419-421, 1995.

[78] J. R. James and G. Andrasic, "Superimposed Dichroic Microstrip Antenna Ar- rays," IEE Proc., Vol. 135, Part H, pp. 304-312,1988.

[79] W. V. T. Rusch, T. S. Chu, A. R. Dion, P. A. Jensen, A. W. Rudge, and W. C. Wong, Chapter 3, in Handbook of AntennaDesign, A. W. Rudge, K. Milne, A. D. Olver, and P. Knight, eds., IEE, Peter Peremus, London, 1982.

[80] G. Andrasic and J. R. James, Microstrip Window Array, Electron. Lett., Vol. 24, pp. 96-97,1988.

[81] M.-S. Wu and K. Ito, "Basic Study on See-Through Microstrip Antennas Con- structed on a Window Glass, in "Proceedings of the IEEE Antennas and Propaga- tion Society International Symposium, 18-25 July, 1992, pp. 499-502.

[82] J. R. James, S. J. A. Kinany, P. D. Peel, and G. Andrasic, "Leaky-Wave Multiple Dichroic Beamformers," Electronics Lett., Vol. 25, pp. 1209-1211, 1989.

1831 J. C. Vardaxoglou, R. D. Seager, and A. J. Robinson, "Realisation of Frequency Selective Horn Antenna Excited from Passive Array," Electron. Lett., Vol. 28, pp. 1955-1956,1992.

[84] M. Negev and C. Samson, "Integrating Multi-channel and Multi-frequency Micro- strip Antenna Array, Microwave & RF Eng., pp. 41-44,1989.

[85] A. Abdelaziz, A. Henderson, and J. R. James, "Dual Band Circularly Polarised Microstrip Array Elements," in Proceedings of the JINA, Nice, France, 1990, pp. 321-324.

322 MULTIFUNCTION PRINTED ANTENNAS REFERENCES 323

[86] A. Henderson, A. Abdelaziz, and J. R. James, Mutual Coupling Between Dual- Band Microstrip Antenna Array Elements, Proceedings of the ICAP, York, 1991, pp. 1348-1351.

[87] A. Abdelaziz, A. Henderson, and J. R. James, "A Multiband Circularly-Polarised Antenna Element," in Proceedings of the ICEAA, Torino, 1991, pp. 429-432.

[88] L. P. Ivrissimtzis, M. J. Lancaster, and M. McN. Alford, "Supergain Printed Arrays of Closely Spaced Dipoles Made of Thick Film High-Tc Superconductors," IEE Proc. Microwave Antennas Propag., Vol. 142, pp. 26-34,1995.

[89] J. R. James and G. Andrasic, Environmental Coupling Loss Effects in Supercon- ducting H F Loop Antenna Design," IEE Proc. Microwave Antennas Propagat., VOI 141, pp. 94-100,1994.

[90] H. Chaloupka, N. Klein, M. Peiniger, H. Piel, A. Pischke, and G. Splitt, "Miniatur- ized High-temperature Superconductor Microstrip Patch Antenna," IEEE Trans. Microwave Theory Tech., Vol. 39, pp. 1513-1521, 1991.

[91] J. R. James and P. S. Hall, eds., Chapters 1 and 14, in Handbook of Microstrip .Antennas, IEE, Peter Perigrinus, London, 1989.

[92] J. P. Daniel, G. Dubost, C. Terret, J. Citerne, and M. Drissi, "Research on Planar Antennas and Arrays: 'Structures Rayonnantes'," IEEE Antennas Propagat. Mag., Vol. 35, pp. 14-38, 1993.

[93] N. I. Herscovici and D. M. Pozar, "Analysis and Design of Multilayer Printed Antennas: A Modular Approach, "IEEE Trans. Antennas Propagat., Vol. 41, pp. 1371-1378,1993.

1941 L. Barlatey, H. Smith, and J. Mosig, "Printed Radiating Structures and Transitions in Multilayered Substrates," Internat. J . Microwave and Millimeter-Wave Com- puter-Aided Eng., Vol. 2, pp. 273-285, 1992.

[95] N. I. Herscovici and D. M. Pozar, "CAD of Multilayer Feeding Networks," Microwave J., pp. 84-96, 1994.

[96] B. Huder and W. Menzel, "Flat Printed Reflector Antenna for mrn-Wave Applica- tions,'' Electron. Lett., Vol. 24, pp. 318-319, 1988.

[97] D. N. Black and J. C. Wiltse, "Millimeter Wave Characteristics of Fresnel Zone Plates," IEEE M T - S Dig., Las Vegas, pp. 437-440,1987.

[98] M. A. Gouker and G. S. Smith, "A Millimeter-Wave Integrated-Circuit Antenna Based on the Fresnel Zone Plate," IEEE Trans. Microwave Theory Techn., Vol. 40, pp. 968-977,1992.

1991 M. Patel and J. Thraves, "Design and Development of a Low Cost, Electronically Steerable, X-Band Reflectarray Using Planar Dipoles," Microwaves 94, Wembley, London, pp. 174-179,1994.

[loo] D. T. McGrath, "A Lightweight constrained Lens for Wide Angle Scan in Two Planes," in Proceedings, 1986 Antenna Applications Symposium, Robert Allerton Park, September 1986.

[ lo l l M. L. VanBlaricum, "Photonic Systems for Antenna Applications," IEEE An- tennas Propagat. Mag., Vol. 36, pp. 30-38,1994.

[I021 T. K. Chang, R. J. Langley, and E. A. Parker, "An Active Square Loop Frequency Selective Surface," IEEE Microwave Guided Wave Lett., Vol. 3, pp. 387-388, 1993.

[I031 J. R. James, P. S. Hall, and C. Wood, Microstrip Antenna Theory and Design, IEE, Peter Peregrinus, London, 1981.

[I041 E. V. Sohtell, Chapter 22,in Handbook of Microstrip Antennas, J. R. James and P. S. Hall, eds. IEE, Peter Peregrinus, London, 1989.

[lo51 K. Fujimoto and J. R. James, eds., Mobile Antenna Systems Handbook, Artech House, Dedham, MA, 1994.

[I061 P. Newham and G. Morris, Chapter 20, in Handbook of Microstrip Antennas, J. R. James and P. S. Hall, eds., IEE, Peter Peregrinus, London, 1989.

[lo71 K. Fujimoto, T. Hori, S. Nishimura, and K. Hirasawa, Chapter 19, in Handbook of Microstrip Antennas, J. R. James and P. S. Hall, eds., IEE, Peter Peregrinus, London, 1989.

[I081 H. Kobayashi et al., "Flexible Microstrip Patch Applicator for Hyperthermia," IEEE AP-S Symp. Dig., pp. 536539,1989.

[lo91 H. Meinke, "Aktive Antenna," Nachrichtentechn. Z., Vol. 19, pp. 697-705, 1966.

[I101 H. An, B. K. J. C. Nauwelaers, and A. R. Van de Capelle, "Broadband Active Microstrip Antenna Design with the Simplified Real Frequency Technique," IEEE Trans. Antennas Propagat., Vol. 42, pp. 1612-1619,1994.

[I l l ] H. An, B. K. J. C. Nauwelaers, and A. R. Van de Capelle, "Broadband Active Circularly Polarized Microstrip Antennas," in 23rd European Microwave Confer- ence Proceedings, Turnbridge Wells, UK, 1993, pp. 345-347.

[I121 M. G. Keller, D. Roscoe, Y. M. M. Antar, and A. Ittipiboon, "Active Millimetre- Wave Aperture-Coupled Microstrip Patch Antenna Array," Electron. Lett., Vol. 31, pp. 2-3, 1995.

[I 131 C. C. Huang and T.-H. Chu, "Radiating and Scattering Analyses of a Slot-Coupled Patch Antenna Loaded with a MESFET Oscillator," IEEE Trans. Antennas Propagat., Vol. 43, pp. 291-298, 1995.

[I141 B. K. Kormanyos, W. Horokopus, Jr., L. P. B. Katehi, and G. M. Rebeiz, "CPW-Fed Active Slot Antennas," IEEE Trans. Microwave Theory Tech., Vol. 42, pp. 541-545,1994.

[115] T. Razban, M. Nannini, and A. Papiernik, "Integration of Ocsillators with Patch Antennas," Microwave J., pp. 104-110,1993.

[I161 P. S. Hall, "Analysis of Radiation from Active Microstrip Patch Antennas," in Proceedings of the JINA, Nice, France, 1990, pp. 446-449.

[I171 J. Lin and T. Itoh, "Two-Dimensional Quasi-Optical Power-Combining Arrays Using Strongly Coupled Oscillators," IEEE Trans. Microwave Theory Tech., Vol. 42, pp. 734-741, 1994.

[I181 J. A. Navarro, L. Fan, and K. Chang, "Active Inverted Stripline Circular Patch Antennas for Spatial Power Combining," IEEE Trans. Microwave Theory Tech., Vol. 41, pp. 1856-1863,1993.

[I191 P. Liao and R. A. York, "A New Phase-Shifterless Beam-Scanning Technique Using Arrays of Coupled Oscillators," IEEE Trans. Microwave Theory Tech., Vol. 41, pp. 1810-1815, 1993.

[I201 D. W. van der Weide, "Planar Antennas for All-Electronic Terahertz Systems, J. Opt. Soc. Am., B, Vol. 11, pp. 2553-2560,1994.

[I211 P. S. Hall and P. M. Haskins, "Microstrip Active Patch Phased Array with dc Bias Phase Control," in Proceedings of the JINA, Nice, France, 1992.


[I221 P. M. Haskins, P. S. Hall, and J. S. Dahele, "Polarization-Agile Active Patch Antenna," Electron. Lett., Vol. 30, pp. 98-99, 1994.

11231 R. B. Waterhouse and N. V. Shuley, "Scan Performance of Infinite Arrays of Microstrip Patch Elements Loaded with Varactor Diodes," IEEE Trans. Antennas Propagat., Vol. 41, pp. 1273-1280,1993.

[I241 C.-H. Ho, L. Fan, and K. Chang, "New FET Active Slotline Ring Antenna," Electron. Lett., Vol. 29, pp. 521-522, 1993.

[I251 X.-D. Wu, K. Leverich, and K. Chang, "Novel FET Active Patch Antenna," Electron. Lett., Vol. 28, pp. 1853-1854, 1992.

[I261 X.-D. Wu and K. Chang, "Novel Active FET Circular Patch Antenna Arrays for Quasi-Optical Power Combining," IEEE Trans. Microwave Theory Tech., Vol. 42, pp. 766-771, 1994.

[I271 D. B. Rutledge, Z. B. Popovic, R. M. Weikle, 11, M. Kim, K. A. Potter, R. C. Compton, and R. A. York, "Quasi-Optical Power-Combining Arrays," 1990 IEEE MTT-S Dig., pp. 1201-1204,1990.

[I281 A. Pance and M. J. Wengler, "Microwave Modelling of 2-D Active Grid Antenna Arrays," IEEE Trans. Microwave Theory Tech., Vol. 41, pp. 20-28, 1993.

11291 D. B. Rutledge, Z. B. Popovic, and M. Kim, "Millimeter Wave Grid Oscillators," 13th Int. Con$ Infrared Millimeter Waves, SPIE, pp. 1-2, 1989.

11301 A. Pance and M. J. Wengler, "Transmission Line Equivalent Circuitsfor 2-D Active Grid Antenna Arrays," in Proceedings of the IEEE Antennas and Propagation Society International Symposium, 18-25 July 1992, pp. 289-292.

[I311 H. S. Tsai, M. J. W. Rodwell, and R. A. York, "Planar Amplifier Array with Improved Bandwidth Using Folded-Slots," IEEE Microwave Guided Wave Lett., Vol. 4, pp. 112-1 14, 1994.

[I321 T. Mader, J. Schoenberg, L. Harmon, and Z. B. Popovic, "Planar MESFET Transmission Wave Amplifier," Electron. Lett., Vol. 29, pp. 1699-1701, 1993.

[I331 J. R. James, G. D. Evans, and A. Fray, "Beam Scanning Microstrip Arrays Using Diodes," IEE Proc., Vol. 140, Part H, pp. 43-51,1993.

[I341 V. K. Varadan and V. V. Varadan, "Smart Skin Antenna Technology," Proc. SPIE, Vol. 1916, pp. 189-196,1993.

11351 C. Vergnolle, T. Lemoine, and B. Dumont, "Materials Requirements for Micro- wave Antenna into Aircraft Skins," Proc. SPIE, Vol. 1916, pp. 197-219, 1993.

11361 I. Saha and S. K. Chowdhury, "Experiments on Impedance and Radiation Proper- ties of Concentric Microstrip Ring Resonators," Electron. Lett., Vol. 31, pp. 421422,1995.

[13q P. P. Smyth, M. McCullagh, D. Wisely, D. Wood, and S. Cassid, "Optical Wireless Local Area Networks Enabling Technologies," 8. T. Tech. J. , Vol. 11, pp. 56-64, 1993.

[I381 G. Andrasic and J. R. James, "Height Reduced Superdirective Array with Helical Directors," Electron. Lett., Vol. 29, pp. 2002-2004, 1993.

El391 J. Huang, "Bandwidth Study of Microstrip Reflectarray and a Novel Phased Reflectarray Concept," in IEEE AP-SIURSI Symposium Digest, Newport Beach, California June 1995, pp. 582-585.

CHAPTER SEVEN

Superconducting Microstrip Antennas

JEFFERY T. WILLIAMS, JARRETT D. MORROW, DAVID R. JACKSON, and STUART A. LONG

7.1 INTRODUCTION

Dramatic technological breakthroughs have been made in the development of high-temperature superconductors since their discovery in 1986, led by advances in the deposition of high-temperature superconducting (HTS) thin flms on relatively low-loss substrate materials. High-quality superconducting transmission lines, filters, and resonators have been developed [I-51; and recently, superconducting antennas with enhanced efficiencies have been demonstrated [6-161. The success of these devices and the rapid maturation of deposition and etching technologies have made plausible the near-term application of high- temperature superconducting devices in high-frequency systems.

The use of superconductors in the construction of passive antennas does not, in general, affect their radiation characteristics [17]. These characteristics are usually associated with the physical construction of the antenna, and therefore the antenna's radiation pattern and directivity will be unaffected by the use of superconducting materials. This independence implies that the radiation resistance and external reactance of the antenna will also be independent of the conducting material. Superconductors do, however, affect the input impedance, radiation efficiency, and frequency behavior of particular types of antennas. These changes are a result of the reduction in ohmic loss and the contributions of

Advances In Microstrip and Printed Antennas,, Edited by Kai Fong Lee and Wei Chen. ISBNO-471-04421-0 0 1997 John Wiley & Sons, Inc.

326 SUPERCONDUCTING MICROSTRIP ANTENNAS

the internal reactance, which is directly associated with the effective penetration depth of the fields into the superconductor.

For the most part, the primary advantage of using superconducting materials in antenna systems is the reduction of the loss associated with transmission line matching circuits, filters, and feed networks, particularly at microwave and millimeter-wave frequencies where the ohmic losses begin to significantly affect system performance. For large antenna arrays with long, elaborate corporate feed networks, the use of HTS transmission lines can substantially increase the gain of the antenna. These benefits become more apparent as the number of radiating elements in the array becomes large.

In addition to the feed line losses, we must include the losses associated with the individual radiators to obtain the overall efficiency of the antenna array. For instance, the efficiency of a microstrip patch antenna is limited by the power dissipated by ohmic losses in the patch element and the ground plane, dielectric loss in the supporting substrate, and undesirable excitation of surface-wave radiation. The level of surface-wave excitation increases with increasing substrate thickness and dielectric constant. For this reason, in many designs, the substrate upon which the microstrip antenna is patterned is electrically thin (< 0.011,). On these thin substrates, coupling into the surface waves is small. Unfortunately, this benefit is often mitigated by a substantial decrease in the radiation efficiency due to conductor and dielectric loss. These losses can be significantly reduced by constructing the antenna from thin films of high-temperature superconductor on low-loss substrates since high-quality HTS materials have microwave surface resistances that are one to two orders of magnitude less than that of copper at 77 K. Therefore, properly designed microstrip antennas and antenna arrays show a marked improvement in efficiency when constructed from high-quality HTS films.

In this chapter, we will begin with a discussion of some of the general properties of high-temperature superconductors and then consider the application of these materials in microstrip transmission line feed networks and microstrip patch antennas. We will also demonstrate how the use of HTS materials can improve the gain of microstrip antenna arrays. We will conclude by sum- marizing the results of some interesting superconducting microstrip antenna investigations.

7.2 BASICS OF SUPERCONDUCTIVITY

At present, the exact mechanism of superconductivity in high-temperature copper oxide materials is of much debate; however, there are indications that this mechanism is similar in some aspects to that of low-temperature superconductors. With this assumption in mind, we will begin with a short summary of the basic properties associated with superconducting materials (for a detailed discussion the reader is referred to references [18-211, followed by a general discussion on the characteristics of high-temperature superconductors.

BASICS OF SUPERCONDUCTIVIN 327

7.2.1 General Properties of Superconductors

The superconducting state is quite remarkable in that it possesses two dramatic, yet seemingly independent macroscopic properties: (1) zero direct-current (DC) electrical resistivity below a critical temperature T, and (2) near-perfect diamagnetism in the presence of a weak magnetic field. The first property, zero DC resistivity, is often misconstrued as implying that a pure superconductor will have zero alternating-current (AC) resistivity, which is certainly not the case as we shall discuss. The second property, near-perfect diamagnetism, results in the exclusion of magnetic flux from the interior of the superconductor, except within a thin region at the surface. The expulsion of magnetic flux from a superconductor was demonstrated experimentally by Meissner and Ochsenfeld in 1933 [23] and is referred to as the Meissner eflect. It is the Meissner effect that is demonstrated in the floating magnet experiment, and it is required that a material possess this property before it can be classified as a superconductor. It is this property that distinguishes a superconductor with zero resistivity (which is only true at DC) from a perfect electric conductor.

The superconducting state is an ordered (lowest energy) state in which conduction carriers (electrons or holes) form loosely associated pairs (Cooper pairs) through interactions with the lattice (phonon interactions). The carrier- lattice-carrier interaction is such that the repulsive forces between the carriers are overcome. The distance over which the paired carriers interact is defined as the coherence length, which is dependent upon the superconductor material and the physical state of the superconductor (i.e., the level of impurities, surface effects, and material defects). The paired carriers flow along the superconductor in a coherent fashion without interruption, and therefore without loss. This flow constitutes the superconductive current. The nature of the carrier pairing has been explained for low-temperature superconductors in an elegant microscopic theory developed by Barden, Cooper, and Schrieffer [24], which is commonly referred to as the BCS theory. For high-temperature superconductors, the exact mechanism of the pairing is unclear, as we shall discuss in the next section.

At a temperature of 0 K, all of the carriers are in the ground or superconducting state, and there is no resistance to current flow (i.e., no losses). As the temperature is increased, some of the carriers are excited out of the ground state by thermal lattice vibrations. This excitation of individual carriers tends to break up the Cooper pairs, producing a mechanism for the flow of both normal conduction carriers (which constitutes a normal current) and paired carriers. The AC losses in superconducting materials are associated with the flow of these normal carriers.

Since the paired carriers in an ideal superconductor flow without resistance, only a vanishing small electric field is required to initiate their movement. Therefore, at zero frequency (DC) there will be no electric field parallel to the surface of the superconductor, and thus no normal conduction current (i.e., no loss). At nonzero frequencies (AC), the superconducting current must react to a changing field. However, the paired carriers have a certain amount of

328 SUPERCONDUCTING MICROSTRIP ANTENNAS BASICS OF SUPERCONDUCTIVITY 329

momentum due to their motion and cannot react instantaneously to the changing field. This lagging current will induce an electric field along the surface of the conductor, which in turn will drive a normal current that produces ohmic loss. Qualitatively, this effect is similar to the current in an inductor lagging the applied voltage.

In addition to being destroyed by temperatures above Tc, superconductivity can be destroyed by sufficiently high current densities and magnetic fields and by very high operating frequencies. At frequencies above the energy-gap frequency, the energy absorbed by the material results in the excitation of carriers to the normal state, eventually destroying the superconducting behavior. The energy gap (energy-gap frequency) is a function of temperature (T), decreasing from a maximum at OK to zero at the critical temperature T,. For temperatures well below T,, very little energy will be absorbed from photons which have energies less than the energy gap (frequencies less than the energy-gap frequency). Therefore, the superconducting state remains intact. A remarkable consequence of the high transition temperatures of the copper-oxide superconductors is a marked increase in the energy-gap frequency. HTS materials have energy-gap frequencies well into the infrared (> 10 THz), whereas the low-Tc superconductors have energy-gap frequencies only slightly above the millimeter-wave region (< I THz). As a consequence, the usable frequency range for the high-Tc materials is at least an order of magnitude greater than that of the low-Tc superconductors.

For superconductors at temperatures below T,, the superconducting state will be destroyed if the current density exceeds the critical current density. This critical current is a function of the temperature, the geometry, and the physical state of the superconductor and is related to whether the magnetic field produced at the surface by the current exceeds the critical magnetic field strength associated with the superconductor.

To discuss the critical magnetic field, consider again a superconductor below T,. As a consequence of the diamagnetic property of superconductors, a screening current is established at the surface of the superconductor to cancel the magnetic field in its interior. There is a certain amount of energy required to establish this screening current; and as the applied magnetic field strength increases, so does the amount of expended energy. At a particular field strength (Hc), which is a function of temperature, the amount of energy required to expel the magnetic flux becomes greater than that required for the material to transition to its normally conducting state. Therefore, for magnetic fields above Hc, the superconducting state will be destroyed and the fields will penetrate the material. The penetration of the magnetic flux depends upon the geometry, the orientation of the field with the surface, and the superconductor type (type I or type 11).

In a type I superconductor, below Hc(T), the material is superconducting and there is no flux penetration (beyond a very small distance from the surface). However, when the applied field becomes greater than H,(T) the material transitions to its normal state and the flux penetrates the sample completely. For a type I1 superconductor, there are two critical field values: the lower critical field

Hcl(T) and the upper critical field Hc2(T), where H,,(T) < Hc2(T). When the applied field is below Hcl(T), the material is superconducting and there is no flux penetration. Above HC2(T) the material returns to the normal state and the field penetrates the sample completely. However, when the applied magnetic field strength is between Hc,(T) and Hc,(T), the flux will partially penetrate the material, resulting in an organized structure that contains both normal and superconducting regions. This is defined as the mixed state of the superconductor.

In the mixed state, outside the regions of flux penetration, the material remains superconducting. When the applied field is below Hc2(T), these superconducting regions are usually well connected. The regions of flux penetration (usually called pinning centers or vortices) are considered to be in a transitional stage between the normal and superconducting states. They are often cylindrical in form with an effective radius of approximately one to two coherence lengths. In an ideal material, the spatial distribution of these vortices is regular and is a function of the applied magnetic field and the current density through the superconductor. When the applied field isjust above Hcl(T), the vortex spacing is large, decreasing to zero at Hc2(T). Circulating the penetrating flux is a current that serves to screen the flux from the superconducting regions. Although the mechanism of superconductivity is usually the same for type I and type I1 superconductors, the mixed-state behavior of the type I1 allows for larger critical current densities and magnetic field strengths, since the currents are no longer restricted to flow in a thin region near the surface. Therefore, type I1 superconductors are better suited for higher-power applications. The relative difference between Hc(0) for a type I and Hc2(0) for a type I1 superconductor can be as great as three orders of magnitude. Copper oxide high-temperature superconductors are type 11. For high-temperature superconductors, poH,, is on the order of 0.001 [TI and poHc2 is on the order of 5-10 [TI, at 77 K.

7.2.2 High-Temperature Superconductors

High-temperature superconductors (interpreted strictly, high-temperature implies critical temperatures above 30 K; but more commonly, it implies Tc above 77 K) are inherently different from their low-temperature counterparts in that they are copper oxide materials, as opposed to metallic conductors. Within the general classification, high-temperature superconductivity has been found in the following families: LaSrCuO, YBaCuO, BiSrCaCuO, TIBaCaCuO, and HgBaCaCuO. Each family of materials has at least one superconducting phase. Alist of some of the most common phases studied, with their approximate critical temperature, is given in Table 7.1. In the following discussion, we will concentrate on the properties that are common to these various classes of materials, except for the HgBaCaCuO materials which are relatively new and not yet well characterized for high-frequency applications. Differences will be specified on an individual basis. Many of our specific examples, however, will be for the YBa2Cu,0, material, since it has received the most study and has many desirable properties for high-frequency applications.


TABLE 7.1 Common High-Temperature Copper Oxide Superconductors

Material Critical Temperature (K)

YBa,Cu,O, 93 T12Ba2CaCu208 110 T12Ba2Ca2Cu,0,, 123 Bi2Sr2CaCu208 90 Bi2Sr2Ca,Cu,0,, 110 HgBa2Ca2Cu,0, 135

0 Copper

Oxygen

FIGURE 7.1 YBa,Cu,O, unit cell.

The crystal structure of the high-Tc materials is related to that of a simple perovskite unit cell, in which a metal ion (anion) is in the center of a cube of cations, surrounded by an octahedral configuration of oxygen atoms. This structure is illustrated in Figure 7.1, which shows the unit cell of YBa,Cu,O,. In general, the unit cells for these superconductors are orthorhombic or tetragonal in cross section, depending on the material and oxygen content (e.g., YBa,Cu,O, is orthorhombic and YBa2Cu30, is tetragonal).

The mechanisms for superconductivity in these new materials is still the subject of much debate. One generally accepted theory is that it is due to the flow of carrier pairs in the Cu-0 planes, of which there are two for each unit cell of the YBaCuO material shown in Figure 7.1. (In this figure, the Cu-0 planes lie just above and below the Y layer). The orbitals of the Cu and 0 atoms are strongly

linked in these planes, thereby accommodating conduction in the Cu-0 or a-b plane. Perpendicular to these planes, conduction is poor. This weak conduction along the c-axis of the material is attributed to the relatively weak linkage between the Cu and 0 orbitals across the Y layer. As a result, the conductivity of these materials is highly anisotropic. This feature has serious implications in the application of high-Tc materials.

We should also mention that the pairing mechanism between carriers in the high-Tc materials has not been well established [22,25]. Presently, it is unclear whether phonon (i.e. lattice vibration) interactions, or some other bonding mechanisms are responsible. In addition, layers other than the Cu-0 layer may also contribute to conduction. For example, the top and bottom layers of the YBa2Cu,0, unit cell consist of Cu-0 chains. (These chains are unique to the YBaCuO family.) The role of these chains in the conduction process is still an open question. In addition, high residual losses at very low temperature suggest to some that for HTS materials there are some nonpaired carriers at OK; in other words, pairing is not complete.

High:T, superconductors are used in two basic forms: bulk and thin film. (Less common are thick films that have many characteristics similar to polycrystalline bulk materials.) Bulk superconductors are simply independent polycrystalline or single-crystal samples of the material, whereas thin-film superconductors are polycrystalline or-single (epitaxial) crystal films of superconductor grown on a substrate material. There are several interesting structural features of these " materials that affect their electrical characteristics. Most of these features are a result of the processing techniques used in the manufacture of the sample; and although we will not discuss these techniques in any detail, we will make reference to some of the more common procedures.

The first high-temperature~superconductor samples were in polycrystalline bulk form. The DC resistance of these materials dropped rapidly at the transition temperature, and they demonstrated the Meissner effect. However, when compared to the low-T, materials, specifically niobium and even normally conducting materials such as copper and silver, they had relatively poor AC electrical characteristics. These high AC losses were attributed to several factors, such as lossy or insulating boundaries between the grains (individual crystals within the material), poor orientation of the grains, and the presence of other superconducting phases, all of which resulted in poor connections between the individual crystals in the polycrystalline material. In addition, roughness, poor connectivity between regions and impurities on the surface of the sample contributed to the high frequency losses.

Many of these factors are eliminated in single-crystal bulk materials, which have very low microwave surface resistances. Unfortunately, large single-crystal samples cannot presently be grown. Advances in bulk material fabrication (e.g., the liquid-phase, or melt-textured, process [26]) have produced highly oriented, large area samples. These materials have large critical current densities and low surface resistances and represent a significant technological advance toward the eventual application of bulk superconducting materials.


The early technological difficulties associated with the development of large high-quality bulk samples amplified the interest in thin-film superconductors. Like early bulk samples, the first thin films had many of the same defects that led to high losses. However, rapid advances in material deposition techniques have overcome many of the initial problems. Laser ablation and sputtering deposition techniques yield very high quality thin films on a variety of substrate materials (SrTiO,, MgO, LaAlO,, ZrO,(Y,O,) and r-plane A1,0,). These films are highly oriented, with their c-axis perpendicular to the substrate (such that the plane of best conduction, the a-b plane, is parallel to the substrate, as is required for most thin-film applications), have near pure epitaxy (essentially single crystal), and are well connected with relatively smooth, clean surfaces. For orthorhombic structures, such as YB~,c~,o,, twin boundary defects occur. For superconductors in which twinning has occurred, adjacent grains or regions are rotated by 90 degrees; as a result, the a (and b) axes of adjacent grains are oriented perpendicular to one another. The most common cause of twinning in HTS thin films is due to twinning in the substrate, which is then reflected in the epitaxially grown films. In high-quality films, the boundaries between the twin regions are very thin, on the order of a few monoatomic layers, and the adjacent regions seem to be reasonably well connected. The effects of these twin boundaries on the macroscopic conductivity is unclear.

The best films have been deposited on SrTiO, substrates; however, SrTiO, has extremely poor electrical characteristics (i.e., a very large dielectric constant that varies dramatically with temperature, and a high loss tangent) and is therefore inappropriate for most high-frequency applications. The basic requirements for microwave and millimeter-wave substrate materials on which high-quality film can be grown are as follows:

Good lattice match with the superconducting material, or the ability to support buffer layers that provide a good lattice match

0 Nonreactive with superconductor or buffer layer at processing temperatures Low loss tangent

0 Low dielectric constant (if possible)

At present, the substrate materials that best satisfy these requirements and are most widely used are LaAlO,, MgO, ZrO,(Y,O,), and r-plane A1,0, (sapphire). MgO is a popular substrate for many high-frequency applications because it has a relatively low dielectric constant (approximately 10). However, MgQ does not have as good a lattice match with HTS materials as does SrTiO, and LaAlO,. It is also hydroscopic (absorbs water) and therefore can have a variable loss tangent depending upon the amount of water it has absorbed. Sapphire has an extremely low loss tangent and is a very durable and machinable substrate material; however, is it highly anisotropic (r-plane cut) and it chemically reacts with the HTS film at processing temperatures. In most situations, a buffer layer, such as

TABLE 7.2 Microwave Properties of Common Substrates Used with High-Temperature Superconductors

Dielectric Constant Loss Tangent Substrate Material (Nominal) (Nominal)

LaAIO, 24 lo4 NdGaO, 23 lo-4 A1203 11 9.4

111.4 MgO 10 lo-' Zr02(YZ03) 29

CeO,, must be used to pacify the sapphire. Another substrate with good mechanical properties is ZrO,(Y,O,), or YSZ. Like sapphire, however, a buffer layer must be used, and YSZ has a high dielectric constant (approximately 24-27). Films on LaAl0, have been widely tested and found to have very good electrical characteristics. LaAlO, is presently the substrate material of choice for high-frequency superconducting thin-film applications, but the disadvantages of LaAIO, substrates include their high dielectric constant (approximately 21-25), brittleness, and large number of twin regions. In Table 7.2 we have listed the electrical properties of some of the substrates commonly used with HTS thin films.

7.2.3 Characteristics of High-Temperature Superconductors

With the advances made in the deposition and patterning of superconducting thin films, applications for these materials have become feasible. Leading the list of possible thin-film applications are passive microwave and millimeter-wave circuit elements (e.g., planarlintegrated transmission lines, filters, couples, antennas, resonators, and delay lines). To successfully design such superconducting elements, a knowledge of their electrical properties is required. In this section we will examine some of the basic high-frequency electrical properties of high-T, superconducting thin films. Many of the characteristics that will be discussed apply directly to bulk superconductors, and most of the properties given can be extrapolated to lower frequencies; however, we will limit the discussion to the microwave characteristics of HTS thin films.

The primary advantage of using superconducting materials in high-frequency devices is the reduction in the ohmic losses compared to identical devices constructed from normal conductors. Therefore, the electrical parameter of most interest is the surface resistance of the material. The surface resistance, R,, is a measure of the time-average power dissipated per unit area of surface. It has units Q/n and is the real part of the surface impedance Z,, given by


The imaginary part of the surface impedance is the surface reactance, which is related to the surface inductance by X,=jwL,, and it is a measure of the time-average stored energy per unit area of the surface. Many laboratories have measured the surface resistance of high-Tc superconductors at microwave and millimeter-wave frequencies. Of the vast array of high-Tc superconductors, the YBa,Cu,O, and Tl,Ba,CaCuO, materials generally have the lowest high- frequency surface resistances. The highest-quality films have surface resistances on the order of 150-500 pQ/n at 10GHz and 77K, and most commercially available films have surface resistances less than 1 mQ/n at 10 GHz and 77 K.

If one assumes that the relationship between the current and electric field in the conductor is local (i.e., the mean-free path length or coherence length is small compared to the field penetration depth; and hence Ohm's law, J = aE, applies) and that the fields decrease exponentially into the good conductor, the surface impedance for a thick conductor is

For a normal conductor, the conductivity is assumed real and constant; therefore the surface resistance and reactance are equal and have an w1I2 frequency dependence.

The coherence lengths for the copper oxide superconductors are extremely small and anisotropic, approximately 1-2nm in the a-b plane and less than 0.6 [nm] along the c-axis at OK. Such small coherence lengths suggest that the relationship between the superconducting current and electric field in these materials is local, indicating that conduction in these materials will be sensitive to material boundaries, defects, and uniformity. In addition, since the high-Tc superconductors have a local field-current relationship, the concept of a simple surface impedance is valid as long as we assume that the magnetic fields are weak enough that the flux is excluded from the interior of the superconductor. For stronger magnetic fields, such that the superconductor is within the mixed state, the field relationships are much more complicated, as we shall discuss later. In general, however, for strong magnetic fields, R, is greater than its weak-field limit.

For superconductors, the conductivity has an appreciable imaginary part as a consequence of the kinetic energy associated with the free-flowing paired carriers. The complex conductivity for HTS materials is a macroscopic constitu- tive parameter of the material that is a function of frequency and temperature and for which no exact theory has been developed. This is not the case for many low-temperature superconductors since an accurate model, the Mattis-Bardeen equations [27], for the complex conductivity has been derived from BCS theory. This model assumes the extreme anomalous limit where the field penetration into the superconductor is much smaller than the coherence length. Unfortunately, the Mattis-Bardeen equations cannot be successfully applied to high-Tc materials, which have field penetration depths much larger than the coherence

lengths. In fact, it is still unclear whether the mechanisms for current flow in the high-Tc materials are the same as those for the low-T, materials. Therefore, for relatively weak fields, the simple two-fluid model is more practical [18,19]. As an approximate empirical model, it adequately predicts the behavior of both low- and high-T, superconductors, revealing much of the important electrical character of these materials. The two-fluid model assumes that a fraction of the conduction carriers are in the superconducting state and the remainder are in the normal state. The current is then assumed to have two components: a superconducting component (J,) and a normal conduction current (J,),

I The normal component of current satisfies Ohm's law for normal carriers,

where a, is the normal-state conductivity. In the classical two-fluid model, J, satisfies the London equations [18,19,28]:

aJsc E London's first equation: - at - pol2 (7.5)

H London's second equation: V x J,, = -- n2

where 1 is the effective field penetration depth. This effective penetration depth is a measure of the penetration of the fields into the superconductor, much the same as the skin depth is for normal conductors. However, it is fundamentally different from the skin depth in that it is an intrinsic property of the material, and it is independent of frequency. Substituting Eqs. (7.3)-(7.6) into Maxwell's equations, a time harmonic wave equation is obtained. From the associated dispersion relation we can define the complex conductivity as

J = oE = (a, - jo,)E

and a, is the normal-stateconductivity of the HTS material T = T,. Normal loss mechanisms and other effects, such as grain boundary losses and residual losses, are included in a,. To account for the temperature dependence of the density of

I carriers in the superconducting and normal states, a temperature dependence is


assigned to the effective penetration depth and a corresponding function of temperature f(T) is assigned to a,. The temperature dependence of these parameters is discussed below.

Another interesting phenomenological two-fluid model (one based on the presence of two kinds of current carriers) has also been introduced 1291. This model replaces London's first equation with an equation that empirically accounts for the AC losses in high-T, superconductors that cannot be readily described by the physics of the material. This new equation is

where I; is an empirical parameter introduced to account for experimentally observed losses. With this expression the resulting complex conductivity is

and

This model reduces to the classical London two-fluid model when I; + a. We will assume this limit for the remainder of this chapter.

The exact temperature dependence for high-T, materials is not yet established. Many results suggest that the following temperature dependence is appropriate [30-341:

where 40) is the effective penetration depth as T approaches 0 K. The values for a that have been reported range from 1.1 to 4. Many experimental observations seem to indicate, however, that a square-law (a = 2) dependence is most appropriate. Therefore, for the remainder of this chapter we will use a = 2. For copper oxide superconductors, the effective penetration depth is anisotropic: approximately 0.14-0.25pm along the c-axis and on the order of 0 . 4 0 - 0 . 5 0 ~ perpendicular to this direction. It is sensitive to the quality of the material, increasing with irregularities such as grain boundaries and defects, impurities, and the presence of other superconducting phases. For high-quality YBaCuO thin films,

BASICS OF SUPERCONDUCTIVITY 337

an is approximately equal to 3 x 106S/m, t(0) is 0.14pm, and the critical temperature Tc is 93 K.

Using these temperature-dependent quatities (2 and a,) the complex conductivity in (7.7) is

Substituting this conductivity into expression (7.2), the surface impedance Z, for a thick superconductor (several penetration depths thick), we obtain

From this equation we see that the surface resistance and surface inductance for a thick superconductor are given by

and

When the superconductor cannot be considered thick, the electrical properties of the superconductor cannot be approximated by Eq. (7.16). In this case a commonly used expression, obtained by modeling the superconducting layer as a section of transmission line with an open-circuit condition at the air interface,

where t is the thickness of the superconductor. Equation (7.19) reduces to the well-known Z, = l/(at) limit as t +O. All of these approximate expressions for Z,, R,, and Ls assume that (a,/a,) << 1, which is generally true for temperatures below 0.9T,. In fact, it should be noted that the two-fluid model begins to lose

HTS MlCROSTRlP TRANSMISSION LINES AND ANTENNAS 339 338 SUPERCONDUCTING MlCROSTRlP ANTENNAS

validity as the temperature approaches T,. A few important observations about this expression are that the surface resistance for a superconductor varies as the square of w and roughly as the cube of 4 T ) . This frequency behavior is in marked contrast to the wllZ frequency dependence of normal conductors. Also, the surface inductance for thick superconductors is directly proportional to the effective penetration depth. This property is often used to determine 47').

The two-fluid model as presented in this section closely models the response of HTS materials for low-level RF fields. However, as the R F magnetic fields increase, unexpectedly high losses and even nonlinear behavior are observed, effects that are not accounted for in this simple model. There is an apparent dependence of the surface resistance and effective penetration depth on the magnetic field strength [36-381. These effects have important implications for high-power applications because they lead to decreased device efficiency, intermodulation distortion, and harmonic generation. The modeling of field dependence effects is usually divided into three general regions: low magnetic fields (0.5Hc1 < H < H,,), intermediate magnetic fields (H,, < H < 5-10HCl), and high magnetic fields (H > 5-lOH,,). For low values of H, one would not generally expect field-dependence effects; however, experimental observations of HTS materials exhibit such effects. In the relatively low field level region, the unexpectedly high losses and field strength dependence are associated with nonlinear behavior of the weak links that exist between the superconducting grains. In this region, an "effective medium" is usually defined to model the field-dependent effects. This technique is described in detail in reference [39]. In the intermediate magnetic field strength region, in addition to the weak-link effects, flux penetration begins to occur and the density of paired carriers is reduced. The effects in this region appear to be similar to those for low-temperature superconductors; hence, the classical Ginzburz and Landau theory [37, 401 has been used to successfully model HTS materials for moderate RF magnetic field levels. In the high-field region, however, the behavior is further complicated by strong hyster- esis effects. As a result, few models that predict the high-field characteristics of HTS materials have been proposed. One model that has been used with some success to characterize the nonlinear effects in high-power striplines is the Bean critical state model 1371.

The high-field behavior of high-temperature superconductors is an area of much interest and debate. These effects are difficult to quantify experimentally, and it is even unclear whether or not many of the observed effects are associated with intrinsic properties of the HTS materials or with defects introduced in fabrication, or measurement issues such as localized heating effects. Many researchers are currently conducting investigation~ to help resolve these questions.

7.3 HTS MlCROSTRlP TRANSMISSION LINES AND ANTENNAS

High-temperature superconductors offer many interesting possibilities for the designers of microstrip antenna systems. With transition temperatures above

that of liquid nitrogen, these systems can be cooled with simple, cost-efficient cryogenic systems or by the ambient dark-side temperatures in space (approximately 70-80K). As already mentioned, the primary advantage of using superconductors in antenna systems is the reduction of ohmic losses in the feed lines and, in some cases, the individual antenna elements. A common misconception, however, is that the use of superconductors will automatically allow for the miniaturization of the antennas. Strictly speaking, if one is only taking advantage of the reduced surface resistance of superconducting materials, miniaturization is not possible since most antenna designs require specific electrical dimensions (dimensions in terms of wavelengths) [71]. On the other hand, some antennas can be reduced in size through the use of high dielectric constant materials, and then be made more efficient by using superconductors with their inherent lower surface resistances. However, the only antenna designs that can truly be miniaturized using superconducting materials must also take advantage of the magnetic energy stored in the kinetic motion of the superconducting carriers, the kinetic inductance of the material. We will discuss this phenomenon in the next section.

In this section, we first discuss some of the fundamental properties of superconducting microstrip transmission lines and rectangular microstrip patch antennas. We then examine the propagation along superconducting transmission lines and the efficiency of normally conducting and superconducting microstrip feed networks, followed by a discussion of the efficiency and bandwidth of microstrip patch antennas.

7.3.1 Superconducting Transmission Lines and Feed Networks

The use of superconducting transmission lines has two immediate benefits: the reduction of ohmic losses and the elimination of conductor dispersion. This can be demonstrated by considering the classical distributed-element model for a transmission line. In this model the telegraphist's equations are used to determine the voltage and current along the transmission line, which is represented by a cascade of lumped elements R, L, C and G that represent, respectively, the series resistance per unit length, series inductance per unit length, shunt capacitance per unit length, and shunt conductance per unit length. For TEM modes, the voltage and currents are uniquely defined. For other modes, the definitions are not unique; however, the distributed-element model can still be made self-consistent. Assuming that the mode of interest propagates as e-?', the complex propagation constant y is given by

This expression can be solved directly for cc and P; however, for this discussion we will neglect the dielectric loss (i.e., assume G = 0) for simplicity. Thus, the


following expressions are obtained for the phase and attenuation constants:

HTS MICROSTRIP TRANSMISSION LINES AND ANTENNAS 341

transmission line and mode; and R, and Ls are the surface resistance and inductance for the conductors, respectively. These expressions for R and Lin are valid for relatively thick conductors (thick compared to a penetration depth). The R, and Ls terms in this case are given by Eqs. (7.17) and (7.18), respectively, and are assumed to be the same for all the transmission line conductors. For thin conductors, alternate expressions for R and L, must be used [41].

Notice in Eq. (7.26) that we have separated the series inductance into two quantities: the internal inductance L,, which accounts for magnetic energy storage within the conductor; and the external inductance L,,,, which accounts for magnetic energy storage external to the conductor. The inductance effects due to kinetic energy storage in the motion of the paired carriers in the superconductors (kinetic inductance) are included in Lin.

Another convenient form for the capacitance per unit length is in terms of the geometrical factor for a homogeneous, air-filled guide Gi and the effective permittivity for the guided mode e:", where

and

If the losses are assumed to be small, such that R << AL, then Eqs. (7.21) and (7.22) are approximated by

and

In this equation, E0 is the electric field inside the air-filled guide and V is the corresponding voltage.

For microstrip transmission lines, approximate expressions for the geometrical factors can be given in terms of general formulas for the characteristic impedance (23, effective dielectric constant (e:"), and propagation constant (y = a + jb) of microstrip. These formulas are usually obtained from quasi-static analysis, numerical computations, or empirical observations. In terms of these quantities, the geometrical factors for microstrip transmission lines can be written as

For microstrip and many other transmission line structures, suitable general forms R, L, and C are

and

where a, is the attenuation constant associated with conductor loss, and C0 (=eOGi) is the capacitance per unit length for the homogeneous, air-filled microstrip guide. Common expressions for Z,, ac, &Eff, and C0 are given in reference [42].

where [ is the contour along the boundary of the conductor cross section; S is the cross section of the guide; G,, G,, and G, are geometric factors for the particular

342 SUPERCONDUCTING MICROSTRIP ANTENNAS HTS MICROSTRIP TRANSMISSION LINES AND ANTENNAS 343

Substituting Eqs. (7.25)-(7.28) into Eqs. (7.23) and (7.24), we obtain the following expressions:

and

where c is the speed of light and 1, is the intrinsic impedence, both associated with free space. Note that both of these expressions contain the term (L,/p,). For thick conductors, from Eqs. (7.2) and (7.18) we find that this term is

- for a normal conductor

for a superconductor

where 6 is the classical skin depth for a normal conductor,

and 1 is the effective penetration depth for the superconductor. Therefore, in comparing the attenuation and phase constants for equivalent normally conducting and superconducting transmission lines, we need to examine not only the relative values of the surface resistance, but also the relative values of 6 and 1. For example, at 10 GHz and 77 K the skin depth for OFHC copper (oxygen-free, high-conductivity copper, a = 40 x lo7 S/m at 77 K) and the effective penetration depth for YBa,Cu,O, are both approximately equal to 0 . 2 5 ~ . For typically dimensioned transmission lines, however, the internal inductance is small compared to the external inductance, as will be shown in a later example. Hence, from Eq. (7.33), the attenuation constant for a typical copper transmission line at lOGHz and 77K is approximately a factor of (R,,, j R , .,,,,) greater than an identical YBCO line. For the highest-quality films, this ratio can be as high as approximately 60-70. (For a frequency of 10 GHz and a temperature of 77 K, R,,,, is approximately 10mR/n and RS,,,,, is on the order of 0.15mi2/0 for the highest-quality films.) The results for a more specific example are shown in Figure 7.2. In this figure we have plotted the attenuation constant in dB/cm for a 5 0 4 microstrip transmission line, at 20GHz, on a LaAIO, substrate. Three cases are shown: YBaCuO conductors at 77K, and copper conductors at 77 K and 300K. The copper is assumed to have a conductivity of 5.8 x 107S/m at room temperature (300 K) and a value of 40 x lo7 S/m at 77 K. The two-fluid

FIGURE 7.2 Attenuation constant for a 20-GHz microstrip transmission line on an LaAlO, substrate.

model described in the previous section is used to characterize the YBaCuO superconductor. For this model, the following parameters, which are representative of a high-quality YBaCuO thin film, are used: a,= 3 x 106S/m, 1(0) = 0.15 p , T, = 90 K, and t = 0.25 pm. From Figure 7.2, we notice that the attenuation constant for the copper microstrip line is significantly larger than that for the YBaCuO line. At 20 GHz the 77 K copper line has an attenuation constant approximately 20 times larger than an identical YBaCuO line. As expected, the attenuation constant for all of the microstrip lines increases with decreasing substrate thickness.

Recall that the phase velocity for a particular mode is given by

If the phase velocity is independent of frequency, the mode is dispersionless. Substituting Eq. (7.32) into this expression, we obtain

Since the effective penetration depth is frequency-independent, we conclude from Eq. (7.34) that superconducting transmission lines that have frequency-independent geometrical factors (such as stripline) are free from material dispersion.

344 SUPERCONDUCTING MlCROSTRlP ANTENNAS HTS MICROSTRIP TRANSMISSION LINES AND ANTENNAS 345

FIGURE 7.3 Ratio of internal to external inductance (multiplied by 112) for a YBaCuO microstrip line.

Equivalent normally conducting lines, however, experience material dispersion (due to the frequency dependence of the skin depth) when the ratio of the internal-to-external inductance (second term in the parentheses in Eq. (7.37)) is appreciable. However, for microstrip transmission lines, any slight material dispersion is usually neglected since it is overwhelmed by the dispersion associated with the quasi-TEM nature of the dominant mode.

Another interesting property of superconducting transmission lines is also apparent in Eq. (7.37). Namely, as the ratio of the internal inductance to external inductance becomes appreciable, which occurs as the fraction of magnetic energy stored in the conductor increases, the phase velocity decreases. This situation is often facilitated by reducing the dimensions of the structure [41,43,44]. Such slow-wave behavior is ideal for use in delay lines and phase shifters and is generally only practical in superconductors since the losses in normally conducting lines become prohibitive. A plot of the second term in Eq. (7.37) is shown in Figure 7.3, for the YBaCuO microstrip transmission line example of Figure 7.2. It is apparent from this figure that no appreciable slowing will occur for normally dimensioned microstrip lines. Significant slow-wave behavior can only be realized when the dimensions for the microstrip (trace and ground-plane conductor thickness, strip width, and substrate thickness) are extremely small C41,441. -

One of the primary advantages of using superconducting materials in antenna systems is the reduction of the loss in large transmission line feed networks, particularly at high frequencies where the ohmic losses of normal conductors are quite large. To demonstrate this we will consider a square corporate-fed array of

FIGURE 7.4 An example of a 2N x 2N (N = 2) square corporate-fed array.

linearly polarized, printed microstrip elements, as shown in Figure 7.4. For this discussion we will only be considering losses associated with the feed. The antenna elements are assumed, for simplicity, to be matched to their corresponding feed line and the radiation efficiency of each element is assumed to be 100%. In addition, we will also assume a uniform array where all of the elements are excited with equal amplitude and phase.

For a square corporate-fed array with 2N antenna elements on a side, the total number of elements in the array is 22N. Assuming that all of the microstrip feed lines have the same characteristic impedance and have quarter-wave matching transformers at each Tee junction, it is straightforward to show (see Appendix) that the efficiency of the array, which only has loss in the transmission line feed network, is

where a is the attenuation constant [nepers/m] for the microstrip feed lines, d is the distance between the antenna elements, and qt is the efficiency of each quarter-wave matching transformer. If all of the feed lines have the same characteristic impedance, 11, is given by

where 1, is the free-space wavelength, and a, and E:" are the attenuation constant [nepers/m] and effective dielectric constant for the quarter-wave section, respectively. The derivations for Eqs. (7.38) and (7.39) are summarized in the Appendix. (Expressions for the microstrip parameters are given in reference [42].)

346 SUPERCONDUCTING MlCROSTRlP ANTENNAS HTS MICROSTRIP TRANSMISSION LINES AND ANTENNAS 347

1 10 100 1000 Number of Elements

FIGURE 7.5 Efficiency of a 20-GHz square microstrip-fed array on a LaAIO, substrate (e, = 23 and tan 6 =

As an example, the efficiency of a 20 GHz corporate microstrip feed as a function of the number of array elements is shown in Figure 7.5. In this example we assume that the element spacing is 1,/2 and the substrate is 0.254-mm-thick lanthanum aluminate (LaAIO,), with a relative permittivity of 23 and a loss tangent of The results in Figure 7.5 are representative of a 5 0 4 microstrip feed fabricated from copper and YBaCuO superconductor. The material parameters for the copper and YBaCuO conductors used in the previous examples are assumed here.

From Figure 7.5 we notice that as the number of elements in the array increases, the efficiency of the copper array decreases noticeably. On the other hand, the efficiency for the YBaCuO array remains relatively flat on this scale. For modest-quality YBaCuO films the efficiency will be less than that shown in this example, but it will remain well above that of the copper array. This example also demonstrates that the increase in efficiency realized by using a superconducting feed network only becomes appreciable when the number of array elements is large. Therefore, due to the scale limitations of present HTS thin-film fabrication technology a large HTS feed network is only feasible for high-frequency arrays. These results only represent the efficiency of the feed network, which is a single component of the overall efficiency for the antenna system. To obtain the overall efficiency, we must also account for losses in the other components of the system, in particular the antenna elements. The overall gain (G) of the antenna array is given in terms of the feed efficiency and the antenna element efficiency q, as

where D is the directivity of the array. The antenna element efficiency is the subject of the next section.

7.3.2 Superconducting Microstrip Patch Antennas

The antenna element efficiency for a microstrip antenna can be expressed in terms of the power lost due to losses in the dielectric (P,) and conductors (PJ of the structure, radiation into surface waves (P,,), and radiation into space (P,,). In terms of these quantities, we define the antenna element efficiency q, as

where Pin is the total input power. The element efficiency can also be expressed in terms of the individual quality factors of the resonant microstrip antenna, as discussed in Chapter 5. In this section we will summarize the specific results from Chapter 5 that are used for the examples to follow. First, we express the total quality factor (Q) for the antenna as

I where Us is the total energy stored by the antenna and o, is the resonant angular frequency. Similarly, we can write a general expression for the individual dielectric, conductor, surface wave, and space wave quality factors as

where x = d, c, sw, or sp. Thus, the total quality factor is given from Eq. (5.9) as

Combining Eqs. (7.42)-(7.44) with Eq. (7.41), we obtain

It is obvious from these expressions that the overall efficiency of a microstrip antenna is increased by increasing the percentage of power radiated into space.

To obtain a measure of the amount of the total radiated power that is lost to radiation into the surface waves, we define the radiation efficiency of a microstrip


antenna q, as

As shown in Chapter 5, the radiation efficiency for a rectangular microstrip patch is approximately equal to that of a horizontal electrical dipole. Therefore, from Eqs. (5.47), (5.48), (5.49) and (5.51), we obtain

where n is the refractive index of the substrate (n = &), h is the thickness of the substrate, and

In these equations we have assumed that the substrate materials are nonmagnetic (p, = 1). The radiation efficiency can also be expressed from Eq. (5.43) in terms of a radiation quality factor Q, as

For a microstrip patch antenna, QR is given from Eq. (5.43) by

Q~=(L+L)-' Qsp Qaw = q r ~ s p

where, from Eq. (5.67),

The factor p is given by Eq. (5.65). For patches on high-permittivity substrates, the patch dimensions are small relative to Lo; therefore, p is approximately equal to one. Note that the surface-wave quality factor can be obtained from Eq. (7.50) as

As discussed in Chapter 5, the dielectric and conductor quality factors can be determined from a cavity model analysis of the microstrip patch antenna. The dielectric Q is given from Eq. (5.40) by the simple expression

where tan 6 is the loss tangent of the dielectric substrate. The conductor Q is given from (5.41) by

where Rrd and Rr' are the surface resistances of the ground-plane and patch conductors, respectively. Thus, the antenna element efficiency is obtained by substituting Eqs. (7.51)-(7.54) into Eqs. (7.44) and (7.45).

In addition to the antenna efficiency, we can also express the impedance bandwidth (VSWR < 2) as a function of the total quality factor of the antenna and the resonant frequency fo. From Eq. (5.30), the unnormalized impedance bandwidth is given by

From Eqs. (7.16)-(7.19) we recognize that the surface impedance is a strong function of temperature. As a result, we expect from the expressions presented that the efficiency and bandwidth will vary with temperature due to their dependence on the surface resistance. Another property of the microstrip patch antenna that we expect will change with temperature is the resonance frequency, f,. This is due to the dependence off , on the surface reactance of the conductors. The change in resonance frequency can be determined using a cavity perturbation analysis [45]. Using the cavity model fields, presented in Chapter 5, the resulting resonance frequency for a microstrip antenna is

where X,P"' and XPd are the surface reactances of the patch and ground-plane conductors, respectively, and h is the substrate thickness. The frequency f, is the resonance frequency for the patch antenna when the ground plane and patch are

. assumed to be perfect electric conductors. For superconducting microstrip antennas, the surface reactance expressions given in Eqs. (7.16) and (7.19) can be used.


FIGURE 7.6 Total antenna efficiency of a 20-GHz rectangular microstrip patch antenna on a LaAIO, substrate (E, = 23 and tan 6 = 1 0 - 9

FIGURE 7.7 Impedance bandwidth of a 20-GHz rectangular microstrip patch antenna on a LaAl0, substrate (8, = 23 and tan 6 =

In Figures 7.6 and 7.7 we have plotted the antenna efficiency and impedance bandwith, respectively, as a function of normalized substrate thickness for three different cases. Each represents a 20-GHz rectangular microstrip patch with an aspect ratio (W/L) of 1.5, on a LaAlO, substrate with a dielectric constant of 23 and a loss tangent of We have assumed that for each antenna the ground plane and the patch are constructed from the same material. For the copper

antennas at 300 K and 77 K the surface resistances used correspond to conductiv- ities of 5.8 x lo7 S/m and 40 x lo7 S/m, respectively. For the YBaCuO antenna the parameters of the two-fluid model described in the previous section are assumed. The resulting surface resistance is 0.67m0/o at 77K. This value is consistent with that for a very good film.

From Figure 7.6 we observe that for very thin substrates the antenna efficiency is small, limited by the ohmic losses of the conductors and the dielectric losses. Since the conductor losses are quite high for the copper antennas, the efficiencies for these antennas are small for thin substrates. In contrast, we notice that the efficiency for the HTS antenna is relatively high for the thinner substrates. The efficiency for this superconducting antenna is primarily limited by the dielectric loss tangent. For each antenna the efficiency increases as the substrate thickness increases. The efficiency for the superconducting antenna reaches a maximum at approximately h/Ao z 0.003, while the maximum for the copper antennas is reached for h/Ao greater than 0.02. At the maximum, the space-wave radiation is the dominant loss mechanism. Beyond these corresponding maxima, the loss of energy due to radiation into the TM, surface wave of the conductor-backed substrate becomes significant. For thicker substrates the surface-wave loss becomes much larger than the combined conductor and dielectric loss, and as a result the efficiencies for the normal metal and superconducting antennas become approximately equal. These plots clearly demonstrate that as the thickness of the substrate increases, the surface-wave loss increases.

The plots for the impedance bandwidth shown in Figure 7.7 demonstrate that, in general, the bandwidth increases with increasing substrate thickness. The only exception occurs when the antenna has a very low efficiency due to extreme conductor loss. In this region the impedance bandwidth actually increases with increasing loss (decreasing substrate thickness). This characteristic is similar to that for other antennas when the radiation loss becomes small relative to the ohmic losses. The key piece of information from this figure is that the bandwith for antennas on LaAIO,, with its high dielectric constant, are very small, as can be seen from Eq. (5.69).

In Figure 7.8 we have plotted the resonance frequency versus temperature for the same 20-GHz microstrip antenna, for two cases: The patch and ground plane are YBaCuO superconductors, and the patch and ground plane are perfect electricconductors. The substrate and material parameters are the same as in the previous examples, and the YBaCuO films are assumed to be 0.25 pm thick. The surface reactance expression from Eq. (7.19) is used for both the HTS patch and ground plane. For this example, the electrical parameters of the substrate are assumed to be constant with temperature. From Figure 7.8 we observe a substantial shift in the resonance frequency for the HTS antenna as the temperature changes. These results are consistent with experimental observations, as we will show in a later section.

For comparison we have also plotted the efficiency and bandwith for a resonant patch with W/L= 1.5 at 20-GHz YBaCuO microstrip antenna at 77 K on a couple of lower-dielectric-constant substrates. These results are shown in


FIGURE 7.8 Rmnance frequency of a 20-GHz rectangular microstrip patch antenna on FIGURE 7.10 Impedance bandwidth of a 20-GHz YBaCuO rectangular microstrip a LaAIO, substrate (E , = 23 and tan 6 = 10-7. patch antenna on three different substrates (tan 6 = lo-').

-.--

FIGURE 7.9 Total antenna efficiency of a 20-GHz YBaCuO rectangular microstrip FIGURE 7.1 1 Total antenna efficiency of a 20-GHz copper rectangular microstrip patch patch antenna on three different substrates (tan 6 = 10-7. antenna on three different substrates (tan 6 = lo-').

Figures 7.9 and 7.10. For each case the loss tangent of the substrate is assumed to be lo-'. It is readily apparent from these figures that using lower-dielectric- constant substrates increases the element efficiency for either (a) very thin substrates where conductor losses dominate or (b) thick substrates where surface- wave losses dominate. Also, as expected, the bandwidth increases by decreasing the dielectric constant. Another interesting observation is that the surface-wave

loss is relatively insensitive to the dielectric constant for the higher 8, substrates. Similar plots for 77 K copper antennas are shown in Figures 7.1 1 and 7.12. The general results are the same as for the HTS antenna. However, we note that on low-loss, low-dielectric-constant substrates, cooled copper microstrip elements have efficiencies that rival equivalent HTS elements on high-dielectric-constant substrates over a wide range of substrate thickness. Unfortunately, low-loss


FIGURE 7.1 2 Impedance bandwidth of a 20-GHz copper rectangular microstrip patch antenna on three different substrates (tan 6 =

substrates (tan 6 < lo-') with dielectric constants on the order of 2.2 are not commonly available (with the exception of low-loss foam or honey-comb materials with E, x 1, but these materials are often not appropriate for monolithic circuit fabrication).

7.4 DESIGN CONSIDERATIONS

There are many significant issues that must be considered when designing monolithic HTS microstrip antennas. The most prominent are related to the dielectric substrate. At present, the substrate material that best satisfies all of the electrical requirements (low loss, reasonable dielectric constant), and on which very high quality HTS thin films can be grown, is lanthanum aluminate (LaAlO,). LaA10, has a good lattice match with YBaCuO; therefore, the films grown on these substrates are highly oriented, have fewer grain boundaries, and are more uniform than those grown on other microwave compatible substrate materials. As a result, good YBaCuO films on LaAIO, substrates have low surface resistances (typically on the order 0.5-0.75 mR/n at 10 GHz and 77 K) and high transition temperatures (approximately 89-93 K). Unfortunately, LaAIO, is far from an ideal substrate material. It has a relatively high dielectric constant for microwave and antenna applications, and it is extremely fragile and difficult to machine. In addition, LaAIO, is subject to a high degree of twinning which weakens the substrate and is often blamed for introducing loss in the HTS films because the twinning is reflected in the film, causing weak links and grain boundaries. To make matters worse, LaAIO, experiences a phase transition at

DESIGN CONSIDERATIONS 355

the temperatures required for the deposition of HTS films. Thus, the characteristics of the substrate often change during the deposition process. Another result of the high degree of twinning is that the dielectric constant of LaAIO, varies not only from sample to sample, but even over an individual substrate. Reported values of the dielectric constant for LaA10, range from 21 to 25, although most accept a value of between 23 and 25. This uncertainty and variation in the dielectric constant causes uncertainty and variation in device performance. LaAIO, does, however, have a relatively low loss tangent. The reported values range from approximately to [46]. Several other competing substrate materials exist, but for various reasons (usually because films grown on them have higher surface resistances) they have yet to gain universal acceptance. These include MgO, YSZ, NdGaO,, and r-plane A1,0, (sapphire). The primary disadvantage of r-plane sapphire is that it is highly anisotropic. Also, since sapphire is chemically incompatible with HTS materials at the processing temperatures required to obtain good superconducting properties, buffer layers are required. Commonly used buffer layer materials are CeO,, MgO, and YSZ [47].

The relatively high value of the dielectric constants for LaAlO,, YSZ, and NdGaO, do allow for the miniaturization of microstrip devices, such as patch antennas. In an antenna array, this results in more room between the radiators, thus allowing for more flexibility in the layout and the inclusion of other devices. However, as a consequence of the high E, the edge impedance of patch antennas becomes extremely high (see Eq. (5.74)) and the impedance bandwidth is reduced. Although it is difficult to accurately measure high values of edge impedance for a rectangular microstrip patch antenna, they are well over 1000 Cl for 0.254 mm thick LaAlO, substrates [48]. As a result, directly coupled feeds must be inset well into the patch, and these significant inset distances produce input impedances that are extremely sensitive to the inset depth. In addition, they preclude the construction of directly coupled circularly polarized elements since such elements generally require orthogonally fed modes that would be significantly perturbed by the large inset distances. Aperture or electromagnetically coupled feeds present design difficulties associated with alignment and cooling. An attractive alternative feed mechanism for planar antenna structures is gap coupling. Instead of directly connecting the microstrip feed line to the patch elements, a small gap is introduced between the end of the line and the edge of the antenna. When appropriately dimensioned, gap coupling provides a simple, yet effective, impedance transformer between the low-impedance feed line and the high-impedence patch [48].

To help offset the reduced bandwidth resulting from the use of a high E,

substrate material, the thickness of the substrate can be increased. This approach, however, has a significant drawback because increasing the substrate thickness also increases surface-wave losses, as demonstrated in the previous section. For many applications the effects of increased surface-wave excitation are generally more serious than the reduced bandwidth. Designs with multiple layers of dielectric materials offer potential solutions to some of these problems; however, these designs are much more complicated, and they present cooling problems


because in practice it is difficult to ensure low-loss thermal and electrical bonds between the layers.

Another important design consideration is cooling. The ultimate goal of most HTS antenna designs is to use liquid nitrogen as the cyrogen, which has a boiling point of 77 K. Liquid nitrogen is relatively inexpensive and easy to handle. In general, liquid nitrogen is used in an open-cycle cooling system where the superconducting device is often either fully or partially immersed in the cyrogen. Open-cycle systems require a continuous resupply of cyrogen. An alternate, yet more costly, method of cooling HTS devices is the use of a closed-cycle helium refrigerator. In these refrigerators, the superconducting devices are usually housed in an evacuated chamber and connected to a cold finger. Closed-cycle systems do not dissipate the cyrogen, but they are much more expensive than open-cycle systems. To cool an antenna the cyrogenic housing (cryostat) must be designed to simultaneously allow for the efficient cooling of the antenna and also provide a electromagnetically transparent window through which the antenna can radiate. The design of an effective cryostat can be quite involved, and the cooling systems often represents a significant fraction of the total antenna system cost. Of particular concern is the heat-lift capacity of the cooler, the thermal mass of the HTS devices and fixtures, and the thermal loading of the connecting cabling. When possible the mounting fixtures, radomes, and cyrogenic platform must be designed to minimize their influence on the antenna.

7.5 EXPERIMENTAL RESULTS

To date, only a rather limited number of HTS antenna studies have been conducted. Many have been directed toward superdirective arrays and electrically small antennas. In this section we will present results from some of the studies that demonstrate the specific properties of HTS microstrip antennas.

In our first example we will show the results from the direct measurement of the efficiencies of copper and YBaCuO rectangular microstrip patch antennas [14]. These antennas were fabricated from 0.25-pm-thick YBaCuO films deposited on 0.508-mm LaAlO, substrates using an in-situ-scanned, large-area laser ablation system. The planar structures were patterned using standard photo- lithography with a negative photoresist, and the films were etched using ion- beam milling. The measurements were made in a two-stage, closed-cycle helium cryogenic refrigerator with a hemispherical quartz radome so that the efficiencies and patterns of the antennas could be measured as a function of temperature in a high-vacuum environment.

The patch design that was used in this study is shown in Figure 7.13. In this design a coplanar-waveguide (CPW) feed line is used. This CPW line is terminated in a loop to provide a monolithic, low VSWR feed [49]. A very good impedance match is obtained for CPW-loop-fed patch antennas over a broad range of feed positions. Furthermore, measured results indicate that the radiation from the CPW line and loop do not alter the principal-plane radiation

Top view

EXPERIMENTAL RESULTS 357

Edge view

FIGURE 7.1 3 CPW-loop-fed microstrip patch antenna.

patterns of the patch antenna. An extended Wheeler method was used to accurately measure the efficiency of a 4.9-GHz copper antenna and an identical 4.9-GHz YBaCuO antenna. The measured efficiencies versus temperature are shown in Figure 7.14. Note that the HTS antenna has a fairly sharp transition near 89 K. Below this temperature the efficiency of the HTS antenna (both patch and ground plane are YBaCuO) is greater than that of the copper structure (ground plane and patch are OFHC copper). At 77 K the measured efficiency for the YBaCuO antenna is approximately 97%, compared to a predicted value (also shown in the figure) of 95%. For the copper antenna at 77 K the measured efficiency is approximately 77%, compared to a predicted value of 74.5%. These results offer validation of the equations presented earlier. The equations discussed in the previous sections were used for the analysis of these antennas.

358 SUPERCONDUCTING MICROSTRIP ANTENNAS EXPERIMENTAL RESULTS 359

20 30 40 50 60 70 80 90 Temperature [K]

FIGURE 7.14 Measured antenna efficiency for a YBaCuO and a copper CPW-fed rectangular patch antenna at 4.9 GHz.

FIGURE 7.1 5 (a) Direct-coupled rectangular microstrip patch antenna. (b) Gap-coupled circular microstrip patch antenna. (From reference [46], 0 1992 IEEE.)

A more extensive experimental investigation of HTS microstrip antennas and arrays is summarized in reference [SO]. In this investigation, similar efficiency versus temperature responses as those shown in our first example were obtained for direct-coupled rectangular and gap-coupled circular YBaCuO patch antennas (Figure 7.15). Examples of the efficiencies measured using the Wheeler- cap method are shown in Figure 7.16 [48]. Results are given for HTS and gold antennas with copper ground planes. The HTS antennas were fabricated on 0.25-mm-thick LaAIO, substrates. The YBaCuO films for the directly coupled antennas were deposited using off-axis sputtering and had a Tc of approximately

FIGURE 7.16 Measured efficiencies for YBaCuO and gold, direct- and gap-coupled patch antennas. (From reference [46], 0 1992 IEEE.)

-.t HTS measured

28.0 0 50 100 150 200 250 300

Temperature (K)

FIGURE 7.1 7 Resonance frequency of direct-coupled rectangular patch antenna. (From reference [4q, 0 1992 IEEE.)

89 K, and the films for the gap-coupled antennas were deposited using a laser ablation system (Tc - 84.5 K). The films were wet etched using a 1% H3P04 solution. The measurements were made in a two-stage closed-cycle helium refrigerator. A plot of the measured resonance frequency for the direct-coupled antenna is shown in Figure 7.17. Notice that, as the temperature approaches the transition temperature, the resonance frequency for the antenna decreases


0.81 . . 8 . 8 . , , , . 1 0 50 100 150 200 250 300

Temperature (K)

FIGURE 7.18 Measured bandwidths for YBaCuO and gold, direct- and gap-coupled patch antennas. (From reference [46], o 1992 IEEE.)

dramatically. This change is a consequence, as demonstrated in the previous section, of the increase in the effective penetration depth (and, hence, the surface inductance) of the film as the temperature increases. The change in the resonance frequency of the gold antenna is due to the 2% decreasein the dielectric constant of LaAIO, from 300K to approximately 20 K. Plots of the measured bandwidth are shown in Figure 7.18.

The relative gains for a linearly polarized four-element direct-coupled rectangular YBaCuO patch array and a linearly polarized four-element gap-coupled circular YBaCuO patch array, compared to an identical array of gold, are shown in Figure 7.19. As expected from the results shown in the previous section, the gain improvement is rather modest since the number of elements in the array is small. But these results do demonstrate that a gain improvement can be realized by using HTS materials. The relative efficiency of a linearly polarized 64-element direct-coupled rectangular Tl,CaCu,O, patch array, compared to an identical gold array at 30 GHz, is shown in Figure 7.20 [a. These results show a rather significant gain improvement for the HTS array.

For the next example, we show some results for a four-element array of circularly polarized, 20-GHz YBaCuO microstrip antennas fabricated on a 0.254-mm-thick LaAIO, substrate [13]. The layout of the array is shown in Figure 7.21. The design uses a microstrip feed network with gap-coupling to excite orthogonal modes on square microstrip patch elements. A phase differential of 90" is established by making the length of one of the orthogonal feed lines a quarter-wavelength longer than the other. The gap size (exaggerated in the figure) is 15pm and is designed to provide a good match to the patch. All

EXPERIMENTAL RESULTS 361

Temperature (K)

FIGURE 7.19 Gains of 20-GHz, four-element YBaCuO arrays relative to gold arrays. (From reference [46], Q 1992 IEEE.)

0

Temperature (K)

FIGURE 7.20 Efficiency of a 30-GHz, 64-element TlCaBaCuO array relative to a gold array. (From reference [7], 1992 IEEE.)


FIGURE 7.21 A 20-GHz, four-element gap-coupled circularly polarized microstrip array.

Theoretical Measured FIGURE 7.22 Theoretical and measured spinning-linear radiation patterns for 20-GHz YBaCuO array in Figure 7.21.

microstrip lines are 500, with the exception of the 35-a quarter-wave matching sections at the tee junctions. The spacing between the element centers is L,/2. The ground plane is a 2-pm-thick layer of silver, evaporated on the back of the substrate. The YBaCuO films were 0.25-pm thick. An identical antenna was fabricated using copper for the microstrip patches, feed lines, and ground plane. The theoretical and measured spinning-linear patterns for this array design are shown in Figure 7.22. There is relatively good agreement between these patterns.

EXPERIMENTAL RESULTS

40 50 60 70

Temperature (K)

FIGURE 7.23 Gain of 20-GHz, four-element YBaCuO array, in Figure 7.21, relative to a room-temperature copper array.

A plot of the measured gain of the YBaCuO microstrip array relative to the room temperature copper array is shown in Figure 7.23. This plot shows a sharp transition at approximately 85 K, with the relative gain increasing above 0 dB for temperatures below 82 K. In addition to the measured gain, a point which shows the theoretically predicted relative gain of 1.67 dB at 77K is provided. This value is very close to the measured result. At 30 K the measured relative gain increases to 3.4dB.

Herd et al. [51] have designed and tested a 20-GHz, 16-element microstrip array with a proximity-coupled YBaCuO feed network. The structure, shown in Figure 7.24, consists of 16 copper rectangular patches printed on a 1-mm-thick quartz superstrate that also functions as a window for the vacuum environment of the cryo-chamber. This superstrate is separated from the YBaCuO feed network by a small vacuum gap. Small 0.5-mm-thick Teflon spacers are used to maintain a fixed gap spacing. Small YBaCuO microstrip patches on a 0.254-mm- thick LaA10, substrate are used to electromagnetically couple to the larger patches on the quartz. A thin copper film is evaporated on the backside of the LaAlO, substrate as a ground plane for the HTS patches and the feed network. The primary purpose for this proximity-coupled design is to improve the bandwidth of the antenna. The measured gain versus frequency at 80 K for the HTS feed and an identical room temperature copper feed is shown in Figure 7.25. Over most of the approximately 10% operating band, the HTS antenna has significantly higher gain.

FIGURE 7.24 A 20-GHz, 16-element proximity-coupled microstrip array. (From reference [49].)

HTS array at 80K - - Copper array at 290K -------

L I I

FIGURE 7.25 Gain for the antenna in Figure 7.24 with a YBaCuO feed at 80K and a room-temperature copper feed.

APPENDIX 365

7.6 SUMMARY

The intent of this chapter was to provide a brief introduction to high-temperature superconductivity and to discuss the application of these materials in the fabrication of microstrip antennas. We have presented a simple empirical model for high-temperature superconductors and used it to predict the performance of HTS patch antennas. Results of experiments that demonstrate some of these theoretical predictions have also been shown.

From our discussion it is obvious that HTS materials are not appropriate for most monolithic antenna applications. The added complexity of cryogenic cooling and the required (at least currently) use of high-dielectric substrates preclude their use in most systems. However, HTS materials, when incorporated in designs such as those demonstrated in this chapter, do offer potential gain improvements for antenna systems that can accommodate the added constraints of the superconducting environment.

APPENDIX

In this appendix the expression for the efficiency of a corporate feed for a 2N x 2N array [Eq. (7.3811 is derived, along with the expression for the efficiency of the quarter-wave transformer [Eq. (7.3911. The corporate feed is assumed to have the same characteristic impedance for all lines. At each tee junction there is a 2: 1 quarter-wave impedance transformer that changes the impedance level. The antennas are spaced a distance d apart and are assumed to be perfectly matched with the feed lines. The corporate array is assumed to be fed by an incoming feed line that extends a distance of d/2 beyond the edge of the array.

In the corporate feed, loss is due to power dissipation in the quarter-wave transformer sections and power loss in the lines (which is the dominant loss mechanism). The total number of transformers encountered by going from the input feed line to any given antenna is 2N. Hence, the overall efficiency of the feed network is

where q, is the quarter-wave transformer efficiency, and q, is the line efficiency, which we define as the efficiency of the corporate feed when the only power loss is associated with the feed lines. Expressions for these quantities are derived in the following sections.

A.l Line Efficiency

The line efficiency q, is given by


where L is the total line length measured from the beginning of the input to any one of the antennas. The line length measured from the center of the array to any particular antenna is

The extra line length due to the input feed line is assumed to be

The total line length is then L = LC + L,. From Eq. (7.58) we then have

which is the same as Eq. (7.38).

A.2 Transformer Efficiency

We assume a quarter-wave matching transformer with a characteristic impedance Z,, and load impedances 2, and Z, connected to each end z = - L and z = 0, respectively. ~ h d s e impedances are related by Zo = m. Assuming that L is a'quarter-wave length (kL= 42), the input and output currents are related by

where I, is the input current a t z = - L, and I, is the output current a t z = 0. The current on the quarter-wave line as a function of z can be written in terms of I, and I, as

where zL =Z,/Zo is the normalized load impedance. In terms of this current, the total power dissipated on the quarter-wave line is

REFERENCES 367

where a, is the attenuation constant (nepers/m) for the quarter-wave transmission line.

The power flowing out of the transformer is expressed in terms of the output current I, as

P , = @zl1212 (7.65)

Under the assumption of small losses, the output power is approximately equal to the input power (Po,, x Pi,,); hence, from these equations we obtain

The transformer efficiency, defined as (Pin -Pd)/Pin, is then

Assuming that Z, = Z1/2 and the transformer is a quarter-wavelength long, we rewrite this equation as

which is the same as Eq. (7.39).

REFERENCES

[I] G. C. Liang, D.Zhang, C. F. Shih, M. E. Johansson, andR. S. Withers, "High-Power High-Temperature Superconducting Microstrip Filters for Cellular Base-Station Applications," IEEE Trans. Appl. Supercond., Vol. 5, No. 2, pp. 2652-2655,1995.

[2] G. Subramanyam, V. J. Kapoor, and K. B. Bhasin, "A Hybrid Phase Shifter Circuit Based on TlCaBaCuO Superconducting Thin Films," IEEE Trans. Microwave Theory Tech., Vol. 43, No. 3, pp. 566-572,1995.

[3] S. H. Talisa, M. A. Janocko, C. Moskowitz, J. Talvaccio, J. F. Billing, R. Brown, D. C. Buck, C. K. Jones, B. R. McAvoy, G. R. Wagner, and D. H. Watt, "Low and High Temperature Superconducting Microwave Filters," IEEE Trans. Microwave Theory Tech., Vol. 39, No. 9, pp. 1455-1461,1991.

[4] W. G. Lyons, R. R. Bonetti, A. E. Williams, P.M. Mankiewich, M. L. O'Malley, J. M. Hamrn, A. C. Anderson, R. S. Withers, A. Menlenberg, and R. E. Howard, "High-Tc Superconductive Microwave Filters," IEEE Trans. Magn., Vol. 27, NO. 2, pp. 2537-2539,1991.

[5] L. C. Bourne, R. B. Hammond, McD. Robinson, M. M. Eddy. W. L. Olson, and T. W. Jones, "A Low Loss Microstrip Delay Line in T1,CaBa,Cu2O8," Appl. Phys. Lett., Vol. 56, pp. 2333-2335, 1990.

368 SUPERCONDUCTING MICROSTRIP ANTENNAS REFERENCES 369

[6] M. A. Richard, K. B. Bhasin, C. Gilbert, S. Metzler, G. Koepf, and P. C. Claspy, "Performance of a Four-Elemenet Ka-Band High-Temperature Superconducting Microstrip Antenna," IEEE Microwave Guided Lett., Vol. 2, No. 4, pp. 143-145, 1992.

[A L. L. Lewis, G. Koepf, K. B. Bhasin, and M. A. Richard, "Performance of TlCaBaCuO 30 GHz 64 Element Antenna Array." IEEE Trans. Appl. Supercond., Vol. 3, No. 1, pp. 2844-2847, 1993.

[8] L. P. Ivrissimtzis, M. J. Lancaster, T. S. M. Maclean, and N. McN. Alford, "High- Gain Series Fed Printed Dipole Arrays Made of High-Tc Superconductors," IEEE Trans. Antennas Propagat., Vol. 42, No. 10, pp. 1419-1429,1994.

[9] J. S. Herd, D. T. Hayes, J. P. Kenney, L. D. Poles, K. G. Herd, and W. G. Lyons, "Experimental Results on a Scanned Beam Microstrip Antenna Array with a Prox- imity Coupled YBCO Feed Network," IEEE Trans. Appl. Supercond., Vol. 3, No. 1, pp. 2840-2843,1993.

[lo] R. J. Dinger, D. R. Bowling, and A.M. Martin, "A Survey of Possible Passive Antenna Applications of High-Temperature Superconductors." IEEE Trans. Microwave Theory Tech., Vol. 39, No. 9, pp. 1498-1507,1991.

[11] L. P. Ivrissimtzis, M. J. Lancaster, and N. McN. Alford, "A High-Gain YBCO Antenna Array with Integrated Feed and Balun," IEEE Trans. Appl. Supercond., Vol. 5, NO. 2, pp. 3199-3202,1995.

[12] H. Chaloupka, N. Klein, M. Peiniger, H. Piel, A. Pischke, and G. Splitt, "Miniatur- ized High-Temperature Superconductor Microstrip Patch Antenna,'' IEEE Trans. Microwave Theory Tech., Vol. 39, No. 9, pp. 1513-1521,1991.

[I31 J. D. Morrow, J. T. Williams, M. F. Davis, D. Licon, D. H. R. Rampersad, D. R. Jazdyk, S. A. Long, and J. C. Wolfe, "Circularly-Polarized, 20 GHz High Tempera- ture Superconducting Microstrip Antenna Array," IEEE Trans. Appl. Supercond. (to be published).

[14] R. L. Smith, J. T. Williams, M. F. Davis, D. H. R. Rampersad, D. R. Jackson, S. A. Long, and J. C. Wolfe, "Design and Experimental Characterization of a Coplanar Waveguide Fed High-Temperature Superconducting Microstrip Antenna," IEEE Trans. Antennas Propagat. (to be published).

[15] L. P. Ivrissimtzis, M. J. Lancaster, and M. McN. Alford, "Supergain Printed Arrays of Closely Spaced Dipoles Made of Thick Film High-Tc Superconductors," IEE Proc. Microwave Antennas Propagat., Vol. 142, No. 1, pp. 26-34, 1995.

[16] H. Chaloupka, "Superconducting Multiport Antenna Arrays," Microwave Optical Tech. Lett., Vo. 6, No. 13, pp. 737-744, 1993.

[ l q R. C. Hansen, "Superconducting Antennas," IEEE Trans. Aerospace Electron. Syst., Vol. 26, NO. 2, pp. 345-355, 1990.

[I81 M. Tinkham, Introduction to Superconductivity, Malabar, R. E. Krieger, 1980. [I91 T. Van Duzer and C. W. Turner, Principles of Superconducting Devices, Elsevier,

New York, 1981. [20] T. P. Orlando and K. A. Delin, Foundations of Applied Superconductivity, Addison-

Wesley, New York, 1991. [21] M. R. Beasley, "High-Temperature Superconductive Thin Film," Proc. Proc. IEEE,

Vol. 77, No. 8, pp. 1155-1163,1989.

[22] M. R. Beasley, "Recent Progress in High-Tc Superconductivity: What Would Make a Difference?" IEEE Trans. Appl. Supercond., Vol. 5, No. 2 pp. 141-151,1995.

[23] W. Meissner and R. Ochsenfeld, "Ein Neuer Effekt bei Eintritt der Supraleitfahig- keit," Naturwissenschaften, Vol. 21, pp. 787-788,1933.

[24] J. Bardeen, L. N. Cooper, and J. R. Schrieffer, 'Theory of Superconductivity," Phys. Rev., Vol. 108, pp. 1175-1204, 1957.

[25] A. W. Sleight, "Chemistry of High-Temperature Superconductors," Science, Vol. 242, pp. 1519-1527,1988.

[26] K. Salama, V. Selvalanickam, L. Gao, and K. Sun, "High Current Density in Bulk YBa,Cu307," Appl. Phys. Lett., Vol. 54, pp. 2352-2354,1989.

[27l D. C. Mattis and J. Bardeen, 'Theory of Anomalous Skin Effect in Normal and Superconducting Metals," Phys. Rev., Vol. 111, pp. 412-417,1958.

[28] F. London and H. London, "The Electromagnetic Equations of the Superconduc- tor," Proc. R. Soc. London, Vol. 171, pp. 71-88,1935.

[29] L G. Ma and I. Wol& "Modeling the Microwave Properties of Superconductors," IEEE Trans. Microwave Theory Tech., Vol. 43, No. 5, pp. 1053-1059,1995.

[30] L. Drabeck, G. Gruner, J. J. Chang, A. Inam, X. D. Wu, L. Nazar, T. Venkatesan, and D. J. Scalapino, "Millimeter-Wave Surface Impedance of YBa2Cu,07 Thin Films," Phys. Rev. B, Vol. 40, pp. 7350-7354,1989.

[31] E. J. Pakulis, R. L. Sandstrom, P. Chaudhari, and R. B. Laibowitz, "Temperature Dependence of Microwave Losses in Y-Ba-Cu-0 Films," Appl. Phys. Lett., Vol. 57, pp. 940-941, 1990.

[32] 0. G. Vendik and A. Y. Popov, "Bipolaron Theory to the Microwave Surface Resistance of High-Temperature Superconductors," Philos. Mag. Lett., Vol. 65, pp. 219-224,1992.

[33] W. N. Hardy, D. A. Bonn, D. C. Morgan, R. Liang, and K. Zhang, "Precision Measurements of the Temperature Dependence o f t in YBa,Cu,O,.,,: Strong Evi- dence for Nodes in the Gap Function," Phys. Rev. Lett., Vol. 70, pp. 3999-4002,1993.

'

[34] A. M. Neminsky and P. N. Nikolaev, '"Temperature Dependence of Anisotropic Penetration Depth in YBa2Cu307 Measured on Aligned Fine Power," Physica C, Vol. 212, pp. 389-394,1993.

[35] R. L. Kautz, "Picosecond Pulses on Superconducting Striplines," J. Appl. Phys., Vol. 49, pp. 308-314,1978.

[36] D. E. Oates, A. C. Anderson, D. M. Sheen, and S. M. Ali, "Stripline Resonator Measurements of Z, versus H , in YBa,Cu307-, Thin Films," IEEE Trans. Micro- wave Theory Tech., Vol. 39, No. 9, pp. 1522-1529,1991.

[37] D. E. Oates, P. P. Nguyen, G. Dresselhaus, M. S. Dresselhaus, C. W. Lam, and S. M. Ali, "Measurements and Modeling of Linear and Nonlinear Effects in Stripline," 3. Supercond., Vol. 5, No. 4, pp. 361-369,1992.

[38] D. E. Oates, P. P. Nguyen, G. Dresselhaus, M. S. Dresselhaus, and C. C. Chin, "Nonlinear Surface Resistance in YBa,Cu307-, Thin Films," IEEE Trans. Appl. Supercond., Vol. 3, No. 1, pp. 1114-1118,1993.

[39] J. S. Herd, J. Halbritter, and K. G. Herd, "Microwave Power Dependence of HTS Thin Film Transmission Lines," IEEE Trans. Appl. Supercond., Vol. 5, No. 2, pp. 1991-1993,1995.


[40] C. W. Lam, D. M. Sheen, S. M. Ali, and D. E. Oates, "Modeling the Nonlinearity of Superconducting Strip Transmission Lines,' IEEE Trans. Appl. Supercond., Vol. 2, No. 2, pp. 58-65,1992.

[41] D. Nghiem, J. T. Williams, and D. R. Jackson, "A General Analysis of Propagation Along Multiple-Layer Superconducting Stripline and Microstrip Transmission Line," IEEE Trans. Microwave Theory Tech., Vol. 39, No. 9, pp. 1553-1565,1991.

[42] R. E. Collin, Foundations for Microwave Engineering, New York: McGraw-Hill, 1992.

[43] J. M. Ponds, J. H. Claassen, and W. L. Carter, "Measurements and Modeling of Kinetic Inductance on Microstrip Delay Lines," IEEE Trans. Microwave Theory Tech., Vol. 35, No. 12, pp. 1256-1262, 1987.

[44] J. C. Swihart, "Field Solution for a Thin-Film Superconducting Strip Transmission Line," J. Appl. Phys., Vol. 32, pp. 461-469,1961.

[45] R. F. Harrington, Time-Harmonic Electromagnetic Fields,New York: McGraw-Hill, 1961.

[46] J. Konopka and I. Wolff, "Dielectric Properties of Substrates for Deposition of High-T, Thin Films Up to 40 GHz," IEEE Trans. Microwave Theory Tech., Vol. 40, No. 12, pp. 2418-2425,1992.

[47] X. D. Wu, S. R. Foltyn, R. E. Muenchausen,D. W. Cooke, A. Pique,D. Kalokitis, V. Pendrick, and E. Belohoubek, "Buffer Layers for High-T, Thin Films on Sapphire," J. Supercond., Vol. 5, No. 4, pp. 353-359, 1992.

[48] M. A. Richard, K. B. Bhasin, and P. C. Claspy, "Superconducting Microstrip An- tennas: An Experimental Comparison of Two Feeding Methods," IEEE Trans. Antennas Propagat., Vol. 41, No. 7, pp. 967-974,1993.

[49] R. L. Smith and J. T. Williams, "An Electromagnetically Coupled Coplanar Waveguide Feed for Microstrip Antennas:' Electron. Lett., Vol. 28, No. 25, pp. 2272-2274,1992.

[50] M. A. Richard, "An Experimental Investigation of High-Temperature Supercon- ducting Microstrip Antennas at K- and Ka-Band Frequencies," NASA Contractor Report, No. 191089,1993.

[51] J. S. Herd, L. D. Poles, J. P. Kenney, J. S. Derov, M. H. Champion, J. H. Silva, M. Davidovitz, K. G. Herd, W. J. Bocchi, S. D. Mittleman, and D. T. Hayes, "Twenty GHz Broadband Microstrip Array with Electromagnetically Coupled High-Tc Superconducing Feed Network," IEEE Trans. Microwave Theory Tech., Vol. 44, NO. 7, pp. 1384-1389,1996.

CHAPTER EIGHT

Active Microstrip Antennas

JULIO A. NAVARRO and KAI CHANG

8.1 INTRODUCTION

Typical radio-frequency (RF) front-end layouts have an obvious progression from an input component to the output at the antenna. Traditionally,microwave components have remained within guided-wave structures far away from the antenna terminals. Within the nonradiating circuits, metallic enclosures are used to shield them away from each other and the antenna. However, once a signal reaches the antenna, it radiates directly into free space and the fields are not so easily controlled. Devices and structures near the antenna can disturb radiation patterns which, in turn, can disrupt the component and subsystem performance. These are the problems and challenges which are met when components are attached directly to an antenna. In this chapter, we describe conventional transmitters/receivers, define the concept of active integrated antennas, and review most implementations described in the literature.

The conventional subsystem uses a modular approach as shown in Figure 8.1. It uses separately designed components and antennas interconnected via transmission lines. Although there are all sorts of transmission lines, most systems have previously relied on waveguides and coaxial cables. Similarly, there are many types of antennas and these often take the shape of an aperture or wire (i.e. horn, dipole, etc.). The types of components and antennas determine the type of transition required (i.e., apertures, probes, loops, etc.).

In the conventional approach, there is freedom to optimize the performance of components and antennas independently because there is an obvious distinction between the circuit components and the radiating structure. Although this

Advances in Microstrip and Printed Antennas, Edited by Kai Fong Lee and Wei Chen. ISBN 0-471-04421-0 0 1997 John Wiley &Sons, Inc.

INTRODUCTION 373

modular approach has many advantages, they are often quite bulky, expensive to manufacture, and difficult to reproduce. A modified conventional approach replaces waveguides, coaxial circuits, and interconnections with microwave integrated circuits (MICs), thereby reducing the overall size and weight of the system. Further miniaturization has been demonstrated with monolithic MICs (MMICs). In MMICs, solid-state devices are fabricated simultaneously with transmission lines and distribution networks to create phase-shifters, switches, oscillators, mixers, and amplifiers. Complete subsystems are created and later coupled to antennas to complete the RF front-end. In these improvements, there still remains a well-defined boundary between where the guided-wave structure ends and the radiator begins.

The integrated antenna approach differs from other, more conventional approaches in that there is no obvious distinction or boundary between the microwave component and the antenna. Packaged devices (or MICs, MMICs) lie within the volume normally associated with the radiating structure. Compo- nent functions are embedded directly at the terminals of the antenna. The antenna serves both as a load and as the radiator for the component. The type of solidkate device and antenna determines the final microwave component realized and its classification (i.e., passive or active). The following guidelines can be used to differentiate between a passive integrated antenna and an active integrated antenna (i.e. active antenna).

1. Passive integrated antennas are antennas incorporating one or more passive solid-state devices and circuits for switching, tuning, modulating, detecting, or any other functions which d o not purposely generate new R F frequencies. These antennas have an input and/or output R F port.

2. Active integrated antennas are antennas incorporating one or more.active solid-state devices and circuits to amplify or generatenew R F frequencies. This category usually involves a negative resistance device for R F power generation or amplification, although the use of passive nonlinear devices for R F multiplication and/or mixing is also included. In the case of amplifiers, mixers, and multipliers, an R F input and/or output port is required. An R F port can also be used with a radiating oscillator for external stabilization of the signal.

Typical integrated antennas have focused primarily on a single function such as detection, amplification, or oscillation. However, more complicated functions require combinations of several devices and/or MMICs. In this fashion, all possible R F component functions can be localized within the antenna structure to provide the smallest possible subsystem. The smallest possible subsystem, however, is not without its share of problems. Due to strong coupling between the fields of the circuit and the radiator. there is considerable degradation of both the - component and antenna performance. If a single substrate is used, its properties cannot be separately optimized for the circuit or the antenna. The combination of

3 7 4 ACTIVE MICROSTRIP ANTENNAS THE EARLY HISTORY O F INTEGRATED ANTENNAS 3 7 5

antennas and circuits on a single substrate often forces a significant trade-off in the overall performance. Solid-state devices and MICs may also require direct- current (DC) biasing lines near the antenna which can disturb currents flowing on the radiating surfaces. Similarly, the antenna may have to be modified to accommodate these devices which often degrade radiation characteristics. Fur- thermore, the small surface area of an integrated antenna limits the amount of power it can handle. Many configurations have been devised to address integration issues as well as the power limitations of a single integrated antenna.

8.2 THE EARLY HISTORY OF INTEGRATED ANTENNAS

The integrated antenna concept may appear to be in its infancy, but the idea is not new. It could be argued that Hertz introduced the concept with his end-loaded transmitter and resonant square-loop antenna receiver in 1893 [I]. Neither the transmitter nor the receiver used any matching networks between the circuit and antenna terminals. The dipole served as the tank circuit for the transmitter, and the resonant square-loop was the only frequency filter for the receiver. Spark-gap transmitters which operate along these lines were widely used at the beginning of the twentieth century. These transmitters offered little control over frequency stability or unwanted harmonics and caused widespread interference. They were subsequently banned from commercial applications by the Federal Communica- tions Commission (FCC) in 1934.

Transmitters had to be filtered and stabilized to meet stringent regulations. This control over the performance of the transmitter was accomplished within the circuit away from the antenna as in conventional approach. These issues could not be addressed at the time with an integrated antenna. For these reasons, both commercial and military transmitters implemented to date have avoided the use of an integrated or active antenna.

The integrated antenna concept surfaced again three decades later when Frost described a parametric amplifying antenna in June 1960 [2]. Several investigators from Ohio State University funded primarily by the United States Air Force, demonstrated both diode- and transistor-integrated antennas 13, 41. Using a tunnel diode and a spiral antenna, Boehnker, Copeland and Robertson demonstrated a mixer-integrated antenna which they described as an ''antennaverter." They also used a traveling-wave antenna together with tunnel diodes to operate as a traveling-wave amplifier which they called an "antennafier." Figure 8.2 shows both amplifier and downconverter implementation of these integrated aerials. The amplyfying antenna or "antennafier" is shown as a series of slots integrated with diodes which are fed by a stripline. The "antennaverter" or downconverting antenna is realized using a broadband conical spiral integrated with a tunnel diode. The measurement setup is shown along with the converting performance from 15OMHz to 1 GHz. In 1961, Pedinoff [S] demonstrated a slot amplifier. A thorough description of a tunnel- diode-integrated dipole antenna amplifier was later shown by Fujimoto [6, 71.

INCIDENT WAVE / ARRAY OF RADIATING

AT FREQUENCY Wt ELEMENTS SUCH AS SLOTS

\

.UP PUMP INPUT

STRIPUNE LOADED WITH DIODES

GENERATOR

LOCAL

p DIPOLE

FIGURE 8.2 Early integrated antennas [3,4]: (a) Sketch of a traveling-wave parametric antennafier; (b) measurement apparatus; (c) measured performance of the conical spiral antennaverter.

376 ACTIVE MICROSTRIP ANTENNAS

A single "antennafier" demonstrated a gain of 10-dB and 6-dB noise figure at 420 MHz.

8.3 DIODE-INTEGRATED ACTIVE MICROWAVE ANTENNAS

It took many years for active diode integrated antennas to return to the literature. The usefulness of the integrated approach was in the microwave- and millimeter- wave bands, but device technology had not advanced enough to take advantage of it. In 1979, Kwok and Weller 18) showed the use of the BARITT diode for Doppler-sensing applications. Armstrong et al. [9] went on to demonstrate an active BARITT-integrated microstrip patch antenna Doppler sensor in 1980. As a radiating oscillator coupled directly to free space, an active antenna is very sensitive to changes in its immediate vicinity. Variations in its environment (i.e., temperature, relative motion) are translated into shifts in the operating frequency. These shifts make an active antenna ideal for Doppler sensing. A BARITT diode was integrated with a microstrip patch antenna and used as a self-oscillating mixer (SOM). The diode was integrated on the same substrate using a patch antenna for radiation and an open microstrip stub for impedance matching. Its use as a proximity detector highlights a practical application for individual active antennas. As shown in Figure 8.3, it is a typical active antenna product: simple, compact, and inexpensive. The proximity detector application does not require excessive amounts of power and can be used in automatic door openers, burglar alarms, and other commercial applications. However, the use of the BARITT diode was short-lived, and this type of integrated antenna approach was filed away for several years.

During the 1980s, improvements in solid-state devices and integrated circuit techniques had made millimeter-wave operating frequencies more accessible. Integrated circuits increased in its uses and functionality. Monolithic circuits began to replace hybrid integrated circuits. Improvements in packaging technology made antenna integrations possible by reducing their effects on the antenna structure. Early in the decade, investigators began to miniaturize circuits and bring them closer to the antenna.

In 1982, the varactor-integrated microstrip patch antenna was introduced by Bhartia and Bahl [lo]. The simple integration turns a narrowband antenna (< 2 %)into a fairly wideband tunable element(- 30%). The quick-tuning ability of the solid-state varactors makes it an ideal preselector for receiving systems. The loading effect on the antenna input impedance gives it potential to remove scan blindness in phased arrays. This successful integration opened possibilities for other devices and different functions. However, this valuable contribution stirred very little interest. At the time, more emphasis was placed on circuit level power combiners to overcome power limitations of single solid-state devices.

In 1984, the first monolithic Gunn-integrated endfire antenna was developed by Wang and Schwa= [Ill. The Gunn diode uses a uniplanar coplanar- waveguide (CPW) resonator coupled to a tapered slot antenna for measurement. Since it was not intended to be an active antenna the tapered-slot radiator was

DIODE-INTEGRATED ACTIVE MICROWAVE ANTENNAS 377

eat sink

FIGURE 8.3 BARITT-diode microstrip Doppler sensor. (From reference [9], with permission from IEEE.)

not an integral part of the Gunn oscillator design. Instead, it was a means of avoiding the use of a coaxial connector for a direct frequency measurement. The clever technique allowed measurement of the oscillating frequency using only an antenna and spectrum analyzer.

In 1984 and 1985, Thomas et al. [12, 131 reported a Gunn-integrated rectangular microstrip patch antenna operating at X-band frequencies. The active microstrip patch was a compact, inexpensive microwave source which could be used for Doppler-sensing or spatial-power-combining applications. The design consists of a Gunn diode and a rectangular microstrip patch antenna. The antenna serves as a resonator and load for the radiating oscillator. The active device is biased to oscillate at 10.891 GHz. This hybrid integration does not use any external RF matching networks unlike the BARITT Doppler sensor above. By varying the diode position along the antenna, the device can be matched for efficient RF power generation. A high-impedance line at a low-impedance point on the mtch is used to provide DC bias to the active device. The design also -- -..- r ~

provides a means for external injection-locking and stabilization. The fields for this rectangular patch antenna and design as an oscillator can be

approached in the following manner. For a rectangular microstrip patch antenna with a resonant length Land width Was shown in Figure 8.4, the fields under the patch antenna may be written as

378 ACTIVE MICROSTRIP ANTENNAS DIODE-INTEGRATED ACTIVE MICROWAVE ANTENNAS 379

where the reactances cancel. The conditions for oscillation are

FIGURE 8.4 Microstrip patch antenna configuration.

where Vo is the voltage at a patch corner, h is the height of patch substrate over the ground plane, and m and n depict the mode of operation. The resonant frequency for the lowest-order mode (m = 0, n = 1) is given by (neglecting fringing effects),

where c is the speed of light and E, is the relative dielectric constant of the substrate material.

For the dominant mode, the real part of the input impedance is a minimum at the center of the patch (i.e. L/2) and is maximum near the radiating edges of the patch. The impedances at different points along the patch are needed to match the active device and ensure that oscillations are sustained. The real part of the input impedance seen at a position y along its resonant length is

where Ro is the radiation resistance at the edge of the patch. If we neglect discontinuities and perturbations, the solid-state device can be matched by solving Eq. (8.3) for the device position:

where - R, is the real part of the device impedance (- R, + jX,), G, is the patch radiation conductance, and G,,, is the mutual conductance of the two radiating edges.

The active antenna integration will begin to oscillate if R, is approximately 20% greater than the input resistance (R,) seen by the device at the frequency

A packaged device is typically large with respect to the antenna, which will disturb the fields within the antenna. If the device could be integrated without disturbing the antenna (i.e., unpackaged, monolithically), the far-field patterns of the patch radiator would be closer to ideal. These disturbances often cause large deviations from calculated radiation patterns. Active antennas often exhibit irregular patterns and high cross-polarization levels (CPLs), and the need for biasing lines further degrades the radiation performance. In the radiation patterns reported by Thomas et al. [13],'the relative size of the diode package to the antenna causes a very high H-plane cross-polarization component ( + 2 dB higher than copolarization component).

The following year in 1986, an IMPATT integrated circular microstrip patch was shown by Michael Dydyk [14]. Similar to the rectangular patch antenna, the fields within a circular patch on a thin substrate can be expressed as

where r and 4 are the radial and angular coordinates for the circular configuration. J , is the Bessel function of order 1, and the prime sign indicates differentia- tion with respect to the argument.

The diameter D for a particular frequency of operation is determined for the fundamental mode from the equation (neglecting fringing effects)

where fo is the fundamental operating frequency, c is the speed of light, and the substrate has a dielectric constant E,.

Similar to the rectangular configuration, the real part of the input impedance is needed to match an active device. This is given by

where r is the device position on a patch of diameter D and Ro is the radiation resistance at r = 012.

The IMPATT-integrated circular patch configuration was also demonstrated by Perkins [IS, 161. Figure 8.5 shows the configuration of the active antenna. The


FIGURE 8.5 IMPATT-integrated circular patch antenna. (From reference 1161, with permission from Microwave Journal.)

design has a much improved cross-polarization level and better overall radiation performance than previous active antennas. The circuit design provided an external port for injection locking and stabilization. Perkins' active circular patch antenna operates at 6.8 GHz with an effective radiated power of 41.5 dBm. The principal plane patterns are smooth and symmetric, and the cross-polarization component is 8 dB below the maximum of the copolarization.

In 1987, Young and Stephan [17] used the Gunn-integrated active microstrip patch antennas as distributed oscillators. The antenna configuration is shown in Figure 8.6a. The active microstrip patch antenna uses a symmetrical D C bias low-pass filter and a probe-fed patch edge-coupled section. The configuration exhibits smooth principal plane patterns as shown in Figure 8.6b, but no cross-polarication levels are mentioned. The probe feed can be used to extremely tune, monitor or injection-lock the active antenna.

In 1988, Hummer and Chang [la, 191 also investigated Gunn-integrated microstrip antennas for spatial power combining. A single active antenna shown in Figure 8.7a exhibited 15 mW at 10.1 GHz. A 3-dB tuning range of 839 MHz was achieved from 9.278 to 10.117 GHz. The power and frequency responses versus D C biasing voltage for a single active antenna are shown in Figure 8.7b. Figure 8 . 7 ~ shows a plot of injection-locking bandwidth versus locking gain. The locking bandwidth and locking gain are parameters which can be used to determine the active antenna's external Q-factor.

The following formula describes the external Q-factor [I81


FIGURE 8.6 Gunn-integrated microstrip patch antenna: (a) configuration; (b) radiation patterns. (From reference [17], with permission from SPIE.)

where A f is the single-side locking-bandwidth for an injected signal of power Pinj, and the active antenna oscillates at f, with an output power of P,. The active antenna was externally injection-locked with a stable source connected to a standard-gain horn antenna. Through the Friis transmission equation, both the injected power and the oscillator power can be calculated.

An obvious path toward a more compact and inexpensive active antenna design is to use a monolithic integrated active antenna. Typically, the high e, of monolithic substrates using GaAs are ideal for devices, but they reduce the radiation efficiency of the antenna. However, devices are directly fabricated with the antenna without package parasitics or integration discontinuities. Such a monolithic active antenna chip would be ideal for developing a large array of

382 ACTIVE MICROSTRIP ANTENNAS DIODE-INTEGRATED ACTIVE MICROWAVE ANTENNAS 383

10.2

9.8

9.4 - Frequency

9.0 8 9 10 11 12 13 14 15

DC Bias voltage (volts) (b)

101 I I I I 1 1 ' 1 22 24 26 28 30 32 34 36

Gain (dB)

FIGURE 8.7 Gunn-integrated active antenna: (a) configuration; (b) output power as a function of frequency and bias voltage for a single active antenna; (c) injection locking bandwidth as a function of locking gain. (From references 1181 and [19], with permission from IEEE.)

distributed sources. One such integration shown in Figure 8.8a uses two IMPA'IT diodes which feed the edges of a microstrip patch antenna and have a DC biasing network as well as an open stub for frequency trimming. The monolithic active antenna operates at 43.3 GHz with an output power of 27 mW at 7.2% DC-to-RF conversion efficiency [20,21]. Figure 8.8b shows very good principal plane patterns, but no cross-polarization levels are mentioned. Half- power beamwidths in the H plane are approximately 80°, and those in the E plane are over 120". Figure 8 . 8 ~ shows the output power and conversion efficieny versus biasing current of the active antenna at 43.3 GHz. The IMPATT- integrated monolithic configuration is also ideally suited for coupling to a rectangular waveguide or for a planar array. The configuration was used by Shillue et al. [22] within a quasi-optical resonator in 1989. A single antenna was stabilized by the open resonator at 56.097 GHz, thereby improving the spectral purity of the signal.

Aperture coupling separates active devices away from the antenna which solves many of the radiation problems which occur due to device integration and DC biasing. The use of an aperture-coupled patch for hybrid and monolithic

Angle (degrees) (b)

10.0

5.0 -s- eff 0.0 10.0 15.0 20

DC current (mA) (c)

FIGURE 8.8 Monolithic IMPATT active antenna: (a) configuration; (b) radiation patterns; (c) output power and efficiency. (From reference [20], with permission from IEEE.)

circuit integration was proposed by Chang et al. [23,24] in 1988. As shown in Figures 8.9a and 8.9b, the circuit is isolated from the antenna by a metallic ground plane and coupling occurs through an aperture. All spurious feedline and device radiation problems are minimized. Active devices are biased on the back side away from the antenna, and the two substrates can be optimized separately. This configuration uses a circular aperture on a thick metal support layer, which increases heat-sinking volume and provides more structural support.

A different type of antenna called a notch or tapered slot antenna was integrated with a Gunn diode by Navarro, Shu, and Chang in 1990 [25, 261. Unlike a microstrip patch antenna, the notch radiates primarily in the endfire direction. The configuration is similar to that shown by Wang and Schwarz [l l] except that the antenna is 'an integral part of the oscillator. The design uses a CPW resonator coupled to a stepped-notch antenna via slotline. Figures 8.10a and 8.10b show the configuration and equivalent circuit. A Gunn diode is placed in a heat sink at the open terminals of the resonator. The configuration exhibits a clean and stable bias-tuned signal from 9.2 to 9.47 GHz with a power output of 14.2 + 1.5 dBm and a cross-polarization level of - 10 dB. Figure 8 .10~ shows the bias voltage versus frequency and power output.


To active devices

Circular aperture I I pxc) patcj antenna

Circular aperture hick ground plane

V / / / / / / / A

Microstrip line (b)

FIGURE 8.9 Aperture-coupled microstrip to patch antenna circuit for active array: (a) top view; (b) cross-sectional view. (From reference [24], with permission from IEEE.)

The stepped notch antenna design was modified and improved with the addition of a varactor by Navarro et al. [27] in 1991. Figure 8.11a shows the active varactor-tunable coupled slotline-CPW notch antenna configuration. The circuit consists of a notch antenna integrated with a varactor-tuned coupled slotline-CPW resonator. A Gunn and a varactor diode are placed at either end of the coupled slotline-CPW resonator. The notch antenna couples to the resonator via slotline near the center. Unlike the stepped notch design, where the Gunn diode feeds both slotlines symmetrically, in the coupled slotline-CPW design the Gunn diode feeds only one slotline which couples to the adjacent slotline where the varactor is mounted 1281. The coupled slotline-CPW resonator design allows the integration and biasing of two devices without the use of filters or DC blocks. Varactor tuning keeps the output power more level over a wide frequency range


Resonator I 1

pped - notch

Slotline Gunn

W I .

Z1 = 90 ohms al I. t m

22 = 114 ohms 7_3 = 145 ohms -- 24 = 185 ohms 25 = 235 ohms 26 = 299 ohms 27 = 380 ohms Dimensions in millimeten

9.2 .+ - g 9.15 M i7j 9.1 '

9.05

Bias voltage (volts) (C)

FIGURE 8.10 Integrated active notch antenna: (a) circuit configuration; (b) equivalent circuit; (c) frequency and power versus bias voltage for the active stepped notch antenna. (From reference [25], with permission from IEEE.)


by maintaining the Gunn bias constant. The slotline steps were modified to a smooth taper for improved radiation and matching bandwidth [29]. Figure 8.11b shows the experimental frequency and power output versus varactor tuning voltage for a Gunn bias of 13.5 volts. A theoretical tuning curve predicted an approximately 2% larger tuning range. The configuration exhibits bandwidth from 8.9 to 10.2 GHz with an output power of 14.5 f 0.8 dBm for varactor

Varactor bias level (volts)

FIGURE 8.11 Integrated active notch Gunn VCO: (a) circuit configuration; (b) frequency and power versus varactor bias voltage; (c) H-plane pattern comparison of a passive and active notch antenna at 10.2GHz; (d) E-plane pattern comparison of a passive and active notch antenna at 10.2GHr (From reference [28], with permission from IEEE.)


H plane cross-pol.

Passive E plane -

ACtlVC E plane ,

Active antenna -. E plane cross-pol. .- - .. h-, '1

\ / .! Passive antenna

E plane cross-pol.

1'

FIGURE 8.1 1 (continued)

voltages of 0-30 V. This is equivalent to over 14% electronic tuning bandwidth. Figures 8 . 1 1 ~ and 8.11d show a comparison between a passive and an active notch antenna radiation patterns at 10.2 GHz. The cross-polarization level is less than -10 dB at 10.2 GHz. Other investigators have shown notch antennas integrated with detectors well into the submillimeter wavelengths. Ekstrom et al.


FIGURE 8.12 Dual Gunn-integrated microstrip patch. (From reference [32], with permission from Electronics Letters.)

[30] demonstrated a bismuth bolometer detector integrated endfire notch antenna at 348 GHz in 1992. Similarly in 1993, Acharya et al. [31] showed a detector integrated endfire notch antenna at 802 GHz. Both configurations demonstrate the submillimeter potential and scalability of this integrated antenna design.

Other investigators sought to improve the radiation performance of typical microstrip patches. York and Compton [32] used a dual Gunn-integrated antenna to provide more power and lower the cross-polarization level. For a patch designed to resonate at 10 GHz, a Gunn-integrated active antenna operated at 10.4 GHz with an output power of 26 mW. By placing a second Gunn diode diametrically opposite of the first as shown in Figure 8.12, power is nearly doubled at an operating frequency of 10.7 GHz. The configuration's symmetry helps to improve the overall radiation pattern and lower the CPL from 2 to 10 dB below the maximum. The approach also demonstrates the ability to combine more than one device under the same antenna.

Luy et al. [33] demonstrated an IMPATT integrated slotline antenna in 1993. The impedance characteristics of the active device were used to determine a good impedance match along the slotline antenna.

An active V-band microstrip patch antenna implementation is shown in Figure 8.13 [34]. It uses a packaged Gunn diode connected to a patch antenna through a microstrip transformer. The Gunn is biased to provide 9.26 mW at 63.24 GHz. It has over 1 GHz of bias tuning bandwidth (- 1.6%) without mode jumps. Although the E-plane patterns or cross-polarization levels are not shown, the H-plane pattern seems overly directive with a 10-dB beamwidth of 30". Another V-band monolithic IMPATT integrated radiating oscillator was shown


Gunn

Patch

FIGURE 8.1 3 A 60-GHz Gum-integrated microstrip patch. (From reference [34], with permission from Electronics Letters.)

by Stiller et al. [35] in 1996. The IMPATTdiode is monolithically integrated on a silicon substrate and matched to the impedance of an asymmetric microstrip patch dipole antenna. The measured oscillating frequency and power were 55.2768 GHz and 6.1 dBm, respectively. The diode efficiency was calculated at 1.4%. The copolarization patterns are typical with a high cross-polarization level.

A variation on microstrip patches is the use of inverted stripline type antennas. Gunn diodes have been integrated with inverted stripline antennas (ISAs). They have been used in spatial power combining and in beam steering applications [36, 3q . These active antennas exhibit good radiation patterns, low cross- polarization levels, easy device integration, and good heat-sinking capacity. Figure 8.14a shows the Gunn-integrated ISA. The diode package could present a significant perturbation on the X-band antenna volume which adversly affects the radiation characteristics and disturbs the oscillating frequency. Radiation patterns for the Gunn-integrated ISA are shown in Figure 8.14b. The cross- polarization level is at least - 10 dB below the peak. The measured HPBWs are 100" in the E plane and 70" in the H plane. A similar passive antenna using a coaxial feed exhibited HPBWs of 105" and 80" in the E and H plane, respectively with a cross-polarization level of - 16 dB. This type of antenna has also been integrated with passive devices such as pins and varactors. Pin diodes can provide electronic control over the radiation efficiency of a microstrip patch [38]. They can be used as microwave switches and/or modulators. In a similar manner, varactors can provide frequency agility [38].

Although a lot of attention has been given to diode integrated antennas, the bulk of new investigations use transistors. The emphasis of most work is to improve the size, conversion efficiency, oscillator quality, and radiation performance of typical active antennas. Although diodes have shown higher operating frequencies and higher output power levels, transistors are lower-priced and provide higher DC-to-RF conversion efficiencies at lower operating voltages.

3 9 0 ACTIVE MlCROSTRlP ANTENNAS

Substrate is press fitted to cavity 7 - Gunn cap is not

C = 12.7 mm I- Mechanical D = 10.4 mm tuning p= 2mm

Bias (a)

Gunn-integrated ISA Passive probe-fed ISA D = 10.4 mm, C = 12.7 mm D = 10.4 mm, C = 12.7 mm p = 2 m m p = 2 m m HPBW: HPBW:

E plane: 100 deg. E plane: 105 deg. H plane: 70 deg. H plane: 80 deg.

CPL: - 10 dB

FIGURE 8.14 Integrated inverted stripline active antenna: (a) circuit configuration; (b) radiation patterns. (From reference [373, with permission from IEEE.)

Smaller operating currents translate to fewer heat-sinking requirements. Fur- thermore, transistors perform a variety of functions using a single technology allowing greater flexibility in a multiple function active antenna design. In both diode- and transistor-integrated active microstrip antennas, testing and interpretation of data need to be done carefully [39].

8.4 TRANSISTOR-INTEGRATED ACTIVE MlCROSTRlP ANTENNAS

The integration of transistors has been essential for the development of active antennas. The use of three-terminal devices has brought on a wide range of

TRANSISTOR-INTEGRATED ACTIVE MlCROSTRlP ANTENNAS 3 9 1

H plane

a .__.- ,o -20 (D

-30 tii 2 -40

-80 -40 0 40 80 Angle (degrees) - -

Angle (degrees) (b)

FIGURE 8.15 FET-integrated feedback patch active antenna: (a) circuit configuration; (b) radiation patterns. Solid and dashed lines are for co- and cross-polarization, respectively. (From reference [49], with permission from Electronics Letters.)

integrated antennas for oscillators, amplifiers, multipliers and other components. Some of the original active integrated aerials of the early 1960s used transistor- integrated dipoles at 150 MHz [40,41]. The mating of an FET transistor to the terminals of a dipole to serve as a VHF amplifier for reception at 700 MHz has been described [42-451. Ramsdale and Maclean [46] used BJTs and dipoles for transmitting applications in 1971. They demonstrated large height reductions in 1974 [47] and later in 1975 [48] using integrated aerials.

The microstrip patch antenna was first integrated with an FET transistor by Chang, Hummer, and Gopalakrishnan 1491 in 1988. Figure 8.15a shows that the patch antenna is a feed back element for the FET oscillator circuit and a radiator. The C-band radiating oscillator circuit operates at 5.7 GHz with a power output of 17 mW. Figure 8.15b shows the principal plane patterns of the FET integrated active antenna. The 3-dB beamwidth is 56" in the E plane and 32" in the H plane


Local oscillator (LO) /

Low-pass filter -4 7 a

FICURE8.16 A 20-GHz notch-integrated receiver. (From reference [51], with permission from John Wiley & Sons.)

with high cross-polarization levels. The erratic radiation patterns may be due to exposed microstrip lines, device interconnections, and impedance mismatches. Chang's configuration was analyzed by Fusco and Burns [50] in 1990.

In 1989, Guttich [51] demonstrated one of the most complete hybrid integrated antennas. A notch antenna and coupled slotlines were integrated with an FET and mixer diodes to create a complete RF front-end. An FET transistor and slotline resonator make the local oscillator (LO) which feeds a pair of diodes 180" out of phase. The diodes are positioned at a slotline T junction with one slotline which tapers out to a notch antenna. The R F comes in from the notch antenna and mixes with the diodes in-phase to make a 20 GHz receiver front-end as shown by Figure 8.16. The local oscillator provides about 3 mW to the diode mixers, which provide 10- to 13-dB conversion loss for the 0- to 8-GHz intermediate frequencies. Unfortunately, the radiation patterns are not discussed.

Leverich et al. [52, 531 integrated an endfire notch antenna with an FET in 1992. The C-band active notch antenna and its radiation performance are shown in Figure 8.17. It oscillates at 6.98 GHz with an output power of 8.9 mW and a 2% bias-tuning bandwidth with a DC-to-RF conversion efficiency of 7.4%. The radiation of the patterns of the active antenna show the E- and H-plane half-power beamwidths to be 40" and 65", respectively. The cross-polarization levels are - 10 dB below the maximum. The integration of FETs provided a more efficient alternative to the Gunn-integrated notch antenna. This integration also

TRANSISTOR-INTEGRATED ACTIVE MICROSTRIP ANTENNAS 393

. . i i i .4

I : :I I -30

I

-90 -60 -30 0 30 60 Angle (deg)

-30 0 -90 -60 -30 0 30 60 90

(c) Angle (deg)

FIGURE 8.1 7 FET-integrated notch oscillator: (a) configuration; (b) E-plane radiation patterns (solid line: copolar, dashed line: cross-polar); (c) H-plane radiation patterns. Solid line: copolar. Dashed line: cross-polar. (From reference [52], with permission from Electronics Letters.)

ACTIVE MICROSTRIP ANTENNAS

IF out A A

Microstrip patch array

FIGURE 8.18 Linear microstrip array active antenna. (From reference [54], with permission from IEEE.)

provides a more wideband antenna for integration than a resonant patch or dipole. Its use in a power-combining array requires a brick-style approach instead of the doubly conformed tile-style approach.

Birkeland and Itoh [54, 551 have introduced several innovative transistor- integrated microstrip patch antenna designs which include multiple transistors on single patches as well as linear arrays of patches. Figure 8.18 shows the linear microstrip array active antenna transceiver configuration. The active antenna provides frequency tuning from 9.50 to 9.54 GHz through a 15-V change in the gate voltage (V,). The antenna uses a 17-antenna series-fed microstrip array to provide a very good fan-beam active antenna. In 1990, Birkeland and Itoh [56] introduced another approach to edge couple FETs to microstrip patches. The integrations operate at 6 GHz with typical EIRPs of 19 dBm. Two and four FETs were integrated with a single patch antenna as shown in Figure 8.19. These were also configured in spatial-power-combining arrays which are the topic of later sections.

Fusco [57] has also investigated an edge-fed transistor integrated active antenna as a more compact design over the feedback amplifier design in 1992. This FET active antenna provides 8 mW at 9.625 GHz (10% DC-to-RF conversion efficiency) with 90 MHz of bias tuning. The radiation performance of the configuration is affected by the patch as well as the open stub used for matching, which causes some asymmetry [58]. Fusco [59] has investigated the FET-integrated patch antenna for Doppler sensing. The FET self-oscillating mixer provides an efficient, compact, low-cost alternative for inexpensive proximity detectors.

Another edge-fed dual-FET-integrated microstrip patch antenna oscillator was demonstrated by Hall and Haskins in 1992 [60] and 1994 [61]. An operating frequency of 2.28 GHz and an external injection-locking signal allows phasing of individual elements for beam steering. The external probe-feed at each patch for the injection-locking signal may prove costly in a large array, but it provides an


FIGURE 8.1 9 Two- and four-FET edge-coupled active patch antenna. (From reference [56], with permission from IEEE.)

accurate and stable injection-locking signal for beam steering. Array patterns are smooth with beam steering of 40".

Another approach was introduced by Birkeland and Itoh in 1991. It uses a directional microstrip coupler to develop two-port FET oscillators [62]. The port can be used for external injection locking. It uses probe coupling to connect patch to the antennas for radiation. The design has an increase in injection- locking bandwidth which is essential for an array of oscillators (500 MHz at 6 GHz). The same configuration was later modified with an input and output antenna [63]. The input signal at the input patch is amplified and retransmitted through the output patch. A ground plane isolates the input signal from the amplified output signal as shown in Figure 8.20. It has been successful in several active arrays.

In 1990, York et al. [64] introduced a compact FET-integrated microstrip patch antenna shown in Figure 8.21a. Unlike previous designs, the FET is integrated within the patch antenna structure. A narrow slit splits the patch to provide DC isolation between the drain and gate during biasing. The active antenna requires vias to connect the FET source leads and a quarter-wave stub on the gate side of the antenna to ground. The drain terminal is biased through a low-pass filter using a capacitor and inductive line. Typical operating voltage


Receive patch

1 match match I

Microstrip 1 cou~ler n

patch

Amplifier (a)

patch

Side view

Ground plane

Transmit patch

Via wire PTFE

Foam tape

Receive patch (b)

FIGURE 8.20 Two-port FET active antenna: (a) schematic of oscillator element; (b) top view and side view. (From reference [63], with permission from IEEE.)

for maximum power output was 6 V at 40 mA. The active antenna oscillates at 8.2GHz with about 250 MHz of bias tuning range. As shown in Figure 8.21b, the principal radiation patterns are relatively smooth with a cross-polarization component 8 dB below the maximum. The EIRP is about 40mW with a DC-to- R F conversion efficiency of 5%. The compact active antenna is ideally suited for quasi-optical power-combining arrays.

A CPW-fed FET-integrated slot-CPW antenna amplifier configuration was shown by Wu and Chang [65] in 1993. With a slight increase in biasing complexity, the transistor amplifies an outgoing signal as shown in Figure 8.22.


.,&y6\~// , Stub, shorted

- -5 m '0 E plane

FIGURE 8.21 Compact FET-integrated active antenna: (a) configuration; (b) radiation patterns. (From reference [64], with permission from Electronics Letters.)


FIGURE 8.22 FET-integrated notch amplifier. (From reference [65], with permission from Electronics Letters.)

The active amplifier antenna has a gain of 7 dB at 9.2 GHz with a return loss of 20dB over a bandwidth of 1.55 GHz. The active antenna amplifier has a gain of over 14 dB over a 1.75-GHz bandwidth. It added over 7 dB of gain over a passive antenna at 9.2GHz. The principal planes are smooth and well-behaved, and cross-polarization levels are 13 dB below the maximum. The configuration makes an ideal single antenna amplifier, but its use in a spatial array would be limited in its present form. A large array would require an R F feed distribution network in a brick-style array approach which increases complexity and losses.

A push-pull FET-integrated active antenna design was introduced by Wu et al. [66] in 1992. The dual patch configuration allows separate loading of the drain and gate ports of the FET, which simplifies the design. The dual FET split patch antenna configuration shown in Figure 8.23 generated 47mW at 8.1 GHz. The patterns are very smooth and symmetrical with a CPL of - 12 dB. A similar active antenna was later introduced by Wu and Chang [67] in 1994. It uses a single transistor and two circular patches to load the transistor terminals. As shown in Figure 8.24, the single active antennas produces good radiation patterns. A single module exhibited an EIRP of 120 mW at 8.4 GHz with a CPL of - 6 dB.


0 20 40 60 80 100 120 140 160 180 Angle (deg)

-25- 0 20 40 60 80 100 120 140 160 180

Angle (deg)

(b)

FIGURE 8.23 Dual FET-integrated split patch active antenna: (a) configuration; (b) radiation patterns. (From reference [66], with permission from Electronics Letters.)

400 ACTIVE MICROSTRIP ANTENNAS TRANSISTOR-INTEGRATED ACTIVE MICROSTRIP ANTENNAS 401

Gate bias (a)

0 i- -----.. H plane -5 - H cross

-90 -70 -50 -30 -10 10 30 50 70 90 Angle (deg)

(b)

FIGURE 8.24 Dual circular patch FET-integrated active antenna: (a) circuit configuration of a FET active circular patch antenna, W = 0.5 mm, D = 6.5 mm; (b) E- and H-plane radiation patterns of the single element active antenna. (From reference [67, with permission from IEEE.)

Another FET-integrated slotline antenna oscillator was demonstrated by Moyer and York [68] in 1993. The cavity-backed slot antennas used MESFETs and a combination of CPW and slotline to develop the active antenna. The configuration demonstrates improvements of a cavity over a ground plane. The cavity is used to remove problems encountered in the elevation plane as well as reducung H-plane cross-polarization levels. A similar configuration was shown by Vaughan and Compton [69] in 1993 for a 10-GHz active slot dipole antenna fed by a CPW oscillator. Kormanyos et al. [70] used this configuration to obtain the highest-frequency quasi-optical slot oscillator in 1994. The InP HFET uses slotline and CPW configurations in much the same way as that shown by other investigators. Active slot antennas operated at 155 GHz with 10 pW of output power. Similarly, 215-GHz active antennas with 1 pW of power were demonstrated. A 20-GHz version was investigated by Kormanyos et al. [71]. Figure 8.25 shows the K-band configuration and radiation performance of the structure.

s l i t ground plane 136 Pm+ p ,.Li for drain bias

11 gate blaS

Angle (deg) (b)

FIGURE 8.25 FET-integrated slot antenna oscillator: (a) CPW circuit layouts for the 20-GHz oscillators showing the capacitive bypassing to allow application of DC bias; (b) measured radiation patterns of a 20-GHz slot oscillator on a 2.6-cm silicon substrate lens. (From reference [71], with permission from IEEE.)

A slotline ring resonator antenna was integrated with an FET by Ho et al. [72,73] in 1993. Very good radiation patterns and performance were shown at 7.73 GHz. An active slot dipole active amplifier was shown by Wu and Chang [74] in 1993. The active amplifier antenna operates at 7.1 GHz with a return loss of 18 dB over a bandwidth of 800 MHz. The FET-integrated slot dipole amplifier


added 7 dB of gain over the passive antenna. The radiation patterns are well-behaved, and cross-polarization levels are 11 dB below the maximum.

In 1994, Navarro, Fan and Chang [75] modified the ISA structure to integrate with an FET as shown in Figure 8.26. The transistor requires three DC blocks to accommodate the drain, gate, and source terminals. D C biasing can be achieved from behind the ground plane or etched to the edges of the antenna. A chip resistor connected across the source to gate simplifies biasing to the device. The FET-integrated ISA provides 57 mW at 5.69 GHz when biased at 3.8 V and 26 mA. The 3-dB bias-tuning range is approximately 1% for a 1-V change in The sliding ground plane allows a mechanical tuning range of nearly 6%. The HPBW in the E- and H-plane patterns are 46" and 64", respectively. The cross-polarization levels are - 19.3 dB below the maximum. The principal planes of the active antenna show smooth radiation patterns and low cross-polarization levels. Probe-fed antennas of similar dimensions exhibit HPBWs of 51" and 61" in the E- and H-plane patterns, respectively. The cross-polarization levels of the passive antenna are also - 19.3 dB with a gain of 10.2 dBi. The effective isotropic radiated power of the active antenna is 594 mW. Approximating the active antenna gain with the passive antenna gain of 10.2 dB results in an oscillator power of 57 mW and of DC-to-RF conversion efficiency of 57%.

Further integrations using this antenna structure have since been carried out by Flynt et al. [76]. A completely integrated ISA transceiver has been demonstrated as shown in Figure 8.27. It uses the FET ISA as the transmitter and local oscillator (LO), which pumps a pill-type mixer diode. The transceiver is unique in that it integrates both the oscillator and mixer functions within the volume of the antenna. Transmit-to-receive isolation is provided through orthogonal polarization. Preliminary results at 5.8 GHz exhibit a 5.5-dB isotropic mixer conversion loss for a 200-MHz RF frequency. The addition of another device has affected the radiation performance of the antenna. The E- and H-plane HPBWs are 49" and 67", which differ from the 46" and 64" measured without the mixer diode. Differences may be due to differences in the antenna dimensions, feedlines, cavity depth, and diode package.

A folded slot antenna configuration was shown by Tsai et al. [77] in 1994. Unlike the previously mentioned amplifier antenna, the input and output ports occur through folded slot antennas. The input and output are polarized orthogonal to each other for isolation. The peak effective power gain in the transmission mode is 11 dB at 4.3 GHz with 10% bandwidth for a single cell. A similar amplification concept is shown by Mader et al. [78]. A linearly polarized wave is received by a rectangular patch, amplified by a MESFET, and retransmitted by another patch. A single-amplifier combination had a 7.1-dB gain at 10 GHz with over 5 dB of gain from 9 to 11 GHz. A 4 x 6 array showed 21-dB gain enhancement over a single amplifier. The design is also flexible in receiving one type of polarization and transmitting another. A single amplifier module demonstrated a circular output from a linear input a t 10 GHz with 6.8-dB gain and 0.3-dB axial ratio. Tasi and York [79a] developed reflection amplifier module for quasi-optical arrays which differs from the arrays shown above. Two orthogonal


Transmit polarization

FIGURE 8.27 Complete active integrated antenna transceiver: (a) top view; (b) side view. (From reference [76], with permission from IEEE.)

polarized patches use a resistive feedback amplifier module to receive an incoming signal and retransmit the signal with orthogonal polarization. An isotropic power gain of 17 dB at 4.2 GHz with 1% bandwidth was measured. Another quasi-optical amplifier was shown by Sheth et al. [79b]. It is a nine-element HEMT amplifier array. It has a gain of 5.5 dB at 10.9 GHz with a 3-dB bandwidth of 1 GHz. The E-plane pattern shown agrees with the calculated pattern, but the H-plane pattern and CPL are not mentioned.

An active patch antenna with very good oscillating characteristics was demonstrated by Martinez and Compton in 1994 [80,81]. Figures 8.28a and 8.28b show the active integration which uses coupled feedback from a patch nonradiating edge to maintain oscillations and the equivalent circuit. The FET patch antenna oscillator operates at 9.84 GHz with 25-MHz tuning range and a + 1-dB power deviation. The EIRP is 360 m W with a DC-to-RF conversion efficiency of 58%. Radiation patterns, however, were irregular with a high cross-polarization level as shown in Figure 8 . 2 8 ~ for the E plane and in Figure 8.28d for the H plane.

The poor radiation performuce of the original circuit was improved with the symmetrical circuit shown in Figure 8.29a [80]. The modified circuit had an EIRP of410mW with a 44% conversion efficiency. Figures 8.29b and 8.29~ show that the E- and H-plane patterns are smooth and relatively symmetric with a CPL of - 12 dB. The E-plane pattern has an approximately 30" squint off broadside. The configuration is readily integrated as an amplitude-modulated active antenna. The 10-GHz active antenna oscillator/modulator has 3-dB modulation bandwidth of 1.4 GHz. The spectral oscillator jitter is below 50 kHz, and the single-sideband noise is - 65 dBc/Hz at 10 kHz from the carrier. The intermodulation distortion is less than -20 dBc for all modulation powers.

A voltage-controlled transistor oscillator using a varactor diode and multilayer design was introduced by Haskins, Hall, and Dahele in 1992 [82,83]. It uses

Excess

Gate Bias -

<: -- > < -- - .

Drain It & Z

Source Leads Grounded

2 L i- co-E plane i P -15 ../ ...-..... cross-E plane j I

FIGURE 8.28 FET-integrated feedback active patch: (a) the layout of the entire microstrip-patch oscillator; (b) the equivalent lumped-element circuit showing feedback applied to the gate; (c) E-plane radiation patterns; (d) H-plane radiation patterns. (From reference [80], with permission from IEEE.)


Excess Gate

Drain Bias

-90 -60 -30 0 3 0 60 9 0 Received Angle (deg)

(c)

.- S a -20

i 0

? -30 .- - m - 2

-40

FIGURE 8.29 FET-integrated symmetrically fed back patch: (a) a linearly polarized- radiating oscillator, where two balanced pickups quench unwanted cross-polarized radiation; (b) E-plane radiation patterns; (c) H-plane radiation patterns. (From reference [80], with permission from IEEE.)

--.--.. cross-E plane -

.. ...... .... - ..... _.... .. ..,. ..... .. ... : : . ..... -..

. . .. . . . : .. . . > . . . . . . . .... : : . . :: : i :..; /

f I $ 3 , ,: : :

a BAR-28 dipode to provide 100 MHz of tunning range at 2.2 GHz for the active antenna. Another VCO active antenna was shown by Liao and York [84]. The configuration is similar to that shown by Martinez and Compton in that the patch serves as feedback from the drain to the gate through a coupled line section.

-90 -60 -30 0 30 60 $90 Received Angle (deg)

The transistor requires vias to ground for the source leads, along with a quarter- wave stub on the gate terminal. The VCO operates at 8.45 GHz with 150 MHz of tunning bandwidth (1.8%). The VCO phase noise is -90 dBc/Hz at 100 kHz from the camer. The EIRP of a 10-element linear array was 10.5 W at 8.43 GHz. Beam steering from - 10 to 20' was demonstrated by a linear array. The VCO active antenna has since been improved to provide a much wider tuning bandwidth [85]. The active antenna electronically tunes from 6.8 to 8.1 GHz with a 3-dB variation in output power. This represents a very useful 17% electronic bandwidth for beam steering power combiners. The EIRP is 29.5 mW with a DC-to-RF conversionefficiency of 11%. The radiation paterns are smooth with a CPL of - 10 dB.

An aperture-coupled FET integrated microstrip patch antenna was shown by Shen et al. [86]. The integrated antenna operates at 4.893 GHz with an output power of 4.81 mW. The radiation patterns show half-power beamwidths of 40" and 52" in the E and H plane, respectively. Another aperture-coupled design was shown by Simons and Lee [87] in 1992. They introduced a dielectric resonator- stabilized HEMT oscillator active antenna using a CPW-aperture-coupled microstrip patch antenna. It operates at 7.6 GHz with approximately 1.1 mW of output power and a CPL of - 20 dB.

Some of the most promising active antenna investigations deal with electro- optical applications. Transistors are ideal candidates for millimeter-wave power generation through optical interaction. A 60-GHz CW generator realized through optical mixing in FET integrated antennas has been shown by Plant et al. [88]. Three-terminal devices such as the high-electron-mobility transistors (HEMTs) 1891 and heterojunction bipolar transistors (HBTs) [go] can also be used. Optically driven solid-state devices can generate microwaves by mixing two continuous wave lasers or by using a mode-locked laser [91]. The use of fiber-optic lines throughout a complex circuit and later converting it to micro-

I waves at an antenna appears to be an attractive alternative to current ap- nroaches.

The integration of a complete monolithic chip at the terminals of an antenna for a variety of functions was the next logical step shown by Simons and Lee [92] in 1993. They integrated a MMIC amplifier with an antipodal notch. Each module consists of a receive antenna, an amplifier, and a transmit antenna. The combination has a power-added efficiency of 14% and a gain of 11 dB over the frequency band. This integration is an ideal active antenna with potential for multiple functions. The monolithic chip can be miniaturized and optimized on gallium arsenide or silicon and later integrated with an antenna whose characteristics are optimized on a low E, substrate. Simons and Lee [93] later showed a similar setup to demonstrate a spatial frequency multiplier. The multiplier uses a GaAs MMIC amplifier chip with a 5 f 1 dB gain from 2 to 22 GHz. The

DIODE ARRAYS FOR SPATIAL POWER COMBINING 409 408 ACTIVE MICROSTRIP ANTENNAS

X-band Signal

horn

& 10 MHz phase lock Mixer : reference signal

.---------__.-a

Receiver

frequency, fo - (b)

FIGURE 8.30 Spatial frequency multiplier using notch antennas: (a) schematic illustrating an experimental setup for frequency multiplication and space power combining; (b) measured second harmonic output power at a fixed fundamental frequency of 9.3 GHz. (From reference [93], with permission from IEEE.)

power-added efficiency at a power output of 0.5 W is 14%. The antenna configuration as shown in Figure 8.30a uses a linear tapered slot antenna (LTSA). The spatial multiplier maintains relatively constant second harmonic power as the input is varied from 2 to 10 GHz. The maximum output power occurs at 9.3 GHz. Figure 8.30b shows that the second harmonic power output varied from -40 to 0 dBm for a - 10 to + 10 dBm variation of the fundamental input power at a frequency of 9.3 GHz. The maximum efficiency of 8.1% occurs at a power output of 10 dBm. The hybrid integration of MMICs and antennas greatly increases the multifunction capabilities of integrated antenna systems.

Many other oscillators [94-961, amplifiers 197-991, receivers C100-1031, and transponders [104] have been shown in the literature. Recent papers have embarked in full 3D field simulations of active antenna structures, including solid-state devices [105,106]. Such an undertaking will allow accurate analysis to understand and correct many radiation problems often encountered with active antennas. These transistor-integrated antennas are essential for multifunction integration because they allow a variety of different operations. They make ideal oscillators and transceivers which can be applied to single or large arrays. The increased DC-to-RF efficiency and lower operating levels are ideal for distributed oscillators in a power-combining array. The innovations provide a wide range of options to successfully develop such a power-combining array.

All the different configurations described have various strengths and applications. If they share a common weakness, a single active antenna cannot meet the

power requirements of most systems. Typically, a large number of active integrated antennas are needed to reach high power levels. Also, since active devices are the cost drivers in current designs, it is essential to mass-produce active antennas to lower the per unit cost. Given a low-cost, reliable active antenna, large arrays of distributed radiating oscillators can be developed to provide high-power with electronic beam steering. An active array system provides graceful degradation during device failures and avoids complex, lossy RF distribution networks. Areas of concern for an active array are heat dissipation, stability, integration, and DC control. Several investigators have studied arrays of radiators to obtain overall performance and characteristics [107,108].

8.5 DIODE ARRAYS FOR SPATIAL POWER COMBINING

Power combining has come about due to power limitations of solid-state devices. Most commercial and military applications require much more power than that available from single devices. Higher power can be realized through the combination of several devices at the chip level, circuit level, or in space 1109, 1101. Spatial power combining can be accomplished within an open resonator (i.e., quasi- optical) or through radiation in space. In the 1960s several investigators used arrays of diodes and transistors for power amplification and beam control. In 1963, Copeland, Robertson, and Verstraete [40,41] used four transistor-integrated dipoles for beam control in a linear array at 150 MHz. Figure 8.31 shows a schematic of a single antennafier and a four-element linear array. This represents one of the original developments of the concept of spatial power combining and active antenna beam manipulations.

In 1968, Staiman et al. [11 l] used an array of transistor amplifiers to create a spatial power combiner. In 1974, a concept using injection-locked distributed oscillators demonstrated spatial power combining and beam steering [I 121. Figure 8.32 shows the beam steerable array configuration and performance. Phase shifts are induced by an external injection-locking pulse. These concepts found little use until the mid-1980s when active antennas and spatial power combining were widely sought to solve power deficiencies of solid-state devices at microwave and millimeter wavelengths.

In 1983, Wandinger and Nalbandian [I131 demonstrated an open-cavity resonator for power combining. This combining method is referred to as a quasi- optical power combiner due to its similarities to laser cavities. Two separate oscillators oscillated directly into the modes of the open resonator defined by two reflecting surfaces. Coupling between the oscillators was due to the modes of the open resonator which allows injection-locking or synchronization for power combining. This power-combining scheme is ideally suited for active antennas. It requires radiating oscillators, which are in fact defined as active antennas. However, it took a few years for the connection between active antennas and quasi-optical resonators to take place.

ACTIVE MICROSTRIP ANTENNAS

{ E

U \ Mid-point of dipole

(a)

FIGURE 8.31 Antennafier and array: (a) the transistorized dipole antennafier; (b) four- element antennafier array. (From reference [41], with permission from IEEE.)

In 1985, Camilleri and Itoh [114] used slot antennas active antenna quasi- optical power combining. Another spatial multiplying diode array was demonstrated in 1987 by Nam et al. [115]. The configuration uses a microstrip to feed an array of diode-loaded slotline antennas. The diodes are positioned to maximise the radiation performance of the multiplier. A 26 dBm, 5.4 GHz input is multiplied to 10.8 GHz.

An article by James Mink [I161 in 1986 and the subsequent supported by the United States Army Research Office allowed the development of active antennas

Radiating elements

DIODE ARRAYS FOR SPATIAL POWER COMBINING 41 1

R.F. locking source (4 GHz)

(a) output input Electric Field

Broadside Position Applied Phase Shifts (0'. 0.. 0.. 0') Phase Errors (-20'. +20e. -20'. +Zoo)

I Calculated -------- I I Measured -

Electric Field ( Shifted Position Applied Phase Shifts (+go*. 0'. Phase Enon (-20'. +zoo. -20'

Calculated -------- Measured -

FIGURE 8.32 Beam steering: (a) block diagram of complete system; (b) dependence of oscillator frequency output on base voltage change in free-running and harmonically locked modes; (c) antenna radiation patterns. (From reference [112], with permission from IEEE.)

41 2 ACTIVE MICROSTRIP ANTENNAS

for quasi-optical power combining. Mink describes the use of an array of currents within a quasi-optical cavity. The large resonator dimensions provide the array of sources with a very high-Q cavity for stability. The array spacing and number of distributed oscillators determine the effficiency with which the energy couples to the main resonator mode. The technique provides a viable alternative for power combining at very high millimeter-wave frequencies. The large resonator dimensions and ease of integration have the potential to overcome low solid-state powerlevels. The technique is not as costly as conventional cavity combiners, nor is it as limited by multimoding effects, tight machining tolerances, or conductor losses.

In 1986, Stephan [117,118] demonstrated the use of Gunn-integrated patch antennas for spatial power combining and even proposed a beam-steering method not unlike that mentioned by Al-Alani et al. [112]. In 1987, Young and Stephan [I191 used the open resonator approach to stabilize the free-running microwave sources. Similarly, Cogan et. al. [I203 used a quasi-optical cavity for power combining in 1987. An X-band model was used to demonstrate the distributed oscillator concept for power combining and beam steering [121].

In 1988, Camirelli and Bayraktarouglu [20,21] used a monolithic integrated IMPATT patch antenna for spatial power combining. They showed power combination of two and three elements in the H plane. Injection-locking is ensured by using 50-Q microstrip lines between the active antennas. Figure 8.33a demonstrates in-phase and out-of-phase coupling (i.e. phasing between the two active antenna elements in an array), while Figure 8.33b shows H-plane beam sharpening versus number of elements in the spatial-power-combining arrays.

In 1989, Chang et al. [24] used aperture-coupled microstrip patch antennas for spatial combining. Figure 8.34 shows the H- and E-plane patterns of a two-element array of active antennas. As expected, patterns are smooth and symmetric; however, a 25" beam shift occurs along the E plane. The beam is steered because of the injection-locked phase difference between the two active antennas. In 1994, Lin and Itoh [I223 also used aperture-coupled antennas for power combiners in a 4 x 4 array. The array uses strongly coupled G u m oscillators on one substrate aperture-coupled to patch antennas through a circular hole in a thick metal ground plate. Interconnecting lines between the G u m oscillators ensure strong coupling for injection locking, while chip resistors suppress undesired modes. Individual oscillators provide an average of 1 dBm of power at 11.80 0.05 GHz. Table 8.1 lists the frequency and power outputs of the individual oscillators, 1 x 4,2 x 4 and 4 x 4 arrays. The first four data columns list the individual measured oscillating frequencies and output powers. The columns labeled 1 x 4 array depicts power combining between four antennas for each row of the planar array. Similarly, the 2 x 4 column lists the output frequency and power for an eight-element power combiner. Finally, the entire array is used as a power combiner with an output of 21.5 dBm and an operating frequency of 11.75 GHz.

Table 8.1 shows that the EIRP is proportional to the square of the number of elements. The E plane pattern of the array is as predicted, but the H-plane nulls

DIODE ARRAYS FOR SPATIAL POWER COMBINING 41 3

I

-150 -50 50 Angle (degrees)

FIGURE 8.33 Spatial combiner radiation patterns: (a) H-plane patterns of two-element array injection-locked in- and out-of-phase; (b) H-plane patterns of one-, two-, and three-element array injection-locked in phase. (From reference [Zl], with permission from IEEE.)

are not as expected. Figure 8.35a shows the dependency of EIRP versus number of oscillators in an array. Figure 8.35b shows the spatial power combiner's radiation patterns. There is relatively good agreement with calculated results in the E plane, while the H-plane nulls are not very well defined for the active array. The configuration moves active devices away from the antenna, allowing separate optimization of the circuit and the antenna.

In 1988, Hummer and Chang [la, 191 demonstrated a two-element E plane power combiner using Gunn-integrated rectangular patches. The active antennas were synchronized via mutual coupling, and they exhibited relatively smooth patterns as shown in Figure 8.36a. The combiner's output power was 30 mW at


I l l ,

-80 -40- 0 40 80 Angle (degrees)

FIGURE 8.34 Aperture-coupled spatial power combiner: (a) H-plane pattern of a two- element aperture-coupled active array; (b) E-plane pattern of a twoelement aperture- coupled active array. Solid line: combiner. Dashed and dotted lines: single devices. (From reference [24], with permission from IEEE.)

10.42 GHz, which is twice that seen for a single patch. Combining power and frequency versus biasing voltage showed a mode jump at a bias voltage of 15.45 V [24]. The jump causes an out-of-phase power combination between the two elements. Figure 8.36b shows in-phase and out-of-phase combiner patterns as well as performance. This phase inversion would later be exploited to steer a spatial power combiner's beam merely by altering the individual oscillator frequencies.

41 6 ACTIVE MICROSTRIP ANTENNAS DIODE ARRAYS FOR SPATIAL POWER COMBINING 41 7

-... Aon --- B on - Both on

1 10 100 Number of oscillators

E plane 0

B f -10 3 2 -20 - Measured B .- - - Calculated m -30 w a

-40 -90 -60 -30 O 30 60 90

Angle (degrees)

H plane 0

B -0 -- -10 1 -20 - Measured

B .- - .. Calculated -30

(r

-40 -90 -60 -30 0 30 60 90

'Angle (degrees) (b)

FIGURE 8.35 Aperture-coupled spatial-power combinec (a) measured EIRP; (b) measured and calculated radiation patterns of a 4 x 4 array. (From reference [122], with permission from IEEE.)

-80 ' d o 0 40 80 Angle (degrees)

(a)

DC bias voltage - V = 1 4 . 5 1 ~ --.a V = 15 .87~

-- Angle (degrees)

(b)

FIGURE 8.36 Two-element integrated patch-Gunn device combiner performance: (a) measured E-plane pattern of a two-element array; (b) pattern broken up above 15.45 V. (From reference [24], with permission from IEEE.)

amplitude and phase. The elements were synchronized through an external partially reflecting dielectric surface. The dielectric layer in front of the array ensures stable injection locking for all elements in the array.

In 1993, aV-band power combiner using 60-GHz pulsed IMPATT oscillators was shown by Davidson et al. [126]. Due to the high operating frequency, the package strongly affects the frequency of oscillations. Eight of these active antennas combined to produce over 2 W of CW power. Given the 61 W of DC power required to drive the array computes to approximately 3.3% conversion efficiency. Pulsing was accomplished using a 2-ps rise time, low-duty cycle, 4-kHz bias.

Ton view -Patch with diode

- Bias lines

Brass heat -sink and ground plane

Side view Dielectric , substrate

- ~

Angle (deg)

i --Calculated

-10 t

-15 : : . .I .q . . \ \ i i i ' i -20 1 ! i : :

, i : \ !

. . : . t :: : . . . :: : . . .

-90 -45 0 45 90 Angle (deg)

(c)

FIGURE 8.37 Gunn-integrated 4 x 4 spatial combiner: (a) 4 x 4 array configuration; (b) E-plane and (c) H-plane patterns at 9.6 GHz for the active array. The theoretical results are calculated by combining the pattern of a single patch with a 4 x 4 array factor. The dielectric slab above the array (4 =4) has a small effect on the patterns. Good qualitative agreement between the measured and calculated curves indicates that the elements are nearly in phase with similar amplitudes. (From reference [125], with permission from IEEE.)

Receivad power (dBrn)


9.498 GHz \ - z \-, 9.499 GHz I I

I \

; 56.80 rnW , , , I . , ---* .-__-

9.498 GHz 9.497 GHz

-90-75 -60-45-30-15 0 15 30 45 60 75 90 Angle, (degrees)


Navarro and Chang [36,37] have been used the Gunn diode integrated ISAs to demonstrate both spatial-power-combining and beam-steering capabilities. A 2 x 2 beam-steering array was shown in 1993 using active inverted stripline antennas. The array operated at 9.5 GHz with an EIRP of 3.8 W and an RF combining efficiency of 89%. The single-element and array configuration as well as radiation performance are shown in Figure 8.38. Also shown are the radiation


TABLE 8.2 Linear Array Frequency Distribution for Beam Scanning

Active Active Active Active Linear Antenna Antenna Antenna Antenna 1 x 4 #I #2 #3 #4 Maximum Arrays (GHz) (GHz) (GHz) (GHz) Scan Angle E plane (1 x 4) 9.3307 9.3157 9.3157 9.3001 + 20"

9.3097 9.3244 9.3247 9.3397 - 16" H plane (4 x 1) 9.3639 9.3422 9.3395 9.3179 + 21"

9.3273 9.3410 9.3400 9.3553 - 13"

patterns for a single element and for the beam-steered array. A total of 15" of phase shift was demonstrated by merely varying the bias voltage to each oscillator.

Four element E- and H-plane linear arrays of active Gunn-integrated inverted stripline antennas were also used for spatial-power-combining beam-steering demonstrations. The 1 x 4 E- and H-plane configurations are shown in Figure 8.39 along with their respective radiation pattern measurements. Maxi- mum E-plane beam scanning demonstrated was 36", while maximum H-plane beam scanning was 34". Table 8.2 shows the frequency distribution of the two linear arrays along with the resulting scan angle.

The beam scanning shown above used only mutually coupling to maintain injection locking among the four sources. There was no interconnections between active antennas or any external locking inputs. Although simple, the scan angle is limited by the low coupling levels. When using this method, lower-quality factor oscillators and increased mutual coupling can increase the scan angle. Mutual coupling due to space waves is increased by a partially reflecting surface such as a low dielectric substrate. The increase in mutual coupling between active antennas helps to maintain injection lock over a wider frequency range, which results in wider scanning angles. Other investigators have since demonstrated larger beam scanning angles using linear arrays of transistors. The area of distributed oscillators for beam steering is an important application for active antenna arrays.

8.6 TRANSISTOR ARRAYS FOR SPATIAL POWER COMBINING

As described in the previous section, spatial power combiners in the early 1960s used both diode and transistor integrated antennas [40,41]. Improvements and innovations continued in the late 1960s and 1970s [I l l , 1121. In the 1980s, the Gunn and IMPATT diode were well established and were used extensively to develop active antennas. As active antennas developed, however, the need or higher efficiencies and lower operating levels brought a resurgence of transistor integrations. The flexibility of the transistor which can be used as an oscillator, amplifier, switch or tuning is another clear advantage over diodes in integrated antenna applications.

TRANSISTOR ARRAYS FOR SPATIAL POWER COMBINING 423

The concept of spatial power combining using distributed amplifiers was shown by Staiman et al. [11 l] in 1968. It provided an alternative to circuit-level cavity combiners, but it was not used by others in the field for several years. Over a decade later, a paper by Durkin et al. [I271 in 1981 discussed an IMPATT oscillator power combiner using a similar approach.

Transistors have been configured within broadside and endfire radiators. They have also been configured within grid-type structures to develop oscillators, amplifiers and other types of components. They have been investigated extensively over the last decade, and a complete description is not possible within this chapter. Grids differ from active antenna spatial power combiners in that a grid's unit cell may not operate as the intended quasi-optical component by itself. Devices in a grid are very strongly coupled to each other, and the quasi-optical component relies on the collective interaction of all of its devices. References [128-1311 describe some key developments in quasi-optical grid components.

With respect to transistor-integrated active antennas in spatial power combiners, there have been many investigators and several different types of antennas used. Slot antennas and transistors were used by Kawasaki and Itoh [132-1341 in the 1990s. The active slot antennas are simple and compact.

Birkeland and Itoh [56] have shown that circuit level and spatial power combining can be used together efficiently. Multiple transistor devices at each active patch antenna provides this flexibility. Two-, three- and four-element E-plane arrays were demonstrated with EIRPs of 22.9, 28.9 and 31.7 dBm at 10 GHz, respectively. Figure 8.40 shows the array configuration and the radiation pattern of the three-element linear array. Asymmetry in the combiner patterns may be due to phase and power deviations of individual active antennas within the array. Another spatial power combiner shown by Birkeland and Itoh [I351 uses their two-port oscillators. A linear array of two-port oscillators showed a locking bandwidth of 453 MHz at 6 GHz (7.5%) with an injected power of 10.3 dBm. The array showed an EIRP of 28.2 W CW with an isotropic conversion gain of 9.9 dB at 6 GHz. The radiation patterns are very good with very low cross-polarization levels. Relatively stable gain and EIRP over bandwidth and are demonstrated.

In 1990, York and Compton [I251 used their compact FET integrated patch to demonstrate a 4 x 4 array of active antennas at 8.27 GHz. Several interesting observations are discussed such as method of synchronization and stabilization, testing procedures, and coupled-oscillator theory to describe the array of distributed oscillators. Figure 8.41 shows a 4 x 4 array of FET-integrated microstrip patches along with radiation patterns. The array operates at 8.27 GHz, delivering an EIRP of 10 W at an efficiency of 26%. This compares very well with a similar 4 x 4 Gunn-integrated patch antenna array which operated at 9.6 GHz with an EIRP of 22 W at an efficiency of 1% . The arrays demonstrate good H-plane patterns and low cross-polarization levels.

In 1993, Leverich et al. 1531 used FET-integrated notch antennas configured in 1 x 4 and 2 x 2 arrays for spatial power combiners. A 1 x 4 H-plane linear array has nearly one wavelength spacing. A 5-mm-thick Plexiglas (E, = 2.6) at


FIGURE 8.40 Dual FET edge-fed spatial combiners: (a) array configuration; (b) radiation pattern of a three-element array. (From reference [56], with permission from IEEE.)

one-half wavelength in front of the linear array was used to synchronize the spatial combiner. A 93% RF combining efficiency was measured for the four active antennas. The H-plane narrowed from 65" to 15'. A 1 x 4 E-plane array demonstrated 15" half-power beamwidth and an 83% R F combining efficiency. These antennas were then set up in a planar 2 x 2 array with E- and H-plane spacing of one wavelength. The combining efficiency of the 2 x 2 array was 72%. The E- and H-plane half-power beamwidths are both 25". Endfire notch antennas integrated with amplifiers have also been shown by Hwang et al. [136]. This investigation uses transistor-integrated notch antennas within a dielectric slab medium. Others have used variations on this useful endfire antenna for many successful spatial power combiners [92,93].

An 8- and a 16-element MESFET array combiners with 5.54 and 17.38 W of EIRP at 10 GHz were demonstrated by Balasubramaniyan and Mortazawi in 1993 [137]. The arrays exhibit excellent radiation patterns in both principal planes which agree well with the theoretical prediction. Measurements for one and two active antennas are 0.058 Wand 0.266 W EIRP, respectively. Mortazawi

Gate bias resistor

n FET with

To other devices (a)

I I I I -90 -60 -30 0 30 60 90

Angle (deg)

FIGURE 8.41 FET-integrated spatial combiner. (a) Sketch of the array which uses Fujitsu FSXO2 MESFETs, showing bias arrangement and individual element design. Elements measure 11 mm by 15mm and the spacing of the elements is 0.671, between centers. The bias inductor reduces element interactions along the bias line. (b) E-plane and H-plane patterns for the 4 x 4 MESFET array. The measurements were made at 8.27 GHz using a flat 2.5-cm-thick dielectric reflector with a dielectric constant of 4. The good patterns indicate in-phase operation. (From reference [125], with permission from IEEE.)


and De Loach [I381 have analyzed spatial power combiners using an extended resonance technique. Very good combining results have been demonstrated for various planar spatial power combiners.

In 1994, Wu and Chang [67] used FET-integrated dual circular patches for spatial power combining. A two-element array had an EIRP of 520 mW at

ground

Angle, (degrees)

(b)

FIGURE 8.42 Active FET array for beam steering. (a) Diagram illustrating the experimental four-element FET array. A simple active patch design using zero gate bias was used with dimensions chosen empirically for operation at 1OGHz. An array spacing of d = 0.861, was used to give the desired angle of coupling. (b) Comparison of measured radiation patterns at three different scan angles. Continuous beam scanning was possible from - 15" to + 12.5' by adjusting the end-element frequencies through the control of DC voltages, which is close to the maximum k 17" predicated by the theory. The scan range was limited by the large antenna spacing. (From reference [145], with permission from IEEE.)

TRANSISTOR ARRAYS FOR SPATIAL POWER COMBINING 427

8.4GHz with a CPL of - 13 dB. A four-element linear array had an EIRP of 1.3 W at 8.4 GHz with a CPL of - 16 dB. A 2 x 2 array achieved an EIRP of 1.5 W at 8.4GHz with a CPL of - 16dB. A 2 x 4 array showed an EIRP of 3.8 W at 8.99 GHz.

There have been many other transistor-integrated active antenna spatial power combiners using conventional patches, endfire antennas, or apertures coupled patches [139]. Some investigations have used MESFETs [140,141] or HEMTs [142]. Although each configuration has its advantages and uniqueness, each attempts to develop an efficient spatial power combiner which does not degrade in component or antenna performance while increasing in reliability and output power. Of course, the intent is to use these approaches to bring about an overall lower cost for microwave and millimeter-wave systems.

One of the most exciting areas with respect to active antennas used as distributed oscillators has been the ability to steer the radiation beam through the control of DC voltages. Beam steering has been demonstrated by several investigators over the past decade. This was shown in the previous section with diode-integrated antennas. With respect to transistor-integrated beam-steering arrays, there are several successful demonstrations by Liao and York C143-1461 and Lin and Itoh [147, 1481. Figure 8.42 shows results from Liao and York's investigations. Four FET-integrated patches were used to demonstrate a beam- steerable phased with beam-steering capability of - 15" to 12.5'. An increase in beam steering was shown through stronger coupling between the oscillator elements. I t scans from -30" to +40a 11461. Lin and Itoh's beam-steering array configurationis different from that used by Liao and York. Figure 8.43 shows the configuration [148]. Upto 33' of steering has been shown with this approach.

n LT Patch Antenna

Termination Resistor

..... FET Amplifier

FIGURE 8.43 Circuit structure of the unilateral injection-locking-type active phased array. (From reference [148], with permission from IEEE.)


One of the approaches toward an active array has been the use of an amplifier at the terminals of the antenna. An amplifying active antenna using conventional microstrip patches with an integrated amplifier at its terminals shows excellent radiation patterns and very good efficiency as demonstrated by Robert, Razban, and Papiernik [149]. Many investigators have graviated toward this design because it provides simplicity and function. Since the distribution network carries very little power, microstrip losses encountered are relatively small compared with the amplified output of the array. This inherently ensures a high DC-to-RF conversion efficiency. Since the antenna is left untouched, the radiation patterns are very smooth and symmetric. This approach has been adopted by several large corporations for the development of the next generation of phased arrays [lSO, 1511.

8.7 SYSTEM APPLICATIONS

From 1987 to the present, active antenna articles and applications have grown steadily. As solid-state devices improve and MMICs shrink in size, the benifits from integration with antennas increase. The concept of integrated antennas in conjugation with spatial and quasi-optical power combining techniques provides the means to overcome the power deficiencies of single solid-state devices at millimeter-wave frequencies. Its successful implementation can fulfill many of the needs of commercial and military applications. Many different configurations have been shown, and very high operation frequencies have been reached. Active integrated antennas, however, have also been presented by many investigators with a strong and difficult challenge to overcome: the ability to efficiently combine guided wave components within the volume of a space-wave device, the antenna.

Over the past decade there have been countless configurations of integrated and active integrated antennas. The majority of these designs use some variation of a microstrip patch antenna. As work in this area matures, publications emphasize the power combining array aspect of the designs over the single- element characteristics. From the overall system point of view, an active antenna array poses a difficult challenge. In comparison with a conventional transmitter which may use a single high-power Gunn diode as a waveguide source, an array of low-power Gunn diodes requires more biasing lines, chokes, and a method of synchronization. If these problems are solved, the array of diodes or transistors has several advantages such as graceful degradation, lower per unit diode costs, and the adaptability of a set of distributed sources.

Different types of antennas offer various advantages, while dictating how an array of sources must be configured. The notch antenna with all of its beamwidth flexibility and wide impedence bandwidth requires the use of brick-style approach in the development of an array. This approach has shown increased surface area for devices and heat-sinking, but it requires depth. For many applications where depth is not available, an alternative tile approach is required.


RF distribution TFN

Connector boss

FIGURE 8.45 Ka-band 16-element phased array: (a) module assembly; (b) antenna configuration. (From reference [150], with permission from IEEE.)

CONCLUSIONS AND FUTURE TRENDS 431

In these instances, planar, broadside radiators such as microstrip patches or dipoles are used. A planar broadside radiator can also be constructed from a resonant slotline. Several investigators have used the active slotline antenna for spatial power combination. There are several possible configurations such as slotline dipoles, loops, or rings. Unlike a microstrip patch, this antenna is a bidirectional radiator which makes it ideal for spatial amplifier applications. However, it presents some problems for distributed oscillators. The use of a reflector plane or cavity has demonstrated some success for using this type of antenna in power combining.

If instead of a single device, one integrates a MMIC, there is the potential of a wide variety of functions. By localizing each front-end function at the terminals of each antenna, one can reduce RF losses and develop a completely electronically adaptable array. This would only be possible if the per unit cost of each antenna were very low, which occurs only in very large volumes.

A brick-type array has been demonstrated by Fitzsimmons et al. [152,153] of the Boeing Company in 1994, and 91-element phased arrays have been shown at 20 and 44 GHz. The array architecture allows repeatable independent access to each module. It is hermetically sealed and has a low parts count duplicated at each antenna. It is held with mechanical fasteners without the use of wire or solder connections. It has shown very good performance with large scanning angles of up to 70' and provides a lower-cost alternative to the tile type described above. Figure 8.44 shows the brick-style approach configuration.

Major issues in the design of an active antenna array system include cost, weight, manufacturability, and reliability [154]. In the complete transceiver, integration of multiple layers becomes critical. These layers combine active devices and circuits, DC power and control lines, RF distribution networks, and antennas in relatively small volumes. Figure 8.45 shows a Ka-band transmit array built for the NASA-Lewis Research Center using this integration approach and based on the aperture-coupled microstrip antenna [150]. This method is called a tile array approach.

8.8 CONCLUSIONS AND FUTURE TRENDS

The field of active antennas has come a long way over the past decade. With the rapid improvement of solid-state materials and devices and the need for more power at ever-increasing frequencies, active integrated antennas have flourished. Just about every type of component has been integrated at the terminals of an antenna. From the late 1980s throughout the 1990s, hundreds of concepts and ideas have been put forth and demonstrated. From these concepts, several ideas remain which will continue to evolve over the coming years: distributed oscillator beam steering, spatial amplification through the use of grids or active antenna arrays, detector-integrated antennas for digital beam-forming approaches, transceiver antenna for receive and transmit applications and active antennas as inexpensive Doppler sensors and decoys.


Each of these ideas continues to develop. In the coming years, with the recent FCC ruling (December 1995) to open up the millimeter-wave region for commercial applications, many new applications will spring up. Old applications will move up in frequency to avoid the clutter and interference of the lower microwave regions. Other applications will require more instantaneous bandwidth to ex- change more data faster [155, 1561.

There are many growing applications in the automotive market for sensors such as collision warning, automatic cruise control, back-up detector, blind-spot sensors, noncontact and remote identification, global positioning systems and wireless communications. In security and surveillance, smaller, more efficient sensors and transceivers continue to be in high demand. With improved materials, devices, components and better integration, the cycle continues. Each year, more applications with higher performance in smaller alocated spaces spring up.

As active antennas improve, they will begin to fill some of these needs. As thousands and thousands of integrated antennas are manufactured, many of the problems associated with them will be overcome. This will open up other applications, and the trend will continue. In the end, having solved all the integration difficulties we currently experience, the smallest, most efficient transceiver will be created on the terminals of an antenna. It will have high performance and be very inexpensive. It will be used in surveillance, security, communications, and radar. Its low cost will makemany of the high-tech systems used today such as phased-arrays available as commodities to consumers. We look forward to this day.

Because of the page limit, many materials and results have to be deleted. The readers are advised to consult references or a more detailed book [I571 for additional information.

ACKNOWLEDGMENTS

We would like to acknowledge the US. Army Research Office for sponsoring most of the developments described in this chapter, including the work done in our laboratory. We would also like to thank Mr. Lu Fan for this critical review of the manuscript.

REFERENCES

[I] R. Hertz, Electric Waves, MacMillan, New York 1893. [2] A. D. Frost, "Parametric Amplifier Antenna," Proc. IRE, Vol. 48, p. 1163, 1960. [3] C. H. Boehnker, J. R. Copeland, and W. J. Robertson, "Antennaverters and

Antennafiers-Unified Antenna and Reciever Circuitry Design," in Tenth Annual Symposium on the USAF Antenna Research and Development Program, 1960.

REFERENCES 433

[4] J. R. Copeland and W. J. Robertson,"Design of Antennaverters and Antemafiers," Electronics, pp. 68-71, 1961.

[5] M. E. Pedinoff, "The Negative-Conductance Slot Amplifier," IRE Trans. Micro- wave Theory Tech., Vol. MTT-9, No. 6, pp. 557-566,1961.

[6] K. Fujimoto, "Analysis and Design of Tunnel-Diode-Loaded Dipoles," in Thirteenth Annual Symposium of the Antenna Research and Development Program, 1963.

[7] K. Fuzimoto, "Active Antennas: Tunnel-Diode-Loaded Dipole Antennas," Proc. IEEE, Vol. 53, p. 174,1965.

[8] S. P. Kwok and K. P. Weller, "Low Cost X-band MIC BARITT Doppler Sensor," ZEEE Trans. Microwave Theory Tech., Vol. 27, No. 10, pp. 844-847,1979.

[9] B. M. Armstrong, R. Brown, F. Rix, and J. A. C. Stewart, "Use of Microstrip Impedence-Measurement Technique in the Design of a BARITT Duplex Doppler Sensor," IEEE Trans. Microwave Theory Tech., Vol. MTT-28, No. 12, pp. 1437- 1442,1980.

[lo] P. Bhartia and I. J. Bhal, "Frequency Agile Microstrip Antennas," Microwave J., Vol. 25, No. 10, pp. 67-70,1982.

[11] N. Wang and S. E. Schwarz, "Monolithically Integrated Gunn Oscillator at 35 GHz," Electron. Lett., Vol. 20, No. 14, pp. 603-604, 1984.

[12] G. Morris, H. J. Thomas, and D. L. Fudge, "Active Patch Antennas," in Military Microwave Conference, pp. 245-249, London, England, 1984.

1131 H. J. Thomas, D. L. Fudge, and G. Morris, "Gunn Source Integrated with Micro- strip Patch," Microwaves RP, Vol. 24, No. 2, pp. 87-90,1985.

[14] M. Dydyk, "Planar Radial Resonator Oscillator," IEEE M W - S Int. Microwave Symp. Dig., pp. 167-168, 1986.

[I51 T. 0 . Perkins 111, "Microstrip Patch Antenna with Embedded IMPATT Oscil- lator," IEEE Antennas and Propagat. Int. Symp. Dig., pp. 447-450,1986.

1161 T. 0. Perkins 111, "Active Microstrip Circular Patch Antenna," Microwave J., Vol. 30, No. 3, pp. 109-1 17, 1987.

[l;rl S. L. Young, and K. D. Stephan, "Radiation Coupling of Inter-Injection-Locked Oscillators," SPIE, Millimeter Wave Technology IV and Radio Frequency Power Sources, Vol. 791, pp. 69-76, 1987.

[I81 K. A. Hummer and K. Chang, "Spatial Power Combining Using Active Microstrip Antennas," Microwave Opt. Tech. Lett., Vol. 1 , No. 1, pp. 8-9,1988.

[19] K. A. Hummer and K. Chang, "Microstrip Active Antennas and Arrays," IEEE MTT-S Int. Microwave Symp. Dig., pp. 963-966,1988.

[20] N. Camirelli and B. Bayraktarouglu, "Monolithic Millimeter Wave INPATT Oscillator and Active Antenna," IEEE M7T-S Int. Microwave Symp. Dig., pp. 955-958,1988.

[21] N. Camirelli and B. Bayratarouglu, "Monolithic Millimeter Wave IMPATT Oscillator and Active Antenna," IEEE Trans. Microwave Theory Tech., Vol. 36, No. 12, pp. 1670-1676,1988.

[22] W. P. Shillue, S. C. Wong, and K. D. Stephan, "Monolithic IMPATT Millimeter- Wave Oscillator Stabilized by Open Cavity Resonator," IEEE MTT-S Int. Micro- waue Symp. Dig., pp. 739-740,1989.

434 ACTIVE MICROSTRIP ANTENNAS REFERENCES 435

[23] X. Gao, and K. Chang, "Network Modelling of an Aperture Coupling Between Microstrip Line and Patch Antenna for Active Array Applications," IEEE Trans. Microwave Theory Techniques, Vol. 36, No. 3, pp. 505-513,1988.

[24] K. Chang, K. A. Hummer, and J. L. Klein, "Experiments on Injection Locking of Active Antenna Elements for Active Phased Arrays and Spatial Power Combiners," IEEE Trans. Microwave Theory Tech., Vol. 37, No. 7, pp. 1078-1084, 1989.

[25] J. A. Navarro, Y. H. Shu, and K. Chang, "Active Endfire Antenna Elements and Power Combiners Using Notch Antennas," IEEE M?T-S Int. Microwave Symp. Dig., pp. 793-796, 1990.

[26] J. A. Navarro, K. A. Hummer, and K. Chang, "Active Integrated Antenna Elements," Microwave J., Vol. 35, pp. 115-126,1991.

[273 J. A. Navarro, Y. H. Shu, and K. Chang, "Wideband Integrated Varactor-Tunable Active Notch Antennas and Power Combiners," IEEE MTT-S International Microwave Symposium Digest, pp. 1257-1260, 1991.

[28] J. A. Navarro, Y. Shu, and K. Chang, "Broadband Electronically Tunable Planar Active Radiating Elements and Spatial Power Combiners Using Notch Antennas," IEEE Trans. Microwave Theory Tech., Vol. MTT-40, No. 2, pp. 323-328,1992.

[29] J. A. Navarro and K. Chang, "Broadband Electronically Tunable Planar Active Radiating Elements and Spatial Power Combiners Using Notch Antennas," Microwave J., Vol. 35, No. 10, pp. 87-101, 1992.

[30] H. Ekstrom, S. Gearhart, P. R. Acharya, G. M. Rebeiz, E. L. Kollberg, and S. Jacobsson, "348 GHz Endfire Slotline Antennas on Thin Dielectric Membranes," IEEE Microwave Guided Wave Lett., Vol. 2, No. 9, pp. 357-358, 1992.

[31] P. R. Acharya, H. Ekstrom, S. S. Gearhart, S. Jacobsson, J. F. Johansson, E. L. Kollberg, and G. M. Rebeiz, 'Tapered Slotline Antennas at 802 GHz," IEEE Trans. Microwave Theory Tech., Vol. 41, No. 10, pp. 1715-1719,1993.

[32] R. A. York and R. C. Compton, "Dual-Device Active Patch Antenna with Im- proved Radiation Characteristics," Electron. Lett., Vol. 28, No. 11, pp. 1019-1021, 1992.

[33] J. F. Luy, J. Bueschler, M. Thieme, and E. Biebl, "Matching of Active Millirneter- Wave Slotline Antennas," Electron. Lett., Vol. 29, No. 20, pp. 1772-1774, 1993.

[34] D. S. Hernandez and I. Robertson, "60 GHz Active Microstrip Patch Antenna for Future Mobile Systems Applications," Electron. Lett., Vol. 30, No. 9, pp. 677-678, . 1994.

[35] A. Stiller, K. M. Strohm, E. Sasse, E. Biebl, and J. F. Luy, "A Radiating Monolithic Integrated Planar Oscillator at 55 GHz," IEEE Microwave Guided Wave Lett., Vol. 6, No. 2, pp. 100-102, 1996.

1361 J. A. Navarro and K. Chang, "ElectronicBeam Steering of Active Antenna Arrays," Electron. Lett., Vol. 29, No. 3, pp. 302-304, 1993.

[37] J. A. Navarro, Lu Fan, and K. Chang, "Active Inverted Stripline Circular Patch Antennas for Spatial Power Combining," IEEE Trans. Microwave Theory Tech., Vol. MTT-41, No.'lO, pp. 1856-1863. 1993. . .

[38] J. A. Navarro and K. Chang, "Low Cost Inverted Stripline Antennas with Solid- State Devices for Commercial Applications," IEEE MTT-S Int. Microwave Symp. Dig., pp. 1771 - 1774, 1994.

[39] M. Gouker, "Toward Standard Figures-of -Merit for Spatial and Quasi-Optical Power-Combined Arrays," IEEE Trans. Microwave Theory Tech., Vol. M1T-43, NO. 7, pp. 1614-1617,1995.

[40] J. R. Copeland, W. J. Robertson, and R. G. Verstrate, "A Transistorized Beam- Control Array," Thirteenth Annual Symposiumofthe USAF Antenna Research and Development Program, 1963.

[41] W. J. Robertson, J. R. Copeland, and R. G. Verstrate, "Antennafier Arrays," IEEE Trans. Antennas Propagat., Vol. AP-2, pp. 227-233,1964.

[42] H. Meinke, "Tunnel Diodes Integrated with Microwave Systems," Radio and Electronic Engineer, Vol. 31, No. 2, pp. 76-80, 1966.

[43] H. Meinke and F. M. Landstorfer, "Noise and Bandwidth Limitations with Transistorized Antennas," IEEE Antennas Propagat. Int. Symp. Dig., 1968.

[44] F. M. Landstorfer, "Applications and Limitations of Active Aerial at Microwave Frequencies," Eur. Microwave C o d , pp. 141-144,1969.

[45] E. A. Killick, "Introduction to Scanning and Active Antennas," Eur. Microwave Conf., pp. 122-123,1969.

[46] P. A. Ramsdale and T. S. M. Maclean, "Active Loop-Dipole Aerials," Proceedings of the IEE, Vol. 118, No. 12, pp. 1698-1710,1971.

[47] T. S. M. Maclean and P. A. Ramsdale, "Short Active Aerials for Transmission," Int. J. Electron., Vol. 36, NO. 2, pp. 261-269, 1974.

1481 T. S. M. Maclean and G. Morris, "Short Range Active Transmitting Antenna with Very Large Height Reduction," IEEE Trans. Antennas Propagat., Vol. 23, No. 3, pp. 286-287,1975.

[49] K. Chang, K. A. Hummer, and G. Gopalakrishnan, "Active Radiating Element Using FET Source Integrated with Microstrip Patch Antenna," Electron. Lett., Vol. 24,No. 21, pp. 1347-1348,1988.

[50] V. F. Fusco and H. 0. Burns, "Synthesis Procedure for Active Integrated Radiating Elements," Electronic Lett, Vol. 26, No. 4, pp. 263-264, 1990.

[51] U. Guttich, "Planar Integrated 20 GHz Reciever in Slotline and Coplanar Wave- guide Technique," Microwave and Optical Technology Letters, Vol. 2, No. 11, pp. 404406,1989.

[52] K. Leverich, X. D. Wu, and K. Chang, "New FET Active Notch Antenna," Electronics Lett., Vol. 28, No. 24, pp. 2239-2240, 1992.

[53] K. Leverich, X. D. Wu, and K. Chang, "FET Active Slotline Notch Antennas for Quasi-Optical Power Combining," IEEE Trans. on Microwave Theory and Tech., Vol. 41, No. 9, pp. 1515-1518, 1993.

[54] J. Birkeland and T. Itoh, "Quasi-Optical Planar FET Transceiver Modules," IEEE MTT-S Int. Microwave Symp. Dig., pp. 119-122,1989.

1551 J. Birkeland and T. Itoh, "FET-Based Planar Circuits for Quasi-Optical Sources and Transceivers," IEEE Trans. Microwave Theory Tech., Vol. 37, NO. 9, pp. 1452-1459,1989.

[56] J. Birkeland and T. Itoh, "Spatial Power Combining using Push-Pull FET Oscil- lators with Microstrip Patch Resonators," IEEE MTT-S Int. Microwave Symp. Dig., pp. 1217-1220,1990.


[57] V. F. Fusco, "Series Feedback Integrated Active Microstrip Antenna Synthesis and Characterization," Electron. Lett., Vol. 28, No. 1, p ~ . 89-91. 1992. - - , -~ ~ --

[58] D. S. McDowall and V. F. Fusco, "Electromagnetic Far-Field Pattern modeling for an Active Microstrip Antenna module," Microwave Opt. Tech. Lett., Vol. 6, No. 5, pp. 275-277,1993.

[59] V. F. Fusco, "Self-Detection Performance of Active Microstrip Antennas," Elec- tron. Lett., Vol. 28, No. 14, pp. 1362-1363, 1992.

[60] P. S. Hall and P. M. Haskins, "Microstrip Active Patch Array with Beam Scan- ning,' Electron. Lett., Vol. 28, No. 22, pp. 2056-2057,1992.

[61] P. S. Hall, I. L. Morrow, P. M. Haskins, and J. S. Dahele, "Phase Control in Injection-Locked Microstrip Antennas," IEEE MTT-S Int. Microwave Symp. Dig., pp. 1227- 1230,1994.

[62] J. Birkeland and T. Itoh, "Two-Port FET Oscillators with Applications to Active Arrays," IEEE Microwave Guided Wave Lett., Vol. 1, No. 5, pp. 112-113, 1991.

[63] J. Birkeland and T. Itoh, "An FET Oscillator Element for Spatially Injection Locked Arrays," IEEE MTT-S Int. Microwave Symp. Dig., pp. 1535-1538, 1992.

[64] R. A. York, R. D. Martinez, and R. C. Compton, "Active Patch Antenna Element for Array Applications," Electron. Lett., pp. 494-495, Vol. 26, No. 7, 1990.

[65] X. D. Wu and K. Chang, "Compact Wideband Integrated Active Slot Antenna Amplifier," Electron. Lett., Vol. 29, No. 5, pp. 496-497, 1993.

[66] X.D. Wu, K. Leverich, and K. Chang, "Novel FET Active Patch Antenna," Electron. Lett., Vol. 28, No. 20, UP. 1853-1854. 1992. - > ? -- --

[67] X. D. Wu and K. Chang, "Novel Active FET Circular Patch Antenna Arrays for Quasi-Optical Power Combining,"IEEE Trans. Microwave Theory Tech., Vol. 42, NO. 5, UP. 766-771.1994. - -

[68] H. P. Moyer and R. A York, "Active Cavity-Backed Slot Antenna Using MES- FETs," IEEE Microwave Guided Wave Lett., Vol. 3, No. 4, UP. 95-97. 1993.

[69] M. J. Vaughan and R. C. Compton, "Resonant-Tee CPW Oscillator and the Application of the Design to a Monolithic Array of MESFETs," Electron. Lett., Vol. 29, No. 16, pp. 1477-1479,1993.

[70] B. K. Kormanyos, S. E. Rosenbaum, L. P. B. Katehi, and G. M. Rebeiz, "Mono- lithic 155 GHz and 215 GHz Quasi-Optical Slot Oscillators," IEEE MTT-S Int. Microwaue Symp. Dig., pp. 835-838,1994.

[71] B. K. Kormanyos, W. Harokopus, L. P. B. Katehi, and G. M. Rebeiz; "CPW-Fed Active Slot Antennas," IEEE Trans. Microwave Theory Tech., Vol. MTT-42, No. 4, pp. 541-545,1994.

[72] C. H. Ho, L. Fan, and K. Chang, "On the Study of Passive and Active Slotline Ring Antennas," IEEE Antennas Propaga. Int. Symp. Dig., pp. 656-659,1993.

[73] C. H. Ho, L. Fan, and K. Chang, "New FET Active Slotline Ring Antenna," Electron. Lett., Vol. 29, No. 6, pp. 521-522, 1993.

[74] X. D. Wu and K. Chang, "Compact Wideband Integrated Active Slot Dipole Antenna Amplifier," Mocrowave Opt. Tech. Lett., Vol. 6, No. 15, pp. 856-857,1993.

[75] J. A. Navarro, L. Fan, and K. Chang, "Novel FET Integrated Inverted Stripline Patch," Electron. Lett., Vol. 30. No. 8, pp. 655-657, April 1994.

REFERENCES 437

[76] R. Flynt, L. Fan, J. A. Navarro, and K. Chang, "Low Cost and Compact Active Integrated Antenna Transceiver for System Applications," IEEE MTT-S Int. Microwave Symp. Dig., pp. 953-956, 1995.

[77] H. S. Tsai, M. J. W. Rodwell, and R. A. York, "Planar Amplifier Array with Improved Bandwidth using Folded-Slots," IEEE Microwave Guided Wave Lett., Vol. 4,No. 4, pp. 112-114, 1994.

1781 T. Mader, J. Schoenberg, L. Harmon, and 2. B. Popovic, "Planar MESFET Trans- mission Wave Amplifier," Electron. Lett., Vol. 29, No. 19, pp. 1699-1701, 1993.

1791 a. H. S. Tsai and R. A. York, "Polarization-Rotation Quasi Optical Reflection Amplifier Cell," Electron. Lett, Vol. 29, No. 24, pp. 2125-2127, 1993.

b. N. Sheth, T. Ivanov, A. Balasubramaniyan, and A. Mortazawi, "A Nine HEMT Spatial Amplifier," IEEE MTT-S Int. Microwave Symp. Dig., pp. 1239-1242, 1994.

[SO] R. D. Martinez and R. C. Compton, "High-Efficiency FET/Microstrip-Patch Os- cillators," IEEE Antennas Propagat. Mag., Vol. 36, No.1, pp. 16-19, 1994.

[81] R. D. Martinez and R. C. Compton, "A Quasi-Optical Oscillator/Modulator for Wireless Transmission," IEEE MTT-S Int. Microwave Symp. Dig., pp. 839-842, 1994.

[82] P. M. Haskins, P. S. Hall, and J. S. Dahele, "Active Patch Antenna Element with Diode Tuning," Electron Lett., Vol. 27, No. 20, pp. 1846-1847,1991.

[83] P. S. Hall, "Analysis of Radiation from Active Microstrip Antennas," Electron. Lett., Vol. 29, No.l,pp. 127-129, 1993.

[84] P. Liao and R. A. York, "A 1 Watt X-band Power Combining Array Using Coupled VCOs," IEEE MTT-S Int. Microwave Symp. Dig., pp. 1235-1238,1994.

[85] P. Liao and R. A. York, "A Varactor-Tuned Patch Oscillator for Active Arrays," IEEE Microwave Guided Wave Lett., Vol. 4, No. 10, pp. 335-337,1994.

1861 Y. Shen, R. Fralich, C. Wu and J. Litva, "Active Radiating Oscillator Using a Reflection Amplifier Module," Electron. Lett., Vol. 28, No. 11, pp. 991-992,1992.

[87] R. N. Simons and R. Q. Lee, "Planar Dielectric Resonator Stabilized HEMT Oscillator Integrated with CPW/Aperture Coupled Patch Antenna:' IEEE MTT-S Int. Microwave Symp. Dig., pp. 433-436,1992.

[88] D. V. Plant, D. C. Scott, D. C. Ni, and H. R. Fetterman, "Generation of Millimeter- Wave Radiation by Optical Mixing in FETs Integrated with Printed Circuit Antennas," IEEE Microwave Guided Wave Lett., Vol. 1, No. 6, pp. 132-134, 1991.

[89] D. V. Plant, D. C. Scott, D. C. Ni, and H. R. Fetterman, "Optically-Generated 60 GHz mrn-Waves Using AIGaAsfInGaAs HEMTs, Integrated with Both Quasi- Optical Antenna Circuits and MMICs," IEEE Photon. Tech. Lett., Vol. 4, pp. 102-105,1992.

[go] D. C. Scott, D. V. Plant, and H. R. Fetterman, "60GHz Sources using Optically Driven Heterojunction Bipolar Transistors," Appl. Phys. Lett., Vol. 61, pp. 1-3,1992.

[91] D. V. Plant, D. C. Scott, and H. R. Fetterman, "Optoelectric mm-Wave Sources," Microwave J., Vol. 36, No. 4, pp. 62-72, 1993.

[92] R. N. Simons and R. Q. Lee, "Space Power Amplification with Active Linearly Tapered Slot Antenna Array," IEEE MTT-S Int. Microwave Symp. Dig., pp. 623-626,1993.


[93] R. N. Simons and R. Q. Lee, "Spatial Frequency Multiplier with Active Linearly Tapered Slot Antenna Array," IEEE MTT-S Int. Microwave Symp. Dig., pp. 1557- 1560,1994.

[94] T. Razban, M. Nannini, and A. Papiernik, "Integration of Oscillators with Patch Antennas," Microwave J., Vol. 36, No. 1, pp. 104-110, 1993.

[95] Z. Ding, L. Fan, and K. Chang, "A New Type of Active Antenna for Coupled Gunn Oscillator Driven Spatial Power Combining Arrays," IEEE Microwave Guided Wave Lett., Vol. 5, No. 8, pp. 264-266, 1995.

[96] M. Kiyokawa, T. Matsui, and N. Hirose, "Dielectric Loaded Gaussian Beam Oscillator in the 40 GHz Band," IEEE MTLS Int. Microwave Symp. Dig., pp. 75-78,1995.

[97] G. F. Avitabile, S. Maci, G. Biffi Gentili, F. Ceccuti, and G. F. Manes, "A Basic Module for Active Antenna Applications," IEE 8th International Conference on Antennas and Propagation, Edinburgh, U.K., pp. 303-306,1993.

[98] H. An, B. K. J. C. Nauwelaers, G. A. E. Vandenbosch, and A. R. Van de CapeUe, "Active Antenna Uses Semi-balanced Amplifier Structure," Microwaves RF, Vol. 33, NO. 13, pp. 153-156, 1994.

[99] J. S. H. Schoenber, S. C. Bundy, and Z. B. Popovic, "Two-Level Power Combining Using a Lens Amplifier," IEEE Trans. Microwave Theory Tech., Vol. MTT-42, No. 12, pp. 2480-2485,1994.

[loo] R. Gillard, H. Legay, J. M. Floch, and J. Citerne, "Rigorous Modeling of Receiving Active Microstrip Antenna," Electron. Lett., Vol. 27, No. 25, pp. 2357- 2359,1991.

[ lo l l H. An, B. Nauwelaers, and A. Van de Capelle, "Noise Figure Measurement of Receiving Active Microstrip Antennas," Electron. Lett., Vol. 29, No. 18, pp. 1594- 1596,1993.

[I021 J. J. Lee, "G/T and Noise Figure of Active Array Antennas," IEEE Trans. Antennas Propagat., Vol. AP-41, No. 2, pp. 241-244, 1993.

[I031 U. Dahlgren, J. Svedin, H. Johansson, 0. J. Hagel, H. Zirath, C. Karlsson, and N. Rorsman, "An Integrated Millimeter-Wave BCB Patch Antenna HEMT Receiver," IEEE M T T - S Int. Microwave Symp. Dig., pp. 661-664,1994.

[I041 K. Cha, S. Kawasaki, and T. Itoh, "Transponder Using Self-Oscillating Mixer and Active Antenna," IEEE MTT-S Int. Microwave Symp. Dig., pp. 425-428,1994.

[I051 V. A. Thomas, K. M. Ling, M. E. Jones, B. Toland, J. Lin, and T. Itoh, "FDTD Analysis of an Active Antenna," IEEE Microwave Guided Wave Lett., Vol. 4, No. 9, pp. 296-298,1994.

[I061 B. Toland, J. Lin, B. Houshmand, and T. Itoh, "Electromagnetic Simulation of Mode Control of a Two Element Active Antenna," IEEE M V - S Int. Microwave Symp. Dig., pp. 883-886, 1994.

[I071 D. E. J. Hurnphery, V. F. Fusco, and S. Drew, "Active Antenna Array Behavior," IEEE Trans. Microwave Theory Tech., Vol. MTT-43, No. 8, pp. 1819-1825,1995.

[I081 J. Lin and T. Itoh, "Active Integrated Antennas," IEEE Trans. Microwave Theory Tech., Vol. MTT-42, No. 12, pp. 2186-2194,1994.

[lo91 K. J. Russell, "Microwave Power Combining Techniques," IEEE Trans. Micro- wave Theory Tech., Vol. MTT-27, No. 5, pp. 472-478,1979.

REFERENCES 439

[l 101 K. Chang and C. Sun, "Millimeter-Wave Power-Combining Techniques," IEEE Trans. Microwave Theory Tech., Vol. MTT-31, No. 2, pp. 91-107,1983.

[Il l] D. Staiman, M. E. Breese, and W. T. Patton, "New Technique for Combining Solid-state Sources," IEEE J. Solid-state Circuits, Vol. SC-3, No. 3, pp. 238-243, 1968.

[I121 A. H. ALAN, A. L. Cullen, and J. R. Forrest, "A Phase-Locking Method for Beam Steering in Active Array Antennas," IEEE Trans. Microwave Theory Tech., Vol. MTT-22, NO. 6, pp. 698-703,1974.

[I131 L. Wandinger and V. Nalbandian, "Millimeter-Wave Power Combiner Using Quasi-Optical Techniques," IEEE Trans. Microwave Theory Tech., Vol. MTT-31, NO. 2, pp. 189-193,1983.

[I141 N. Camilleri and T. Itoh, "A Quasi-Optical Multiplying Slot Array," IEEE Trans. Microwave Theory Tech., Vol. 33, No. 11, pp. 1189-1195,1985.

[I151 S. Nam, T. Uwano, and T. Itoh, "Microstrip-Fed Planar Frequency Multiplying Space Combiner," IEEE Trans. Microwave Theory Tech., Vol. 35, No. 12, pp. 1271-1276,1987.

[116] J. W. Mink, "Quasi-Optical Power Combining of Solid-state Millimeter-Wave Source," IEEE Trans. Microwave Theory Tech., Vol. MTT-34, No. 2, pp. 273-279, 1986.

[I171 K. D. Stephan, "Inter-injection-Locked Oscillators with Applications to Spatial Power Combining and Phased Arrays," IEEE MTT-S Int. Microwave Symp. Dig., pp. 159-162,1986.

[I181 K. D. Stephan, "Inter-Injection-Locked Oscillators for Power Combining and Phased Arrays," IEEE Trans. Microwave Theory Tech., Vol. MTT-34, No. 10, pp. 1017-1025,1986.

[119] S. L. Young and K. D. Stephan, "Stabilization and Power Combining of Planar Microwave Oscillators with an Open Resonator," IEEE MTT-S Int. Microwave Symp. Dig., pp 185-188,1987.

[I201 K. I. Cogan, F. C. De Lucia, and J. W. Mink, "Design of a Millimeter-Wave Quasi-Optical Power Combiner for IMPATT Diodes," in Millimeter Wave Technology W a n d Radio Frequency Power Sources, SPIE, Vol. 791, pp. 77-81, 1987.

[I211 W.A. Morgan and K. D. Stephan, "An X-band Experimental Model of a Millimeter-Wave Inter-injection-Locked Phased Array System," IEEE Trans. Antennas Propagat., Vol. 36, No. 11, pp. 1641-1645,1988.

[I223 J. Lin and T. Itoh, 'Two-Dimensional Quasi-Optical Power-Combining Arrays Using Strongly Coupled Oscillators," IEEE Trans. Microwave Theory Tech., Vol. 42, NO. 4, pp. 734-741, 1994.

[I231 R. A. York and R. C. Compton, "A 4 x 4 Active Array using Gunn Diodes," IEEE Antennas Propagat. Int. Symp. Dig., pp. 1146- 1149,1990.

[I241 D. B. Rutledge, Z. B. Popovic, R. M. Weikle, M. Kim, K. A. Potter, R. Compton, and R. A. York, "Quasi-Optical Power Combining Arrays," IEEE MTT-S Int. Microwave Symp. Dig., pp. 1201-1204,1990.

[I251 R. A. York and R. C. Compton, "Quasi-Optical Power Combining Using Mutually Synchronized Oscillator Arrays," IEEE Trans. Microwave Theory Tech., Vol. 39, No. 6, pp. 1000-1009,1991.

440 ACTIVE MICROSTRIP ANTENNAS REFERENCES 441

[I261 A. C. Davidson, F. W. Wise, and R. C. Compton, "A 60 GHz IMPATT Oscillator Array with Pulsed Operation," IEEE Trans. Microwave Theory Tech., Vol. 41, No. 10, pp. 1845-1850,1993.

[I271 M. F. Durkin, R. J. Eckstein, M. D. Stringtellow, and R. A. Neidhard, "35 GHz Active Aperture," IEEE MTT-S Int. Microwave Symp. Dig., pp. 425-427,1981.

[I281 Z. B. Popovic, M. Kim, and D. B. Rutledge, "Grid Oscillator," Int. J. Injrared Millimeter Waves, Vol. 9, No. 7, pp. 647-654, 1988.

[I291 D. B. Rutledge, 2. B. Popovic, R. M. Weikle, M. Kim,K. A. Potter,R. C. Compton, and R. A. York, "Quasi-Optical Power-Combining Arrays," IEEE MTT-S Int. Microwave Symp. Dig., pp. 1201-1204,1990.

[I301 R. M. Weikle, M. Kim, J. B. Hacker, M. P. DeLisio, Z. B. Popovic, and D. B. Rutledge, "Transistor Oscillator and Amplifier Grids," Proc. IEEE, Vol. 80, No. 11, pp. 1800-1809,1992.

[I311 T. Mader, S. Bundy, and Z. B. Popovic, "Quasi-Optical VCOs," IEEE Trans. Microwave Theory Tech., Vol. 41, No. 10, pp. 1775-1781,1993.

11321 S. Kawasaki and T. Itoh, "A Layered Negative Resistance Amplifier and Oscillator Using FETs and a Slot Antenna," IEEE MTT-S Int. Microwave Symp. Dig., pp. 1261-1264,1991.

[I331 S. Kawasaki and T. Itoh, "40 GHz Quasi Optical Second Harmonic Spatial Power Combiner Using FETs and Slots," IEEE MTT-S Int. Microwave Symp. Dig., pp. 1543-1546,1992.

[I341 S. Kawasaki and T. Itoh, "Quasi-Optical Planar Arrays with FETs and Slots," IEEE Trans. Microwave Theory Tech., Vol. MTT-41, No. 10, pp. 1838-1844,1993.

[I351 J. Brikeland and T. Itoh, "A 16 Element Quasi-Optical FET Oscillator Power Combining Array with External Injection Locking," IEEE Trans. Microwave Theory Tech., Vol. 40, No. 3, pp. 475-481, 1992.

[I361 H. S. Hwang, T. W. Nuteson, M. B. Steer, J. W. Mink, J. Harvey, and A. Paolella, "A Quasi-Optical Dielectric Slab Power Combiner," IEEE Microwave Guided Wave Lett., Vol. 6, No. 2, pp. 73-75, 1996.

[I371 A. Balasubramaniyan and A. Mortazawi, ''Two-Dimensional MESFET-Based Spatial Power Combiners," IEEE Microwave Guided Wave Lett., Vol. 3, No. 10, pp. 366-368,1993.

[I381 A Mortazawi and B. C. De Loach, "Spatial Power Combining Oscillators Based on an Extended Resonance Technique," IEEE Trans. Microwave Theory Tech., Vol. 42, No. 12, pp. 2222-2228, 1994.

[I391 T. Ivanov and A. Mortazawi, "A Two-Stage Spatial Amplifier with Hard Horn Feeds," IEEE Microwave Guided Wave Lett., Vol. 6, No.2, pp. 88-90, 1996.

[I401 C. C. Huang and T. H. Chu, "Radiating and Scattering Analyses of a Slot-Coupled Patch Antenna Loaded with a MESFET Oscillator," IEEE Trans. Antennas Propagat., Vol. 43, No. 3, pp. 291-298,1995.

[I411 Y. Shen, C. Laperle, N. Sangary, and J. Litva, "A New Active Array Module for Spatial Power Combiners and Active Antennas," IEEE Trans. Microwave Theory Tech., Vol. 43, No. 3, pp. 683-685, 1995.

[I421 M. G. Keller, D. Roscoe, Y. M. M. Antar and A. Ittipiboon, "Active Millimeter- Wave Aperture-Coupled Microstrip Patch Antenna Array," Electron. Lett., Vol. 31, NO. 1, pp. 2-3, 1995.

[I431 R. A. York, "Non-linear Analysis of Phase Relationships in Quasi-Optical Oscil- lator Arrays," IEEE Trans. Microwave Theory Tech., Vol. 41, No. 10, pp. 1799- 1809,1993.

[I441 P. Liao and R. A. York, "Phase-Shifterless Beam-Scanning Using Coupled-Oscil- lators: Theory and Experiment," IEEE Antennas Propagat. Int. Symp. Dig., pp. 668-671,1993.

[I451 P. Liao and R. A. York, "A New Phase-Shifterless Beam-Scanning Technique Using Arrays of Coupled Oscillators," IEEE Trans. Microwave Theory Tech., Vol. 41, No. 10, pp. 1810-1815, 1993.

[I461 P. Liao and R. A. York, "A Six-Element Beam-Scanning Array," IEEE Microwave Guided Wave Lett., Vol. 4, No. 1, pp. 20-22,1994.

11471 S. Nogi, J. Lin and T. Itoh, "Mode Analysis and Stabilization of a Spatial Power Combining Array with Strongly Coupled Oscillators," IEEE Trans. Microwave Theory Tech., Vol. 41, No. 10, pp. 1827-1837,1993.

[I481 J. Lin, S. T. Chew, and T. Itoh, "A Unilateral Injection-Locking Type Active Phased Array for Beam Scanning," IEEE MTT-S Int. Microwave Syrnp. Dig., pp. 1231- 1234,1994.

[I491 B. Robert, T. Razban and A. Papiernik, "Compact Active Patch Antenna," in IEE 8th International Conference on Antennas and Propagation, Edinburgh, U.K., pp. 307-310,1993.

[I501 S. Sanzgiri, W. Pottenger, D. Bostrom, D. Denniston, and R. Q. Lee, "Active Subarray Module Development for Ka-Band Satellite Communication Systems," IEEE Antennas Propagat. Int. Symp. Dig., pp. 860-863,1994.

[I511 J. A. Navarro, K. Chang, J. Tolleson, S. Sanzgiri, and R. Q. Lee, "A 29.3 GHz Cavity-Enclosed Aperture-Coupled Circular-Patch Antenna for Microwave Cir- cuit Integration," IEEE Microwave Guided Wave Lett., Vol. 1, No. 7, pp. 170-171, 1991.

[I521 G. W. Fitzsimmons, B. J. Lamberty, D. T. Harvey, D. E. Riemer, E. J. Vertat- schitsch, and J. E. Wallace, "A Connectorless Module for an EHF Phased-Array Antenna," Microwave J., Vol. 37, No. 1, pp. 114-126,1994.

[I531 "Integrated Circuit Active Phased-Array Antenna (ICAPA)," Contract No. F19628-90-C-0168, Rome Laboratories, John P. Turtle, Technical MonitorIEEAA, Don McMeen, Boeing Program Manager.

[I541 D. E. Riemer, "Packaging Design of Wide-Angle Phased-Array Antenna for Frequencies Above 20 GHz," IEEE Transactions on Antennas and Propagation, Vol. 43, NO. 9, pp.915-920,1995.

[I551 G. J. Erickson, G. W. Fitzsimmons, S. H. Goodman, D. T. Harvey, G. E. Miller, D. N. Rasmussen, and D. E. Riemer, "Integrated Circuit Active Phased Array Antennas for Millimeter Wave Communications Applications," IEEE Antennas Propagat. Int. Symp. Dig., pp. 848-851,1994.

[I561 E. J. Vertatschitsch and G. W. Fitzsimmons, "Boeing Satellite Television Airplane Receiving System (STARS) Performance," in International Mobile Satallite Confer- ence, Ottawa, Canada, June 6-8,1995.

[I571 J. A. Navarro and K. Chang, Integrated Active Antennas and Spatial Power Combining, John Wiley, New York, 1996.

CHAPTER NINE

Tapered Slot Antenna.

RICHARD Q. LEE and RAINEE N. SIMONS

9.1 INTRODUCTION

Tapered slot antennas (TSAs), also known as notch antennas, belong to the general class of endfire traveling-wave antennas (TWAs). Being a printed antenna, TSA has many advantages such as low profile, low weight, easy fabrication, suitability for conformal installation, and compatibility with microwave integrated circuits (MICs). In addition, TSA has demonstrated multioctave bandwidth, moderately high gain (7-10 dB), and symmetrical E- and H-plane beam patterns. Despite its superior performance, TSA has not been able to

broad interest in the r&earchcommunity since the early work reported by Lewis et al. [I] in 1974. Some possible explanation could be that TSA lacks the versatility of microstrip antennas which are capable of multifunctional operations such as dual frequencies and dual polarizations (LP,CP). As a result, the fundamental operation of TSA is not yet fully understood, and the designs of these antennas have primarily been based on empirical results due to lack of established design rules. This chapter will focus on the empirical development of the tapered slot antennatarrays.

The chapter begins with an up-to-date review of some typical planar TSA designs and their performance characteristics. In general, all designs differ only in the taper profile of the slot and the feeding methods. A variety of taper profiles are illustrated in Figure 9.1. The discussions on taper profile will focus mainly on the linearly tapered slot antenna (LTSA) and the vivaldi antenna [2]. In addition, two important variants of LTSA will also be presented and discussed: (1) the

Advances in Microstrip and Printed Antennas, Edited by Kai Fong Lee and Wei Chen ISBN 0-471-04421-0 0 1997 John Wiley & Sons, Inc.

444 TAPERED SLOT ANTENNA

linearly tapered V-antennas (V-LTSA) (Figure 9.2) and (2) LTSA of antipodal geometry (Figure 9.3). These antennas are relatively new, and only limited information is available. An important step in the design of a broadband antenna is the choice of a suitable feeding technique. With the exception of the antipodal geometry, all other TSAs are fed by a slo&ne. Hence the dis&sion on the feeding methods will focus mainly on the design and measured characteristics of a suitable transition between a slotline and any other transmission line. Moreover, this chapter will present experimental results on impedance characteristics and near-field distribution. For completeness, a brief summary of numericalJanalyti-. cal methods that have been developed by several researchers over the years for analyzing the performance of single TSAs as well as arrays with TSA elements will also be provided. These studies are useful in predicting blindness in array beam scanning [3]. Finally, we will highlight throughout the chapter some important applications of the TSAs.

9.2 BASIC GEOMETRIES

Figures 9.la-g show seven TSA designs of planar geometry that have been reported up to this date. In all cases, the basic radiation mechanism is similar. The antennas differ from each other only in the taper profile of the slot which constitute the radiating region of the antenna. In general, there are only three basic profiles: (1) nonlinear taper (exponential or vivaldi, tangential, and parabolic) [2,4,5], (2) linear taper [6,7], and (3) constant width [8,9]. The TSAs with constant width generally have one or more transitional regions of either linear or nonlinear profile as shown in Figure 9.le-g. A variant of the linear taper is the broken linear taper which is shown in Figure 9.lh. Of the seven designs presented in Figure 9.1, only the vivaldi and the linearly tapered slot antenna have been extensively studied over the years, and very limited data are available for the other designs.

A new variant of the LTSA and vivaldi generally known as the V-antennas have recently been introduced [lo]. Figure 9.2 shows the schematics of the V-LTSA and the V-vivaldi or "bunny-ear" [ll]. The V-antenna has a finite width ground plane which enhances the antenna performance by suppressing surface- wave and parallel-plate modes between conductors. The planar V-antenna in sandwich structure is capable of submillimeter applications and has been demonstrated at a wavelength of 1 1 9 ~ [12].

Planar TSAs, either with or without a supporting dielectric substrate, can be fabricated using photolithographic technique. These antennas have two common features: (1) Both the radiating slot and ground plane are on the same side of the substrate, and (2) the antenna is fed by a balanced slotline. One serious drawback of planar-type TSAs is in the fabrication and impedance matching of the slotline. Since a slotline fabricated on a low dielectric constant substrate has relatively high impedance which makes matching to a microstrip feed very difficult, the slotline-to-microstrip transition often limits the operating

BASIC GEOMETRIES 445

FIGURE 9.1 TSA with different tapered profiles excited by a slotline: (a) exponential, (b) tangential, (c) parabolic, (d) linear, (e) linear-constant, (f) exponential-contant, (g) step-constant, and (h) broken-linear.

446 TAPERED SLOT ANTENNA FUNDAMENTALS 447

FIGURE 9.2 Schematics of V-antennas excited by a coplanar stripline: (a) V-LTSA and (b) V-vivaldi. The shaded area is metal.

bandwidth of the TSA. To surmount the impedance matching difficulty, TSA of antipodal geometry was introduced [13]. The antipodal TSA, shown in Figure 9.3, is formed by gradually flaring the strip conductors of the balanced microstrip on opposite sides of the dielectric substrate by an angle a with respect to the antenna axis, thus allowing the antenna to be excited by a microstrip feed. Recently, a two-layer balanced antipodal vivaldi with a stripline feed has demonstrated a reduction in cross-polarization by 15 dB across an 18:l band C 141.

FIGURE 9.3 Schematic of an antipodal LTSA excited by a microstrip line. The portions indicated by the dotted lines are on the opposite side of the substrate.

The TSA, typically a few free-space wavelengths (1,) in length, is formed by gradually increasing the width of a slotline from its feed end to an open end of width generally greater than 1,/2 [6]. Published results have confirmed that geometrical parameters such as length, width, and taper profile of the TSA have direct impact on the impedance, directivity, bandwidth, gnd radiation patterns. Since TSA is a traveling-wave antenna, the dielectric thickness and the dielectric constant of the substrate control the rate at which electromagnetic energy radiates away, and therefore contribute to the efficiency of the antenna. The dimension of the ground plane which affects both the circuit and radiation characteristics of the TSA is another important design parameter. The induced current on theedge of the ground plane along the termination of the slot aperture has been found to have great impact on the E-plane pattern [15]. Furthermore, results for the V-LTSA indicate that the finite-width ground plane suppress surface-wave and parallel-plate modes between conductors to produce very low cross-polarization (- 30 dB at boresight) and symmetrical radiation patterns in both E and H planes [lo]. Other important design considerations which could impact the overall antenna performance are the ground plane and dielectric overlay effects. Besides its primary use as a radome, the overlay with parasitic element placed over a fed TSA can actually improve the antenna performance. Finally, the method selected for feeding the TSA is of utmost importance for wideband operation. A variety of proven feeding techniques will be discussed in Section 9.6.

9.4 FUNDAMENTALS

An antenna is basically a mode transformer [16]. Transmission of electromagnetic energy by an antenna consists in transforming a guided wave into a plane wave propagated in free space under a matched condition. Referring to Figure 9.4, continuous interaction between the guided wave and the plane


- Source

Longitudinal slot

FIGURE 9.4 Interaction between the guided wave and the plane wave.

wave can be maintained only if the free-space wavelength, A,, and the guided wavelength, 5, satisfy

Hence, in order for the antenna to radiate energy in the ? direction at an angle, 8, to the x axis, the guided wavelength, Ap must be greater than or equal to the free-space wavelength, a,; that is,

a, = .lo/cos 8 2 a,.

Accordingly, the phase velocity of the guided wave, v, must be

where c is the velocity of light. Traveling waves with up 2 c are called "leaky" waves or "fast" waves, which continuously lose energy through radiation. In general, leaky waves cannot be supported in terms of TE or TM waves alone, but by hybrid modes involving TE-TM coupling with complex propagation constant. Traveling waves with up < c are called "surface" waves, sometimes also referred to as "trapped" waves or "slow" waves. Surface waves attenuate exponentially away from the surface and radiate only at the edge of the guided structure. To obtain endfire radiation (8 = 0°), it is necessary to have a guided wave whose velocity is equal to the velocity of the wave generated in free space; that is, up = c.

FUNDAMENTALS 449

(-k,<k<kd Invisible Visible Invisible region region region

Backward endfire Foward endfire radiation radiation

FIGURE 9.5 Wavenumber k diagram.

The wave phenomenon associated with the TSA described above can be represented on the wavenumber k diagram shown in Figure9.5. The wavenumbers + k, and - k, denote free-space waves propagatingin the forward and backward directions, respectively. For a wave propagating in a nondispersive medium, the wavenumber satisfies the dispersive relation

where p and e are the permeability and permittivity of the medium, respectively. 'Hence for free space, the above relation reduces to

where p, = 471 x lo-' henry/meter and E , = 8.85 x 10-l2 farad/meter. By combining the above two relations and when up > c, we obtain

The interval (- k,, + k,) which allows the guided wave and the external medium to be matched to produce radiation is called the "visible" region, while the part of the spectrum with k < - ko and k > k , where the nonradiated energy continues in the state of guided waves in the line is called the "invisible" region. Endfire radiation occurs when the wavenumber k equals to + k,. For an endfire traveling-wave antenna, Hansen-Woodyard have shown that the antenna has maximum directivity if the wavenumber k satisfies the following condition CIA:

where L is the length of the antenna. The Hansen-Woodyard condition states that the antenna has higher directivity by slightly slowing the wave guided by the radiating structure. Physically, this represents a small translation of the spectrum


toward the "invisible" region to produce a finer main lobe in the endfire direction. However, the translation of the spectrum also produces a relative increase of the sidelobes.

A tapered slot antenna can have two principal mechanism of radiation: (1) traveling-wave mechanism [8], and (2) resonance mechanism 161. The main, nonresonant, traveling-wave mechanism of radiation is produced by higher- order Hankel function modes generated by waves traveling down a curved path along the antenna [2]. TSAs with a traveling-wave mechanism of radiation generally have lengths of 21 , s L I 121, and termination widths of W 2 6,/2. TSAs with lengths shorter than one free-space wavelength radiate through resonance mechanism. These antennas generally have low gain and broad patterns which are often accompanied by small ripples.

The traveling-wave mechanism of radiation in the TSA has been reported as attributed to leaky waves (v, 2 c) by some investigators [6] and surface waves (v, < c ) by others [8]. However, these claims have not been supported by experimental results, and the exact radiation process is still not yet well understood. Strictly speaking, a surface wave is one that propagates along an interface between two different media without radiation, with such radiation being interpreted to mean energy converted from the surface wave field to some other form [18]. To support a surface wave, the surface between the two homogeneous media must be straight in the direction of propagation. Departure from this condition such as any slight curvature in the direction of propagation or the truncation of the guiding structure can result in radiation. The simplest case of wave propagation over a flat metal surface is the inhomogeneous plane wave, or Zenneck wave. These fields exist even if one of the two media is free space [19]. However, the Zenneck wave has a very small rate of decay. Hence, the surface must be coated with dielectric to be an effective slow wave structure. As an example, at a frequency of IOGHz, an uncoated metal surface has a decay coefficient, p, approximately given by

where p0 = 4n x lo-' henry/m is the permeability for free space, and a = 6 x lo7 mho/m is the conductivity for copper. Consequently, the field falls to l/e at a height of 70m. Clearly, with such a small rate of decay normal to the surface, it would be difficult to identify this surface wave. By coating the metal surface with a dielectric having a thickness t = 0.16cm and relative dielectric constant E, = 2.5, the corresponding decay coefficient in free space at the frequency f = 10 GHz can be approximated by

Now, the field falls to l/e of its surface value at a height of 2.38 cm. Since the phase velocity is inversely proportional to E, of the medium, the effect of loading the

FUNDAMENTALS 451

surface is to reduce the phase velocity v, to a value substantially below the free-space velocity c. The effect of dielectric thickness, t, on the behavior of a TSA has been experimentally investigated [7]. In these experiments, the dielectric thickness is characterized in terms of an effective dielectric thickness, ten = (a) t. It has been experimentally observed that TSA of length of 4-101, and substrate thickness in the range of 0.0036, I t,< 0.011, generally exhibits standard traveling-wave characteristics of broad bandwidth and low sidelobes. Surface waves supported by thick dielectrics generally give rise to poor radiation patterns and reduced antenna efficiency. Thus increasing the dielectric thickness at first results in increased antenna gain and with higher sidelobes; further increase results in asymmetric E- and H-plane patterns. Vivaldi antennas have also been found to exhibit similar dielectric thickness effects; that is, the thinner dielectric antennas are well behaved, while the thicker ones show some anomalous effects. In general, H-plane patterns are less sensitive to the thickness of the dielectric

It has been experimentally demonstrated that a tapered slot antenna can radiate energy effectively without any supporting dielectric substrate [20]. Since surface wave antennas require a dielectric-coated or corrugated metal surface to store, propagate, and radiate electromagnetic energy, energy radiated from a TSA fabricated on an uncoated metal surface can be considered to come predominantely from leaky waves as a result of transformation of guided waves in the slotline into traveling waves. Energy traveling along a uniform slotted metal sheet is tightly bound to the slot region when the slot width is very small compared to the free-space wavelength, and radiation occurs only at the termination of the slotline. However, close confinement can be achieved only if the guide wavelength, I,, is roughly 30-40% of the free-space value [21]. Progressive radiation of the energy carried by a guided structure can be achieved by placing a series of discontinuities along the guide to create suitable perturbation of its characteristics which could be a variation in the refractive index, or a variation in the thickness or antenna shape. In the case of a TSA fabricated on an uncoated metal surface, energy radiates as a result of the gradual flaring of the slot width which increases the guide wavelength, A,, and characteristic impedance, Z, of a slotline. Thus, a leaky wave is generated when a closed or an open waveguide structure supporting a guided wave is perturbed either continuously or at periodic internal to effect a change in Lq For a TSA fabricated on a dielectric substrate of thickness t at a specified frequency, a 20% increase in the slot width produces a 6% increase in Z, and a 1% increase in 6,/6, [22]. Because of the continuous changes in 1, along the tapered slot region, the TSA is capable of multioctave bandwidth from below 2 GHz to above 40 GHz [2].

The TSA radiates most of its power in the endfire direction. The direction of radiation is determined by the Poynting vector, E x H, which is defined by the electromagnetic field distributions along the TSA. The total field can be considered as a combination of six field components corresponding to (1) the case of a dielectric-air interface in a TSA and (2) the case of a TSA without a supporting


Top view z

I Side view (b)

FIGURE 9.6 Field distribution in the tapered slot region of a TSA: (a) with a supporting dielectric and (b) without a supporting dielectric.

substrate. The field components for both cases are depicted in Figures 9.6a and 9.6b, respectively. As shown, Ex, E,, and Hz are the possible field components for case (1) and Ez, H, and H, for case (2). The fields for the first case are the Zenneck waves, which are supported by a dielectric-air interface and decay exponentially away from the surface [19].

One principal limitation in the use of a TSA for broadband application is in obtaining a broadband transition at points of truncations. There are essentially two transition regions in the structure which must individually possess broadband behavior: (1) the transition from the dominant slotline mode to the traveling wave at the feed end and (2) the transition from the open end of the TSA to free space. Broadband operation requires a perfect impedance match at both transitions. Since for a given slot width the characteritic impedance varies with

ANALYTICAL METHODS 453

Stripline open adjustment

Slot short adjustment

FIGURE 9.7 Scheme for tuning a TSA.

frequency, the truncation of the tapered slot radiating region at the feed and the open ends imposes limits on the highest and the lowest frequency that the TSA can operate. In the case of mismatch at these two transition regions, standing waves, in addition to the nonresonant traveling waves, will exist simultaneously in the tapered slot region. Resonances resulting from the standing waves often reduce the overall bandwidth of the TSA. In the case of stripline-fed TSA, various schemes using MMIC tuning circuitry for compensating the mismatch have been studied. Results reveal that the TSA could be electrically tuned to the required low- and high-frequency limits by varying the length of the stripline open and slotline short terminations [23]. Such a compensating scheme is shown schematically in Figure 9.7.

9.5 ANALYTICAL METHODS

Because of complex geometry and large ground plane, analytical methods that work well for other planar antennas cannot be applied directly to the tapered slot antenna. The difficulties in the analysis are also caused by the nonuniformity of the wave in the tapered slot region where, for a given permittivity of the supporting dielectric substrate, the impedance and the propagation coefficient vary with slot width. Analytical methods that have been proposed so far for tapered slot antennas include: (1) the 2-D TLM method [24], (2) the moment method [25-273, (3) the equivalent source method [28], (4) the stepped approximation method [15,29,30], (5) the conjugate gradients-fast Fourier transform method 1311, and (6) the finite-difference time-domain (FDTD) method [32]. All proposed methods have demonstrated reasonably good agreement with meas-


FIGURE 9.8 Stepped approximation method for a TSA.

ured data, but, in general, most of these methods have some serious drawback and limitations. For example, the TLM method simulates the wave propagation in a structure replaced by a three-dimensional mesh of transmission lines, while the moment method is based on the numerical solution of the reaction integral equation of the surface currents defined over the entire conducting surface. Both methods require lengthy computing time, and therefore, they are suitable only for small antenna structures. The same holds true for the FDTD method, which generally requires a supercomputer for implementation. The stepped approximation method replaces the tapered section of the TSA by a number of uniform slot sections of progressively increasing width (usually five sections per free-space wavelength) as shown in Figure 9.8. The analysis is essentially a two-step process: (1) The dispersion characteristics and the electric field distribution E,(R') of an infinite slotline with uniform width are obtained using the spectral Galerkin's technique [33], and (2) the far field E(R) for each uniform section is obtained by integrating the surface magnetization vector MS(R1), over each slot aperture S' with the conducting half-sheet Green's function developed by Tai [34]:

where jwpoMs(R') = - n x Es(R') and G,,(R,R1) is the electric dyadic Green's function of the second kind with the observation and source points denoted by R,R' respectively. The total far-field is obtained by summing the contribution


from all different sections. The analysis assumes that the lateral edges of the TSA are at infinity and that power conservation is enforced at each step discontinuity, implying no reflection or radiation at the step junction. The effects of termination of the structure are taken into account by adding a small reflected wave. Despite its simplified approach, the stepped approximation method has demonstrated excellent agreement as compared to rigorous full-wave analysis and experimental results. Because ofits wide acceptance by researchers, we will present this method in greater detail below.

9.5.1 Analysis of Uniform Slotline by the Spectral Domain Approach

According to the technique outlined in reference [33], a hybrid mode solution is required to determine the dispersion characteristics and the aperture field distribution of a slotline shown in Figure 9.9. The fields are decomposed into TE wave with the magnetic scalar potential function &'(x, y ) and in T M wave with the electric scalar potential function @(x, y) in the three regions i = l ,2,3. By defining the Fourier transform as

where r] is the tranform variable. The hybrid fields in the spectral domain can be written as

Metallization -. kw-d 4

FIGURE 9.9 Slotline cross section.


where z, = jopi, y, = j u q , and k, = m a . The quantities pi and ci are, respectively, the permeability and permittivity of the three regions, and k, is the unknown propagation constant along the z direction. The transforms of the scalar potential for the regions 1 ,2 , and 3 are given by

whzre 6;(q, Y) and &f(q, Y) satisfy the Helmholtz equation V' &,(q, y) + k:mi(q, y) = 0, which in Fourier domain can be simplified to

w h e r e y ~ = q 2 + k ~ + k ~ , k l = k s = k o , k 2 = ~ ~ i t h i = 1 , 2 , 3 a n d k o b e i n g the free-space wavenumber. The eight unknown coefficients, Ae, Ah, ..., De and Dh are to be evaluated from the following boundary and continuity conditions.

At y = 0 (dielectric-air interface):

At y = d, (slot-conductor surface):

0, 1x1 z w/2 = { e x , I x 1 < w/2 = E x ) ,

(f) Hxl - Hx2 = {fx) 1x1 L w/2 1x1 < w/2

where w is the slot width; jx(x) and jz(x) are the unknown surface current components at y = d, 1x1 2 w/2, and e,(x) and e,(x) are the unknown fields in


the slot region at 1x1 < w/2. Since only tangential components are required by the boundary conditions, we need to evaluate only the x and z components of the electric and magnetic fields. By applying boundary conditions (a), (b), and (c) in spectral domain, we can express, Ae(q), Ah(q), Be(q), Bh(q), De(q), and Dh(q) in terms of Ce(q) and Ch($. We next apply boundary condition (d) a t y = d and Ix 1 < w/2 in spectral domain to solve for Ce(q) and Ch(q) in terms of tx(q) and t,(q), which are the Fourier transforms of ex(x) and e,(x), respectively. Finally, by applying boundary condition (e) and (f) at y = d and 1x1 2 w/2, we obtain a set of coupled equations of the form

In the above equations, coefficients r l (q, k,) . . . r4(q, kJ are known function of q and k,, and Jx(q) and J,(q) are Fourier transforms of j,(x) and j,(x), respectively.

To solve the coupled equations, we expand the slot fields ex(x) and e,(x) in an infinite series of known basis functions as

The transforms of the slot fields can then be written as

where a, and b, are the unknown coefficients and ~:(q) and ~',(q) are the Fourier transforms of the known basis functions. Applying Galerkin's method, we obtain


The above equations can be written in matrix form with matrix elements given by

Since the slot fields and the surface currents vanish in complementary domain of x, the right-hand sides of Eqs. (9.3) and (9.4) which consist of inner products of J,(q)eXq) and J,(q)&;(q) can be proved to be zero using Parseval's theorem. The dispersion relationship is obtained by solving for the values of k, which render the determinant of the coefficient matrix of Eqs. (9.3) and (9.4) to zero for a given k , and slotline geometry. The effective dielectric constant can be computed from k, by

The definition of the characteristic impedence is somewhat arbitrary for the slotline due to the non-TEM nature of the problem. One possible choice is to define it as

where V, is the slot voltage and Pa,, is the time-averaged power flow along the slotline given by

where * denotes the complex conjugate. Using Parseval's theorem, the above equation can be written as


The voltage can be obtained by integrating the electric field distribution across the slot of width w:

The basis functions are so chosen that the behavior of E, and Ex near the edge of the metal strip is properly accounted for. For the fundamental mode of the slot, the longitudinal (z-directed) component is an odd function of x, whereas the transverse (x-directed) component is an even function of x. The basis functions are chosen as [35].

= O for Ix 1 2 w/2 (9.5)

e x = ( ' ) 2 1 ( ) for 1x1 1 w/2,m = 1.2,. . .

=O for Ix l rO (9.6)

where T, and U, are Chebyshev polynomials of the first and second kind, respectively. The Fourier transforms of the given basis functions can be found in closed form as

9.5.2 Far-Field Computation

In order to use Tai's results directly to compute the far fields, the x and z axis of the tapered slot antenna were retated by 90" as shown in Figure 9.8. With the new coordinates, the component e,(z) contributes only to the cross-polarization; hence, only e,(z) is needed to compute the copolar component of the far field [I 51.

460 TAPERED SLOT ANTENNA FEEDING TECHNIQUES 461

From Eq. (9.5), the transverse slot field e,(z) can be written as

Based on the assumption of constant power flow along the slot, all mode coefficients can be determined in terms of a';, the amplitude of the first transverse basis function.

where Zb is the characteristic impedence for the ith section determined by the method outlined in Section 9.5.1. By including the phase factor and normalizing the mode coefficients a t in the ith section such that a: = 1, the z-directed slot field in the ith section is given by

The pattern function, gdO, d ) , for an x-directed two-sided infinitesimal slot on a conducting half-plane is required to compute the radiated field of the TSA. The pattern function first given by reference 1341 and by reference [15] for an infinitesimal slot located a t (x', z') has the form

where v = k0x1sin O(1+ cos 4) and F(o) is the Fresnel integral defined by

The far field EL from the ith section is obtained by integrating the field distribution (5.9) over the ith section with the pattern function (5.10); that is,

The expression for Eg can be obtained in a closed form given by [15]

E plane:

H plane:

where

Ci = ('O/'?ith section, kO = 2 7 4 , U & = k O ~ f s l ( c i - 01,

c:,, = koxi,,(ci + sin O), of, , = kox~ , , ( c i + cos 4) , I$,, = koxk.,(ci - cos 4) ,

qfi,l= k o ~ f i , ~ ( c ~ - I ) , 4;,, = koxf, l(ci + 1) pi,, = koxt,,(l + cos 4)

and xf and x i are the lower and upper coordinates of the ith section, respectively. Ef(.) can be determined from Eqs. (9.7) and (9.9). In general, only one mode is needed to obtain a convergent solution for the slot characteristics and the radiation patterns.

9.6 FEEDING TECHNIQUES

Almost always an isolated TSA is excited by a slotline. However, to build systems, the TSA has to be integrated with other microwave circuits using a common transmission media. Hence for most practical purposes, feeding a TSA is synony- mous to building a transition between slotline and other transmission media. These transitions should be very compact and have low loss for constructing large and efficient arrays, respectively. In addition, these transitions should have small parasitics for wide bandwidth, and hence electromagnetic coupling is preferred over wire bonding or solder connection. Several approaches to design these transitions have been outlined in the literature. The approaches are divided


into two categories by the form of electrical coupling, namely, electromagnetic coupled transitions and directly coupled transitions. Transitions which make use of microstrip line, conventional coplanar waveguide (CPW), grounded coplanar waveguide (GCPW), grounded coplanar waveguide with finite width top ground planes (FCPW), and stripline belong to the former category. Transitions which

FIGURE 9.10 Feeding techniques for planar TSA: (a) coaxial line, (b) microstrip line, (c) CPW, (d) air-bridge/GCPW, (e) FCPWIcenter-strip, (f) FCPW/notch, (g) microstrip/coupled microstrip/slotline, and (h) stripline.

incorporate coaxial line, bond wires or ribbons, and microstrip power splitter and phase shifter combination belong to the latter category. Typical examples of the above transitions are illustrated in Figure 9.10. Physical layout may also play an important role in the choice of a transition design. Hence it is worthwhile to mention that the feedline and the slotline are in-line in the transitions shown in Figures 9.10d, e, and 9.10h and are orthogonal in the rest of the cases. In addition, feeding techniques in Figures 9.10a and 9.10b are the most commonly used methods for exciting TSA. The remaining are new concepts introduced only recently. In addition to the techniques described above, there are other feeding techniques developed for antipodal TSA and V-TSA. A brief description of each technique is provided in this section. In the description that follows, fo and I, are the design frequency and the corresponding free-space wavelength. The substrate thickness and relative dielectric constant are represented by t and E,, respectively.

Coaxial Line Feed. The coaxial line feed provides a direct path for coupling of fields across the slot. The slotline-to-coaxial transition is constructed by electri-

1 cally attaching the outer conductor of a coaxial cable to the ground plane on one

I side of the slot, while attaching the extended inner conductor to the other side directly across the slot. To aid the transition design, an equivalent circuit based on the assumption that the inner conductor of the coax follows a circular path across the slot has been developed 1361. The equivalent circuit predicts tha; the slot imvedance will be transformed to a lower value: and to match to a 50-52 coaxial cable, a slot impedance of about 75 R is needed. In practice, a slotline with an impedance of less than 100 R has a slot width of only a few thousandths of an inch which cannot be fabricated accurately with conventional etching techniques. Without a proper impedance transformer, the slotline-to-coaxial transition generally has a 3:1 bandwidth with VSWR less than 2.0. To overcome the high impedance mismatch, a wedge-fed transition, shown in Figure 9.11, has been developed and has demonstrated a measured return loss better than 13 dB and VSWR less than 1.6 from 3.5 to 22 GHz [37]. However, pattern degradations were observed over almost the entire frequency band due to interference from the wedge transition [38].

Microstrip Line Feed. A simple microstrip/slotline transition consists of an open- circuited microstrip line which is extended past the center of the slotline one- quarter of a guide wavelength I, minus a "length extension" Al. The length extension is due to fringing at the end of the open-circuited line, which makes the line appeared electrically longer. The length extension can be approximated using the following expression [39]:

where eeff is the effective dielectric constant, w, is the linewidth, and t is the substrate thickness. The microstrip-slot transition can be approximated by the


Semirigid coaxial cable

FIGURE 9.11 Schematic for a wedge-fed transition. (From reference [38], with permission from University of Illinois, Urbana-Champaign.)

equivalent circuit shown in Figure 9.12 [37]. An impedance match between the microstrip and the slotline can be achieved at a given frequency by making

Zom = n2ZOs

where

n = cos (2nut/Ao) - cot (q) sin (2nut/Ao)

q = 2nut/Ao + tan-'(u/v)

where As is the slotline wavelength. To achieve proper impedance match, multi-step quarter-wave transformer is sometimes needed. The bandwidth is

FEEDING TECHNIQUES 465

s below substrate

W I I

FIGURE 9.1 2 Microstrip-fed transition: (a) coupling section and (b) equivalent circuit. (From reference [37], with permission from Microwave Journal.)

considerably broadened when the microstrip is terminated by a radial stub and the slotline is terminated by an elliptical shaped cavity as shown in Figure 9.13. According to the authors [38], the introduction of the elliptical cavity tends to shift the operating bandwidth of the microstrip-to-slotline transition down in frequency. As a result, the slotline is chosen as the low-frequency stub, while the high-frequency stub is constructed by simply shortening the length of the microstrip stub. A vivaldi with radial and elliptical stubs shows measured return loss of better than 10 dB from 2.8 to 18.8 GHz.

Conventional Coplanar Waveguide (CPW) Feed. In a CPW, both the signal line and the ground plane are on the same side of the printed circuit board. The normal propagating mode on this transmission line is the quasi-TEM or the coupled slotline odd mode with the electric fields in the two slots oriented in


FIGURE 9;13 Bandwidth broadening with a radial stub and elliptical cavity. (From reference [37], with permission from Microwave Journal.)

the opposite directions. This structure can also support a non-TEM mode or the coupled slotline even mode with the electric fields in the two slots oriented in the same direction. The non-TEM mode is dispersive and is usually suppressed. This is done by maintaining the two ground planes at equal potential which in a practical circuit is implemented by an air bridge. Coplanar waveguides offer several advantages over conventional coaxial or microstrip line for monolithic or hybrid microwave integrated circuit (MMIC or MIC) applications; these include ease of parallel and series insertion of both active and passive components and high circuit density. In addition, coplanar waveguide feed has lower radiation loss, can be characterized using CPW wafer probe equipment, and provides the extra degree of freedom of being able to choose the center conductor width independently for the line impedance, leading to lower dispersion and conductive losses.

Two new techniques for exciting a TSA using conventional CPW have been reported. In the first technique shown in Figure 9.10c, only one-half of the CPW transitions into a slotline and excites the TSA. The other half is terminated in a short circuit [40]. A vivaldi excited by this technique exhibits a broader bandwidth than that excited with the conventional microstrip feed. In the second technique, an air-bridge is used to couple power from the open end of a conventional CPW to a TSA. A variant of the conventional CPW is the grounded CPW (GCPW) which has an additional ground plane on the opposite side of the substrate. Figure 9.14 shows a typical transition belonging to the second technique. In this feed, the CPW is terminated in a tapered open circuit of length L, which is about Ig(,,, 42, where I, is the guide wavelength at the design frequency f, of 18GKz. The width S of the CPW center strip conductor at the open end 0.0191,. The slotline of the LTSA is terminated in a curved short circuit of length Ag(,,,,,/4 beyond the bridge. The width of the slotline is the same as that of the

I . I M ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ + j Top Metalization

substrate / '0% 4,

Bottom Metalization

FIGURE 9.1 4 CPW feed directly coupled to a LTSA by an air-bridge: (a) top metalization and (b) bottom metalization.

Frequency, GHz

FIGURE 9.15 Measured return loss at the CPW port for an air-bridge feed.

CPW which is indicated as w. The radii of curvature r , and r , of the slotline are approximately 1,(,,,,,/6. The TSA used in the experiment has a length, L, of 4.11, and a taper angle, 2u, of 10.6". A 0.00508-cm-wide gold ribbon bridges over the slotline connecting the open end of the conductor-backed CPW to the opposite edge of the slotline. Results presented in Figure 9.15 show a measured return loss of better than 10 dB from 16.7 GHz to 20.7GHz [41].

Conductor-Backed Finite Ground-Plane Coplanar Waveguide Feed (FCPW). Exciting the tapered slot antenna using a conductor-backed finite ground-plane CPW offers many advantages over the conventional CPW feed described above.


' I1 w I I!!

Dielectric substrate Boer

FIGURE 9.16 Schematic illustrating CPW strip-to-slot transition: (a) bottom metalization and (b) top metalization.

The FCPW has fewer parallel-plate modes, lower conductor losses, and better isolation between adjacent feeds in an array [42]. Unlike the conventional CPW-fed TSA, the FCPW etched on the opposite side of the substrate is electromagnetically coupled to the TSA. Figures 9.10e and 9.10f show two FCPW-fed TSA designs that have demonstrated very wide bandwidth. The TSAs for both designs have a length, I , of 6.6cm and a tapered angle, 2u, of 11.2". Although both TSAs are excited by FCPW, the mechanism of coupling power to the antenna is quite different. In Figure 9.10e, the power coupling is through a CPW strip-to-slot transition, while in Figure 9.10f, the coupling is through a CPW slot-to-slot transition. The layout of the CPW strip-to-slot transition is shown in details in Figure 9.16. As indicated in the figure, the finite ground planes of the CPW is connected to the antenna ground plane through via holes to ensure good impedence match and odd-mode operation. For efficient power coupling, the center strip conductor of the FCPW is extended to form a CPW-to-slotline transition with the TSA. The distance L, from the short termination of the slotline, as well as the distance L, from the open termination of the extended center strip conductor to the CPW-to-slotline junction, is about a quarter of a wavelength at the center frequency fo of 20GHz. An equivalent circuit for the microstrip-to-slot transition is shown in Figure9.17. In the figure, C,, and Zo, are the open circuit capacitance and the characteristic impedance of the FCPW center strip conductor extension, respectively, while L,, and Z,, are the short-circuit inductance and the characteristic impedance of the slotline, respectively. Estimates of these parameters are given in reference 1433. The measured return loss for the CPW strip-to-slot transition coupled TSA is shown in Figure 9.18. Results show return loss of better than lOdB over a bandwidth of 20 GHz centered at 20GHz [41].


(b)

FIGURE 9.1 7 Equivalent circuit for the CPW strip-to-slot transition. (From Microstrip Line and Slotline by K . C . Gupta, R. Garg, and I. J. Bahl, Artech House, Inc., Norwood, MA.)

FIGURE 9.18 Measured return loss for the center strip coupled LTA.


Top Metaliration

Bottom Metalization

FIGURE 9.19 LTSA electromagnetically coupled to FCPW feed: (a) top metalization and (b) bottom metalization.

Figure 9.19 shows the schematic of the TSA with CPW slot-to-slot transition described earlier in Figure 9.10f as a feed. The FCPW which is etched on the opposite side of the substrate is placed at right angles to the slotline of the TSA. To improve coupling, two notches of width w and lengths L, and L, are cut from the FCPW ground plane located directly above the slotline of the TSA. A pair of bond wires are attached to both sides of the notch to suppress any spurious slotline modes generated at the discountinuity. The FCPW and the slotline are terminated in short circuits. The 10-dB return loss bandwidth for the electromagnetically coupled FCPW feed is approximately the same as the air-bridge coupled feed but significantly worse than the CPW strip-to-slot feed. Results of the measured return loss are displayed in Figure 9.20.

Microstrip-to-CoupledMicrostrip Feed. Figure 9.10g shows the schematic of an LTSA fed with a microstrip-to-slotline transition. This transition is similar in construction to that reported in reference [44]. The two side arms of the microstrip T junction are bent to form a circle with arc lengths a-b and a-c differing by lg(micraatrip). Hence the fields at the locations b and c are 180" out of phase. This phase difference is responsible for exciting the odd mode on the coupled microstrip lines b-d and c-e. The following equation can be used for the design of the transition [45]:


40° 17.5 18.9 20.3 21.7 23.1 24.5

Frequency, GHz

FIGURE 9.20 Measured return loss for the electromagnetically coupled feed.

-

Mlcrostrip mode

Coupled microstrip odd - mode

Slotline mode

FIGURE 9.21 Electric field distribution along the microstrip/coupled microstrip/slotline transition.

where Z,,, Z,,, and Z,, are the characteristic impedances for the microstrip, slotline, and coupled microstrip, respectively. The values of Z,, and Z,, are arbitrarily chosen, and Z,, is computed from the equation given above. The electrical field distribution at the various cross sections is shown in Figure 9.21. To demonstrate this feed concept, an LTSA excited by the microstrip-to-coupled microstrip-to-slotline transition was fabricated on a high-resistivity silicon wafer. The length L and the aperture width W are chosen as 1.331, and 0.51,


respectively, where 1, is the free-space wavelength at a design center frequency, f,, of 10 GHz. The tapered angle, 2a, is 21". The measured return loss is better than 10dB with over 8% bandwidth at 9.0 GHz.

BalancedStripline Feed. A stripline-fed notch radiator is shown in Figure 9.10h. The stripline placed symmetrically between two ground planes excites two tapered slot antennas of the same design. Power is coupled to the TSA by a perpendicular intersection of the stripline center conductor and slotline. The stripline is terminated in an open circuit, and the slotlines are terminated in short circuits. Stripline feeding approach offers more flexibility to achieve input match with stacked antenna geometry. Previous study indicated that the input VSWR of the TSA can be changed by varying the open-circuited stripline and shorted slotline termination lengths 1223.

Microstrip-to-Balanced Microstrip Feed for Antipodal TSA. The feed structure, shown in Figure 9.22, consists of a conventional microstrip on a dielectric substrate of thickness, t, with the ground plane tapered to a width equal to the strip width, w,, (0.071 cm), to form balanced microstrip [72]. The radius R, of the arc is arbitrarily chosen as one half free-space wavelength (1,/2) at the design frequency f,, which is 18 GHz for this particular design. The taper helps matching the characteristic impedance of the conventional microstrip (50 R) to the balance microstrip. Unlike the slotline, the balanced microstrip is relatively easy to realize

Dielectric substrate we 1

FIGURE 9.22 Antipodal LTSA and feed network: (a) top metalization and (b) bottom metalization.

FIGURE 9.23 Electric field distribution at cross sections , . of (a) conventional microstrip, (b) balanced microstrip, and (cl (c) antenna radiating edge.

wideband impedance match. To match the input impedance of the TSA, the characteristic impedance of the balanced microstrip is chosen to be approximately 160 C2, which is twice the input impedance of a regular half TSA above a ground plane without a dielectric. The electric field lines at various cross section along the feed and the antenna are shown in Figure 9.23. The electric field lines which are spread out in the conventional microstrip concentrate between the metal strips of the balanced microstrip and finally rotate while traveling along the axis of the antenna. The measured return loss at the coaxial input port of the feed network is shown in Figure 9.24. The return loss is observed to be better than lOdB over a frequency range extending from 8 to 32 GHz, a significant improvement over the conventional CPW-fed TSA of Figure 9.10~ described earlier [40].

Uniplanar Microstrip-to-Coplanar Stripline (CPS) Feed for V-TSA. The schematic for a uniplanar microstrip-to-coplanar stripline (CPS) feed exciting a V- TSA is shown in Figure 9.25a [lo]. The feed network should work for TSA of any tapered profile. In the feed network, a microstrip line of characteristic impedance, Z, = 50R, and width, w,, is coupled to two orthogonal microstrip lines of characteristic impedance, 70R, and width, w,, through a quarter-wave stepped impedance-matching transformer of width, w,. The characteristic impedance of 70C2 is chosen for easy fabrication. In an ideal transition, the mean path length of

476 TAPERED SLOT ANTENNA CHARACTERISTICS OF TSA 477

FIGURE 9.26 Vivaldi antenna in finline mount.

frequencies, these feed structures are generally not satisfactory for most applications due to excessive losses. Instead, waveguides are often used to minimize losses and to achieve adequate shielding of circuits. Figure 9.26 shows a wideband waveguide-to-finline transition for feeding a TSA [46]. The finline which excites the antenna is inserted inside the waveguide, making contact with the upper and lower waveguide walls. A detailed description on how to design the transition is given in reference [47].

9.7 CHARACTERISTICS OF TSA

Since no design rule exists, a good understanding of the antenna characteristics would facilitate the task of designing the TSA. Based on previous work, it is well known that TSA generally has wider bandwidth and higher directivity than printed patch elements and is capable of producing symmetrical radiation patterns. However, other characteristics of TSA-such as mutual coupling and impedance, and so on, which are important parameters in the design-are not readily available from the literature. Provided below are experimental data illustrating some important characteristics of TSA described in Section 9.2.

9.7.1 Radiation Characteristics

Being a traveling-wave antenna, the phase velocity, and hence the guide wavelength A,, of a TSA varies with changes in substrate thicknes, dielectric constant, and taper shape. Since the gain is proportional to L/1,, and the beamwidth is proportional to @, geometric parameters such as length, width, taper profiles, and so on, will impact the radiation patterns, directivity, and cross-polarization level of the antenna. Other parameters such as substrate

FIGURE 9.27 TSA with linear (1) and exponential (2, 3,4) taper profiles.

thickness, ground plane, and parasitic superstrate have also been found to have direct effects on the radiation characteristics. Some experimental results of these effects are presented below:

Effect of Curvature on TSA with Supporting Substrate. The effects of the taper profile and the curvature of the mounting structure on TSA were experimentally investigated. Four TSAs with same length L = 0.931, and same terminating slot width W = 0.681,, but with different taper profiles were studied at a frequency of 11 GHz. The antennas, shown in Figure 9.27, were fabricated on 10-mil-thick RTIDuroid substrate (E, = 2.2) and were labeled #1 to #4, with #1 being linearly tapered and #4 having the smallest radius of curvature-that is, largest rate of change in taper profile. The exponential tapers were generated from the equation

y(x) = (ax + b)ecx

where a, b, and c are parameters chosen to produce the desired profile with c = 0 corresponding to the LTSA case. The effects of taper profiles on the half-power beamwidth (HPBW) and cross-polarization levels are displayed in Figures 9.28 and Figures 9.29, respectively. Results indicate that HPBW increases with decrease in the radius of curvature for the E and the diagonal D plane, while the opposite holds true for the H plane. The cross-polarization generally improved with decrease in the radius of curvature except for the E plane, which did not show any improvement. The cross-polarization levels for the E and H plane are better than 15dB, while that for the D plane is only about 6dB below the copolarization levels. Typical radiation patterns for TSA #1, #2, and #3 are shown in Figure 9.30. For these relatively short TSA, the H-plane pattern is significantly broader when compared to the E- and D-plane patterns. Ripples appearing in the patterns are common for short antennas with L 121,.

Measured data at 11 GHz for TSA with taper profiles the same as those in Figure 9.29, but fabricated on thin brass sheet without supporting dielectric, exhibit radiation characteristics similar to that shown in Figure 9.28; that is, the HPBWs for the E plane become broader with decreases in radius of curvatures, but the opposite holds true for the H plane. However, the curvature effect on the brass sheet TSA is not as strong as for the TSA with suporting dielectric. The


FIGURE 9.28 Half-power beamwidth for TSA with different taper profiles: (a) E plane, (b) H plane, and (c) D plane.

HPBWs for both the E and H planes of the brass sheet TSA show only slight changes as the taper profiles varied from #1 to #4.

To study the effect of curvature of mounting structure, TSA #1 was tested at 11 GHz on a curved surface of a foam cylinder of radius 9 cm (3.31,) and 15 cm (5.52,). When the curvature is in the transverse direction of the antenna, results indicate that the curvature effect of the mounting structure generally degrades the directivity of the E plane but improves the directivity of the H plane by less than 1 dB. However, the curvature effect has a large impact on the cross-polarization of the E plane which increases by more than 7 dB. The degradation is more severe with the 9-cm cylinder. When the curvature is in the longitudinal direction of the

CHARACTERISTICS OF TSA 479

-18 r

FIGURE 9.29 Cross-polarization level for TSA with different taper profiles: (a) E plane, (b) H plane, and (c) D plane.

antenna, degradation of more than IdB in the E-plane directivity but less than 1-dB difference in the cross-polarization was observed. The large increase in the cross-polarization for the first case is due to distortion of the E-field a t the slot termination by the curvature.

Effect of Length, Terminating Slot Width, and Lateral Edge Width. The directivity of a TSA is directly proportional to the length of the antenna, L. This is quite obvious since a longer TSA has a larger radiating aperture which is capable of higher directivity. Any decrease in the length will produce a corresponding


-50 -90 -60 -30 0 30 60 90

Angle, deg

FIGURE 9.30 Typical radiation patterns for TSA tested at 11 GHz: (a) E plane, (2) H plane, and (3) D plane.

-50 I I I I I -90 4 0 -30 0 30 60 90

Angle, deg

-50 ( (b) , I I I I

-90 -60 -30 0 30 60 90 Angle, deg

FIGURE 9.31 Radiation patternsfor an LTSA oflength(1) L = lO.l6cm,(2) L= 6.35 cm, and (3) L = 3.81 cm: (a) E plane and (b) H plane.

decrease in the terminating slot width, U: and an increase in the width of the lateral edge, W,, of the TSA (see Figure 9.8). To find out the effect of the dimensional change of W, on the radiation characteristics, the half-power beamwidth (HPBW) and the gain of a LTSA of various lengths were measured at 13 GHz. To start out, the LTSA having a length of 10.16cm (6.51), a lateral edge of 0.318cm (0.24, and a taper angle, 2u, of 25" is fabricated on 10-mil-thick RTPuroid (E, = 2.2);1 =I,/& is the dielectric wavelength. In the experiment, the antenna length was shortened by 1.27cm (0.811) each time without changing the lateral dimension of the ground plane which is W + 2 W,. Results for the E- and H-plane patterns for L = 10.16cm, 6.35cm, and 3.81cm are shown in Figure 9.31a and 9.31b respectively. As illustrated in the figures, the HPBW increases with decreases in antenna lengths. For L less than 5.08 cm (3.251), the lateral edge W, now with a width of 1.5 cm (0.951) starts introducing abnormality in the E-plane pattern which was predicted analytically in reference [15]. The abnormality in the E plane is caused by the excess current density along the lateral edge of the LTSA. Contrarily, the increase in the width of the lateral edge appears to have very little effect on the H-plane pattern. By reducing the width of the lateral edge to initial value of 0.318 cm, a well-behaved E-plane pattern is recovered; however, the reduction in the lateral dimension of the ground plane considerably broadens and degrades the H-plane pattern. The effects of the increased lateral edge and the reduced ground plane on the E- and H-plane patterns are illustrated in Figure 932a and 9.32b, respectively.

The HPBW and the gain of the LTSA (L = 10.16 cm, W, = 0.318 cm, 2u = 25") measured at 13GHz as a function of antenna length L are displayed in Fig- ures 9.33 and 9.34, respectively. In general, the HPBW is inversely proportional to L, while the gain is directly proportional to L. The HPBW in the H plane increases as L is reduced from its starting value and then tapers off to around 50" for L < 51; however, in the E plane, the HPBW continues to increase as L is reduced.

The effects of antenna length on the radiation characteristics of LTSA of antipodal geometry were also investigated at 20.55 GHz. Figure 9.35 shows the HPBW versus length reduction, Al, for an antipodal LTSA with a starting L = 9.5 cm, W, = 0.9 an, and 2a = 15" fabricated on RT/Duroid substrate (E , = 2.2). The HPBWs of both E and H planes increase as the antenna length is decreased from 9.5 cm to 7.7cm. The increase in the E-plane HPBW is much smaller than that of the H plane.

Effect ofsubstrate. The effect of substrate on the radiation characteristics of TSA has been reported previously for a vivaldi on polyethylene at 18.5 GBz [IS]. The measured HPBW of both the E and H plane as a function of substrate thicknesses are reproduced in Figure 9.36. In general, the H-plane HPBW is narrower than that of the E plane except for the case without substrate, corresponding to the point of zero thickness. The HPBW in the H plane decreases with increases in substrate thickness, while the HPBW in the E plane exhibits characteristics opposite to that of the H plane. The radiation patterns for the TSA without

(a) I -50 I I I I I

-90 -60 -30 0 30 60 90 Angle, deg

-90 -60 -30 0 30 60 90 Angle, deg

FIGURE 9.32 Effect of lateral edge and ground plane size on the radiation patterns of a LTSA with L= 3.81 cm, (1) W, = 0.318 cm, (2) W, = 1.5cm: (a) E plane and (b) H plane.

FIGURE 9.33 HPBW of an LTSA versus normalized length, L/I. I is the dielectric wavelength.


FIGURE 9.34 Gain of an LTSA versus normalized length, L/1. I is the dielectric wavelength.

AL, cm

FIGURE 9.35 Effect of length reduction, 81, on HPBW of an antipodal LTSA (2a = 15") at 20.55 GHz.

substrate were also measured and found to have similar characteristics [18]. Effects of the dielectric substrate on the radiation characteristics of TSA could be quite different from the results described here if the TSA has different shape, length, or operating frequency [8]. For normalized effective dielectric thickness, t.lc/Ao = ( & i ) t / l O , greater than 0.18, the LTSA shows asymmetric beams in the E and H planes. For vivaldi, the dielectric thickness effects are quite similar to those found for LTSAs, that is, the thinner substrate (t,,, = 0.0086) produces


Thickness, cm

FIGURE 9.36 Effect of substrate thickness on HPBW of a vivaldi antenna

a standard traveling-wave antenna, while the thicker one ( t , = 0.028) clearly shows some anomalous effects. For the TSA shown in Figure 9.27 fabricated on bare metal sheet, measured data reveal significantly broader E-plane pattern, but essentially same H-plane pattern as compared to patterns of the same TSA with 10-mil supporting dielectric. Results also indicate that the cross-polarization in both E and H planes are generally lower for TSA without a dielectric medium.

Effect of TaperAngle. Varying the taper angle will change the phase velocity and hence Lg, which will in turn change the beamwidths of the TSA. Gibson obtained approximately constant beamwidths in both E and H planes for a vivaldi fabricated on alumina substrate with taper shape defined by [2]

z = + 0.125 exp (0.052 x)

In general, the taper angle required to produce constant beamwidths in both planes may be different for TSA with different antenna parameters. For an LTSA with L = 12.6c.m (4.2&) and E, = 2.55 fabricated on 30-mil-thick substrate, the taper angle in the range of 15-20" produces nearly identical E- and H-plane HPBW [48], while for LTSA fabricated on 0.13-mrn RTPuroid, changing the taper angle from 11.2" to 16.4' gives essentially the same curve of beamwidth versus normalized length for the H plane, but smaller E-plane beamwidth [8]. For a LTSA with L = 7.62cm and W, = 2.5 cm fabricated on 10-mil RTPuroid (E, = 2.2), we obtained results which indicate that the operating frequency and antenna length have only small effects on the taper angle required to produce constant beamwidths in both planes. Figure 9.37 shows the HPBW as a function of taper angles at 13.5 GHz and 19 GHz. In addition to the usual reduction in beamwidth at higher frequency, the two curves look very similar and the taper angle required to produce roughly the same E- and H-plane beamwidth occurs at around 5" for both frequencies. Figure 9.38 shows the HPBW versus taper angles for a LTSA with reduced length (L = 5.7cm, Wg = 1.5 cm) at 19 GHz. As indicated, the effect of taper angle on the HPBW is essentially the same for both


0 5 1 0 1 5 Z Q 2 5 3 0 Taper angle, deg

FlGURE9.37 HPBW versus taper angle for L=7.62cm at 13.5GHz: (a) H plane, (b) E plane; and at 19 GHz: (c) H plane and (d) E plane.

10 15 20 Taper angle, deg

FIGURE 9.38 HPBW versus taper angle at 19GHz for L=5.7cm: (a) H plane, (b) E plane; and for L = 7.62 cm: (c) H plane and (d) E plane.

the long and reduced length antennas. For the reduced length LTSA fabricated on 20-mil Duroid (E, = 2.2), we found HPBW to be approximately constant at 35" for both E and H planes as the taper angle varied from 5" to 25'. In general, reducing the lateral edge dimension W enerally increased the H-plane beam-

g P width and decreased the E-plane beamwidth.


I

5 0 I I I I I I I I I I I I I ( -90 -75-60-45-30-15 0 15 30 45 60 75 90

Angle, deg

FIGURE 9.39 H-plane patterns at 11 GHz for a LTSA over a ground plane with a foam spacer in between (1) with no ground plane, (2) with a ground plane and no spacer, (3) with a ground plane and a 0.3175-cm foam spacer, and (4) with a ground plane and a 0.635-cm foam spacer. (From reference 1 4 9 1 , ~ 1987 IEEE.)

Effect of Ground Plane and Dielectric Overlay. To study the ground plane effect, the LTSA shown in Figure 9.16 was placed over a copper ground plane separated by foam spacers. Results for the H-plane patterns are displayed in Figure 9.39. With the ground plane placed immediately below the fed LTSA and with no spacer, the beam is scanned by about 50" in the H plane. The amount of scan decreases from 50" to about 35" and to 25" as the foam spacer thickness is increasedfrom zero to 0.3175 cm (0.1 162,) and to 0.635 crn(0.2322,), respectively. In general, the effect of the ground plane diminishes as the distance between the antenna and the ground plane increases. For the E-plane patterns, no significant change was observed except that the LTSA had to be tilted in the elevation to receive full power. For planar TSA designed for dual polarizations (horizontal and vertical), a reflecting ground plane placed on the side of the dielectric substrate parallel to the antenna surface can be used to produce unidirectional radiation [49].

The dielectric overlay was found to have significant effects on the radiation characteristics of the tapered slot antennas in our experiments [SO]. The dielectric overlay alters the guide wavelength and thus increases the electrical length as well as the effective aperture of the antenna. As a result, higher directivity was achieved as indicated by narrower main lobes in the measured radiation patterns. The effect of the overlay was found to be more pronounced in the H plane than in the E plane [SO].


9.7.2 Impedance Characteristics

Since almost all previous studies on TSA have been focused on the radiation characteristics, the impedance characteristics of the antenna is not well understood up to this date; yet this information is of utmost important in the design of a wideband input match transition. In a previous study, the measured input impedance of a fin antenna without a dielectric has been used as the input impedance of a LTSA [8]. Results of this study show that from 4GHz up, the impedance is essentially constant with frequency and is close to 80Q. However, measureddata for TSA with a supporting dielectric have so far not been obtained. Described below are our experimental findings of impedance characteristics of a TSA.

Input Impedance Characteristics. The input impedance of a TSA was measured [73] using a microwave wafer probe and a set of on-wafer Thru-Reflect-Line (TRL) slotline standards. The LTSA, shown in Figure 9.40, is fabricated on 10-mil-thick RTPuroid 6010.5 (E , = 10.5). In the figure, a and L represent the semiflare angle and flare length, respectively. The LTSA is excited through a short length of a slotline by a ground-signal microwave probe (Picoprobe, Inc.) as shown in Figure 9.41. The slotline minimizes the interaction between LTSA input terminals and the parasitic associated with the probe tips. The reflection coefficient of the LTSA is de-embedded from the measured reflection coeffient at the input terminal of the slotline. The de-embedding is done with a HP 8510C network analyzer, a set of TRL on-wafer slotline calibration standards (Fig- ure 9.42), and the NIST de-embedding software [51]. The software runs on an HP 9000 computer and controls the Network Analyzer.

The real and imaginary parts of the de-embedded LTSA input impedance Re(Zi,) and Im(ZiII) as a function of the frequency for u = 5" and L = 2.54cm are

0.0254 r Reference

.017 1 cm ' R ~ ~ ~ T ;:, . . , . . a " ' . . . %%

. , ( E ~ = 10.5) -f- . . ' : I . . .. .' i ._ . .I _. .,' . ': - . ..! .

. . . '. ' ._ .. . . G . . . . ' . 0.318 cm ':',

I . . . . '.

t-i-.--IT FIGURE 9.40 LTSA used in the impedance experiment.


.- Coaxial connector -.

F Siotline

plane \ \-- Antenna mouth Antenna substrate

FIGURE 9.41 Experimental setup.

1 ,- Reference plane

Thru .635 cm

Reflect

Delay line #1 0.749 cm

Delay line #2 389 cm

FIGURE 9.42 TRL on-wafer slotline calibration standards.

shown in Figure 9.43a and 9.43 b respectively. The plots of Zin exhibit a series of resonances over the frequency band. The occurrence of the resonances are attributed to imperfect impedance match transitions at the feed end and the termination end of the LTSA. As the frequency varies from 2 to 26.5 GHz, the normalizedlength of the LTSA (L/Ao) varies from 0.17 to 2.24. The corresponding variation in the normalized termination width of the LTSA ( W/A,) is from 0.03 to 0.4. In an LTSA at the lower end of the frequency band, W/Ao is very small and


-500 0 10000 . 20000 30000

Frequency, MHz (a)

-1 500 I I I 0 10000 20000 30000

Frequency, MHz

FIGURE 9.43 (a) Real and (b) imaginary parts of the input impedance (a= 5", W = 0.455 an, L = 2.54 cm).

hence the electric field intensity is large. The large electric field produces a large wave impedance which in turn results in a large Re(Zin) for the first resonance mode, typically in the range of 25OOQ. On the other hand, at the upper end of the frequency band the effective aperture is large and hence Re&) is small, typically about 145 a. The minimum value of Re&) occurring between the resonances at the high end of the frequency band is about 40 Q, which is approximately half the value predicted in reference [8].

Measurements on several other LTSAs with the same L but with a progressively increased from 5" up to 20" in steps of 2.5" show that at the lower end of the frequency band, Re(Zin) decreases as a increases. Figures 9.44a and 9.44b display Re(Z,) and Im(Zin) for a = 20°, respectively. From Figure 9.44a, Re(&) is about 6500 and 145 0 at the low and high end of the frequency band, respectively. At


-1 00 ' 0 10000 20000 30000

Frequency, M H z (a)

300 r

-400 0 l o w 20000 30000

Frequency, M H z (b)

FICURE9.44 (a) Real and (b) imaginary parts of the input impedance (a=20°, W = 1.859cm, L= 2.54cm).

these frequencies, W varies from 0.1241, to 1.861,. These results also support the above discussion. The minimum value of Re(Zi,) is about 85 R, which is about the same as predicted in reference [8].

Figures 9.45a and 9.45b show Re(&) and Im(Z,) for u = 10" and L = 7.62 cm. The LTSA is about three times longer than the previous cases and therefore has three times more resonances. For this case, the Re(Zin) is initially as high as 1300R for L/1, = 1.5 and then reduces to a value in the range of 55 R to 130R for L/1, > 3.6. It appears that a perfect impedance match at both the high and low end of the frequency band is almost impossible to achieve by varying the flare angle and/or the length of the LTSA alone. As a result, the standing-wave mode and the traveling-wave mode exist simultaneously most of the time in the TSA.


Frequency, M H z (a)

- I

-3000'- 0 10000 20000 30000

Frequency, M H z (b)

FIGURE 9.45 (a) Real and (b) imaginary parts of the input impedance (a= loo, W = 2.69 cm, L = 7.62 cm).

Mutual Coupling Effect. It is well known that mutual coupling could produce profound impacts on the performance of an antenna array causing impedance mismatch and scanning blindness. In general, mutual coupling can occur between two TSAs placed adjacent to each other in the same plane or in stacked arrangement. To study the mutual coupling effects, we measured the amplitude and phase of the coupling coefficient represented by S,, between two identical LTSAs which have dimensions L = 3.81 cm, 2u = 25", and W, = 0.318 cm and are fabricated next to each other on a 10-mil RT/Duroid (E, = 2.2) substrate. The two LTSAs were excited through a short length of a slotline by a pair of ground-signal microwave probes similar to those used in the impedance experiments described above, and the S,, was measured using an HP 8510C network analyzer. The probes were calibrated to the tips using impedance standard substrate (ISS). In the experiment, the coupling coefficients were first measured with the LTSAs


0.0 6.5 13.0 19.5 26.5 Frequency, GHz

FIGURE 9.46 1S2,J versus frequency for two identical LTSAs on (a) a continuous substrate and (b) separate substrates.

--- 0.0 6.5 13.0 19.5 26.5

Frequency, GHz

FIGURE 9.47 Phase of S2, versus frequency.

fabricated on a continuous substrate and later repeated after a narrow slot was cut in the dielectric separating the two LTSAs. In the latter case, couplings between antenna were confined through free space only. Results for the S,, as a function of frequency for both cases are superimposed in Figure 9.46. Based on these results, the following observations can be made: (1) Both antenna configurations exhibit similar S,, characteristics with the LTSA on continuous substrate demonstrating stronger mutual coupling as a result of additional coupling through the supporting dielectric substrate. For frequencies ranging from 1.5 to 20GHz, the differences in mutual coupling between the two cases vary from about 0.5 to 6.0dB. (2) The amplitudes of S,, decrease monotonically with increases in frequency, (3) The S,, curves have the appearance of standing-wave patterns because of mismatch at the feeding and termination ends of the LTSA as previously observed in the input impedance measurements. Figure 9.47 shows a typical plot of the phase as a function of frequency for the S,,. The phase is generally periodic across the frequency band.

Figure 9.48a shows the S,, characteristics of two identical LTSAs as a function of antenna separations for two different dielectric constants (E, = 2.2 and 10.5) and frequencies 1.7 GHz and 4.7 GHz. The two LTSAs on two substrates are placed side-by-side in the same plane, and S,, is measured for several separations. As indicated, the mutual coupling decreases with increases in LTSA separations. The mutual coupling is stronger at the lower frequency (1.7 GHz) and generally with lower dielectric constant. At 1.7 GHz and 0.025 cm spacing, the mutual coupling is about - 3.1 dB but decreases rapidly with frequency.


(4 , I I

1 0.2 0.4 Separation, in.

-40 ( b ) , 1 , 1 , j

0.0 0.2 0.4 0.6 Vertical separation, in.

FIGURE 9.48 1 S,, 1 versus antenna separations: (a) coplanar geometry for (1) E, = 2.2, (2) E, = 10.5 at 1.7GHz, (3) e, = 2.2, and (4) e, = 10.5 at 4.7GHz; (b) stacked geometry for e, = 2.2 at (1) 1.7 GHz, (2) 4.7 GHz, (3) 9.5 GHz, and (4) 15.1 GHz.

The mutual coupling between two identical LTSAs (E, = 2.2) in stacked configuration was also measured as a function of vertical separations at frequencies: 1.7,4.7,9.5, and 15.1 GHz. The results shownin Figure 9.48b are very similar to those of the coplanar case described above. In general, the mutual coupling decreases with increase in either antenna separations or frequency; however, the increase is significantly faster at high frequencies.

To ensure that the difference in mutual coupling between the two cases is not caused by changes in the return loss IS,,] introduced by the isolation slot, we have repeated the same measurements and found essentially no difference in (S,,I for both antenna geometries. Next, by placing the LTSAs on a con-


FIGURE 9.49 A f for TSA with different tapered profiles.

tinuous substrate between two layers of absorber, the mutual coupling level was reduced to -30dB on the average over the entire frequency range, indicating that the predominant coupling mechanism is via space wave between the antennas.

9.7.3 Bandwidth Characteristics

The TSA is capable of multioctave bandwidth over a frequency spectrum ranging from approximately 2 to over 90GHz. To achieve wideband operation, it is generally understood that the TSA is required to operate in a traveling-wave mode with perfect impedance match at both the feed transition and the slot termination. Depending on the feeding method, different schemes for bandwidth broadening have been described in Section 9.6. Effects of other antenna parameters on the bandwidth of a TSA, however, are not as well understood. We will report below some of the experimental findings on the effects of tapered profiles on the bandwidth of the TSA. The bandwidth is proportional to A f, the frequency difference defined by the 2:l VSWR points. As shown in Figure 9.49, the Af; of TSA #1, #2, and #3 (Figure 9.27) in general decrease with the decrease in the

8 9 10 11 12 Frequency, GHz

FIGURE 9.50 Return loss for TSA with different tapered profiles: (1) TSA# 1, (2) TSA # 2, (3) TSA # 3, and (4) TSA # 4.

radius of curvature of the antenna. The return loss measurements, shown in Figure 9.50, clearly indicate a reduction in A f resulting from a change in the taper profile.

For an LTSA with dimensions L = 7 .62~~1, 2a = 20°, and W, = 2.5cm fabricated on 20-mil-thick RTPuroid substrate (E, = 2.2), results indicate very little change in A f as L varies from 7.62 cm to 4.9 cm and as W, varies from 2.5 cm to 1.5cm. Also, varying the tapered angle of the same antenna from 5" to 25" produces no noticeable difference in the Af.

9.7.4 Field Distributions

The magnetic field distribution of a TSAat different frequencies were measured using a coaxial probe which was held perpendicular to the magnetic field lines at a distance of approximately 1 mm away from the antenna surface by an x-y-z positioner. The coaxial probe was constructed from a semirigid coaxial cable with the center conductor extended to form a circular loop and soldered to the outer conductor. The LTSA with dimensions L = 2.54cm and cr = 10" was fabricated on 10-mil-thick RT/Duroid (E, = 10.5). In the experiment, the LTSA was excited with a ground-signal microwave probe (Picoprobe, Inc.) and the magnetic field strength measurement was made by moving the coaxial probe.

Frequency, QHz

0 0 2338 6.659

-5

g -10

d v $ -15

F .J -20 f t I" -25

"01 , , , -35

0.0 0.2 0.4 0.6 0.8 1.0 Distance, in.

FIGURE 9.51 Relative magnitude of H, along x.


-25 0.0 0.2 0.4 0.6 0.8 1.0

Dlstanoe, in.

FIGURE 9.52 Relative magnitude of H , along x.

Both the probes were connected through flexible coaxial cables to a HP 8510C network analyzer which recorded the relative field strength. The network analyzer was calibrated to the ends of the flexible coaxial cables. The following magnetic field components were measured: (1) Hz along z, (2) Hy along z, (3) H , along x, and (4) H, along x (see Figure 9.6). Figures 9.51 and 9.52 show the plots for the relative amplitudes of H, and Hy along x, respectively, at discrete frequencies ranging from 2.0 GHz to 11.0 GHz. The measurement probe starts at the feeding end of the LTSA and moves along the center at 0.0635 cm (0.025-in.) increments. Results exhibit standing-wave patterns along the longitudinal direction of the LTSA. The attenuation in amplitude as the wave propagates down the antenna indicates that power is progressively "leaked away". At higher frequencies, more cycles appear as a result of smaller wavelength. Variations of the relative amplitudes of H , and Hz along z are shown in Figures 9.53 and 9.54, respectively. The measurement probe starts at the center of the LTSA and moves laterally in steps of 0.0635 cm (0.025 in.). Results indicate that the magnetic field lines of H, starts out with maximum amplitude and then decreases with distance in the direction toward the conducting plane. For H , along z, a null exists at the center for all frequencies tested indicating that a phase reversal occurs at the point. The variation of the relative amplitude of Hy, as a function of distance


Frequency, r Gtiz I" 0 2.3207 \

Distance, in.

FICURE 9.53 Relative magnitude of H, along z.

Frequency, GHz

0 23267

Distance, in.

FICURE 9.54 Relative magnitude of Hz along z.


Frequency, GHz

Distance, in.

FIGURE 9.55 Relative magnitude of H, as a function of distance normal to the antenna surface.

normal to the surface is shown in Figure 9.55. Results indicate that the wave decay exponentially away from the surface with a higher rate of decay at a higher frequency. These results confirm that the radiation mechanism for a TSA with a supporting dielectric is predominantly surface waves.

9.8 TAPERED SLOT ANTENNA ARRAYS

Tapered slot antennas are very suitable as radiating elements for arrays of "brick" architecture where TSA elements are arranged in rows or columns connected perpendicularly to a power-combining block. To realize orthogonal polarizations, two TSA elements of like polarization are first combined into a two- element subarray. Two such subarrays are joined (colocating at 90") through a mechanical slot cut in the top of one subarray and the bottom of the other subarray to form a four-element subarray module. These four-element subarray modules can be arranged in square or triangular lattices to form bigger arrays capable of dual or circular polarizations. Figure9.56 shows an 8 x 8 array composed of four-element subarray modules as building blocks. For this array, the average VSWR at boresight from 4 to 18 GHz is below 2.0 [52].

TSA arrays of "brick" construct discussed above have found applications in reflector systems as well as direct radiating arrays for airborne and electronic warfare (EW) systems. In reflector systems, TSA arrays have been used mainly as feeds in the focal plane of Cassegrain reflector systems to create multiple beams, or with integrated diode as receptor element, to sample images at millimeter- wave frequencies [53-541. These focused optical systems create or receive

TAPERED SLOT ANTENNA ARRAYS 499

FIGURE 9.56 Photographs of TSA array of "brick" configuration: (a) 8 x 8 array and (b) orthogonal subarray element pair.

multiple directional beams by switching to one or more individual feeds in the focal-plane array. The important parameters to consider in designing these systems are the aperture efficiency and the crossover level between beams as in the case of an imaging system with large f-number to control off-axis aberration [53]. In general, improvements in the aperture efficiency and angular resolution between beams require close element spacings and narrow feed patterns. The TSA being capable of both narrow beamwidth and close spacing is most suitable as array elements for multibeam imaging systems. Another important advantage of endfire tapered slot antennas is their ability to operate over very wide bandwidths which has made them candidates for wideband radar and EW applications. Active T/R modules can be integrated behind each individual antenna element or orthogonal subarray element pair to form phased arrays capable of electronic beam scanning.

Numerical analysis of an infinite array of tapered slot antennas have been attemped using the finite element method [55], the time domain TLM [56], and the method of moments [57]. These computional techniques have demonstrated reasonably good agreement with measurements obtained from waveguide simulators. One important finding of these analyses is the prediction of scan blindness, which produces total reflection of power at the antenna terminal at certain scan angles or frequencies. The scan blindness is manifested in a very low value of active input resistance for the array or a reflection coefficient having a magnitude of one. It is generally understood that scan blindness in phased arrays results


from mutual coupling effects which can be quite large for close element spacings; however, the exact phenomena creating the blindness are not yet fully understood. A recent study based on the method of moments has identified one class of scan blindness associated with guided waves which propagate across a corrugated surface instead of radiating into space [3]. This type of blindness which occurs in the E plane when the H-plane spacing exceeds A0/2 can be eliminated by installing electrically conducting walls between TSA unit cells [58]. Blindness associated with other antenna parameters such as different array lattices, grid spacing greater than A0/2, and so on, remains poorly understood, and further work is needed before design guidelines can be developed.

Conformal printed circuit flared slot antenna arrays can be flush-mounted over the curved structure of aircraft or vehicles for drag reduction. The first conformal TSA array is a dual-flared slot evolved from a half-wavelength resonant slot design which is flared at both ends and combined at their center [59 ] . Figure 9.57 shows the geometry and polarization circuit of a new conformal

Horizontal

To horizontal element port

Input 50 n To vertical

Single-pole element port triple-throw series pin diode switch

Two single-pole microstrip double-throw series lines pin diode switch

(b)

FIGURE 9.57 Conformal flared slot array: (a) geometry and (b) polarization circuit.

Duroid

Copper

TAPERED SLOT ANTENNA ARRAYS 501

- Feed system

wideband crossed microstrip flared slot having a greater than 3:l bandwidth and capable of polarization diversity. In this design, a crossed flared slot is etched on one side of the copper-clad dielectric, and four 50-a microstrip lines are etched on the other side of the printed circuit board. The two orthogonal flared slots can be driven 0" and 90" to provide for vertically, horizontally, or circularly polarized radiation [49]. In order to obtain unidirectional radiation, a reflecting ground plane is placed on the side of the dielectric substrate parallel to the flared slot surface. To enhance the bandwidth, the element was formed into a cavity-type resonator.

Recently, a K-band circular LTSA array, shown in Figure 9.58, has been proposed for mobile communications [60]. The 16-element array is fed by a 1:16 microstrip line power splitter composed of T junctions and right-angle bends. The output ports of the splitter are electromagnetically coupled to the slotline of the LTSA through a conventional microstrip-to-slotline transition. To achieve tight coupling and fabrication ease, the slotline and the microstrip line characteristic impedance were chosen to be 112 0 and 100 a , respectively. The LTSA of length L = 5 cm and tapered angle a = 35" was fabricated on 10-mil-thick RT/Duroid(e, = 2.2) substrate, and the finished array was placed over a reflecting ground plane to displace the beam above the horizon. The amount of scan in the elevation plane depends on the separation distance between the array and the

Dielectric I ! I .-Duroid foam I

&,,,,,- Coaxial connector

FIGURE 9.58 Circular 16-element LTSA array.


- lhfithout a metal ground plane .----- With a metal ground plane

-1 0 I c-

-20 If

I i

-1 0 I I I I I I I I I I l ( " ) ] -90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90

Angle, deg

FIGURE 9.59 Measured radiation pattern at 19-GHz: (a) H plane and (b) E plane.

ground plane. Figure 9.59 displays the measured E- and H-plane patterns for a separation distance of 0.2861,. Results show an omidirectional pattern in the azimuthal plane and a beam displacement of about 28" in the elevation.

9.9 ACTIVE TAPERED SLOT ANTENNA ARRAY

Because of broad impedance bandwidth and planar geometry, the tapered slot antennas have advantages over microstrip patch antennas as radiators for integrated active antennas. The broad impedance bandwidth provides a wide tuning range, and the planar structure allows easy integration with active devices. Active antenna elements and receivers built by integrating a Gunn diode [61], varactor diode [62], and FET [63] with a tapered slot antenna have exhibited clean and very stable spectra a t the design frequencies of around 9.5 and 21 GHz respectively. Figure 9.60 shows the schematic of the varactor-tuned active notch antenna and its CPW resonator circuit. The circuit was optimized based on a transmission line model shown in Figure 9.61.

The output power of an active oscillator antenna is very small, particularly in the microwave and millimeter-wave region. To obtain higher power, the output

ACTIVE TAPERED SLOT ANTENNA ARRAY 503

Heat sink

FIGURE 9.60 The circuit configuration of a varactor tuned active notch antenna(From reference [62], 0 1991 IEEE.) - Total length = 30.48 mm -4 24 sections of stepped dotline

Free space 377 ohms

Zl = 160 ohms, L1 = 0.685 mm 22 160 ohms, t2 = 3.529 mm 23 = 50 ohms, W = 3.500 rnm 24 = 11 0 ohms, L4 = 7.200 mm 25 = 122 ohms, L5 = 2540 mm

FIGURE 9.61 Equivalent circuit for theoretical analysis. (From reference [62], 0 1991 IEEE.)

from all the oscillators have to be combined using either conventional power combiner or quasi-optical power combiner. The conventional power combining is done with Wilkinson, radial line, or hybrid coupled networks. In the case of quasi-optical combiners, oscillators constructed with IMPATT diodes [64], Gunn diodes [62], MESFETs [65], and HEMTs [66] areintegrated with printed microstrip patch antennas or TSA to form an active antenna array which combines power radiatively in free space. This approach has the advantage of distributing the RF source over a large number of devices, thus eliminating the


Modified Vivaldi antenna --,,

FICURE9.62 Twelve-element omnidirectional active array. (From reference [67], 0 1995 IEEE.)

combining network entirely. Quasi-optical combiners generally have higher combining efficiency because of lower conductor loss and larger dimensional tolerances with the absence of resonance modes. In addition, both antennas and solid-state devices can be integrated on a single semiconductor wafer, thus simplifyingthe array construction. However, to producea coherent radiation, the individual oscillators have to be phase-locked through mutual coupling between oscillators via free space, transmission-line circuit, or external cavities, enabling them to synchronize to a common frequency through interinjection locking. Figure 9.62 shows an omnidirectional, quasi-optical array of 12 vivaldi-coupled oscillator elements which are powered from a single direct-current (DC) power supply [67]. The array was demonstrated to have a high combiningefficiency and remain frequency-locked over a span of 600 MHz at 28 GHz.

Quasi-optical power combining using arrays of antenna-coupled oscillators could provide a low-cost approach to achieve electronic beam scanning by eliminating the need for phase shifters. When the free-running frequencies of the oscillators are within a collective locking range, a constant phase progression can be achieved simply by controlling the free-running frequencies of the outermost array elements [68]. An alternative approach to obtain a linear progression in output phase is to introduce a phase shift between the sourceinjectionpoints. For the four-element LTSA phased array shown in Figure 9.63, beam steering is achieved by using a phase shifter to introduce a phase shift between outermost


Waveguide variable phase power shifter divider

Slgnal 0 generator

FIGURE 9.63 Four-element phased array with active notch antennas. (From reference [69], 0 1987 IEEE.)

elements, and injection locking via coupling network placed between the oscillators 1691.

Another way to obtain high power is through the use of a spatial amplifier. Unlike the spatial oscillator array, the spatial multiplier array does not require injection locking for coherence and stability. Figure 9.64 schematically illustrates a possible arrangement for space power amplification. In this approach, an array of active antenna modules constructed from nonplanar LTSAs and GaAs monolithic microwave integrated circuit (MMIC) multistage power amplifiers receives the signal at lower power and after amplification reradiates the signal into free space. Polarization diversity is employed to permit accurate measure-


-

FIGURE 9.65 Experimental three-element LTSA MMIC array module.

ment of the amplified signal radiated from the array. The advantages of the spatial amplifier array over the quasi-optical oscillators array are that only a single stable low-power source is required, thus greatly simplifying the combiner construction, and that the amplifiers can be individually optimized. Spatial power amplification has been demonstrated with a three-element active array module shown in Figure 9.65. With the amplifiers turned on, the array produced a gain of 30 dB at 20 GHz [70]. Measured E- and H-plane patterns are displayed in Figure 9.66. This design is suitable for constructing a large array using monolithic integration technique. Replacing the MMIC multistage power amplifier with a GaAs MMIC distributed amplifier having a very wide bandwidth and dynamic range, frequency multiplication, and space power combining was demonstrated with the same active LTSA array module which receives signal at the fundamental frequency of 9.3 GHz and, after multiplication and amplification, radiates the second harmonic signal into free space [71]. Results obtained indicate a fundamental-to-second-harmonic conversion efficiency of 8.1%. For good conversion efficiency, a high-power source is required. Figure 9.67 shows the measured radiation patterns of the horn antenna which collects the power at the second harmonic frequency of 17.9GHz. As shown, the spatially combined second harmonic signal is 50dB above the noise level.


FIGURE 9.66 Measured radiation patterns of the horn antenna showing space power amplification: (a) H plane and (b) E plane.


Amplifier

-1 0

-90 -75 -60-45 -30-15 0 15 30 45 60 75 90 Angle, deg

(a)

. - -90-75 -60-45 -30-15 0 15 30 45 60 75 90

Angle, deg (bl

FIGURE 9.67 Measured radiation patterns of the horn antenna showing space power combining at the second harmonic frequency of 17.9GHz: (a) H plane and (b) E plane.


9.10 CONCLUSION

In this chapter, we have presented an up-to-date review of some important work in TSA, including arrays of both active and passive types. As we pointed out, as of this date, there is no established design guidelines that can be readily applied to the design of this type of antennas. T o aid the design and understanding of the radiation process in TSA, we have provided an in-depth discussion of the impedance and radiation characteristics that are either derived from previous publications or from our own findings. Although much work has been done, further work is still required particularly in the development of CAD software for TSA, and new applications for this type of antennas.

REFERENCES

[I] L. R. Lewis, M. Fassett, and J. Hunt, "A Broadband Stripline Array Element," in 1974 IEEE AP-S International Symposium, Atlanta, GA, June 1974, pp. 335-337.

[2] P. J. Gibson, "The Vivaldi Aerial,"in 9th European Microwave Conference, Brighton, UK, September 1979, pp. 101-105.

[3] D. H. Schaubert and J. A. Aas, "An Explanation of Some E-Plane Scan Blindnesses in Single-Polarized Tapered Slot Arrays," in 1993 IEEE AP-S International Sympo- sium, Vol. 3, Ann Arbor, MI, June 1993, pp. 1612-1615.

141 N. Fourikis, N. Lioutas, and N. V. Shuley, "Parametric Study of the Co- and Crosspolarization Characteristics of Tapered Planar and Antipodal Slotline An- tennas," IEE Proc., Part H, Vol. 140, No. 1, pp. 17-22,1993.

[5] A. Podcameni, M. M. Mosso, and A. D. Macedo Filho, "Dielectric Overlay Com- penated Slotline Printed Antennas," in International Symposium on Antennas(JINA), Nice, France, November 1986, pp. 180-183.

[6] S. N. Prasad and S. Mahapatra, "A Novel MIC Slot-line Antenna," in 9th European Microwave Conference, pp. 120-124, Brighton, UK, September 1979; also IEEE 'Ram. Ant. Propagat., Vol. AP-31, No. 3, pp. 525-527,1983.

[7] P. R. Acharya, J. F. Johnsson, and E. L. Kollerg, "Slotline Antenna for Millimeter and Submillimeter Waves," in 20th European Microwave Conference, Budapest, Hungary, pp. 353-358,1990.

181 K. S. Yngvesson, D. H. Schaubert, T. L. Korzeniowski, E. L. Kolberg,T. Thungren, and J. F. Johansson, "Endfire Tapered Slot Antennas on Dielectric Substrates," IEEE Trans. Antennas Propagat., Vol. AP-33, No. 12, pp. 1392-1400,1985.

[9] B. Milord and C. Letrou, "Contribution to the Design of Non-uniform Slotline Antennas," in International Symposium on Antennas (JINA), Nice, France, Novem- ber 1992, pp. 93-96.

[lo] R. N. Simons, N. I. Dib, R. Q. Lee, and L. P. B. Katehi, "Integrated Uniplanar Transition for Linearly Tapered Slot Antenna," IEEE Trans. Antennas Propagat., Vol. 43, NO. 9, pp. 998-1002, 1995.

[11] J. J. Lee and S. Livingston, "Wide Band Bunny-Ear Radiating Element," in 1993 IEEE AP-S International Symposium, Ann Arbor, MI, June 1993, pp. 1604- 1607.

REFERENCES 51 1

[I21 T. L. Hwang, D. B. Rutledge, and S. E. Schwarz, "Planar Sandwich Antennas for Submillimeter Applications," Appl. Phys. Lett., Vol. 34, No. 1, pp. 9-11, 1979.

1131 E. Gazit, "Improved Design of the Vivaldi Antenna," IEE Proc., Part H, Vol. 135, No. 2, pp. 89-92, 1988.

[14] J. D. S. Langley, P. S. Hall, and P. Newham, "Novel Ultrawide-Bandwidth Vivaldi Antenna with Low Crosspolarisation," Electron. Lett., Vol. 29, No. 23, pp. 2004- 2005,1993.

[I51 R. Janaswamy and D. H. Schaubert, "Analysis of the Tapered Slot Antenna," IEEE Trans. Antennas Propagat., Vol. AP-35, NO. 9, pp. 1058-1065,1987.

[16] G. Broussaud and J. C. Simon, "Endfire Antennae," in Advances in Electronics and Electron Physics, Vol. 19, Academic Press, New York, 1964, pp. 255-308.

[I71 W. W. Hansen and J. R. Woodyard, "A New Principle in Directional Antenna Design," Proc. IRE, Vol. 26, pp. 333-345,1938.

[18] H. M. Barlow and J. Brown, Radio Surface Waves, Oxford University Press, Amen House, London, 1962.

[I91 J. Zenneck, "Uber Die Fortpflanzung Ebener Elektromagnetischer Wellen Langs Einer Ebenen Leiterilache UndIhre Beziehung Zur Drahtlosen Telegraphie," Ann. Phys., 23, pp. 846-866,1907.

[20] D. C. Hogg and W. E. Legg, "A Finline Radiator," Bell Syst. Tech. J., Vol. 52, No. 7, pp. 1249-1253,1973.

1211 G. H. Robinson and J. L. Allen, "Slot Line Application to Miniature Femte Devices," IEEE Trans. Microwave Theory Tech., Vol. MTT-17, No. 12, pp. 1097-1101,1969.

[22] M. L. Reuss, Jr., "A Cursory Investigation of a Slotline Radiator," NRL Memoran- dum Report 2796,1974.

[23] K. Simon, J. Wendler, R. Pozgay, and M. Schindler, "MMIC Compensation Network for Phased Array Element Mismatch," Contract Report RAY/RD/ S4248A, Naval Research Laboratory, 1990.

[24] F. Ndagijimana, P. Saguet and M. Bouthinon, 'Tapered Slot Antenna Analysis with 3-D TLM Method," Electron. Lett., Vol. 26, No. 7, pp. 468-470, 1990.

1251 R. Janaswamy, "An Accurate Moment Method for the Tapered Slot Antenna," IEEE Trans. Antennas Propagat., Vol. 37, No. 12, pp. 1523-1528,1989.

[26] J. F. Johansson, "A Moment Method Analysis of Linearly Tapered Slot Antennas," in 1989 IEEE AP-S International Symposium, Vol. 1, San Jose, CA, pp. 383-386, 1989.

[27] A. Koksal and F. Kauffman, "Moment Method Analysis of Linearly Tapered Slot Antennas," in 1991 IEEE AP-S International Symposium, Vol. 1, London, Ontario, pp. 314-317,1991.

[28] X. H. Yang and W. X. Zhang, "An Equivalent Source Analysis for Tapered Slot Antennas," in International Sympasium on Antennas (JINA), pp. 96-99,1990.

[29] S. S. Zhong and N. Zhang, "Analysis of the Tapered Slotline Antenna on a Dielectric Substrate," in 1988 IEEE AP-S International Symposium, Vol. 3, Syracuse, NY, pp. 1174-1177,1988.

[30] P. R. Acharya, H. Ekstrom, S. S. Gearhart, S. Jacobson, J. F. Johansson, E. L. Kollberg, and G. M. Rebeiz, "Tapered Slotline Antennas at 802 GHz," IEEE Tans. Microwave Theory Tech., Vol. 41, No. 10, pp. 1715-1719,1993.

51 2 TAPERED SLOT ANTENNA

[31] M. F. Catedra and J. A. Alcaraz," Analyses of Microstrip and Vivaldi Antennas Using a CGFFT Scheme That Allows the Study of Finite Dielectric Sheets with Arbitrary Metallization on Both Sides," in 1989 IEEE AP-S International Sympo- sium, Vol. 3, San Jose, CA, pp. 1332-1335,1989.

[32] E. Thiele and A. Taflove, "FETD Analysis of Vivaldi Flared Horn Antennas and Arrays," IEEE Trans. Antennas Propagat., Vol. 42, No. 5, pp. 633-641,1994.

[33] T. Itoh and R. Mittra, "Dispersion Characteristics of Slot Lines," Electron. Lett., Vol. 7, No. 13, pp. 364-365, 1971.

[34] C. T. Tai, Dyadic Green's Function in Electromagnetic Theory, 2nd ed., IEEE Press, New York, 1993.

[35] R. Janaswamy and D. H. Schaubert, "Dispersion Characteristics for Wide Slotlines on Low-Permittivity Substrates,"IEEE Trans. Microwave Theory Tech.,Vol. MTT- 33, NO. 8, pp. 723-726, 1985.

- -

[36] J. B. Knorr, "Slot-LineTransitions," IEEE Trans. Microwave Theory Tech., Vol. 22, No. 5, pp. 548-554, 1974.

[37] Y. H. Choung and W. C. Wong, "Microwave and Millimeter-Wave Slotline Transi- tion Design," Microwave J., Vol. 37, No. 3, pp. 77-89, 1994.

[38] K. M. Frantz and P. E. Mayes, "Broadband Feeds for Vivaldi Antennas," in Proceedings of the Antenna Applications Symposium, Monticello, IL, 1987.

[39] E. 0. Harnmerstad, "Equations for Microstrip Circuit Design," in 5th European Microwave Conference, Hamburg, Germany, pp. 258-272, 1975.

[40] A. Nesic, "Endfire Slotline Antennas Excited by a Coplanar Waveguide," in 1991 IEEE AP-S International Symposium, Vol. 2, London, Ontario, pp. 700-702,1991.

[41] R. N. Simons, R. Q. Lee, and T. D. Perl, "New Techniques for Exciting Linearly - Tapered Slot Antenna with Coplanar Waveguide," Electron. Lett., Vol. 28, No. 7,

pp. 620-621,1992. [42] R. N. Sirnons and R. Q. Lee, "Coplanar Waveguide Aperture Coupled Patch

Antennas with Ground Plane/Substrate of Finite Extent," Electron. Lett., Vol. 28, NO. 1, pp. 75-76. 1992. - -

[43] K. C. Gupta, R. Garg, and I. J. Bahl, Microstrip Lines and Slotlines, Artech House, Dedham, MA, 1979.

[44] R. N. Simons, S. R. Taub, R. Q. Lee, and P. G. Young, "Microwave Characteriz- ation of Slot Line and Coplanar Strip Line on High-Resistivity Silicon for a Slot Antenna Feed Network," Microwave Opt. Tech. Lett., Vol. 7, No. 11, pp. 489-494, 1994.

[45J N. M. H. El-Minyawi, "Single Sided Slotline Microstrip Transition," IEE Proc., Part H, Vol. 134, No. 1,pp. 101-102, 1987.

[46] T. Thungren, E. L. Kollberg, and K. S. Yngvesson, "Vivaldi Antennas for Single Beam Integrated Receivers," in 12th European Microwave Conference, Finland, pp. 475-480,1982.

1471 J. H. C. van Heuven, "A New Integrated Waveguide-Microstrip Transition," IEEE Trans. Microwave Theory Tech., Vol. 24, No. 3, pp. 144-146, 1976.

[48] P. S. Kooi, T. S. Yeo, and M. S. Leong, "Parametric Studies of the Linearly Tapered Slot Antenna (LTSA)," Microwave Opt. Tech. Lett., Vol. 4, No. 5, pp. 200-207,1991.

REFERENCES 51 3

[49] M. J. Povinelli, "A Planar Broad-Band Flared Microstrip Slot Antenna," IEEE Trans. Antennas Propagat., Vol. AP-35, No. 8, pp. 968-972,1987.

[50] R. N. Simons, R. Q. Lee, T. D. Perl, and J. Silvestro, "Effect of a Dielectric Overlay on a Linearly Tapered Slot Antenna Excited by a Coplanar Waveguide," Microwave Opt. Tech. Lett., Vol. 6, No. 4, pp. 223-225, 1993.

[51] NIST De-embedding Software, Program DEEMBED, Rev. 4.04,1994. [52] M. J. Povinelli, "Experimental Design and Performance of Endfire and Conformal

Flared Slot (Notch) Antennas and Application to Phased Arrays: An Overview of Development," in Proceedings of the Antenna Applications Symposium, Monticello, IL, September 1988.

[53] K. S. Yngvesson, J. F. Johansson, Y. Rahmat-Samii, and Y. S. Kim, "Realizable Feed-Element Patterns and Optimum Aperture Efficiency in Multibeam Antenna Systems," IEEE Trans. Antennas Propagat., Vol. 36, No. 11, pp. 1637-1640,1988.

[54] T. L. Korzeniowski, D. M. Pozar, D. H. Schaubert, and K. S. Yngvesson, "Imaging System at 94 GHz Using Tapered Slot Antenna Elements," in Proceedings of the 8th International Conference on Infrared & Millimeter Waves, Miami, FL, pp. w6.3, 1983.

[55] D. T. McGrath, "Phased Array Antenna Analysis Using Finite Element Methods," Ph.D. dissertation, Air Force Institute of Technology, 1993.

[56] F. German, S. Sanzgiri, and D. Doyle, "Analysis of Flared Slot Antennas for Phased Array Applications," in 1993 IEEE AP-S International Symposium, Vol. 3, Ann Arbor, MI, pp. 1600-1603,1993.

[57] P. S. Simon, K. McInturff, R. W. Jobsky, and D. L. Johnson, "Full-Wave Analysis of an Infinite, Planar Array of Linearly Polarized, Stripline-Fed, Tapered Notch Elements," in 1991 IEEE AP-S International Symposium, Vol. 1, London, Ontario, pp. 334-337,1991.

[58] G. J. Wunsch and D. H. Schaubert, "Effects on Scan Blindness of Full and Partial Crosswalls Between Notch Antenna Array Unit Cells," in 1995 IEEE AP-S Internd- tional Symposium, Vol. 4, Newport Beach, CA, pp. 1818-1821,1995.

[59] J. W. Eberle, C. A. Levis, and D. McCoy, "The Flared Slot: A Moderately Directive Flush-Mounted Broad-Band Antenna," IRE Trans. Antennas Propagate, Vol. AP-8, pp. 461-468,1960.

[60] R. N. S ions , E. Kelly, R. Q. Lee, and S. R. Taub, "Radial Microstrip Slotline Feed Network for Circular Mobile Communications Array," in 1994 IEEE AP-S Interna- tional Symposium, Vol. 2, Seattle, WA, pp. 1024-1027, 1994.

[61] J. A. Navarro, Y. H. Shu, and K. Chang, "Active Antenna Elements and Power Combiners Using Notch Antennas,"in 1990 IEEE MTT-S International Microwave Symposium, Vol. 11, Dallas, TX, pp. 793-796, 1990.

[62] J. A. Navarro, Y. H. Shu, and K. Chang, "Wideband Integrated Varactor-Tunable ActiveNotch Antennas and Power Combiners," in 1991 IEEE MTT-S International Microwave Symposium, Vol. 111, pp. 1257-1260, Boston, MA, 1991.

[63] U. Guttich, "Planar Integrated 20 GHz Receiver in Slotline and Coplanar Wavegu- ide Technique," Microwave Opt. Tech. Lett., Vol. 2, No. 11, pp. 404-406,1989.

[64] N. Camilleri and B. Bayraktaroglu, "Monolithic Millimeter-Wave IMPATT Oscil- lator and Active Antenna," IEEE Trans, Microwave Theory Tech., Vol. 36, No. 12, pp. 1670-1676,1988.


[65] J. Birkeland and T. Itoh, "FET-Based Planar Circuit for Quasi-Optical Sources and Transceivers," IEEE Trans. Microwave Theory Tech., Vol. 37, No. 9, pp. 1452-1459, 1989.

[66] R. N. Simons and R. Q. Lee, "Planar Dielectric Resonator Stabilized HEMT Oscillator Integrated with CPW/Aperture Coupled Patch Antenna," in 1992 IEEE MTT-S International MicrowaveSymposium, Vol. I, Albuquerque, NM, pp. 433-436, 1992.

[6i7 M. J. Vaughan and R. C. Compton, "28 GHz Omni-Directional Quasi-Optical Transmitter Array," IEEE Trans. Microwave Theory Tech., Vo1.43, No. 10, pp. 2507-2509,1995,

[68] P. Liao and R. A. York," A New Phase-Shifterless Beam-Scanning Technique Using Arrays of Coupled Oscillators," IEEE Trans. Microwave Theory Tech., Vol. 41, No. 10, pp. 1810-1815,1993.

[69] W. A. Morgan, Jr., and K. D. Stephan, "Inter-injection Locking-A Novel Phase Control Technique for Monolithic Phased Arrays," in Proceedings of the 12th International Conference on Infrared and Millimeter Waves, Lake Buena Vista, FL, pp. 81-82,1987.

[70] R. N. Simons and R. Q. Lee, "Space Power Amplification with Active Linearly Tapered Slot Antenna Array," in 1993 IEEE MTT-S International Microwave Symposium, Vol. 11, Atlanta, GA, pp. 623-626, 1993.

[71] R. N. Simons and R. Q. Lee, "Spatial Frequency Multiplier with Active Linearly Tapered Slot Antenna Array," in 1994 IEEE MTT-S International Microwave Symposium, Vol. 111, San Diego, CA, pp. 1557-1560,1994.

[72] R. N. Simons, R. Q. Lee, and T. D. Perl, 'Non-planar Linearly Tapered Slot Antenna with Balanced Microstrip Feed," 1992 IEEE AP-S International Symposium, Vol. 4, Chicago, IL, pp. 2109-21 12,1992.

[73] R. N. Simons and R. Q. Lee, "Linearly Tapered Slot Antenna Impedance Character- istics," in 1995 IEEE AP-S International Symposium, Vol. 1, Newport Beach, CA, pp. 170-173,1995.

CHAPTER TEN

Efficient Modeling of Microstrip Antennas Using the Finite-Difference Time-Domain Method

SlVA CHEBOLU, SUPRIYO DEY, RAJ MITTRA, and JOHN SVICELJ

10.1 INTRODUCTION

Over the last two decades, microstrip antennas have evolved from simple single patch structures to complex multilayer configurations comprising of multiple feeds and active elements. These antennas are attractive candidates for wireless communication systems because of their conformal low-profile, lightweight characteristics and the ease with which they can be integrated with feeding networks and associated circuitry. Although the initial microstrip antenna designs involving single patches had narrow impedance bandwidths, low polarization purity, poor power handling capabilities, and spurious feed radiation, several new configurations have been proposed to offset these limitations. With the development of these innovative designs and owing to the enormous demand for low-profile, lightweight structures, microstrip antennas have found numerous applications in satellite, personal and mobile communication systems, biomedi- cal detectors, and remote sensing devices. In addition to the present volume, the recent book by Pozar and Schaubert [I] and several other publications [2,3]


51 6 EFFICIENT MODELING OF MICROSTRIP ANTENNAS

provide a good introduction to the issues involved in the design of microstrip antennas and the scope of their applications.

Microstrip antenna systems can be broadly classified into two categories:

1. Large arrays radiating high levels of power, as in satellite transmitting antennas and monopulse tracking radars.

2. Receiving of transmitting antennas for low-power applications in bio- medical probing and cellular or GPS communications. These structures are typically characterized by a single element or by an array with relatively few components.

In this work, the focus is on modeling microstrips antennas that belong to the second group. For a discussion of array analysis, the reader is referred to Chapter 3 of this book.

10.2 A COMPARISON OF VARIOUS CAD APPROACHES

Corresponding to the developments in the experimental design of microstrip radiators, there has been a tremendous increase in the degree of sophistication in the numerical models available for analyzing these structures.

The cavity model [4], proposed in 1980, provides a simple intuitive understanding of the performance of the microstrip antenna. Other approaches with simplifying assumptions are the transmission line model [2], and the multiport network model [5 ] , which characterize the antenna in terms of lumped and distributed circuit elements. Although the accuracy of these approximate models is limited, they are nevertheless useful for the design of simple structures. This is because these models can provide good initial estimates of the performance characteristics of the design and are helpful in predicting the trends in these characteristics with the variation of the design parameters.

In contrast, the full-wave models involve a more rigorous representation of the antenna structure, are abie to analyze arbitrarily-shaped geometries, and can take into account the effect of various types of feeds. In general, these models are much more accurate and are capable of handling a wide variety of structural configurations at the expense of increased computational complexity and time. Some popular full-wave modeling approaches include the Method of Moments (MOM), the Finite Element Method (FEM), and the Finite-Difference Time- Domain (FDTD) technique.

The moment method was initially applied to the problem of microstrip antenna analysis in 1981 [6] and has since been considerably modified to analyze complex structures with increased accuracy [7-121. The MOM analysis can be camed out either in the spatial domain [6-81 or in the spectral domain [9-111. The spatial domain analysis involves the Sommerfeld type of integral equations, while the spectral domain approach has the advantage of evaluating closed-form Green's functions in its formulation. Although this technique is

A COMPARISON OF VARIOUS CAD APPROACHES 51 7

well-suited for handling planar microstrip structures mounted on large ground planes and is capable of modeling a variety of feed structures, it requires extensive preprocessing to construct the requisite Green's functions fo; a given geometry.-~n addition, the results obtained are very sensitive to the type of attachment modes and to the basis and testing functions employed in the formulation. This sensitivity is prominent, especially when electrically thick substrates are involved. Also, an improper choice of the basis functions in this method can result in an ill-conditioned matrix equation, whose solution may pose convergence problems. This is particularily true when the antenna geometry is complex, and the ground plane is modeled as being finite. However, much progress has been made recently toward improving the accuracy and efficiency of the MOM approach, and the reader is referred to Kinayman and Aksun [13] for further details.

Let us now turn briefly to the FEM as a tool for analyzing microstrip antennas. Unlike the MOM, the FEM uses a volumetric approach which enables it to conveniently model various inhomogeneties in the problem. It can also be adapted to model fine structural features without sacrificing accuracy. The ability to use tetrahedral and prismatic elements allows for an accurate geometric characterization of the structure. Another attractive feature of this method is the ability to visualize the fields in the domain over which the problem is being solved. While FEM has seen widespread use in the analysis of microwave circuits, the same cannot be said about its application to microstrip antennas, especially in a complex environment. One reason for this is that the problem of mesh truncation for open regions still poses some diaculties for the commercially available FEM software. It is only recently that Volakis and others [14] have applied FEM successfully towards modeling a variety of printed circuit antennas. Although some of the problems encountered with the FEM approach can be overcome by using a hybrid approach that combines the FEM with MOM [IS, 163, this technique has not yet found widespread use for the patch antenna problem.

The FDTD method [17] is yet another full-wave modeling tool which has received considerable attention in the electromagnetics community and has recently been successfully applied to the problem of modeling different types of antenna structures [18]. This technique is well-suited for handling complex microstrip antenna configurations because it can conveniently model the numerous inhomogeneties encountered in these structures. Furthermore, it has the distinct advantage over the frequency-domain methods that it can generate the characteristics of the patch over a broad band of frequencies with a single simulation. Moreover, this scheme requires O(N) multiplications to update N grid points, whereas the full N x N matrix from the method of moments requires 0(N3) multiplications for its inversion [18]. The matrix-free nature of the algorithm that enables the FDTD method to routinely handle upward of lo6 unknowns on conventional workstations, the potential unconditional stability of this numerical scheme, and its second-order accuracy are some of the attractive attributes of this approach.

51 8 EFFICIENT MODELING OF MICROSTRIP ANTENNAS

Simple microstrip antenna structures were first modeled using the FDTD method by Reineix and Jecko [19] in 1989. Since then, many different configurations such as parasitically coupled patches [20], active antennas [21], two- element phased arrays [22], and microstrip antennas mounted on curved surfaces [23] have been successfully analyzed with this approach. The papers by Wu et al. 124,251 considerably improved the modeling technique that enabled it to accurately characterize multilayer patch antennas with various feed structures such as microstrip, coaxial, and aperture coupled feeds. In this work, we describe some recent advancements with the FDTD algorithm that improve the computational efficiency of the conventional FDTD method and thereby extend its scope for analyzing complex microstrip antenna configurations. To illustrate the application of the FDTD method, the following structures are analyzed: a single patch mounted on an electrically thick substrate; a two-layer microstrip antenna; and a compact broadband antenna. By comparing the simulation results with the measured data, it is demonstrated that the FDTD technique can accurately model these intricate structures that involve nonplanar stacked dielectrics, shorting pins, and thick substrates.

Following this, the issue of CAD optimization for microstrip antenna design is addressed. Over the last decade, a host of electromagnetic solvers have been developed for commercial applications. One common problem encountered with using these CAD software packages for the design of microstrip antennas is that most of these techniques are suitable for analyzing a given geometry and not directly for design purposes. In other words, given a structural configuration with all the relevant-dimensions, one can use an appropriate CAD software tool to simulate the response of the structure over a desired range nf frequencies. However, the complementary synthesis problem of predicting the structural dimensions for a specified response is usually a much more daunting task.

Ideally, a CAD software package should require little preprocessing and be able to predict, efficiently and accurately, all of the characteristics of a given practical antenna configuration. Also, it should have built-in optimization routines that enable it to choose between several geometrical shapes and estimate that effect of varying a design parameter. For multifeed antennas or multiple patch array configurations, it is important for the software to rigorously model the mutual coupling effects as well.

Presently available software can rarely meet these imposing requirements. A simple technique, such as the cavity model, is only able to quickly estimate the approximate dimensions of single patches mounted on thin, low-permittivity substrates. When investigating a particular class of antennas, one can choose a suitable full-wave modeling tool to accurately analyze a few representative cases and employ interpolation techniques to develop a library of CAD formulas which are useful for design purposes [26]. Although full-wave methods are able to accurately analyze a variety of structural configurations, they are often highly computer-intensive and, hence quite slow. Also, such software packages are usually very expensive and generally require dedicated high-end workstations. These rigorous techniques provide the capability to visualize the field

THE BASIC FDTD ALGORITHM 51 9

distributions which can contribute to the fundamental understanding of the operation of the antenna and can also lead to new design insights. When using full-wave techniques for design purposes, the dimensions generated through simple models are often used as a starting point, and the design process typically requires several numerical iterations to meet a particular specifications. Addi- tional experimental fine tuning may be necessary to account for tolerances in the etching process as well as misalignment in manufacturing and permittivity variation in the dielectric substrates. Another important problem associated with CAD optimization is that there is no guarantee that these numerical iterations would eventually converge to an acceptable solution. Hence, the generation of a new microstrip antenna design to meet certain specifications primarily involves the design experience of the engineer and is facilitated with the availability of fast and accurate CAD tools. Although one can manage experimental design of simple configurations with approximate techniques, the availability of accurate CAD tools becomes a critical factor for the design of arrays which have many elements. For further discussion on this topic, the reader is referred to Pozar and James [I].

While a considerable amount of effort has been directed in the past toward the development of accurate analysis techniques, there has been little research on optimization methods for the systematic design of electromagnetic components. Global optimization routines, such as the Genetic Algorithm and Evolution Strategies, have been successfully applied only recently for the design of multilayer optical filters, frequency surfaces, and broadband antennas [27]. It is anticipated that further research in these areas would facilitate, considerably, the design of microstrip antennas.

While present CAD techniques play an important role in any mictostrip antenna design process, there remains ample scope for future developments in this area, including (a) further advances in modeling techniques and (b) implementation on parallel computers.

10.3 THE BASIC FDTD ALGORITHM

The FDTD algorithm, proposed by K. S. Yee 1171 in 1966, discretizes the Maxwell's equations in both space and time. Since the algorithm has been well documented-~17,181, the details of its implementation are not described here, and only on overview of the method is presented instead. This technique involves the generation of a spatial grid for the electric and magnetic fields over which the solution is desired. In the Yee algorithm, the spatial grid for the electric field is staggered one-half cell with respect to the corresponding magnetic grid. Similari-ly, in the time domain, the corresponding electric and magnetic fields are displaced by half a time step with respect to one another. For example, consider the top view of a microstrip antenna with a microstrip line feed as shown in Figure 10.1. The E-cell grids are shown in solid lines and the H-fields are assumed to be located at the center of each E cell.

520 EFFICIENT MODELING OF MICROSTRIP ANTENNAS

FIGURE 10.1 Stripline-fed patch modeled using a uniform orthogonal grid.

For illustrative purposes, in a 2D problem, the differential form of Faraday's law

is discretized in both space and time using a central difference scheme:

where Ex,, Ex,, E,,, and E,, correspond to the electric fields along the edges of the cell over which the H field is being updated (see Figure 10.1). The superscripts refer to the time instants at which the fields are being calculated. As seen from the above update equation, the electric fields are associated with integer values of the time variable n, while the magnetic fields are staggered in comparison by half a time step. In this scheme, the electric fields are initialized and the magnetic fields are computed from previously available information. This leap-frog integration procedure is repeated to update the electric fields. This time advancing scheme results in an explicit solution technique where, unlike a frequency-domain method, a computationally expensive matrix inversion is not necessary. This feature enables the algorithm to model large problems with a direct scaling in the CPU time and memory requirements, with the maximum size of the problem that can be handled depending only upon the availability of the computational

THE BASIC FDTD ALGORITHM 521

resources. In contrast, with a frequency-domain approach, the task of inverting a large dense matrix becomes increasingly complicated as the size of the problem is extended. Also, since the FDTD update equations involve communication only between the nearest neighboring cells, the algorithm can be conveniently adapted for parallel processing computing platforms.

The central finite differencing procedure ensures the second-order accuracy of the algorithm. To obtain accurate results using this technique, the spatial discretization should be less than 1,/10, where 1, refers the wavelength at the highest frequency of interest. Similarly, to ensure the stability of the algorithm, there is an upper bound for the temporal discretization which is dictated by the Courant limit [18]

For fast computation, it is advantageous to use a large temporal discretization. Moreover, a large value of At reduces the dispersive error in the simulation. Hence, the time step in FDTD simulations is typically chosen to be about 0.95 At,. Also, note that this temporal sampling rate, whichis of the order of 15 fhf, where fhf = ell,, is well above the minimum Nyquist sampling rate of fhf/2 which is needed for recovering frequency-domain information accurately.

The structure being analyzed is first described by using rectangular brick elements of dimensions Ax, and Ay, and Az. Note that the spatial discretizations along the three Cartesian coordinates are chosen to be of the same order to prevent large grid dispersion errors. The boundaries of the structure are made to align with the E-cell edges as shown in Figure 10.1. Each cell has associated with it information regarding the permittivity, permeability, and conductivity of the material filling the cell. Initially, all of the fields are assumed to be zero throughout the mesh. Next, the cells corresponding to the source are excited with a suitable amplitude distribution. Then, as the FDTD algorithm updates the field values in the adjacent cells, the input excitation propagates along the structure. For open structures, absorbing boundary conditions (ABCs) are used to terminate the mesh. These ABCs are designed to absorb the radiation impinging upon them from all angles of incidence over the desired range of frequencies and hence simulate open space conditions. Of course, small amounts of reflections, of the order of 0.01-1% of the incident field, are present due to the imperfect nature of the ABCs.

The discretized time signatures of the desired electric and magnetic fields are observed at suitable locations in the structure. With this information, electrical parameters of interest, voltage and current, are easily calculated. The voltage across two points can be obtained through a line integral of the electric field, and the current flowing along a conductor can be computed via a loop integral of the magnetic field surrounding the conductor. A Fourier transformation of these

522 EFFICIENT MODELING OF MlCROSTRlP ANTENNAS

time signatures yields the discretized frequency of the fields with a frequency spacing A f = l/(N*At), where N corresponds to the number of samples in the time signature. Hence, to obtain a fine resolution in the frequency domain, a large number of time-domain samples are needed. For nonresonant structures, it is possible to terminate the simulation after the response has decayed significantly, and then zero-pad the time signature to obtain the desired frequency resolution. However, for resonant structures, such as microstrip antennas, this procedure is not applicable as the time response of such devices exhibits a slowly decaying ringing behavior. In such cases, extrapolation techniques, described in the next section, can be used to reduce the computation time.

10.4 EFFICIENT FDTD MODELING OF MlCROSTRlP ANTENNAS

Since the conventional Yee's algorithm meshes the entire computational volume using a fixed temporal discretization, modeling complex antenna configurations having fine features with this technique can be prohibitively expensive in terms of memory requirements and computation time. For example, accurate characterization of a typical dual-layer microstrip patch via the conventional FDTD algorithm could requires as much as 400 MB of RAM and the simulation could run for several days on a workstation. Recently, a number of techniques have been developed to improve the computational efficiency of the conventional FDTD method, applied to the problem of modeling microstrip antennas. These efficient techniques typically involve a trade-off between accuracy and speed of computation. This section is based on work which has been reported earlier in references [28-301.

10.4.1 Spatial Discretization

A problem that is commonly encountered when modeling microstrip antenna geometries with a uniform orthogonal discretization is that it becomes necessary to use a small cell size, typically on the order of &/40 to l,,/100, to accurately represent the fine features of the antenna such as coaxial connectors, shorting pins, and substrate thickness. This value of the spatial increment is much smaller than the nominal value of &/lo, which is required to maintain the accuracy of the conventional FDTD algorithm. Similarily, since the Courant stability condition necessitates the time step to be proportionally small, the time signature is highly oversampled. These two requirements can result in a FDTD simulation that has to deal with an excessively large number of cells, and the computation time can go up dramatically. Thus, the conventional FDTD method can be an inefficient approach to modeling microstrip antennas with fine features.

Over the last decade, several approaches have been developed to model fine features of an object in an efficient manner. The applicability of each of these techniques to this class of problems will be explored below, with a view to selecting the most appropriate modeling tool.

EFFICIENT FDTD MODELING OF MlCROSTRlP ANTENNAS 523

Subcell Gridding and Expansion Techniques. In the subcell gridding and expansion techniques [31,32], the geometry is modeled with a uniform fine grid in certain regions enclosing discontinuities and fine features, while a uniform coarse grid is employed elsewhere. In the subgridding appproach [31], spatial and temporal interpolations are used to update the fields on the interface between the fine and coarse grids. It has been found that the accuracy of this model is not good unless the domain of the fine feature region is sufficiently large. The problems under consideration involve fine structural features that may be distributed over the entire volume of the structure, and their dimensions do not necessarily extend over large spatial domains. Hence, these methods are not well-suited for the present purposes.

Subcell Modeling. This technique is commonly employed to model thin sheets, slots, and wires 1181. In microstrip antenna analysis, the thin-sheet approximation is valid even in complex environments, including one where the sheet is in the proximity of several conductors, and is used, where applicable, to reduce the computational domain.

On the other hand, the thin-wire approximation breaks down when there are several conductors in its vicinity as, for instance, in a coaxial cable. The thin-wire model is based on the assumption that the electric fields are normal to the surface of a thin wire. The tangential magnetic fields are presumed to exhibit a l l r dependence in the vicinity of the wire, where r is the radial distance from the center of the wire. In such situations, one edge of a Yee cell can be used to model the thin wire, and the field update equations have to be modified accordingly. Unfortunately, for the structures being investigated here, the original assumption regarding the field behavior is not valid; hence, this model is also not useful for the present problem.

Nonorthogonal, Curvilinear, and Globally Unstructured Grids. To obtain an accurate field solution in an arbitrary structure by using the FDTD algorithm, it becomes necessary to choose a suitable grid discretization such that it accurately models both the geometry and the field variations in the structure, and one approach to doing this is to use a general, finite-element type of nonorthogonal grid [33]. The generalization of the FDTD algorithm to include the surface-curve integral form and the volume surface integral form of Maxwell's equations has led to the development of the hybrid FDTDIFVTD technique [34] which can solve for the fields on a globally unstructured volume grid. However, this approach is not always very robust, because it is not suitable for handling different structures with a minimum amount of preprocessing, which is one of the principal attractive features of the FDTD method.

An alternative strategy is to use the curvilinear FDTD approach [35,36], which employs a structured nonorthogonal grid and is well-suited for modeling patch antennas with curved surfaces [23]. However, for the class of structures analyzed in this work, the curvilinear method turns out to be prohibitively expensive in terms of memory requirements and CPU time, owing to the fact that


it is necessary, in the aforementioned approach, to store the coordinate transformation metrics and because the time required to convert the covariant and contravariant field components back and forth is computationally expensive. In predominantly rectangular geometries, curved objects such as shorting pins and circular coaxial feeds can be simply modeled with square geometries. Since the dimensions of these fine features are very small, this approximation yields good results and obviates the use of the curvilinear FDTD.

Nonuniform Orthogonal Grids. From the earlier discussion, we have seen that an accurate representation of the antenna geometry using a nonorthogonal grid leads to a significant increase in the solution time, and modeling the fine features - using subcell approximations can lead to erroneous results. In this respect, the use of a nonuniform orthogonal grid [37] is a good compromise to increasing the modeling accuracy while preserving the computational speed and accuracy of the FDTD technique.

In this method, the simplicity of the FDTD update equations is retained by using an orthogonal grid. Therefore, the computational speed of this method is the same as the conventional Yee algorithm.

By employing nonuniform spatial increments, this technique allows us to model the geometry more accurately than is possible in the uniform approach, which requires the dimensions of a structure to be integral multiples of the chosen discretizations in the x, y, and z directions. This flexibility in vwying the mesh dimensions is especially advantageous for modeling a circulary polarized (CP) patch antenna accurately, since its characteristics, such as the axial ratio and the input impedance, are very sensitive to variations in the dimensions of the patch and the location of the probe. For instance, in an ordinary C P patch, the ratio of the two sides (a/b ratio) is on the order of 1.01-1.05. Hence, it becomes very di£ficult t o accurately describe these dimensions as well as the feed, and its position on the patch, using a uniform mesh with a fixed spatial discretization. On the other hand, a nonuniform grid can easily model the structural dimensions precisely with a few cells. As an example, the top view of a short-circuited patch modeled with a nonuniform orthogonal grid is shown in Figure 10.2.

With this technique, a fine discretization can be used to model the regions where there is a rapid variation in the fields, and a coarse mesh can be employed in regions where the field is well-behaved. This process can lead to a signscant savings in the memory requirements for the simulations. Also, since microstrip antennas are open radiating structures, the ability to vary the mesh resolution enables us to move the absorbing boundaries of the computational domain farther away from the radiating structure, without an undue increase in the number of cells. This can be quite advantageous when modeling large, complex structures, because the presence of spurious reflections from an imperfect ABC can contaminate the FDTD solution when these boundaries are placed too close to the antenna being modeled.

There are a few restrictions that must be adhered to when the nonuniform orthogonal grid is employed. As a rule of thumb, the growth factor of the mesh

Shorting pin

EFFICIENT FDTD MODELING OF MICROSTRIP ANTENNAS 525

FIGURE 10.2 Short-circuited microstrip patch modeled using a nonuniform orthogonal grid. (Reprinted with permission from Microwave Journal, January 1996, Vol. 39, No. 1.)

(which is the ratio of the spatial steps of two adjacent cells) should be kept below 1.2-1.3 to prevent artificial discontinuities introduced by the abrupt changes in the cell size. However, larger growth rates are acceptable as long as the cell size is very small compared to the wavelength 1381. Also, it should be noted that the nonuniform grid no longer preserves the second-order accuracy that is obtained with the use of the uniform grid. Nevertheless, if the mesh spacing changes slowly, the error can be close to that of a second-order method.

As will be demonstrated in later sections, it is possible to achieve about 40-80% reduction in the problem size and a corresponding decrease in the computation time compared to the conventional FDTD method by using this modeling procedure without an undue sacrifice of the accuracy.

Considering all of these advantages, the nonuniform orthogonal FDTD method is the best approach for modeling predominantly rectangular microstrip antenna geometries. For analyzing circular patches, it is perhaps more advantageous to use a curvilinear mesh [23,35,36]. Recent advances in the contour path FDTD technique [39] may enable one to use a regular grid with the option of locally deforming the mesh to conform to the curvature of the geometry.

Note that although a significant reduction in the computational domain has been achieved through nonuniform spatial discretization, the time step is still determined by the smallest cell size. This issue can be addressed through signal processing techniques to be discussed shortly.


10.4.2 Source Excitation

Microstrip antennas are inherently high-Q structures and are typically designed to operate over a relatively narrow band of frequencies. To obtain the frequency information within this narrow range, it is usual in FDTD analysis to excite the antenna with a sinusoidal signal, operating at the center frequency of the band, and modulate it by an appropriate Gaussian pulse [19]. This type of temporal excitation not only generates the desired modes on the antenna, but also allows the fields to reach their steady-state values quickly. The situation can be further improved by replacing the Gaussian pulse with a standard window function (e.g., Blackman-Harris window), whose spectral response has very low sidelobes. Examples of representative so source excitations are summarized in Table 10.1.

Typically, microstrip antennas are excited by using a coaxial probe or a microstrip feed structure which can be coupled to the patch via an aperture. In either case, it is numerically efficient to exite these transmission lines with a quasi-static distribution obtained from the solution of Laplace's equation. With this form of spatial excitation, the fields settle down to their dominant modal distributions in a few cell lengths; hence, it is possible to use a shorter length of the transmission line for modeling the feed structure.

10.4.3 Phased Array Excitation

In the design of microstrip antenna arrays for attaining broadband CP characteristics, one often has to feed two patches with a 90' phase difference over the frequency range of operation [40]. This is conveniently accomplished via the use of a 90" hybrid coupler in the experimental setup. However, modeling this excitation in the time domain can be difficult.

For single-frequency simulations, we can readily excite two different patches with a particular phase difference, either by having an additional number of space grids between one of the sources and the corresponding observation point or by having a time shift between the two excitations [22]. The latter approach is preferable because it keeps the cable length fixed even when a large phase difference is needed.

For maintaining the phase difference relatively constant over a band of frequencies, signal processing tools such as the Hilbert transform technique can be employed [30].

10.4.4 Extrapolation Techniques

When analyzing microstrip antennas, which are inherently high-Q structures, with the conventional FDTD technique, the simulations are typically run for a very long time to allow the time signatures to decay significantly. Fortunately, this ringing feature of the temporal response is also ideally suited for extrapolation because it is relatively straightforward to approximate the time-domain signature over a short duration with an appropriate set of predefined functions

....... d d d d 9

IpnPldulV


and, subsequently, use this information to extrapolate this signature. Several extrapolation techniques-for example, the Prony's method [41], the autoregressive models [42,43], and the generalized pencil-of-function (GPOF) method 1441-have been successfully employed in the past for this purpose. In the modified GPOF procedure 1291, the decaying discrete temporal date, f(t,,), is represented by using a set of p complex exponentials with strictly negative real parts as follows:

In the above equation, n,,,,,, refers to the initial number of time steps that are skipped over while applying the GPOF algorithm; the complex poles and their corresponding residuals are found by solving a generalized eigenvalue problem.

It has been found that the modified GPOF method is very well-suited for the time-domain signatures encountered in microstrip antenna applications. The present authors tend to favor the GPOF method over the AR technique since it models the time response by using a set of complex exponentials, which correspond to the natural response of the antenna system. Also, the GPOF approach is less sensitive to noise in the sampled data than the Prony's method [44].

As an example, consider a typical time signature of the feed voltage in a microstrip patch antenna as shown in Figure 10.3. The patch is excited with a Gaussian pulse, which has a duration of approximately 2 000 time steps. The data in the first 4000 time steps are disregarded and only those data from the

Coaxially fed microstrip antenna

0 2000 4000 6000 8000 110' Number of time steps

FIGURE 10.3 Time-domain signature of a typical microstrip patch. (Reprinted with permission from Microwave Journal, January 1996, Vol. 39, No. 1.)

EFFICIENT FDTD MODELING OF MICROSTRIP ANTENNAS 529

Vm and Vgpmx

Interpolation using 4000-6000 time steps

4000 4500 5000 5500 6000 6500 7000 7500 8000 Number of time steps

FIGURE 10.4 Results of extrapolation of the time-domain voltage waveform. (Reprinted with permission from Microwave Journal, January 1996, Vol. 39, No. 1.)

4000-6000 time step interval are used to obtain the coefficients of the approximation. Subsequently, this exponential approximation is applied to extrapolate the voltage data to 41,000 time steps and obtain a fine resolution of 25 MHz in the frequency domain. Due to the oversampled nature of these time signatures, the signal is usually decimated before the extrapolation procedure is applied. To validate the results of the extrapolation, the original simulation can also be run for a large number of time steps. Figure 10.4 shows that the interpolated and extrapolated results agree very well with the original data set, derived by using 41,000 time steps.

Figure. 10.5 demonstrates that the frequency response, obtained via the time-domain extrapolation, also agrees well with the original system response. Note that an 85% savings in the computational time has been achieved by applying the extrapolation procedure to a 6000 time-step record, instead of running the actual simulation for 41,000 time steps. For comparison purposes, we also show, in Figure 10.5, the result obtained by using only 6000 time steps and the frequency response derived by using between zero-padding between 6 000 and 41,000 time steps. Note that although the latter method is fairly good for predicting the smooth portion of the spectrum, it is unable to model the poles with sufficient accuracy.

We conclude this section with the observation that, for resonant systems with a few dominant poles in the frequency band of intrest, extrapolation proves to be an indispensable tool which models the late-time response accurately and helps reduce the CPU-time requirements by a significant amount.

530 EFFICIENT MODELING OF MlCROSTRlP ANTENNAS

Frequency response of the Voltage

8 8.5 9 9.5 10 10.5 11 Frequency (GHz)

FIGURE 10.5 Comparing the frequency response obtained using various methods. (Reprinted with permission from Microwave Journal, January 1996, Vol. 39, No. 1.)

10.4.5 Impedance

Proper characterization of the feed structure is essential for obtaining accurate impedance values. A patch antenna excited with a microstrip feedline, or an aperture-coupled feed, can be easily modeled by using a thin-cell approximation and a nonuniform grid spacing. Accurate results have been obtained for patches mounted on high-dielectric-constant substrates [25] by using this approach. On the other hand, the modeling of a coaxial feed is more involved.

There have been three different models proposed for determining the input impedance of a coaxially fed microstrip antenna. The first one, proposed by Reineix and Jecko [19], incorporates the effect of the feed through a via model with an equivalent lumped source resistance. This via model turns out to be oversimplified because it cannot accurately model all of the features of the discontinuity through an equivalent source resistance and is also highly dependent on the value of the source resistance and the via radius used in the simulation.

An accurate model of the coaxially fed patch antenna has been proposed and validated by Wu et al. [24]. In their model, the incident and reflected voltages are monitored separately and the reflection coefficient, s,,, is determined as a ratio of the incident to the reflected voltage in the frequency domain. This approach requires a long coaxial probe so that one can separate the incident voltage pulse from the reflected one. Also, a knowledge of the characteristic impedance of the feed is necessary to be able to translate the s,, information to the input impedance of the antenna.

In all of the previous literature available on this subject, there appears to be an emphasis on using a matched feed in the simulation to determine the input


impedance of the antenna. This can lead to an exorbitant number of cells being used for the feed modeling, especially if the feed is filled with a high-dielectric- constant substrate. However, note that the input impedance of the microstrip antenna is determined solely by the location of the feed rather than the characteristic impedance, Z,, of the probe used in the measurement. Usually, a suitable location on the patch is chosen such that the resonance resistance matches with 2, to allow maximum power transfer to the antenna.

Chebolu et al. [28] have used a slightly different model to calculate the input impedance which is not greatly affected by the choice of the probe used in the simulation. In this approach, the voltage and current are observed at a convenient location-for example, the junction between the patch and the cable. Fourier transformation of this time-domain data yields the input impedance, Zin, of the antenna over a wide range of frequencies at the monitoring plane:

The next step is to convert the calculated input impedance Zin to reflection coefficient data s,, ,,, using the characteristic impedance, Zoex,, of the experimental probe:

The impedance of the experimental probe has been used in the above formula to enable comparison between the computed results and the measurements. These results for the reflection coefficient are then translated to a suitable reference plane, determined by the measurement settings, and compared with the experimental data. For a lossless transmission line, the Smith chart impedance locus simply rotates, depending of the position along the transmission line. Hence, the magnitude of the measured reflection coefficient should agree with Is,, ,.,,I if the model is accurate. Since both the voltage and the current are monitored in this method, it is not necessary to separate out the incident pulse from the reflected one. Note that even in this case, it is beneficial to have a matched probe because the magnitude of the multiple reflections between the probe-patch discontinuity and the absorbing boundaries is minimized. However, it turns out that the contribution of these multiple reflections is usually negligible.

10.4.6 Absorbing Boundaries

For microstrip type of feeds mounted on high-dielectric-constant substrates, a dispersive boundary condition [25,45] is useful, especially if a wideband frequency response is desired. For a coaxially fed patch antenna, a first-order Mur boundary condition [46] is sufficient to absorb most of the incident waves which are propagating longitudinally along the coaxial cable, while a second- order Mur ABC is employed on the remaining boundaries. Despite the assertion


to the contrary [25], the present authors find that a second-order Mur ABC is needed on these boundaries even when the grid spacing is dense.

While modeling these radiating structures, one should carefully select the number of cells required between the outer absorbing boundaries and the patch. The use of too many cells results in an unnecessarily large computational domain, while too few cells lead to significant amount of reflections from the imperfect ABCs. Through experience, it has been found that using a number of cells corresponding to 1,/2 is a good choice. The latest developments in this field, such as the Berenger's Perfectly Matched Layer condition [47,48], lead to a further reduction of the "white-space" between the radiating structure and the ABCs.

In some situations, it becomes necessary to excite coaxial feeds with many bends (see Figure 10.12, for instance). In a conventional FDTD model, the reflections from these discontinuities corrupt the input signal. One approach to overcoming this problem is to implement a numerical absorber within the coax itself to minimize the reflections from the bends.

10.4.7 Radiation Pattern

The radiation pattern of the antenna can be calculated in several ways. For a single-layer patch antenna mounted on a very large ground plane, the current distribution on the surface of the patch can be processed to generate the far-field patterns [19]. For more complex geometries involving stacked patches, it is convenient to monitor the fields on a suitable equivalent surface enclosing the radiating structure and then process this information to obtain the radiation pattern. Two different approaches to computing the radiation pattern will now be discussed.

Wideband-Near-to-Far-Zone Transformation. In many practical applications, information about the radiation pattern of the antenna is desired over several frequencies centered about the resonant frequency of the antenna. This information can be conveniently obtained with a single time-domain simulation used in conjunction with an efficient near-to-far-zone transformation, which involves the following steps:

1. The antenna is enclosed in a closed Huygen's surface, which is conveniently chosen to be a cube whose faces are.about three to five cells inside the absorbing boundaries surrounding the antenna.

2. The equivalent magnetic current, m,(t), is computed from the tangential electric field on the Huygen's surface. Because the tangential magnetic field on the Huygen's surface is not directly available, an average value is used to determine the equivalent electric current, j,(t).

3. Next, the near-to-far-zone transformation [49,50] is applied to these equivalent currents to obtain the time-domain far fields, e,(t), e4!t). There is a minor modification in the implementation of this scheme whlch has not been mentioned in the references. The central finite differencing scheme


employed in this transformation sums up the contributions to the far field due to the equivalent source at the current time step, the previous time step, and the next time step. Hence, this scheme should only be applied until the penultimate time step, and a backward difference scheme should be used, if necessary, for the last time step.

4. Fourier transformation of e,(t) and e4(t) yields the radiation pattern over a band of frequencies.

Typically, the radiation pattern information is needed for at least two planes, namely, the E and the H planes. To obtain a reasonable angular resolution, the far field is monitored at a sufficient number of observation points, say 40. For so many data points, the near-to-far-field transformation slows down the FDTD code significantly, by as much as a factor of two. Also, storing the entire time-domain signature at all these locations places a heavy burden on the memory requirements. To avoid inordinately long computational times, some form of an extrapolation scheme, such as the adaptive extrapolation procedure [51], should be used.

Single-Frequency Near-to-Far-Zone Transformation. An alternative scheme to incorporate near-to-far-field transformation in the frequency domain is useful if the radiation pattern of the antenna is needed only for a few frequencies, for example less than 10. For such cases, the computationally intensive broadband time-domain transformation can be avoided. In this scheme, the antenna is excited with a combination of the desired frequencies, and the electric and magnetic fields are monitored over a suitable Huygen's surface. A running discrete Fourier transform (DFT) can be used to obtain the coefficients of the electric fields at the frequencies of interest. Using this information, the standard frequency domain near-to-far-field transformation yields the radiation pattern at the desired frequencies. Since only the Fourier coefficients are stored in this method, the memory requirement is much smaller than that needed for the wideband near-to-far-field transformation. Furthermore, the speed of the original FDTD algorithm is affected little when this approach is used. Hence, whenever the radiation pattern is needed at a few frequencies, this method turns out to be more efficient than the wideband algorithm.

Before closing this section, it should be mentioned that it is necessary to employ a fine spatial discretization for electrically large antennas to model the near field accurately. With minor modifications in the algorithms described above, one can also compute the power gain and the cross-polarization radiation levels of the antenna under investigation.

10.4.8 Distributed Computing

Microstrip antennas are well-suited for domain decomposition techniques which significantly reduce the computational requirements [24]. For example, a probe- fed patch antenna can be separated into two regions as shown in Figure 10.6.


Microstrip Antenna

Domain 1

FIGURE 10.6 A coaxially fed microstrip antenna.

I

These two regions can be analyzed separately, and the field information at the interface can be transferred through a message passing scheme. With this procedure, the 'whitespace' underneath the patch is not modeled and, hence, significant computational resources can be conserved.

10.4.9 Dielectric Loss Tangent

0

For an accurate modeling of the radiation characteristics of the antenna, it is necessary to account for the loss tangent (tan 6) of the dielectric, since this parameter can significantly alter the magnitude of the input impedance [52]. This feature can be easily incorporated into the FDTD algorithm by introducing an equivalent conductive loss, given by a,,, = w s' tan 6, in the dielectric. Note that an appropriate value of o , which lies within the given frequency range, must be used since the FDTD approaches is not very well-suited for handling dispersive media.

I Coaxial Pmbe N

10.5 SINGLE PATCH MODELING

Although the single microstrip patch antenna has been extensively analyzed over the last 15 years, there are very few publications that document all of the dimensions of the patch, including the size of the ground plane. Nonetheless, the

SINGLE PATCH MODELING 535

single rectangular patch configuration is a good benchmark for testing the accuracy of the FDTD technique. The results reported herein are generated on a DEC-Alpha workstation with 128 MB of RAM.

We consider the problem of calculating the input impedance of two different rectangular microstrip patch geometries, both of which are fed with a coaxial line, and were investigated in references 1531 and [7]. In the first study 1531, the thickness of the substrate was chosen to be 0.0241, at the resonant frequency, while a dielectric thickness of 0.0461, was used in the second case.

10.5.1 Impedance of a Patch Antenna Mounted on a Moderately Thick Substrate

The antenna under consideration consists of a square patch whose dimensions are 2.01 an x 2.01 cm. This antenna is mounted on a substrate with s, = 2.55, tan 6 = 0.002, and thickness t = 0.159 cm and is excited by a coaxial feed along the center of one side. The detailed geometry of the antenna has been described in reference 53. A uniform discretization of 0.65 mm x 0.65 mm x 0.53 mm was used to model the geometry, and a 0.8751, x 0.8751, ground plane was used in the FDTD simulation to accommodate the problem on the available workstation. The patch itself was modeled by using an infinitely thin PEC plane [18]. A spacing of 20 cells was chosen between the radiating structure and the ABCs to allow for proper absorption of the scattered fields. The total computational domain consisted of 131 x 131 x 73 cells-that is, 1.25 million cells. The coaxial lines were terminated using the first-order Mur ABC, while the remaining unbounded regions of the computational volume were truncated with the second-order Mur ABC. The first-order Mur ABC is sufficiently accurate to absorb the transverse electromagnetic waves propagating along the coaxial cable. Since the impedance characteristics were desired over the frequency range of 4.15-4.65 GHz, the loss tangent of the dielectricwas modeled using an effective conductivity a,,, = w0sftan 6, where w, corresponds to the central frequency of 4.4 GHz. Also, a sinusoid at 4.4 GHz modulated with a Gaussian pulse, having a 3-dB cutoff frequency of 0.25 GHz, was used for the temporal excitation.

Figure 10.7 shows a comparison between the two reflection coefficient (s,,) results, obtained from the experimental measurement and the FDTD simulation. Figure 10.7 also displays the results derived by Deshpande and Bailey [53] by using the Method of Moments technique. While the FDTD method is able to estimate the resonant frequency to within an accuracy of 2%, the predicted frequency response is broader than the experimental results. This discrepancy is probably due to the difference in the ground-plane sizes used in the simulation and the experiment. Note that, in this case, the order of accuracy of the FDTD results is similar to that obtained with the moment method. Once the time signatures of the fields have stabilized to their resonant distributions, a plot of the steady-state electric field underneath the patch, shown in Figure 10.8, displays the field variation which is characteristic of a microstrip antenna operating in the TM,, mode.


90

FIGURE 10.7 Input impedance of a single patch antenna mounted on a moderately thick substrate.

FIGURE 10.8 Steady-state electric field distribution on a single patch antenna.

10.5.2 Impedance of a Patch Antenna Mounted on a Thick Substrate

Thick substrates are often used to increase the impedance bandwidth of the antenna. Here, we consider the impedance characteristics of a coaxially fed patch antenna mounted on an electrically thick substrate of thickness 0.0461,. The width and length of the patch are 12mm and 20mm, respectively. The relative permittivity of the dielectric substrate is 2.22, and the loss tangent is 0.001. It is

SINGLE PATCH MODELING 537

FIGURE 10.9 Input impedance of a coaxially fed path antenna mounted on an electrically thick substrate.

important to account for the axial variation of the probe current for substrate thickness greater than 0.021, [Ill . This requirement can be easily met in the FDTD method by using four or more cells to model the thickness of the substrate.

The modeling procedure for this geometry is the same as in the previous example. With a uniform discretization of 0.5 mm x 0.5 mm x 0.51 mm, the maximum size of the ground plane had to be restricted to 1.51, x 1.261, due to memory limitations on the workstation.

Figure 10.9 displays the experimental and simulated impedance characteristics over the frequency range of 6.5 GHz to 11.75 GHz. From this plot, it is seen that the agreement between the two sets of data is not as goodas that obtained by Hall and Mosig [7] by using a thick substrate MOM formulation. There could be several reasons for this discrepancy. First, the dimensions of the ground plane used in the FDTD model were substantially smaller than those in a typical experimental setup, and we will see form the discussion below that the size of the ground plane can have a profound influence on the input impedance. Second, an effective conductivity was used in the FDTD simulation to model the loss tangent of the substrate (tan 6 = 0.001) at the center frequency of 9 GHz. However, with this representation, the effective loss tangent varied from 0.0014 at 6.5 GHz to 0.00077 at 11.75 GHz. This variation in the effective loss tangent could account for part of the discrepancy in the impedance results [11,52]. Although this modeling deficiency could be overcome by using a modified FDTD algorithm which is suitable for treating dispersive media [18], such an algorithm is not only


considerably more complex to implement, but is also slower than the conventional FDTD approaches.

10.5.3 Efiect of a Finite Ground Plane on Impedance and Radiation Pattern

Often, the size of the ground plane and the loss tangent are not specified in many papers dealing with an experimental study of patch antennas. Although the resonant frequency of a patch is not very sensitive to these parameters, they can have a significant effect on its input impedance and the radiation pattern. It is important to model these effects accurately because it is very useful for designing multilayer stacked patch antennas [54,55].

To investigate the effect of a finite ground plane on the input impedance, the patch antenna considered in the previous section was simulated with different sizes of the bottom patch ranging from 1, x 1, to infinity. Initially, the patch antenna was modeled with a ground plane whose size was 1.51, x 1.261, to accommodate the task on the available workstation. Later, the use of the nonuniform grid allowed us to increase the size of the ground plane to 31, x 2.812,. Finally, the infinite ground plane was simulated in the FDTD method by extending the ground plane and the substrate to the absorbing boundaries, and the first-order Mur ABC was used on all boundaries. However, in this approach, there could be significant reflections of the surface waves traveling along the substrate depending on the type of ABC employed in the formulation, and this problem could perhaps be alleviated by using dispersive ABCs of the type suggested by Betz and Mittra [45]. The results of these numerical experiments are shown in Figure 10.10. From this figure, it is seen that the impedance values progressively converge to the experimental ones as the size of the ground plane is increased. Also, it can be inferred that once the ground plane extends beyond 31, x 2.81,, it has an incremental effect on the input impedance. These results indicating that an accurate modeling of the near-fields of the radiating structure is essential to determining the impedance characteristics correctly.

Next, let us consider the pattern of a 21 mm x 14mm patch antenna mounted on a 61 mm x 54mm ground plane, and a dielectric of relative permittivity 2.32 and thickness 3 mm. Since the ground plane is only 2.0Id x 1.8Ad at the resonant frequency of the TM,, mode, it is expected to alter the radiation patterns significantly. Figures 10.11a and 10.11b display the E- and H-plane radiation patterns, respectively, for this structure. Note that there is substantial backlobe radiation in the shadow region of the patch due to edge diffraction effects.

10.6 ANALYSIS OF A TWO-LAYER STACKED PATCH ANTENNA

Recently, nonconformal microstrip antennas involving multiple layers of stacked patches have found applications in GPS communications [54,55]. In this section we consider the FDTD modeling of a two-layer stacked patch array, shown in

ANALYSIS OF A TWO-LAYER STACKED PATCH ANTENNA 539

- Large

-

Frequency (a) (GHz)

-100 0 6 7 8 9 1 0 1 1

Frequency (GHz) (b)

1501

100

- 50 E L1 -

C

x- 0

-50

FIGURE 10.1 0 (a) Real and (b) imaginary parts of the input impedance, as computed through the FDTD method, for various sizes of the ground plane.

- Small i - Large i - ""'-'

-

-

-

Figure 10.12, which is a circularly polarized (CP) antenna used in mobile communications to realize a near-omnidirectional coverage [54]. We investigate the characteristics of this antenna in the frequency range of 1-2 GHz, centered about its first two resonances.

A nonuniform discretization was employed to model the geometry, and the grid size was varied from 0.75 mm x 0.75 mm x 0.75 mm to 3.2 mrn x 3.2 mm x


0

Eplane

FIGURE 10.11 (a) E- and (b) H-plane radiation pattern of the TM,, mode in a patch antenna mounted on a small ground plane.

3.2mm. Although a fine grid was used in describing the features of the coaxial cable and the thickness of the dielectric, the cell size was gradually increased to model other regions of the structure. Note that even at the highest frequency of interest (namely, 2GHz), the largest cell size is approximately 1,147, indicating a very fine spatial discretization. The total computational domain had 106 x 107 x 126 cells, and the smallest cell determined the 1.25 ps time step of the simulation. If the same geometry was modeled with a uniform mesh with a cell size of 1 mm x 1 mm x 1.6mm, we would require a mesh with 244 x 244 x 140

ANALYSIS OF A TWO-LAYER STACKED PATCH ANTENNA 541

Total input

*-way power divider (NARDA 43218-21

d=7l mm erl = 10.5 tl = t2 = 3.12 mm er2 = 3.6 a1 = 29.3 mm, bl s 28.8 mm, gl = 43.6 mm ap = 50.9 mm, b2 = 48.9 mm, g2 = 60.8 mm

a, b - - - Dimensions of patches g - - - Dimensions of ground planes

FIGURE 10.1 2 Two-layer stacked patch antenna.

cells. Compared to the uniform discretization for this case, we see that the use of a nonuniform grid results in a memory saving of 83%, and the RAM requirements reduce from 500 MB to only 90 MB.

For the first two resonant modes of the bottom patch, the electric fields is zero at the center of the patch. Hence, although the coaxial feed of the top patch passes through the center of the bottom patch, it does not significantly perturb the field distributions on the bottom patch. The top and bottom patches are fed one-third of the way along the diagonal to achieve circular polarization together with a good impedance match. Therefore, it is necessary to bend the coaxial cable that feeds the ton ~ a t c h as shown in Figure 10.12. This bend in the cable is modeled by . A using two 90' bends as shown in Figure 10.13. The feeds are excited with a spatial distribution corresponding to the quasi-static Laplace's solution for the coaxial line, and the temporal form of the excitation is a 1.55 GHz sinusoid modulated

I

with a 0.5 GHz Gaussian pulse. The two patches are fed in phase using a two-way 1 power divider. This effect is simulated in the FDTD model by exciting both

patches with the same form of input pulse at locations along the feeds that are equidistant from the patches.


FIGURE 10.13 FDTD model of a two-layer stacked patc- -h array.

Figure 10.14 shows the time-domain signatures of the voltage and the current which are monitored at the intersection of the feed and the patch. The G P O F methodis used on the data from 4000-6000 time steps to extrapolate the response to 25,000 time steps. Although this time response is not as periodic as that of a signal microstrip patch due to the complexity of the structure, excellent agreement was obtained between the actual and extrapolated data, and the latter was postprocessed to yield the input impedance. Note that the application of the extrapolation technique resulted in about 76% savings in the CPU time, which corresponds to a reduction of the simulation time from over 3 days to 16 hours on a DEC-Al~ha workstation.

Figure 10.15 displays a comparison between the experimental and computed reflection coefficients of the two-layer stacked patch array. The two peaks in the impedance curve at f, = 1451 GHz and f, = 1525 GHz correspond to the resonant frequencies of the first two dominant modes of the nearly square antenna. Again, good agreement is achieved between the theory and measurements, which

DESIGN OF A COMPACT BROADBAND ANTENNA 543

0 1000 2000 3000 4000 5000 6000 Number of time steps

(a)

Number of time steps (b)

FIGURE 1 0.1 4 (a) Tie-domain voltage waveform, (b) Time-domain current waveform.

indicates that the FDTD technique is able to accurately predict the response of complex microstrip configurations.

Figure 10.16 shows the TM,, and TM,, modal current distributions on the bottom patch, operating in isolation, after the response has stabilized to its steady-state value. From these plots, we can see the perturbation of the current at the probe location and the charge accumulation along the edges of the patch.

10.7 DESIGN OF A COMPACT BROADBAND ANTENNA

As another example, the FDTD method was used to analyze a compact parasitically coupled broadband microstrip antenna [56]. The antenna configuration,

1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 Frequency (GHz)

FIGURE 10.15 Comparison of the reflection coefficient obtained from the FDTD simulation with experimental results for a two-layer antenna.

FIGURE 10.16 Current distributions on the bottom patch, operating in isolation.

544

DESIGN OF A COMPACT BROADBAND ANTENNA 545

Short~ng pin

To 50R load

Feed point

Shorting pin f 1.41 Shorting pin

FIGURE 10.1 7 Schematic of compact broadband antenna.

shown in Figure 10.17, consists of four short-circuited square patches of length 20mm. The patches are etched on a substrate with a dielectric constant of 2.6, a thickness of 3.2 mm, and a ground plane of dimensions 68 mm x 68 mm. All of the patches are connected to the ground through shorting pins, which are 0.5 mm in diameter. The antenna is excited in the following fashion: Patch 1 is fed by a coaxial probe, while Patch 3 is terminated with a 50 R load, and the remaining two patches serve as parasitic elements.

The measured standing-wave ratio (vswr) of the antenna is shown by a solid line a Figure 10.18. It is evident that the antenna has a 21 vswr bandwidth in the range 1 .O3-1.22 GHz, which corresponds to an impedance bandwidth of 16%, despite the fact that the total area of the antenna is only 42% of that of a half-wave microstrip antenna operating at the same central frequency.

The FDTD grid consisted of 168 x 168 x 54 cells, with dimensions dx = dy = dz = 0.5mm. The coaxial feed and the termination line were modeled as an integral part of the radiating structure. The feedline was excited with a Gaussian pulse with a 3-dB cutoff frequency of 3 GHz. The input impedance of the antenna was calculated by monitoring the voltage V(t) and the current I( t ) at suitable locations inside the coaxial feedline. Fourier transformation of the time-domain data, followed by a calculation of the voltage-to-current ratio V ( f ) / I ( f ) in the frequency domain, yielded the variation of the input impedance over the desired frequency range. These impedance data were then translated to vswr of the antenna and are exhibited by the dotted line in Figure 10.13. The plot shows that the FDTD analysis predicts a somewhat larger bandwidth than that observed experimentally. This may be attributable to the fact that the feed dimensions were not modeled accurately in the FDTD analysis and the shorting pins were


1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 Frequency (GHz)

FIGURE 10.18 VSWR plots of the antenna.

FIGURE 10.19 Electric field distribution under the patch surface.

described by using rectangular rather than circular cross sections. From several experiments,it was observed that the impedance of the antenna was very sensitive to (a) the dimensions of the coaxial cable and (b) the locations of the cable as well as of the shorting pins.

The steady-state distribution of the electric field E, under the patch surface is shown in Figure 10.19. From the plot, it is evident that E, goes to zero on the shorting pins, and is maximum at the edges of the patches opposite to the locations of these pins. We can also observe from this plot that the parasitic

CONCLUSIONS 547

FIGURE 10.20 Current distribution under the patch surface.

patches are well-coupled to the radiating element. Figure 10.20 shows the current distribution on the patch surface.

10.8 CONCLUSIONS

In this chapter, a comprehensive analysis of complex patch antenna configurations has been carried out by using the FDTD method, which is a simple, accurate and versatile technique, well-suited for handling complex microstrip geometries. It can conveniently generate, with a single simulation, information on the various characteristics of the antennas, such as the input impedance and the radiation pattern over the desired frequency range. Also, the ability to visualize the field and current distributions on the patch can provide physical insight into the behavior of these antennas. It was observed that modeling of these intricate structures using the conventional FDTD method can be very computer-intensive, and several recently developed techniques were discussed to improve the computational efficiency of the FDTD algorithm while maintaining its accuracy. These techniques involve the following: choosing the proper type of feed excita- - - -

tion; employing appropriate absorbing boundary conditions; using a nonuniform orthogonal grid; applying extrapolation procedures to time signatures; and using distributed computation. It is possible to achieve significant savings in the computational time and memory requirements through a judicious application of these techniques. This has been demonstrated through the analysis of several complex geometries.

Comparative results between the FDTD method and experiments were presented for a two-layer stacked array and a compact broadband antenna to illustrate the fact that the FDTD approach enables us to compute the resonant


frequencies, the input impedance, and the radiation patterns of complex microstrip structures accurately. In this technique, the effects of a finite ground plane and losses in the dielectric can be conveniently incorporated into the analysis.

I t is hoped that the efficient modeling techniques outline in this work will substantially enhanced the scope of the FDTD method to the analysis of complex microstrip antennas.

REFERENCES

[I] D. M. Pozar and D. H. Schaubert, Microstrip Antennas: The Analysis and Design of Microstrip Antennas and Arrays. IEEE Press, Piscataway, NJ, 1995.

[2] J. R. James and P. S. Hall, Handbook of Microstrip Antennas, Peter Peregrinus, London, 1989.

[3] W. F. Richards, "Microstrip Antennas," Chapter 10, in Antenna Handbook, Y. T. Lo and S. W. Lee, eds., Van Nostrand Reinhold, New York, pp. 10.1-10.74,1988.

[4] W. F. Richards, Y. T. Lo, and D. D. Harrison, "An Improved Theory for Microstrip Antennas and Applications, " IEEE Trans. Antennas Propagat., Vol. 29, No. 1, pp. 38-46,1981.

[5] A. Benella and K. C. Gupta, "Multiport-Network Model and Transirnission Char- acteristics of Two-Port Rectangular Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. 36, No. 10, pp. 1337-1342, 1988.

[6] E. H. Newman and P. Tulyathan, "Analysis of Microstrip Antennas Using Moment Methods," IEEE Trans. Antennas Propagat., Vol. 29, No. 1, pp. 47-53,1981.

[7] R. C. Hall and J. R. Mosig, "The Analysis of Coaxially Fed Microstrip Antennas with Electrically Thick Substratesm," Electromagnetics, Vol. 9, pp. 367-384, 1989.

[8] D. Zheng and K. A. Michalski, "Coaxially Fed Microstrip Antennas of Arbitrary Shape," J. Electromagn. Waves. Appl., Vol. 5, No. 12, pp. 1033-1327,1991.

[9] J. R. Mosig and F. E. Gardiol, "General Integral Equation Formulation for Microstrip Antennas and Scatterers," Proc. Inst. Electr. Eng., Vol. 132, Part H, pp. 424-432,1985.

[lo] J. T. Aberle and D. M. Pozar, "Accurate and Versatile Solutions for Probe-Fed Microstrip Patch Antennas and Arrays," Electromagnetics, Vol. 11, No. 1, pp. 1-19, 1991.

[1 l] W. Chen, K. F. Lee, and R. Q. Lee, "Spectral Domain Full Wave Analysis of the Input Impedance of Coaxially-fed Rectangular Microstrip Antennas," J. Elec- tromagn. Waves Appl., Vol. 8, No. 2, pp. 248-273,1994.

[12] J. P. Damiano and A. Papiernik, "Survey of Analytical and Numerical Models for Probe-Fed Microstrip Antennas," IEE Proc. Microwave Antennas Propagat., Vol. 141, No. 1, 1994.

[I31 N. Kinayman and M. I. Aksun, "Efficient Use of Closed-Form Green's Functions for the Analysis of Planar Geometries with Vertical Connections." (to be published).

[I41 T. Ozdemir and J. L. Volakis, "Finite Element Analysis of Doubly Curved Confor- mal Antennas with Material Overlays," IEEE AP Symp., Vol. 1, pp. 134-137, 1996.

REFERENCES 549

[I51 J. C. Cheng, N. I. Dib, and L. P. B. Katehi, "Theoretical Modeling of Cavity-Backed Patch Antennas Using a Hybrid Technique," IEEE Trans. Antennas Propagat., Vol. 43, NO. 9, pp. 1003-1013,1995.

[16] U. Peke1 and R. Mittra, "A Hybrid MoM/FEM Technique for the Analysis of Cavity-Backed Patch Antennas Embedded in Large Conducting Surfaces." (to be published).

[I71 K. S. Yee, "Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equation in Isotropic Media," IEEE Trans. Antennas Propagat., Vol. 14, NO. 3, pp. 302-307,1966.

[18] A. Tdove, Computational Electromagnetics: The Finite-Difference Time-Domain Method, Artech House, Boston, pp. 92-105, 1995.

[19] A. Reineix and B. Jecko, "Analysis of Microstrip Patch Antennas Using the Finite Difference Time Domain Method," IEEE Trans. Antennas Propagat., Vol. 37, No. 11, pp. 1361-1369,1989.

[20] G. S. Hilton, C. J. Railton, and M. A. Beach, "Modeling Parasitically-Coupled Patch Antennas Using the Finite-Difference Time-Domain Technique," IEE Eighth Int. Con$ Antennas Propagat., Vol. 1, pp. 186-189,1993.

[21] B. Toland, J. Lin, B. Houshmand, and T. Itoh, "FDTD Analysis of an Active Antenna," IEEE Microwave Guided Wave Lett., Vol. 3, No. 11, 1993.

[22] K. Uehara and K. Kagoshima, "Rigorous Analysis of Microstrip Phased Array Antennas Using a New FDTD Method," Electroni. Lett., Vol. 30, No. 2, pp. 100-101, 1994.

[23] T. Kashiwa, T. Onishi and I. Fukai, "Analysis of Microstrip Antennas on a Curved Surface Using Conformal Grids FD-TD Method," IEEE Trans. Antennas Propagat., Vol. 42, No. 3, pp. 423-427,1994.

[24] C. Wu, K. L. Wu, Z. Bi, and J. Litva, "Modeling of Coaxial-Fed Microstrip Patch Antenna by Finite Difference Time Domain Method," Electron Lett., Vol. 27, No. 19, pp. 1691-1692,1991.

[25] C. Wu, K. L. Wu, Z. Q. Bi, and J. Litva, "Accurate Characterization of Planar Printed Antennas Using the Finite-differences Time-Domain Method," IEEE Trans. Antennas Propagat., Vol. 40, No. 5,1992.

[26] W. Chen, K. F. Lee, J. S. Dahele, and R. Q. Lee, "CAD Formula for the Resonant Frequency of a Rectangular Patch Antenna with Dielectric Cover," Proceedings of the Eighth International Conference on Antennas Propagation, IEE Conference Publication, 370, pp. 550-553,1993.

[27] E. Michielssen and D. Weile, "Electromagnatic System Design Using Genetic Algorithms," in Genetic Algorithms in Engineering and Computer Science, G. Winter, J. Periaux, M. Galan, and P. Cuesta, eds., John Wiley & Sons, New York, pp. 354-370,1995.

[28] S. Chebolu, J. Svigeli, and R. Mittra, "Efficient Modeling of Microstrip Antennas Using the Finite Difference Time Domain Method," Proc. Antenna Appl. Symposium, Sec. 111, pp. 1-22, 1994.

[29] S. Chebolu, R. Mittra and W. D. Becker, "The Analysis of Microwave Antennas Using the FDTD Method," Microwave, Vol. 39, No. 1, pp. 134-150, 1996.

[30] S. Chebolu, S. Dey, J. Svigelj, and R. Mittra, "Accurate Characterization of Complex Microstrip Antenna Configurations Using the FDTD Method." (to be published).


[31] S. S. Zivanovic, K. S. Yee, and K. K. Mei, "A Subgridding Method for the Time- Domain Finite-Difference Method to Solve Maxwell's Equation, " IEEE Trans. Microwave Theory Tech., Vol. 39, No. 3, pp. 471-479,1991.

[32] K. S. Kunz and R. L. Luebbers, "A Technique for Increasing the Resolution of Finite-Difference Solution of the Maxwell Equation," IEEE Trans. Electromagn. Compat., Vol. 23, pp. 1320-1323, 1981.

1331 K. Mahadevan, R. Mittra, and P. M. Vaidya, "Use of Whitney's Edge and Face Elements for Efficient Finite Element Time Domain Solution of Maxwell's Equa- tion," J. Electromagnetic Wave and Applications, Vol. 8, No. 9/10, pp. 1173-1191, 1994.

[34] K. S. Yee and J. S. Chen, "Conformal Hybrid Finite Difference Time Domain and Finite Volume Time Domain Technique," IEEE Trans. Antennas Propagat., Vol. 42, No. 10, pp. 1450-1454,1994.

[35] R. Holland, "Finite Differences Solution of Maxwell's Equations in Generalized Nonorthogonal Coordinates," IEEE Trans. Nucl. Sci., Vol. 30, No. 6, pp. 4589-4591, 1983.

[36] J. F. Lee, R. Palandech, and R. Mittra, "Modeling three-Dimensional Discontinui- ties in Waveguides Using Nonorthogonal FDTD Algorithm," IEEE Trans. Micro- wave Theory Tech., Vol. 40, No. 2, pp. 346352,1992.

[37] J. Svigelj, "Efficient Solution of Maxwell's Equations Using the Nonuniform Or- thogonal Finite Difference Time Domain Method," Ph.D. dissertation, University of Illinois at Urbana-Champaign, 1995.

[38] J. Svigelj and R. Mittra, "Grid dispersion error using the nonuniform orthogonal finite difference time domain method," Microwave and Opt. Tech. Lett., Vol. 10, NO. 4, pp. 199-201,1995.

[39] C. J. Railton, I. J. Craddock, and J. B. Schneider, "Improved Locally distorted CPFDTD Algorithm with Provable Stability," Electronics Lett., Vol. 31, pp. 1585- 1586,1995.

[40] S. Dey et al., "A Compact Microstrip Antenna for CP," in IEEE AP Symposium, 1995.

[41] W. L. KO and R. Mittra, "A Combination of FD-TD and Prony's Methods for Analyzing Microwave Integrated Circuits," IEEE Trans. Microwave Theory Tech., Vol. MlT-39, NO. 12, pp. 2176-2181, 1991.

[42] J. Litva, C. Wu, K. L. Wu, and J. Chen, "Some Considerations for Using the Finite Difference Time Domain Technique to Analyze Microwave Integrated Circuits," IEEE Microwave Guided Wave Lett., pp. 438-440, 1993.

[43] V. Jandhyala, E. Michielssen, and R. Mittra, "FDTD Signal Extrapolation Using the Forward-Backward Autoregressive Model," IEEE Microwave and Guided Wave Lett., Vol. 4, No. 6, pp. 163-165, 1994.

1441 T. K. Sarkar and 0. Pereira, "Using the Matrix Pencil Method to Estimate the Parameters of a Sum of Complex Exponentials," IEEE Antenna Propagat. Mag., Vol. 37, NO. 1, pp. 48-55, 1995.

[45] V. Betz and R. Mittra, "A Boundary Condition to Absorb Both Propagating and Evanescent Waves in a Finite-Difference Time-Domain Simulation," IEEE Micro- wave and Guided Wave Lett., Vol. 3, No. 6, pp. 182-184,1993.

[46] G. Mur, "Absorbing Boundary Conditions for the Finite-Difference Approximation

REFERENCES 551

of the Time-Domaln Electromagnetic Field Equations," IEEE Trans. Electromagn. Compat., Vol. 23, pp. 1073-1077,1981.

[473 J. P. Berenger, "A Perfectly Matched Layer for the Absorption of Electromagnetic Waves," J . Computational Phys., Vol. 11, pp. 185-200,1994.

[48] J. Veihl and R. Mittra, "An Efficient Implementation of Berenger's Perfectly Matched Layer for FDTD Mesh Truncation," IEEE Microwave Guided Wave Lett., Vol. 6, No. 2, 1996.

[49] K. S. Yee, D. Ingham, and K. Shlager, "Time-Domain Extrapolation to the Far Field Based on FDTD Calculations," IEEE Trans. Antennas Propagat., Vol. 39, NO. 3, pp. 410-413,1991.

[50] R. J. Luebbers, K. S. Kunz, M. Schneider, and F. Hunsberger, "A Finite-Difference Tie-Domain Near Zone to Far Zone Transformation," IEEE Trans. Antenms Propagat., Vol. 39, No. 4, pp. 429-433,.1991.

[51] I. J. Craddock, P. G. Turner, and C. J. Railton, "Reducing the Computational Overhead of the Near-Field Transform Through System Identification," Electron. Lett., Vol. 30, No. 19, pp. 1609-1610, 1994.

[52] K. F. Lee, S. Chebolu, W. Chen, and R. Q. Lee, "On the Role of Substrate Loss Tangent in the Cavity Model Theory of Microstrip Patch Antennas," IEEE Trans. Antennas Propagat., Vol. 42, No. 1, pp. 110-1 12, 1994.

[53] M. D. Deshpande and M. C. Bruley, "Input Impedance of Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. 30, No. 4, pp. 645-656,1982.

[54] R. Yang, R. Mittra, and M. Itoh, "A New Omnidirectional CP Patch Antenna," IEEE AP Symposium, Vol. 3, pp. 1848-1851,1994.

[55] S.Chebolu, S. Dey, R. Mittra, and M. Itoh, "A Dual Band Stacked Microstrip Array for Mobile Satellite Applications," IEEE Symp., June 1995.

[56] S. Dey and R. Mittra, "A Compact Broadband Microstrip Antenna," Microwave Opt. Tech. Lett., Vol. 11, No. 6, pp. 295-297, 1996.

CHAPTER ELEVEN

Analysis of Dielectric Resonator Antennas

K. M. LUK, K. W. LEUNG, and S. M. SHUM

11 .I INTRODUCTION

The use of low-loss dielectric resonators (DRs) as radiating elements was proposed by Long et al. [I] in 1983. In contrast to the applications in designing miniature microwave filters and oscillators in which higher relative permittivity materials (E, z 25-100) are used, DR antennas are usually fabricated out of lower relative permittivity blocks (E, I 10) in order to have lower Q factors. Initially, the major impetus to investigate the characteristics of DR antennas is attributed to their inherent advantage of no conductor loss. As the conductor loss is increased with the square root of the operating frequency, conventional metallic antennas such as the microstrip antennas may have very low radiation efficiencies when operating at higher frequencies. The class of DR antennas has been designated to hive potkntial applications in millimeter-wave circuits and systems.

A substantial amount of research effort has been devoted to the study of DR antennas in the last decade. It has been demonstrated that dielectric blocks of cylindrical [I], rectangular parallelepiped [2], hemispherical [3], half-split cylindrical [4], and spherical cap [5] shapes can be designed to radiate efficiently through proper choices of feed location and feed dimensions. Different types of feeding structures such as the coaxial probe [I], microstrip line [6], microstrip- fed aperture [7], and coplanar waveguide [8] have been proposed. Bandwidth enhancement techniques have also been studied. By stacking a parasitic DR on top of the fed DR, a cylindrical DR antenna with more than 25% bandwidth for

Advances in Microstrip and Printed Antennas, Edited by Kai Fong Lee and Wei Chen. ISBN 0-471-04421-0 0 1997 John Wiley & Sons, Inc

554 ANALYSIS OF DIELECTRIC RESONATOR ANTENNAS

SWR < 2 has been achieved [9]. An improvement in bandwidth for a CPW- aperture-coupled DR antenna has also been reported, using a similar stacked configuration [lo]. In these two cases, attention has been paid on the broadside HEM,,, mode. For an annular ring dielectric resonator antenna operated at the endfire TM,,, mode, it has been shown that the bandwidth can be improved by introducing an airgap between the DR and the ground plane [ll]. Similarly, bandwidth enhancement can also been obtained for a hemispherical DR antenna with a hollow air gap [12] or with a dielectric coating 131. In reference [14], it has been demonstrated that the introduction of air gaps between the DRs and between the driven DR and the ground plane of a stacked annular ring DR antenna operated at the TM,,, mode can increase the impedance bandwidth significantly. DR antennas with circular polarization have been reported [15- 171. For the design of DR antenna array, it has been observed that the mutual impedance between two hemispherical DR antennas may be significant and should be taken into account [18]. Some successful finite DR arrays have been presented recently [19-211. In addition to their potential applications in the millimeter-wave range, DR antennas with high relative permittivity > 80) have been proposed to be used as low-profile antennas in the lower microwave frequency range (z 1-10GHz) [22,23].

DR antennas are easy to fabricate but difficult to be analyzedrigorously due to the existence of edge-shaped boundaries. For the analysis of the cylindrical DR antennas, one used the perfect magnetic wall approximation to estimate the resonant frequencies of the antennas. More than 20% discrepancy between theory and measurement was found [24]. Van Blade1 [25] employed the perturbation theory to find explicit expressions for various antenna parameters as functions of the dielectric constant of the material used. The method is based on asymptotic expansions of the fields in terns of the inverse powers of the square root of the dielectric constant. This approach is accurate only for very high dielectric constant.

Another method, proposed by Tsuji et al. [26,27], expands the interior and exterior fields into series of spherical harmonics. The tangential electric and magnetic fields are matched at the DR's surface in a least-square sense. By setting the derivative of the least-square error with respect to each modal coefficient to zero, a set of homogeneous algebraic equations for the unknown coefficients is obtained. The complex resonant frequencies of the antenna are then found by searching the zeros of the determinant of the system of equations. The input impedance of the antenna, however, was not considered.

Using the equivalence principle, two coupled integral equations for the equivalent surface electric and magnetic current densities were derived [28,29], which were solved by the method of moments. From the surface current densities, the resonant frequencies, Q factors, and field components inside and outside the dielectric body can be computed. This method has also been extended to the study of input impedance recently [30]. Solving the coupled integral equations, however, is computationally expensive and time inefficient.

ANALYSIS OF APERTURE-COUPLED HEMISPHERICAL DR ANTENNA 555

The input impedance versus frequency, resonant frequencies, and radiation patterns of a hemispherical DR antenna have been investigated [31-331. For the spherical geometry, exact closed-form expressions for the Green's functions of point currents inside the dielectric body can be derived using the modal expansion technique. The feed current and hence the input impedance of the antenna can then be found by the moment method with the Galerkin's procedure. This method is computationally very efficient. Similar results have been obtained independently by Kishk et al. [34].

In this chapter, we present the detail theoretical and experimental results on the study of DR antennas obtained recently by our group in the City University of Hong Kong. In Section 11.2, the input impedance and radiation patterns of an aperture-coupled hemispherical DR antenna excited at the broadside TE,,, mode are studied by the method of moment with the use of an exact Green's function for the dielectric sphere. The theoretical results are confirmed by experiments. DRs of cylindrical shape are of practical importance. They are much more easily available from the commercial market. More importantly, we have the freedom to adjust the ratio between the diameter and the height of the DR in order to optimize the performance of a DR antenna such as gain and cross- polarization level. However, it is difficult to derive an exact Green's function for the dielectric cylinder. Alternatively, we have considered the use of the finite- difference time-domain method (FDTD) to study the cylindrical DR antennas [35]. The method has the potential to study DR antennas of complicated geometries and has attracted a lot of research interest in solving various problems. In Section 11.3, we present our recent results on the investigation of the input impedance and radiation patterns of a probe-fed cylindrical DR antenna excited at the broadside HEM,,, mode by the FDTD method.

11.2 ANALYSIS O F APERTURE-COUPLED HEMISPHERICAL DR ANTENNA

In this part, we will study the input impedance and the radiation patterns of the aperture-coupled hemispherical DR antenna, which is excited at the fundamental broadside TE, , , mode [33]. The aperture-coupled source has several advantages over the probe-fed version [32] such as the feasibility of integration with MMICs and the avoidance of large probe self-reactances at millimeter-wave frequencies. Moreover, drilling a hole for the probe penetration is now not required. While the probe-fed DR antenna uses electric-source excitation, the aperture-coupled version utilizes the magnetic one. Due to the duality of the sources, the position of the source to excite a particular mode is different in the two configurations. For example, in the aperture-coupled case, excitation of the TE,, , mode is strongest when the slot is fed at the center of the DR. This is in contrast to the probe-fed case where the probe should have a certain displacement in order to excite the TE,, , mode properly [32]. Moreover, while a center-fed probe can only excite TM modes [32], a slot aligned with a diameter of the DR can excite TE modes only.


I I

FIGURE 11.1 Geometry of an aperture-coupled hemispherical DR antenna with an I

infinitely long microstripline for the problem formulation. i The analysis consists of two parts: the DR antenna above the ground plane

and the microstripline below the groupd plane. In the former, the mode matching 1 method is employed to determine the exact magnetic field Green's function inside the DR due to an equivalent magnetic current in the slot. Analysis of the latter is based on the reciprocity method, which was used by Pozar [36] to solve

I 1

the problem of the aperture-coupled microstrip antenna.

11.2.1 Problem Formulation

Consider the configuration shown in Figure 11.1. The grounded dielectric slab has dielectric constant E, and height d, whereas the microstrip feedline has width Wf and is assumed to be infinitely long and to propagate a quasi-transverse electromagnetic (TEM) mode. The inset shows the dimensions of the slot, which has length L and width W. To begin with, the equivalence pfinciple is used to replace the aperture field by an equivalent magnetic current M y = My$. Then by enforcing the continuity of the magnetic field Hy across the aperture, one obtains [36]

where H; is the magnetic field inside the DR antenna (z < 0 ) due to My, H; is the magnetic field inside the substrate ( z >0) due to My, H; is the propagating


magnetic field inside the substrate (z > 0 ) due to the microstripline, and

is the voltage reflection coefficient. In Eq. (1 1.2), So and Z , are the surface of the slot and the characteristic impedance of the microstripline, respectively.

Define two Green's function G g y and GEM as the 9-directed magnetic field at 7 ( x , y, 0 ) inside an isolated spherical DR antenna (by image theory) and that inside the grounded dielectric slab, respectively. Both of them are due to a unit magnetic current My@', y', 0) . Equation ( 1 1.1) then becomes

J Js,, Gz , (x , y; x', y') [- 2 M,(x',y')] dS' - G E M ( ~ , y ; ~ ' , ~ ' ) M&',yl)dS' J J,

Note that in the first integral of Eq. (1 1.3), a factor of - 2 has been added to the magnetic current My. The factor of two accounts for the presence of the ground plane, whereas the minus sign ensures that the tangential electric field is equal on each side of the aperture region. From Eqs. (1 1.2) and (1 1.3), the unknown magnetic current M y and reflection coefficient R can be solved. After the reflection coefficient R is found, the equivalent series impedance Z , of the slot can be calculated 1361 from

In actual applications, the slot is usually terminated by an open-circuited stub of length L, x LJ4. The equivalent circuit of the antenna configuration is shown in Figure 11.2, from which the input impedance at the reference plane (x = 0) is readily evaluated:

Z , = Z , - jZ , cot PL, (11.5)

In the next section, the unknowns R and M y are solved using the method of moments.

1 1.2.2 Moment Method Solution

Using the moment method, the unknown magnetic current is first expanded in a set of basis functions f,,(x, y):


I , Open-circuited I I

! stub

FIGURE 11.2 Equivalent circuit of the aperture-coupled hemispherical DR antenna with an open-circuited stub L,.

where Vn's are unknowns to be determined. By choosing piecewise sinusoidal (PWS) modes for My, one has

where

in which h = L/(N + I), y, = - L / 2 + nh, and k , = ko ,,/- are the PWS mode half-length, the center point of the nth expansion mode, and the effective wavenumber of the PWS mode, respectively. In Eq. (11.8), we have assumed that the voltage across the slot is constant, which is a valid assumption for a slender slot (k , W<< 1, W<< L).

Substitution of Eq. (1 1.6) into Eq. (11.3) gives


Using the Galerkin's procedure, the following matrix equation is obtained:

where

On the other hand, insertion of Eq. (11.6) into Eq. (11.2) gives

where the superscript t denotes the transpose of a matrix. From Eq. (11.11) and Eq. (11.15), the unknown Vn7s can be solved via the matrix equation

The evaluations of Y", and Av, are easily performed in the spectral domain [36]:

where

" HM - j (k ,cosk ld+jk2~ , s ink ld) (~ , ,k~-k: ) j k ~ k t ( e r s - 1 ) Gyy (k, , ky )=- + ' 1 Tm

Te T ~ I (11.19a) 1

560 ANALYSIS OF DIELECTRIC RESONATOR ANTENNAS ANALYSIS OF APERTURE-COUPLED HEMISPHERICAL DR ANTENNA 561

Fp(ky) = [ ~ m I . ( y ) e - j k ~ y d y = 2k,(cos k , h - cos k, h) (k: - k:) sin k , h

sin (k , W,/2) Fu(ky) = s-mm /,,(y)e- j k y y d y =

k, W,/2

T, = kl cos k l d + j k , sin k,d

in which ko = w 6, and q , = a, and Pf are the vacuum wavenumber, the vacuum wave impedance, and the propagation constant of the microstripline fields, respectively.

It should be noted that special care must _be taken in calculating Yk, due to surface wave poles of the Green's function GEM. The numerical technique for such integration was discussed by Pozar [37].

For the evaluation of the DR admittance Y", as seen by the slot, the Green's function G$ is required which will be derived in the next section.

11.2.3 Derivation of DR Antenna Green's Function G$

In this section, the Green's function G z y denoting a 9-directed magnetic field Hy inside the DR antenna due to a 9-directed magnetic current M y is derived rigorously. Note that the computation of [V,] as given by Eq. (11.16) is coordinate-independent; hence for convenience, the geometry of the DR antenna configuration is redefined in Figure 11.3, where the hemispherical DR antenna of radius a and of dielectric constant E,, is excited by the slot having offsets xd and yd from the y axis and the x axis, respectively. To begin with, image theory is employed so that an equivalent configuration which is a magnetic current radiating in a spherical DR antenna is obtained. The $-directed magnetic current M y o_n the plane z = 0 is then decomposed into an +-directed component M, and a 4- directed component M,. The potential functions due to the current components are first found, and from them the various field components are found easily [38, p. 2691. It should be mentioned that M , can excite T E to r modes only, whereas M can excite both TE to r and TM to r modes. Therefore one potential function

$ G,, alone is adequate to represent all possible fields excited by M,, but two potential functions G;, and G& are required for the case of M4. The Green's

Microstrip line t

line plane "rs

FIGURE 11.3 The redefined geometry of the antenna configuration: (a) Top view, (b) side view.

function G;, denotes the electric potential due to an Pdirected magnetic point current, while the Green's functions G;, and G& denote the electric potential and the magnetic potential due to a &directed one, respectively. In the following presentation, subscripts p and h are used to denote the particular solution and the homogeneous solution, respectively.

11.2.3.1 Green's Functions Gz+ and G$

(a) Particular solutions

m n

GZ+ = x A,,P: (cos B)ejm6@',(kr') yl,(kr) n=O m= - n

where

and O;(x) = (d/dx)@,(x).


(b) Homogeneous solutions

m n r l a

(1 1 .24)

G A , ~ - f f p; (cos 8) +-jn (kr), r l a M + - n = O m = - n f i 2 ( k 0 r ) r > a (1 1.25)

where the constants k,, k, and E denote the vacuum wave number, the dielectric wave number, and the DR's dielectric permittivity, respectively. P,"(x) is the assocjated Legendre function of the first kind with order m and degree n, and &(x) and Hi2)(x) are, respectively, the spherical Bessel function of the first kind and the spherical Hankel function of the second kind, both of order n and of Schelkunoff type. The unknown modal coefficients A,, and D,, are determined from the boundary conditions at the source point 7 = P' (E,, H,, and H, are continuous while E, is discontinuous by a surface magnetic current M,,), and other modal coefficients B,, Cnm, Enm, and F,,,,, at the DR surface r = a (E,, E,, He, and H,, are all continuous). Following the steps in reference [32], the coefficients are obtained and the results are shown as below (r 5 a):

1 " " d GAP - -

M+ - r, 1 1 dm P: (COS 0') P: (COS 8) cos m (4 - 4') an (kr') Yn (kr) n = 1 m = o

(1 1.27)

1 " " G Z =- Z 1 bn,,,P: (cos 0')P: (cos 0) sinm(4 - 4')4(krr) jn(kr)

sine

(11.28)

(1 1.29) where

I ANALYSIS OF APERTURE-COUPLED HEMISPHERICAL DR ANTENNA 563

1 for m > 0 for m = 0

(11.36)

I

Note that in Eqs. (11.34) and (11.35), ATE = 0 and ATM = 0 are, respectively, the characteristic equations for TE and TM modes as given in reference [39]. Finally

1 the Green's functions GG, and G*+ are given by

11.2.3.2 Green's Function GG. Following the procedure given in reference 1381 (pp. 267-269), the following differential equation for the particular solution G 2 of the Green's function G z , can be derived:

~ 2 ; - - E ~ ( r - r ' ) s ( e - f l s ( 4 - 4 ~ ) (V +k2)---.

r r r2 sin 8 (11.39)

Equation (1 1.39) was solved and the result is given by

where

By matching the boundary conditions at the spherical surface of the DR, the homogeneous solution is obtained as follows:

- .. G z = 1 z h,,, P; (cos 0') P: (cos 8) cos m(4 - 4') Jn(krl) jn ( k ) (1 1.42)

rI2 n = O m = O

564 ANALYSIS OF DIELECTRIC RESONATOR ANTENNAS I ANALYSIS OF APERTURE-COUPLED HEMISPHERICAL DR ANTENNA 565

where

k hnm = 3 [dp)(ka) fii2)'(koa) - - ~ ~ ) ' ( k a ) gP)(k0 a)] (11.43)

k 0

Finally the Green's function Gz, is given by

11.2.3.3 Green's Function G 2 . Define two dyadic Green's functions:

where G$& = r, 4 and p = r, 6,4) is the magnetic field Green's function derived from Gz,, G&, and Gf& [38, p. 2691. The total magnetic field excited by M y is then given by

Now extract the $-directed magnetic field Hy from Eq. (1 1.47) and compare it with the following equation:

the desired Green's function Gz, is obtained (r I a and 6' = 8' = n/2). It was found that the particular solution G, of the Green's function G$ is

a slowly convergent series of Hankel functions. However, Hankel functions of high order have such a large amplitude that they are difficult to handle numerically, and very often the technique of prescaling is required. To avoid these difficulties, recall that G, simply represents a j-directed magnetic field excited by a j-directed magnetic point current in an unbounded dielectric medium, which has been well-studied in the problem of the cylindrical dipole. Realizing this fact, the Green's function G2? can be written as (z = z' = 0)

G~=G,+G,

where

- 1 sin 4' sin 4 " z b,n(n + 1)(2n + 1) P,(cos(& - 4'))j,,(kr1)j,,(kr)

1 cos 4'sin 4 " a C bJ2n + P,,(cos(+ - $))J^:(kr1)jn(kr) 4nwpo r2r' ,,=, 8 4

1 sin $ cos+ " --. a z bJ2n + 1) --; P"(cos(4 - +'))j,,(kr')R (kr) 4nwpo rrt2 ,,=, 8 4

k C O S & C O S ~ ~ 2n+1 a2 --. n o rrl ,,?I b n n ( n + l ) ) ~

P,(cos(4 - $)) Tb(krf) (kr)

I and

e,, = - Hrnf(ka) f iy(koa) - LBF (ka) B!,~)' (koa) A?' - I [ - ko ] (11.53)

In Eq. (11.50), R = ,/(x - xi)' + 0, - y')' is the distance between the field point and the source point on the ground plane. Note that G, is singular as 7 +7. On the other hand, from the physical argument above, a mathematical identity can be established:

1 sin$ sin 4 " =-. x n(n + 1) (2n + 1) P,(cos($ - 4')) cPn(krl) Y, (kr) 4nwp,k r2rf2 ,,=,

1 cos$sin4 " --. a C (2n + I)--; P,(cos(4 - $))QI; (kr') Y,(kr) 4nop0 r2r' ,,=, a 4

1 sin$ cos+ " --. a (2n + 1) - P,(cos(4 - $))a, (kr') Y (kr)

4nop0 rr" ,,=, a 4 WE cos ~ ' C O S lj " (b+L) P: (cos(4 - 4')) On (krl) 'Y,, (kr) --.

4nk rr' ,,=, n(n + 1)

k C O S ~ ' C O S + ~ (2n+l) a2 --. C-- P,, (cos(r#~ - &)) cP; (kr') Y ; (kr) 4nwp0 rr' , ,=,n(n+l)a4a4'


In deriving Eqs. (1 1.51) and (1 1.54), the double summation is reduced to the single summation by using the addition theorem for Legendre polynomials:

" 2 (n-m)! PJcos c) = c -.- P: (cos 0) P: (cos 8') cos m(4 - 4') (1 1.55)

m = o Am (n + M Y

where A, has been defined in Eq. (1 1.36).

11.2.4 Evaluation of Y&

To evaluate Y:,, one may write from Eqs. (11.12) and (11.49) that

where

The evaluation of Y: can be done in a straightforward manner because G, is a smooth and slowly varying function. For Y;,, however, special consideration is needed due to the singularity of G, occurring at F+T1-'. To tackle this problem, first note that Y;, simply represents the self- and mutual admittances in an unbounded dielectric medium. Since such quantities are position independent, we can treat the slot as if it were located along they axis. Moreover, for a slender slot, one can compute the slot admittance using the concept of equivalent radius a, [40] so that the theory developed in the cylindrical dipole can be utilized. The equivalent radius a, of the slot is given by

In the "Richmond form" [41,42], one obtains

where re = J(m and q = G. Note that in Eq. (1 1.60) the expression


in the square brackets is the self- and mutual impedances of an electric dipole of length L and radius a,, which can be computed i n a straightforward manner.

1 1 1.2.5 Single-Cavity-Mode Approximation This section will investigate the use of single-mode approximation of the Green's

1 function G z for the broadside TE,, , mode [43] so as to simplify the expression of the Green's function. The results will be compared with those using the exact solution, and the limitations of the single-mode theory will be discussed. The

1 single-mode Green's function for the broadside TE, ,, mode is given as follows (r a, r' I a and 0 = 8' = 42):

I 3b sin4sin@cos($-@)- 1.

r2J2 . Jl (kr') 2, (kr)

27cwp0 k

3b1 sin 4 cos 4' sin(4 - 4') --. r2r'

.fi (kr) jl (kr) 4 n w o

3 b sin @ cos 4 sin(4 - 4') - +A. . J1 (kr') J^; (kr)

~ Z W F O rrr2 3 kb, cos @ cos 4 cos(4 - 4') - --. .~;(kr')&(kr) (11.61)

8 n w o rr'

To further simplify the problem, the magnetic current of the slot is modeled by a single PWS mode:

where Vo is the unknown amplitude of the aperture field. With this approximation, the reflection coefficient in Eq. (11.15) is now simply reduced to

where r r r r

Y a = -2JJsoJJso My(x, y) GT?, (x, y; x', y') MY(x1, y') dS'dS (1 1.64)


and all other symbols have been defined in Ea. (11.19). Once the reflection - , , I

coefficient R is obtained, the input impedance at the reference plane is obtained I using Eqs. (1 1.4) and (1 1.5).

11 2.6 Single-Cavity-Mode Radiation Field of the DR Antenna

Using the single-mode approximation, the Green's functions G2y and G$ for the I

radiation fields E, and E4 are given by [44]

- 3 sin @ sin(4 - #) GZy7->F") =-. 4n k, ATE rrr2 .jl (kr1)fiy)(k0i-)

3 k cos 4' cos($ - 4') + ------. 8nkoATE rr ' .?,(kr') fi\2)(kor)

- 3 sin 4' cos 0 cos(4 - #) G$F,F1) =-. 4n k, ATE rrf2 .fl (kr')@)(k,r)

3 k cos 4' cos 0 sin($ - 4') --. 8nkoATE rr' .J^; (kr') a(:)(k,,r) (11.68)

From the Green's functions, the electric field Ep (/I = 0,4) can be easily calculated:

In the analysis of the back-lobe radiation from the grounded dielectric slab, the radiation fields are evaluated using the stationary phase method [36,44]. The effect of the feedline is often omitted to simplify the problem [36,44].

11.2.7 Results and Discussions

For Figures 11.4-11.7, the rigorous modal solution [Eq. (1 1.49)] and N = 3 in the MOM are used in the calculations. Figure 11.4 shows the calculated and measurednormalized input impedance for L = 11.0,13.5,16.3 mm. The slots were fed at the center of the DR antenna. Reasonably good agreement between theory and experiment is observed. As seen from the figure, for L= 13.5mm the input impedance of the antenna configuration matches the characteristic impedance (50Q) of the microstripline, confirming the feasibility of the antenna configuration in practical applications. The measured resonant frequency is 3.62 GHz, which is very close to the calculated value of 3.56 GHz (1.65% error). Moreover, it is consistent with the predicted value of 3.68GHz obtained by solving the characteristic equation ATE = 0. The deviation between the calculated resonant frequency (3.65 GHz) and the predicted value (3.68 GHz)is caused by the effects of the slot and of the open-circuited stub. With reference to the figure, the coupling


- Theory 0 3.30 GHz

V 3.56 GHz (Theory) .-.-.-. Experiment 0 3.62 GHz (Exp.)

FIGURE 11.4 Computed and measured normalized input impedance at the reference plane for L=11.0, 13.5, and 16.3mm: a = 12.5mm, ~,=9.5, xd=O.Omm, yd=O.Omm, W = 0.9 mm. W, = 1.45 mm, d = 0.635 mm, E,, = 2.96, L, = 13.6 mm. (From reference [33], copyright 0.1965 IEEE.)

factor (defined as the radius of the impedance circle [45]) increases with the slot length. This suggests that one can achieve impedance matching by simply varying theslot length.

The calculated and measured input impedance for different slot displacement x i s are shown in Figure 11.5. Reasonably good agreements are found. It is interesting to note that the larger the offset x, is, the weaker the TE,,, mode is excited. This is in contrast to the probe-fed case, where a certain displacement from the center of the DR is required to excite the mode properly. The difference in the excitation locations is expected by considering the duality property of the electric and magnetic sources.

The input impedance for different y i s is shown in Figure 11.6. Again, the larger the slot offset y, is, the weaker the coupling between the DR antenna and the slot results. From Figures 11.5 and 11.6, it is found that in order to have the strongest TE,, , mode excitation, one should put the slot a t the center of the DR. Moreover, in addition to the slot length, the slot offsets x, and y, are also parameters to help - achieve the impedance matching.

Figure 11.7 shows the calculated input impedance for different slot width W ' s . With reference to the figure, a wider slot width results in a larger coupling factor (larger impedance radius). This is because more energy can be coupled to the DR intenna from the slot for a larger slot area.

.--.--. 3.56 G H z (Theory) Experiment 3.62 G H z (Exp.)

FIGURE 11.5 Computed and measured normalized input impedance at the reference plane for xd=O.O, 5.0, and 10.5mm: a=12.5mm, ~ ,=9.5 , L=13.5mm, yd=O.Omm, W= 1.3mm, Wf = 1.45mm, d = 0.635mm, E, = 2.96,L, = 13.6mm. (From reference 1333, copyright o 1995 IEEE.)

. . . -. . 3.56 G H z (Theory) Experiment

3.62 G H z (Exp.)

FIGURE 11.6 Computed and measured normalized input impedance at the reference plane for yd=O.O, 3.5, and 5.5mm: a=12.5mm, &,=9.5, L=13.5mm, x,=O.Omm, W= 1.3 mm, Wf = 1.45mm, d = 0.635mm, E, = 2.96, L, = 13.6mm. (From reference [33], copyright o 1995 IEEE.)


0 3.30 G H z

v 3.56 G H z

A 3.90 GHz

FIGURE 11.7 Computed normalized input impedance at the reference plane for W=0.5, 1.3, and 2.0mm: a = 12.5mm, ~,,=9.5, L = 13.5mm, xd=O.Omm, yd=O.Omm, Wf= 1.45mm,d=0.635mm,~,=2.96,L,=I3.6mm.

FIGURE 11.8 Comparison of results using the rigorous solution and the single-mode theory for xd=O.O, 0.5, and 10.5mm: a = 12.5mm, &,=9.5, L=13.5mm, yd=O.Omm, W= 1.3mm, Wf= 1.45mm,d=0.635mm,~,,=2.96,L,=13.6mm.

FDTD ANALYSIS OF PROBE-FED CYLINDRICAL DR ANTENNA 573

Figure 11.8 compares the single-cavity-mode results with the rigorous-solution results for different slot offset xis. With reference to the figure, the single- cavity-mode theory agrees well with the rigorous solution for x, = 0. This is because when x, = 0, all TM modes and some TE modes (e.g., TE,, , mode [46,47]) are eliminated. Moreover, for this particular slot position, the TE, , , mode is strongly excited and the influence of the remaining higher order modes becomes relatively small. When x, is increased to 5.0mm, the single-mode theory becomes less accurate. Nevertheless, since the TE,, , mode is moderately excited at this slot position, the single-mode theory is still a good approximation at frequencies around the resonance of the mode. However, when x, is further increased to 10.5mm, the single-mode solution is no longer a good approximation to the rigorous solution. In this case, the TE, , , mode cannot be excited properly and so the fields inside the DR are strongly influenced by the neglected higher-order modes, causing a relatively large discrepancy between the two results.

Figure 11.9 shows the calculated and measured results of the H plane (Figure 11 9a) and the E plane (Figure 11.9b) radiation field patterns for the broadside TE,,, mode. With reference to the figure, the calculated radiated fields of the DR antenna (the upper half-space) agree reasonably well with the measured ones. For the lower half-plane, however, a relatively large discrepancy between theory and experiment is found due to the feedline diffraction which has been neglected in the theory.

1 1.2.8 Summary

The input impedance and the radiation field patterns of an aperture-coupled hemispherical DR antenna, excited at the broadside TE,,, mode, has been studied theoretically and experimentally. The effects of the slot length L, the slot offsets x, and y,, and the slot width W on the input impedance have been examined. It has been shown that impedance matching can be achieved by varying the parameters.

Both the rigorous modal solution and the single-cavity-mode solution have been considered and compared. It has been found that the single-cavity mode is very accurate when the slot is located at the center of the DR antenna. However, if one wants to predict the result accurately at an arbitrary slot position, the rigorous modal solution is preferred.

11.3 F D T D ANALYSIS O F PROBE-FED CYLINDRICAL D R ANTENNA

In this section, the input impedance and radiation characteristics of the probe-fed cylindrical DR antenna are analyzed using the finite-difference time-domain (FDTD) method. A DR excited by penetrating a coaxial probe inside its body is the original antenna configuration proposed by S. A. Long in 1983 [I]. The geometry of the DR antenna is shown in Figure 11.10. Only recently, this type of antenna was analyzed rigorously by a method of moment (MOM) procedure

574 ANALYSIS OF DIELECTRIC RESONATOR ANTENNAS FDTD ANALYSIS OF PROBE-FED CYLINDRICAL DR ANTENNA 575

Coax~al probe

Ground plane a

2ra Ground plane

FIGURE 11.1 0 Geometry of probe-fed cylindrical dielectric resonator antenna.

based on the surface integral equation formulation for the bodies of revolution coupled to arbitrary objects [30]. However, when this method is applied to analyze more complex configurations (e.g., stacked cylindrical DR antenna or rectangular DR antenna), the process may become very complicated and time- consuming.

Application of the FDTD method to antenna problems has been reported recently [48-501. The present authors have analyzed a stacked DR antenna using similar technique [14]. Two-dimensional cylindrical coordinates were used because the antennas are excited by an axisymmetric coaxial probe and the fields are &independent. But feeding the DR this way can only produce endfire radiation, and the simplified model cannot handle &dependent modes.

Here, the 3-D FDTD method in rectangular coordinates is applied for I

analyzing a probe-fed DR antenna which is operating at HEM,,, mode. This is the preferred mode because it produces a broadside radiation direction [I]. The characteristics of the input impedance and radiation patterns of the DR antenna will be investigated. Compared to the MOM method used in reference [30], the FDTD method is capable of modeling more complicated structures with a relatively simple procedure. The major drawback of the FDTD method is the relatively high requirements of both computational and storage resources. However, because the processing power of both PCs and workstations are increasing at a tremendous rate, this limitation is becoming insignificant.

11.3.1 The FDTD Method

The FDTD method was first proposed by K. S. Yee in 1966 for solving the time-dependent Maxwell's curl equations [35]:

In the calculation, the space containing the structure of interest is divided into number of small element called the "Yee cell." As shown in Figure 11.11, the E fields and the H fields in the "Yee cell" are interleaved both in space and time. This permits the space and time derivatives in the Maxwell's equations to be approximated by central difference operations with second-order accuracy:

8 4 9"'0.5(i,j,k) - +"-0.5(', , -(iAx,jAy, kAz,nAt) = At j k, + 0 [(A t ) 2 ]

a t (11.71b)

where @"'i, j, k) = 4(iAx,jAy, k Az, nAt) is one of the six field components. Ax, Ay, and Az are the space steps in the x, y, and z direction, respectively, and At is the time increment. In this way, six FDTD time-stepping expressions are produced. Two of these equations are shown as follows:


By applying an electromagnetic excitation and setting initial values for all of the field components, the fields are calculated iteratively using these equations for as long as the response is of interest.

11.3.2 Antenna Feed Modeling

Detail modeling of the coaxial probe is straightforward in the FDTD method (see, e.g., reference [48]). However, because the radius of the coaxial probe feeding the DR antenna is usually much smaller than the radius of the DR, this requires large program memory and very long computation time. Alternatively, simplified models using the thin-wire approximation technique can be used [51, 521. The simplest one is the gap voltage model [51]. In this model, a voltage is introduced in the first cell of the feeding wire as shown in Figure 11.12. The value of the corresponding Ez is set to the injected voltage divided by the space step in the z direction:

The voltage is a Gaussian pulse whose spectrum covers the frequency range of interest. This model is analogous to the MOM delta voltage model. Another

FIGURE 11.1 2 The simple gap voltage antenna feed model.


Gap voltage conductor source

FIGURE 11.1 3 Jensen's antenna feed model.

model analogous to the MOM magnetic frill model is also proposed in reference [51], which can also take into account the radius of the coaxial probe. Interested readers can refer to reference [51] for implementation details. These excitation schemes are considered as "hard" in the sense of enforcing the fields at some locations to certain values and neglecting the presence of any reflected waves. Since the reflected waves cannot be absorbed by the source, they are reflected back into the structure under analysis. As a result, the decay of the response becomes slower and the computation time is lengthened.

To shorten the computation time, the feed model proposed by M. A. Jensen 1521 can be used. In this model, the coaxial line connecting the feeding probe is also simulated as shown in Figure 11.13. A gap voltage is introduced inside the coaxial cable, and the same FDTD equations are used to propagate the fields toward the antenna. The other end of the coaxial line is terminated by applying an absorbing boundary condition (ABC). Any reflected wave from the antenna can now go through the coaxial line and absorbed by the ABC. From our experience, the required computation time can be only 50% that of the models using "hard" sources. The thin-wire approximations derived in reference [53] are used to calculate the magnetic fields around the coaxial probe:


where r, and r, are the radii of the coax inner and outer conductors, respectively. This model can only be applied when the radius of the outer conductor of the coax is less than the size of one cell in the antenna region. In addition, all models described here assume the coaxial probe is very thin. To model thick probes, standard FDTD has to be used.

11.3.3 Absorbing Boundary Condition

When applying the FDTD method to antenna problems, ABCs are required to reduce the nonphysical wave reflection from the outer boundaries of the computational domain. The most common ABC is probably the one proposed by G. Mur [54]. Many new ABCs are being proposed, and all claim to have better performance than the Mur's second ABC. Some are easy to implement and some are quiet complicated. In the author's opinion, the ABC introduced by Z. P. Liao [55] is a good choice. It has the advantages of ease of implementation, only using field values located along a straight line perpendicular to the boundary, thus eliminating special handling of the corners, and it has better performance than Mur's ABC. The derivation of Liao's ABC of any order can be found in reference [55]. Here, we only provide the expression for the second-order ABC applied at X = x,:

where

Note that d(x,t) represents a wave incident on the boundary as shown in Figure 11.14. Additional program memories are required for storing the field values at previous time steps.

One disadvantage of the Liao's ABC is the possibility of numerical instability, particularly when single-precision floating point arithmetic is in the FDTD simulation. Since the storage requirements of FDTD method is quiet expensive, double-precision floating-point arithmetic may not always the used. A method is proposed in reference [56] for stabilizing the Liao's ABCs using single-precision arithmetic. However, the optimum solution is machine-dependent and a general formula is not available. According to the author's experience, the second Liao's ABC is easily stabilized and suitable for using in the present problem.


Absorbing Boundary x=x, -+ I I

FIGURE 11.14 Liao's absorbing boundary condition.

11.3.4 Input Impedance Calculation

Using a pulse as the excitation to the antenna, the frequency-dependent characteristics of the antenna can be obtained in one analysis cycle. A Gaussian pulse type of voltage excitation is used which has the following form:

where T denotes the pulse width and is chosen to cover the frequency range of interest, and to is the time delay which enables a smooth "turn on" of the pulse. If the gap voltage type of model is used, this is the final voltage entered into the input impedance calculation. If simulation of the coaxial line is also included, the feed-point voltage can be calculated using the following equation [52]:

The current flowing into the antenna is obtained by performing the line integral of the magnetic fields around the base of the probe at each time step (Figure 1 1.15):

The input impedance of the antenna is determined from the ratio of the Fourier transform of the voltage wave and the Fourier transform of the input


FIGURE 11.15 Calculation of the input current of the antenna.

current wave i.e.,

Either the direct discrete Fourier transform (DFT) of fast Fourier transform (FFT) can be used for the transform process. The F F T is generally more time-efficient than the DFT. However, even if the simple DFT is used, the computation time for the transform process is negligible compared to the time spent in the FDTD simulation.

11.3.5 Far-Field Calculations

To obtain far radiation fields from the FDTD near-field data, a near-to-far field transformation process must be performed. In general, it is based on the field equivalence principle and can be performed either in the frequency domain [57] or in the time domain [58].

According to the field equivalence principle, the electromagnetic fields outside an imaginary closed surface (a virtual surface) surrounding the objects of interest can be obtained if the tangential fields on the closed surface is known. Conse- quently, in the FDTD simulation, the time-domain fields on a surface enclosing the DR antenna are used to calculate the far radiation fields. The virtual surface is illustrated in Figure 11.16.

The frequency-domain near-to-far field transformation is memory-efficient: a recursive DFT algorithm can be used to eliminate the need for storing the whole time sequence of the fields on the virtual surface, which is mandatory in the time-domain transformation. In addition, since the DFT is actually more efficient

FDTD ANALYSIS OF PROBE-FED CYLINDRICAL'DR ANTENNA 581

FIGURE 11.1 6 The virtual surface used for the calculation of the far fields.

than the FFT when the number of observation frequencies M is smaller than log, N, where N is the total number of time steps, the frequency-domain transformation can also be more time-efficient.

Here, radiation patterns are calculated at only one or several frequencies. Therefore, the use of frequency-domain near-to-far field transformations is highly efficient. Furthermore, an efficient recursive algorithm, the Goertzel Algorithm [59] for DFT calculation, is used, which further speeds up the analysis process.

In the Goertzel Algorithm, the DFT is considered as a linear filtering operation with the following system function [59]:

where z is the z-transform variables. After manipulating H,(z), two difference equations can be obtained for calculating the DFT of a time sequence F(n):

where W: = cos(2nklN) - j sin(2nklN). The recursive relations in Eq. (1 1.81a)is iteratedfor n = 0,1,. . . , N, but Eq. (1 1.8lb)is computed only once at a time n = N, which yields the component of F ( t ) at frequency fk = lINkAt, where N is the total number of time steps and At is the time step. Hence, in each FDTD time step and each frequency of interest, only one real multiplication and two additions are required for each tangential field component on the closed surface chosen for far

582 ANALYSIS OF DIELECTRIC RESONATOR ANTENNAS FDTD ANALYSIS OF PROBE-FED CYLINDRICAL DR ANTENNA 583

fields calculation. This is more efficient than the conventional recursive D F T method, which requires two real multiplications and two additions.

Once the frequency-domain near fields on the virtual surface are available at the end of the FDTD simulation, the image theory is applied to remove the ground plane and the far fields are obtained using the following equations [60]:

where

7 = r i is the position vector to the observation point

7' = r'i is the position vector to the source point.

The equivalent current densities and GS are equal to ii x and - 2 x if on the virtual surface, respectively.

11.3.6 Results and Discussions

To verify the numerical computation, the calculated input impedance is compared with existing measured results obtained from reference [30]. The probe- fed DR antenna considered has parameters: &, = 12, a = 2.75 cm, b = 1.4 cm, d = 2.6 cm, I = 2 cm, and r , = 0.381 mm. The space steps used are Ax = 1.72mm, and Az = 1.63mm, and the time step used is At= 3 . 1 3 ~ ~ . The size of the computational domain is 62Ax x 62A y x 31 Az. The simulation is performed for 20,000 time steps to allow the input response become approximately zero. The calculated results using the simple gap voltage feed models and the measured results of the input impedance of the DR antenna are plotted against frequency in Figure 11.17. It can be seen from the figure that the agreement between both calculated and measured results is good.

Next, the effect of using different feeding models is investigated. The calculated input impedance results using the gap-voltage model, the magnetic frill model, and Jensen's model are illustrated in Figure 11.18. It can be seen from the figure that the feed models produce only slightly different results in terms of input impedance. Jensen's feed model is preferable since only about 10,000 time steps are required for the time response to die down, so the computation time is greatly improved. On the other hand, the simple gap voltage model is the simplest for implementation. It is used for subsequent calculations. The effect of varying the probe length is illustrated in Figure 11.19. We can see that the input impedance

100 Calculated 1

-2 5 / Reactance

I I 1.2 1.3 1.4 1.5

Frequency (GHz)

FIGURE 11.1 7 Calculated and measured input impedance for the DR antenna versus frequency.~,=12,a=2.75cm,b=1.4cm,d=2.6cm,1=2cm,andr,=0.381mm.

FIGURE 11.18 Calculated and measured input impedance for the DR antenna versus frequency using different types of antenna feed models. E, = 12, a = 2.75cm, b = 1.4cm, d = 2.6cm, I = 2cm, and r , = 0.381 mm.

125

100

E 75 -

al 0 50-

-0 a P. E 25 .- - 3

E? 0 - -25

increases with the probe length but the resonant frequency decreases. The height of the DR is 2.6 cm, so the two curves show the input impedance for I = 3.03 cm indicate that the probe is passing through the DR. However, since the input impedance doesn't change dramatically, this is feasible during impedance matching especially for large ratios of a and d. Next, the effect of changing probe

- ----- Gap voltage model .-.-.- - Magnetic frill model Jensen's model

-

-

- I I I I

1.2 1.3 1.4 1.5 Frequency (GHz)


.-.-.-.-.-. 1 = 2.38 cm .- ..- ..- 1 = 3.03 cm

Reactance

FIGURE 11 .I 9 Calculated input impedance versus frequency for different probe length. ~=12,a=2.75cm,b=1.4cm,d=2.6cm,andr,=0.381mm.

displacement from the axis of the DR is illustrated in Figure 11.20. From this figure, we can see that for strong coupling of the HEM,,, mode the probe should be located near the edge of the DR. If the probe is placed outside the DR (the curves corresponding to b = 3 cm), the impedance becomes highly capacitive, which should be normally avoided.

For the far-field calculation, the DR antenna considered has the following parameters: E, = 9.2, a = 6.1 mm, b = 4.15 cm, d = 12.2 mm, and I = 5.1 mm. The

.................. b = 0.8 crn a 4 -100 * 3

E-150

-200

-250

- b = 1.2cm - .-.-.- .-.- b = 1.6 cm .-..-..-..- b = 3 c m -

Reactance - \ ..-..-..#" -----" \..... _..-.. _..--- -.._..-- _..-0. .-..

I I I 1.2

I 1.3 1.4 1.5

FIGURE 11-20 Input impedance versus frequency for different probe displacement. ~ ,=12 ,a=2.75cm, b = 1.4cm,1=2cm,andr0=0.381mm.


far fields of the DR antenna are obtained from the FDTD data using the technique described in the previous section. The radiation patterns of the fabricated antenna are measured in an anechoice chamber using an HP85310C antenna measurement system. Both the calculated and the measured radiation patterns are shown in Figure 11.21. The agreement between both results is quiet good. The discrepancies are mainly due to the infinite ground-plane assumption used in the calculation.

Next, the effect of changing the probe position on the radiation patterns of the antenna is investigated. The dimensions of the antenna is unchanged, and the distance of the probe from the center of the DR, b, is varied between 0.2 a and 0.9 a. For each value of b, the probe length is adjusted to maintain impedance matching. The results on radiation patterns for three different values of b/a are plotted in Figures 11.22a to 11.22~. In addition, the E-plane and the H-plane cross-polarization are plotted against b/a in Figure 11.23. From these figures, it can be seen that as b is increased, both the cross-polarization level and the asymmetry of the E-plane pattern is reduced. Hence, the feeding probe should be located as close to the edge of the DR as possible. It is worth noting that the resonant frequency of the antenna only changes slightly when the probe position is changed.

The effect of changing the ratio of the radius and the height of the DR is also studied. The radiation patterns for three different of a/d are plotted in Figure 11.22d to 11.22f. The E-plane and the H-plane cross-polarization are plotted

I--- E Plane Xpol - H Plane xpol/

FIGURE 11.23 E-plane and H-plane cross-polarization level versus bla. e, = 9.2, a = 6.1 rnrn, and d = 12.2rnrn.

588 ANALYSIS OF DIELECTRIC RESONATOR ANTENNAS REFERENCES 589

-30 1 --- E Plane Xpol - H Plane Xpol

FIGURE 11.24 E-plane and H-plane cross-polarization level versus a/d. E, = 9.2, a = 6.lmm, and b=4.l5mm.

phi (degree) 0 i I I I

0 20 4 0 6 0 80 100 120 140 160 180

-5 t I

FIGURE 11.25 Cross-polarization level versus angle 4. E, = 9.2, a = 6.1 mm, b=4.l5mm, l=5.lmm, and d = 12.2mm.

against a/d in Figure 11.24. Again, for each value of a/d, the probe length is adjusted to maintain impedance matching. From these figures, it is observed that small values of a/d produces smaller cross-polarized fields. However, if a/d is smaller than 2.0, it may be difficult to match the input impedance of the antenna

I to 50 R. Since a is fixed in the calculations, the resonant frequency increases when a/d is increased.

1 Finally, the cross-polarization of the DR antenna is considered as a function of the angle 4. The calculated results are plotted in Figure 11.25. The definition of the crdss-polarization used here is

I

As shown in the figure, the cross-polarization level attains a maximum at 4 = 45O

l and 4 = 135".

1 1.3.7 Summary I

Cylindrical DR antennas operating at the fundamental broadside mode, HEM,,, mode, is analyzed using the FDTD method. An efficient FDTD with

I frequency-domain near-to-far field transformation is used to obtain the far fields of the cylindrical DR antenna. The numerical results agree well with experimental results. If adequate computing resources are available, the present method can be extended easily to analyze configuration involving a finite ground plane or stacked DRs.

REFERENCES

[I] S. A. Long, M. W. McAllister, and L. C. Shen, "The Resonant Cylindrical Dielectric Cavity Antenna," IEEE Trans. Antennas Propagat., Vol. AP-31, pp. 406412,1983.

[2] M. W. McAllister, S. A. Long, and G. L. Conway, "Rectangular Dielectric Resonator Antenna," Electron. Lett., Vol. 19, pp. 218-219,1983.

[3] M. W. McAllister and S. A. Long, "Resonant Hemispherical Dielectric Antenna," Electron. Lett., Vol. 20, pp. 657-659, 1984.

[4] R. K. Mongia, "Half-Split Dielectric Resonator Placed on Metallic Plane for Antenna Applications," Electron. Lett., Vol. 25, pp. 462-464,1989.

[5] K. W. Leung, K. M. Luk, and E. K. N. Yung, "Spherical Cap Dielectric Resonator Antenna Using Aperture Coupling," Electron. Lett., Vol. 30, pp. 1366-1367, 1994.

[6] R. A. Kranenburg and S. A. Long, "Microstrip Transmission Line Excitation of Dielectric Resonator Antenna," Electron. Lett., Vol. 24, pp. 1156-1 157, 1988.

[fl J. T. H. St. Martin, Y. M. M. Anter, A. A. Kishk, A. Ittipiboon, and M. Cuhaci, "Dielectric Resonator Antenna,Using Aperture Coupling," Electron. Lett., Vol. 26, pp. 2015-2016,1990.

[8] R. A. Kranenburg, S. A. Long, and J. T. Williams, "Coplanar Waveguide Excitation of Dielectric Resonator Antennas," IEEE Trans. Antennas Propagat., Vol. 39, pp. 119-122,1991.

[9] A. A. Kishk, B. Ahn, and D. Kajfez, "Broadband Stacked Dielectric Resonator Antenna," Electron. Lett., Vol. 25, pp. 1232-1233,1989.


[lo] R. N. Simons and R. Q. Lee, "Effect of Parasitic Dielectric Resonators on CPWIAperture-Coupled Dielectric Resonator Antennas," Proc. Inst. Electr. Eng., Part H , Vol. 140,336-338,1993.

[I11 S. M. Shum and K. M. Luk, "Characteristics of Dielectric Ring Resonator Antenna with an Air-Gap," Electron. Lett., Vol. 30, pp. 277-278, 1994.

[I21 K. L. Wong, N. C. Chen, and H. T. Chen, "Analysis of a Hemispherical Dielectric Resonator Antenna with an Air-Gap," IEEE Microwave Guided Wave Letters, Vol. 3, pp. 355-357,1993.

[I31 N. C. Chen, H. C. Su, K. L. Wong, and K. W. Leung, "Analysis of a Broadband Slot-Coupled Dielectric-Coated Hemispherical Dielectric Resonator Antenna," Microwave Opt. Technol. Lett., Vol. 8, pp. 13-16, 1995.

[14] S. M. Shum and K. M. Luk, "Stacked Annular Ring Dielectric Resonator Antenna Excited by Axi-symmetric Coaxial Probe," IEEE Trans. Antennas Propagat., Vol. 43, pp. 889492,1995.

[I51 M. Haneishi and H. Takazaawa, "Broadband Circularly Polarised Planar Array Composed of a pair of Dielectric Resonator Antennas," Electron. Lett., Vol. 21, pp. 437-438,1985.

[I61 R. K. Mongia, A. Ittipiboon, M. Cuhaci, and D. Roscoe, "Circularly Polarised Dielectric Resonator Antenna," Electron. Lett., Vol. 30, pp. 1361-1363, 1994.

[ l q M. B. Oliver, Y. M. M. Anter, R. K. Mongia, and A. Ittipiboon, "Circularly Polarised Rectangular Dielectric Resonator Antenna," Electronics Letters, Vol. 31, pp. 418- 419,1995.

1181 K. M. Luk, W. K. Leung, and K. W. Leung, "Mutual Impedance of Hemispherical Dielectric Resonator Antennas," IEEE Trans. Antennas Propagat., Vol. 42, pp. 1652-1654,1994.

[I91 G. D. Loss and Y. M. M. Antar, "A New Aperture-Coupled Rectangular Dielectric Resonator Antenna Array," Microwave and Optical Technology Lett., Vol. 7, pp. 642-644,1994.

[20] A. Petosa, R. K. Mongia, A. Ittibipoon, and J. S. Wight, "Design of Microstrip-Fed Series Array of Dielectric Resonator Antennas," Electron. Lett., Vol. 31, pp. 1306- 1307,1995.

[21] K. Y. Chow, K. W. Leung, K. M. Luk, and E. K. N. Yung, "Cylindrical Dielectric Resonator Antenna Array," Electron. Lett., Vol. 31, pp. 1536-1537, 1995.

1221 R. K. Mongia, A. Ittibipoon and M. Cuhaci, "Low Profile Dielectric Resonator 3Antennas Using a Very High Permittivity Material," Electron. Lett., Vol. 30, p p 1362-1363,1994.

[23] K. W. Leung, K. M. Luk, E. K. N. Yung, and S. Lai, "Characteristics of a Low-Profile Circular Disk DR Antenna with Very High Permittivity, "Electron. Lett., Vol. 31, pp. 417-418,1995.

1241 D. Kajfez and P. Guillon, eds., Dielectric Resonators, Artech House, Dedham, MA, 1986.

1251 J. Van Blade], "On the Resonances of a Dielectric Resonator of Very High Permit- tivity," IEEE Trans. Microwave Theory Tech., Vol. 23, pp. 199-208,1975.

[26] M. Tsuji, H. Shigesawa, and K. Takiyama, "On the Complex Resonant Frequency of Open Dielectric Resonators," IEEE Trans. Microwave Theory Tech., Vol. 31, pp. 392-396,1983.

REFERENCES 591

[27] M. Tsuji, H. Shigesawa, and K. Takiyama, "Analytical and Experimental Investiga- tion on Several Resonant Modes in Open Dielectric Resonators," IEEE Trans. Microwave Theory Tech., Vol. 32, pp. 682-633, 1984.

[28] A. W. Glisson, D. Kajifez, and J. James, "Evaluation of Modes in Dielectric Resonators Using a Surface Integral Equation Formulation," IEEE Trans. Micro- wave Theory Tech., Vol. 32, pp. 1609-1616,1984.

[29] A. A. Kishk, H. A. Auda, and B. C. Ahn, "Radiation Characteristics of Cylindrical Dielectric Resonator Antennas with New Applications," IEEE AP-S Newslett., VOL 31, pp. 7-16, 1989.

[30] G. P. Junker, A. A. Kishk, and A. W. Glisson, "Input impedance of Dielectric Resonator Antennas Excited by a Coaxial Probe," IEEE Trans. Antennas Propagat., Vol. 42, pp. 960-966,1994.

[31] K. M. Luk, K. W. Leung, K. Y. A. Lai, and D. Lin, "Analysis of Dielectric Resonator Antenna," Radio Sci., Vol. 28, pp. 1211-1218, 1993.

1321 K. W. Leung, K. M. Luk, K. Y. A. Lai, and D. Lin, "Theory and Experiment of Probe Fed Dielectric Resonator Antenna," IEEE Trans. Antennas Propagat., Vol. 41, pp. 1309-1398,1993.

[33] K. W. Leung, K. M. Luk, K. Y. A. Lai, and D. Lin, "Theory and Experiment of an Aperture-Coupled Hemispherical Dielectric Resonator Antenna," IEEE Trans. Antennas Propagat., Vol. 43, pp. 1192-1 198,1995.

[34] A. A. Kishk, G. Zhou, and A. W. Glisson, "Analysis of Dielectric-Resonator Antennas with Emphasis on Hemispherical Structures," IEEE AP Mag., Vol. 36, pp. 20-31,1994.

[35] K. S. Yee, "Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equations in Isotropic Media," IEEE Trans. Antennas Propagat., Vol. 14, pp. 302-307,1966.

1361 D. M. Pozar, "A Reciprocity Method of Analysis for Printed Slot and Slot-Coupled Microstrip Antennas," IEEE Trans. Antennas Propagat., AP-34, pp. 1439-1446, 1986.

[37l D. M. Pozar, "Input Impedance and Mutual Coupling of Rectangular Microstrip Antennas," IEEE Trans. Antennas Propagat., AP-30, pp. 1191-1196,1982.

[38] R. F. Harrington, Time-Harmonic Electromagnetic Fields, McGraw-Hil1,New York, 1961.

[39] M. Gastine, L. Courtois, and J. L. Dormann, "Electromagnetic Resonances of Free Dielectric Spheres," IEEE Trans. Microwave Theory Tech., Vol. MTT-15, pp. 694-700,1967.

[40] R. W. P. King, Theory of Linear Antennas, Harvard University Press, Cambridge, MA, pp. 16-241956.

[41] J. D. Kraus, Antennas, 2nd edition, McGraw-Hill, New York, pp. 391-392,1988. [42] R. S. Elliott, Antenna Theory and Design, Prentice-Hall, Englewood Cliffs, NJ,

pp. 569-572,1981. [43] K. W. Leung, K. Y. A. Lai, K. M. Luk, and D. Lin, "Input Impedance of Aperture

Coupled Hemispherical DR Antenna," Electron. Lett., Vol. 29, pp. 1165-1167, 1993.

[44] K. W. Leung and K. M. Luk, "Radiation Characteristics of Aperture-Coupled


Hemispherical Dielectric Resonator Antenna," Microwave Opt. Technol. Lett., Vol. 7, pp. 677-679, 1994.

[45] P. L. Sullivan and D. H. Schaubert, "Analysis of an Aperture Coupled Microstrip Antenna," IEEE Trans. Antennas Propagat., Vol. AP-34, pp. 977-984,1986.

[46] K. W. Leung, K. Y. A. Lai, K. M. Lai, K. M. Luk, and D. Lin, "End-Fire TE,,, Mode of Aperture Coupled Hemispherical Dielectric Resonator Antenna," Electron. Lett., 29, pp. 981-982, 1993.

[47l K. W. Leung and K. M. Luk "Moment Method Solution of Aperture-Coupled Hemispherical Dielectric Resonator Antenna using Exact Modal Green's Func- tion," IEE Proc.-Microwave, Antennas and Propagation, Vol. 141, pp. 377-381,1994.

[48] J. G. Maloney, G. S. Smith and W. R. Scott, Jr., "Accurate Computation of the Radiation from Simple Antennas Using the Finite-Difference Time Domain Method," IEEE Trans. Antennas Propagat., Vol. AP-38, pp. 1059-1068,1990.

[49] A. Reineix, and B. Jecko, "Analysis of Microstrip Patch Antennas Using Finite Difference Time Domain Method," IEEE Trans. Antennas Propagat., Vol. AP-37, pp. 1361-1369,1989.

[50] D. Katz, M. Piket-May, A Taflove, and K. Umashankar, "FDTD Analysis of Electromagnetic Wave Radiation from System Containing Horn Antennas," IEEE Trans. Antennas Propagat., AP-39, pp. 1203-1212,1991.

[51] R. J. Luebbers, L. Chen, T. Uno, and S. Adachi, "FDTD Calculation of Radiation Patterns, Impedance, and Gain for a Monopole Antenna on a Conducting Box," IEEE Trans. Antennas Propagation, Vol. AP-40, pp. 1577-1583,1992.

[52] M. A. Jensen and Y. Rahmat-Samii, "Performance Analysis of Antenna for Hand- Held Transceivers Using," IEEE Trans. Antennas Propagat., Vol. AP-42, pp. 1106-1113,1994.

1531 K. Umashankar, A. Taflove, and B. Beker, "Calculation and Experimental Valida- tion of Induced Currents on Coupled Wires in an Arbitrary Shaped Cavity," IEEE Trans. Antennas Propagat., Vol. AP-35, pp. 1248-1257,1987.

[54] G. Mur, "Absorbing Boundary Conditions for Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations," IEEE Trans. Electromagn. Compat., Vol. EMC-23, pp. 1073-1077,1981.

[55] Z. P. Liao, H. L. Wong, B. P. Yang, and Y. F. Yuan, "A Transmitting Boundary for Transient Wave Analysis," Sci. Sin. ser. A, Vol. XXVII, pp. 1063-1076, 1984.

[56] M. Moghaddam and W. C. Chew, "Stabilizing Liao's Absorbing Boundary Condi- tions Using Single-Precision Arithmetic," in Proceedings, 1991 IEEE AP-S Interm- tional Symposium, London, Ontario, Canada, pp. 430-433,1991.

[57l A. Taflove and K. R. Umashankar, "Radar Cross Section of General Three- Dimensional Structures," IEEE Trans. Electromagn. Compat., Vol. EMC-25, 433-440,1983.

[58] R. J. Luebbers, K. S. Kunz, M. Schneider, and F. Hunsberger, "A Finite-Difference Time-Domain Near Zone to Far Zone Transformation," IEEE Trans. A n t e n m Propagat., Vol. AP-31, pp. 429-433,1991.

[59] A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, Prentice-Hall, NJ.

[60] C. A. Balanis, Antenna Theory, John Wiley & Sons, New York, 1982.

index

Active element pattern, 134,135 Active patch antenna, 186,377

circular polarization. 186 dual linear polarization, 186 polarization-angle, 186

Active reflection coefficient, 113, 118 Active slot dipole active amplifier, 401 Active tapered slot antenna army, 502

conversion efficiency, 507 mutual coupling, 503 quasi-optical power combining, 504 spatial amplifier, 505 spatial multiplier army, 505 spatial oscillator, 505

Air gap, 1,43,49,73,113 Angular spectrum of plane waves, 290 Anisotropic. 126 Anisotropic conducting surface, 296 Antenna array, 326 Antenna feed modeling, 576 Aperlurc coupling, 7.71, 126, 127, 133, 142,555 Application drivers, 315 A m y configuration, 138 Array efficiency, 345,365 Asymptotic approximation, 130 Attachment mode, 19,26,27,33,35,36,37 Attenuation constant, 342

Backlobe radiation, 72 Barium strontium titanate, 284 Basis function, 19,23

patch, 19,23 probe, 19.23

Beamfonner, 149 Beam scanning (steering), 278

diode army, 419

transistor-integrated, 427 Bcsscl's function, 144 Boulder Microwave Technologies, Inc., 67,68

Ensemble software, 67.68 Boundary conditions, 4,5,76,77 Bow-tie dipoles, 3 12 Branch-line hybrid divider, 147 Brick-type army, 43 1 Broadband antenna, 543

CAD formulas, 223 bandwidth, 242,243 diictivity, 263 input impedance, 230,254 probe reactaace, 253 Q factors, 233,234 radiation efficiency, 246 radiation patterns, 256 resonance frequency, 231 resonant input resistance, 248,249

CAD model, 230 CAD tools, 5 19 Cavity model, 5, 125,226 Characteristic equations, 563 Characteristic impedance, 80 C h i d materials, 126,285 C h i d substrates, 186 Circular polarization, 143,163, 186 Circularly polarized (CP) antenna, 539 Circularly polarized arrays, 188,362 Circularly polarized patches, 167

elliptical patch, 178 feed arrangement, 167 loop, 178 orthogonal patches, 169 patch with center slot, 178

594 INDEX INDEX 595

Circularly polarized patches (continued) patch with notches, I77 patch with tabs, 177 patch with truncated comer, 178 pentagonal patch, 178 rectangular patch, 177 ring with notches, 178 triangular patch, 178

Closed-form equations, 143 Compact packages, 308 Complex conductivity, 335,337 Complex region, 10, 1 1 Computer-aided design (CAD), 124,223 Conformal array, 306 Coplanarparasitic subarray, 1,35,50,68,83 Co-polarization, 89-94,101-104,585-586,

589 Copper oxide superconductors, 326,328,330 Corporate feed, 139 Cross-polarization, 89-94,101-104.585-587 Current filament, 36 Current ribbon, 5

Delta-gap voltage, 36 Design freedom, 274 Dichroic conductors, 296 Differential spatial phase delay Dielectric constant, 145 Dielectric cover (superstrate), 1.43.278.286 Dielectric material, 277 Dielectric resonator antenna, 553

far-field calculation, 580 input impedance, 555,579 radiation patterns, 555

Dielectric resonators, 553 Dielectric sphere, 555 Differential spatial phase delay, 151 Direct broadcast satellite (DBS), 157 Directivity, 263 Doppler sensing, 376,394 Dual-band operation, 302 Dual-circular polarization, 141 Dual-linear polarization, 141 Dual polarization, 163 Dual polarized arrays, 188 Dual polarized patches, 183 Dyadic Green's functions, 13, 18, 19,564

electric dyadic Green's function, 14, 18 magnetic dyadic Green's function, 14,18 spatial domain, 13, 15, 17,37 spectral domain, 17,34

Earth remote sensing, 154 Effective dielectric constant, 232

Effective length, 224,232 Effective loss tangent, 5,226 Effective propagation constant, 80 Effective width, 225 Eigenfunctions, 225 EIRP, 394,404 Electric cumnt excitation, 7,12 Electric-current model, 256,260 Electric dyadic Green's function, 14, 18 Electric field integral quation, 7 Electrically thick substrate, 37 Electromagnaic coupled patches (EMCP), 53,

54.0-63 Endtire radiation, 448.45 1 Equivalent electric surface currents, 126 Equivalent magnetic currents, 126 Equivalent radius, 566 Equivalence theorem, 126 Expansion mode, 120,127

f/o ratio, I5 1 Fabry-Perot cavity, 3 12 Far field, 13 Feed inductance, 229,252 Feeder simplicity, 302 Ferrite losses, 277 Ferrite material, 126,276,277 Femte substrate, 186,277 Finite difference method, 130 Finite-Difference Time-Domain (FDTD) method,

68,515,516,573 absorbing boundaries, 53 1 absorbing boundary conditions, 52 1,578 curvilinear grids, 523 efficient modeling, 526 extrapolation techniques, 526 nonuniform grids, 524 subshell modeling, 523 Yee algorithm, 5 19

Finite element method, 130,516 Finite ground plane effect, 538 Five-patch cross, 5 1,54 Flat reflector, 149 Floquet modes, 109,133 Floquet theorem, 109 Folded slot antenna, 402 Fourier transform, 6,29,79, 127

discrete Fourier transform (DFT), 580 fast Fourier transform (Fm, 580

Frequency selective surface, 296 Fresnel reflection coefficients, 18 Fringing length 232 Fringing width. 225 Full-wave analysis, 2,4,5,36, 124, 126,516

Gain, 1, 59, 123 Galerkin's procedure, 73.78 GaAs T/R module, 158 Generalized reflection coefficient, 16, 19 Global positioning system (GPS), 516,517 Goertzel algorithm, 581 Grating lobe, 64, 142,202 Green's functions, 3, 13, 14, 15, 17, 18,34, 37,

73,126,557 asymptotic approximation, 130 homogeneous solutions, 562 particular solutions, 561 single-mode approximation, 567

Grid antenna anays, 3 12 Ground plane size, 538 Gunn diodes. 309

Half-power bmwidths, 46,59,88,94, 104 Hammerstad formula, 232 Hansen Woodyard condition, 449 Hemispherical dielectric resonator antenna, 555 High-temperature superconductors, 302,325,

326,329,330,333,338 AC losses, 327,331,336 coherence length, 327,334 Cooper pairs, 327 critical current density, 328 critical magnetic field, 328 energy-gap frequency, 328 high magnetic fields, 338 kinetic inductance, 339 Meissner effect, 327,331 mixed state, 334 near-perfect diamagnetism, 327 penetration depth, 335,336 resistivity, 327 surface impedance, 334,337 surface reactance, 334 surface resistances, 326,333,337 temperature dependence, 336 thin-film superconductors, 33 1 vortices, 329 YBaCuO, 329

Higher-order modes, 143, 170, 194 Horizontal electric dipole, 235,256,269

radiation efficiency, 235 space-wave power, 235 surface-wave power, 236

Horizontal magnetic dipole, 258,269 Hybrid coupler, 167 Hybrid seriedparallel feed, 140

Impedance bandwidth, 1,42,45,46,50,53,63,

72,73,98,107-109,123,349,350,353, 360

Impedance matrix, 127 Infinite array analysis, 125, 132 Infinite array of dual-patches, 114 Input impedance, 22,36,37,43,227,530,539 Integrated antenna, 373

active integrated antenna, 373 active solid state devices, 373 amplification, 373 Baritt Doppler sensor, 376 diode, 376 IMPATT, 379 power generation, 373

early history, 374 mixer-, 374 multifunction capabilities, 408 passive integrated antenna, 373

detecting, 373 modulating, 373 passive solid-state devices, 373 switching, 373 tuning, 373 varactor, 376

Integration of antennas and circuits, 308 Interference suppression, 289 Inverted stripline antennas (ISAs), 389

FET-integrated, 402 Gunn-integrated, 389 integrated transceiver, 402 pins, 389 varactors, 389

Invisible region, 449 Isotropic, 126

James formula, 232 Josephson junction, 312

Leaky cavity, 5 Leaky waves, 448.45 1 Leaky wave antennas. 284 Legendre polynomial, 566 Linearly polarized patches, 1,73 Log-periodic microstrip array, 153 London equations, 335 Loss, 123 Loss tangent, $37, 534 Low sidelobes, 153 Low temperatun superconductors, 326

Magnetic current excitation, 7, 11, 12 Magnetic current model, 257,262 Magnetic dyadic Green's function, 14, 18 Magnetic field bias, 277

596 INDEX INDEX 597

Magnetic frill model, 37 Magnetic wall cavity, 5,26 Marine weather radar1 58 Mars Pathfinder microstrip dipole array, 157 Material boundary conditions, 283 MESFET oscillator, 308 Methods ofmoments, 8, 124, 131,516, 557 Microstrip antenna, 1, 71, 326

air gap, 43, 82 aperture-coupled FET integrated, 407 ape* coupling, 71, 126, 133, 142,382 bandwidth, 1.42, 50,53,63, 72, 73, 128,230 circular patch, 143 coaxial feed (probe-feed), 1.2, 11, 19,35,71,

534 coplanar subanay, 1,35,68,83 CPW-fed-integrated slot-CPW antenna

amplifier, 396 dominant mode, 378 dual-FET-integrated, 394 edge-fed transistor integrated, 394 FET transistor integrated, 392, 395 fields under patch, 377,546 gain, 1.59, 123, 361 Gunn-integrated, 380 half-power beamwidth, 46,59 IMPATT integrated, 388 IMPATT-integrated circular patch, 379 impedance bandwidth, 1,42,50,53,63,72,73 infinite array, 109-1 18, 125

of aperture coupled patches, 109 of dual patches, 114 of patches with air gap, 113

multilayer multipatch, 1,4,35, 68 offset dual-patch, 93 patch in multi-dielectric media, 35,42,68 patch with dielectric cover (superstrate), 43 patch with superstrate and two substrates, 43,

47 patch with superstrate and unwanted air space,

46,49 patch with two superstrates, 45.46 probe-feed (coaxial feed), 1,2, 11, 35 push-pull FET integrated, 398 radiation conductance, 378 rectangular patch, 2, 19,35,143,223 resonant frequencies, 1,5,37,41,45,46,49,

23 1 single patch, 35, 36, 68 stacked patches, 1,35,53-63,68,97, 127, 133,

142 stripline feed, 71 transistor-integrated, 391,394 two-layer five-patch, 99

two-layer three-patch, 103 two-port FET oscillator, 395 U-slot patch, 1,2,63-68

Microstrip arrays, 123, 129 aperture-coupled, 109 bandwidth, 123 design methodology, 137 loss, 123 power handling, 123

Microstrip array applications, 123, 152 commercial, 123, 157 military, 123, 152 space, 123, 154

Microstrip hyperthermia applicators, 286 Microstrip integrated circuits (MICs), 373 Microstrip line arrays, 188

chain antenna, 188 crank line, I88 herring-bone line, 188 rampart line, 188 square-loop line, 188 stripldipole array, 188

Microstrip reflectmy, 133, 148 Microstrip spirals, 184 Microwave integrated circuits (MICs), 373 Millimeter array, 284 Millimeter-wave frequencies, 124 Mixed potential approach, 128 Mode matching method, 556 Moment method,& 124, 126,131,132,516,

557 Monolithic integrated phase-array, 153 Monolithic MICs (MMICs), 373 Multi-dielectric media, 35 Multifunction printed antenna, 273 Multilayer, 1,4,35,68,73, 126, 141 Muhipacting breakdown, 142, 156 Multiple expansion functions, 37,41 Multiple feeds, 24 Multipoint feed, 170 Multipart segmentation model, 125 Mutual admittance function, 80 Mutual coupling, 124, 128, 129, 131,301 Mutual impedance function, 80

Normal-state conductivity, 335 Notch antenna, 383,384

active varactor-tun~ble coupled slotline-CPW, 384

FET transistor integrated, 392 Gunn diode, 383 GUM-integrated, 388,392 stepped, 383 tapered slot, 383

Omnidirectional, 539 Optical interaction, 407 Optically active particles, 285 Optically driven solid-state devices, 407 Orthogonal polarization, 165 Oscillator locking, 309

Parallel feed, 139 Parasitic patches, 1,5,50 Patch arrays. 188 Patch current, 27 Patch feeding, 167 Patch-probe junction, 19.26.36 Periodic structure, 132 p- factor, 24 1,266 Phase array analysis, 526 Phase shifters,l41, 154 Phase velocity, 343 Photonic feeder system, 306 Planary layered medium, 14 Poisson summation formula, 132 Polarization, 164 Polarization agility, 277 Power-combining array, 408 Power-combining configurations, 309 Power division line, 144 Power-handling, 123, 142, 156 Printed antenna, 5,273,275,443 Printed conductor topology, 294 Probe current

advanced model, 41 axial variation, 37 azimuthal variation, 37 simple model, 4 1

Probe, effective width of, 227 Probe reactance, 41,252 Proximity coupled, 126,365

Q of patch, 226,380 conductor Q factor, 234 dielectric Q factor, 234 space-wave Q factor, 235 surface-wave Q factor, 235

Quarter-wave transformer, 140, 144 Quasi-optical methods, 304

Radar crass section, 186,214,286 Radiated power of patch, 242 Radiation efficiency, 231,278,326,350,353,

361 Radiation patterns, 36,48,49, 66,87-110,256,

362,532,540 Reaction, 6, 7 Reactive power dividers, 147

Rectangular patch CAD formulas, 223 tuning range, 277

Reciprocity theorem, 6,73,79 Recursive relations, 16 Reflectatray, 304-306 Reflection coefficient, 22.78, 79, 1 13 Resistive sheet, 289 Resonance frequency, 1.5, 37,41,45,46,49,

23 1,349,352 rectangular patch, 23 1

Resonant array, 138 Resonant resistance, 37.45 Richmond form. 566

Salisbury screen, 289 Scan bandwidth, 1 17 Scan blindness, 134, 136,286 Scattering matrix, 26 Self-admittance function, 80, 134, 137,286 Self-diplexing antennas, 164 Self-impedance function, 80 Self-oscillating mixer, 376 Semiconductor loaded elements, 308 Sequentially arranged, 141 Sequentially rotated arrays, 190

circular polarization, 190 dual polarization, 210 feeding phase. errors, 194 grating lobes, 202,203 higher order modes, 194 multiple reflections, 194 radiation pattern effects, 200

Series feed, 138 in-line feed, 138 out-of-line feed, 138

Shorting pins, 24,26 Simple region, 7.8 Single-mode approximation, 567 Single-point feeds, 177 Singularity, 566 SIR-C antenna, 154 Skewed periodic structure, 109 Slotline antenna, 388

cavity-backed, 400 FET transistor integrated, 392,400

Slotline ring resonator antenna, 401 Slow wave behaviour, 344 Smart skin, 153,274 Smart skin apertures, 274 Space domain approach, 127 S-parameters, 129 Spatial domain Green's functions, 13, 15, 17,

37

598 INDEX INDEX 599

Spatial power combining, 377,409 aperture-coupled microstrip patch antennas,

412 distributed amplifers, 423 FET integrated patch, 423 FET-integrated dual circular patches, 426 Gunn diode integrated ISAs, 419 Gunn-integrated microstrip patches, 413,414 Gunn-integrated patch antennas, 412 Gunn-integrated rectangular patches, 413 injection-loaded distributed oscillators, 409 integrated IMPATT patch antenna, 412 open-cavity resonator, 409 quasi-optical power combiner, 409 hansistor array, 422 transistor-integrated, 427

Spectral domain approach, 37,127,516,559 Spectral domain Green's functions, 17, 34.37,

73 Spiral antenna, 374 Stacked patches, 1,35,53-63,68,97, 127, 133,

142,538,541 Stored energy in patch cavity, 239 Substrate loss, 278 Substrate loss tangent, 37 Substrate materials, 276,332,354

AI2O3 (sapphire), 332,355 La.410,. 332,354 MgO, 332 SrTiO,, 332 2102 (Yz01). 332

Substrate permittivity, 36,45,52 Substrate surface waves, 278 Substrate thickness, 5,37,42,45 Superconducting antennas, 325,339 Superconducting microstrip patch antennas, 347

efficiency, 347,350,365 experimental results, 356 impedance bandwidth, 349,350 resonance frequency, 349,351

Superconducting printed patches, 302 Superconducting transmission lines, 325,339

attenuation constant, 342 efficiency, 345 feed network, 344 phase velocity, 343 slow-wave behavior, 344

Superstrate (dielectric cover), 1,43,4547,278, 286

Superstrate polarizer, 3 12 Surface wave, 126, 127, 129, 134,448 Surface wave power, 236 Synthetic-aperture radars, 154 System applications, 428

Tapered slot antennas, 383,443 analytical methods, 453 antipodal TSA, 446,463 bandwidth characteristics, 494 broadband operation, 452 feeding techniques, 461

balanced microstrip, 472 coaxial line feed 463 conductor-backed finite ground-planar

CPW, 467 coplanar waveguide feed, 466 even mode, 466 grounded CPW (GCPW), 466 high-resistivity silicon wafer, 47 1 impedance match, 464 microstripline feed, 463 microstrip/slotline transition, 463,470,501 notches, 470 odd mode, 465,474 parallel-plate modes, 468 package design, 474 quarter-wave stepped impedance-matching

transformer, 473 slot-to-slot transition, 468 stepped approximation method, 453 stripline-fed notch radiator, 472 strip-to-slot transition, 468 transition design, 463 uniplanar microstrip-to-coplanar stripline

feed, 473 waveguide-to-fdine transition, 476

input impedance, 487 de-embedded, 487 impedance standard substrate (ISS), 492 mutual coupling, 491,493 on-wafter Thm-Reflect-Line (TRL), 487 standing-wave mode, 490,492 traveling-wave mode, 490

linearly tapered slot antenna (LTSA), 443 magnetic field distribution, 495 mechanism of radiation, 450 radiation characteristics, 476

cross-polarization, 477 ,

curvature effect, 477,478 dielectric overlay effect, 486 gain, 48 1,483 ground-plane effect, 486 half-power beamwidth, 481-485 lateral edge width effect, 479,482 length effect, 479,483 slot width effect, 479 substrate effect, 48 1,484 taper angle effect, 484

surface wave antenna, 45 1

surface waves, 5,448,498 vivaldi, 443 V-antennas, 444

Tapered slot antenna arrays, 498 brick architecture, 498 circular LTSA array, 501 finite element method, 499 flared slot antenna, 500 method of moments, 499 scan blindness, 499 time domain TLM, 499

TEM mode, 20 Test mode, 120, 127 Thin substrate, 5.37.536 3D filed simulations, 408 Tile array, 43 1 Transmission line model, 4, 125 Transverse electric (TE), I6 Transverse magnetic (TM), 5, 16 Traveling wave array, 138, 153,284 Triple-band, 302 Truncated substrate, 260 Tuning, 277 Tunnel diode, 374 T/R module, 125, 154, 158

MMIC, 141

Two-fluid model, 335 complex conductivity, 335 effective penetration depth, 335,336 normal-state conductivity, 335 surface impedance, 337 surface inductance, 337 surface resistance, 337 temperature dependence, 336

U-slot patch, 1,2,63-68

Varactor diode, 309 Varactor diode reactive loading, 305 Variable frequency FET oscillator, 308 Visible region, 449 VSWR (SWR), 42,46,67,84,90,91,94,96,

100,110,165,546

Waveguide simulators, 135 Wilkinson splitter bower divider), 147, 167

Yee cell, 575

Zeeneck wave, 450,452 Zonal plate antenna, 304 Zonal rings, 304,306

advances.in.microstrip & printed antennas-wiley1997.lee

Documents