CIRCULARLY POLARIZED RECTANGULAR DIELECTRIC RESONATOR ANTENNAS FOR

PERSONAL COMMUNICATIONS

Lieutenant Commander P.N. Dombowsky, CD

A thesis subrnitted to the Department of Electrical and Cornputer Engineering

Royal Military CoUege of Canada Kingston, Ontario

In partial fulfillment of the requirements for the degree of

Master of Engineering

November 1996

O Copyright 5y P.N. Dombowsky, 1996 This thesis may be freely used within the Department of National Defence, but the copyright for open publication remains the property of the author.

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ABSTRACT

CIRCULARLY POLARIZED RECTANGULAR DIELECTRIC RESONATOR ANTENNAS FOR PERSONAL COMMUNICATIONS

by Lieutenant Commander P.N. Dombowsky

Currently, a rapid growth of "persona1 communications" is underway which is spurring the development of many varied technologies, including antenna design. Some areas of "personal communications" include - Global Positioning Systerns (GPS), Cellular telephones (incl. Terrestrial and Satellite), indoor/outdoor wireless communications (e.g. cornputer networks) etc. - all of which operate maidy in the L and S bands.

The word "personal" implies mobile, tnerefore, antenna designs must be small. lightweight and inexpensive yet still posses properties of high efficiency, 'wide bandwidth', and the ability to optirnize directivity, gain and polarization (particularly circular) to meet specific requirements. Many different antenna technologies are k i n g investigated such as Microsmp Patch and Ferrite Resonator Antemas.

Recently, a new single feed circularly po larized Dielectric Resonator Antenna (DRA) was reported that could offer some promise in this area of communications. The antenna elements use mutually orthogonal nearly degenerate modes to generate circular polarization with low axial ratios over a wide fkequency band and beamwidth. In this thesis, the performance of these antennas in the S band has k e n investigated and characterized in terms of parameters such as: far field patterns, radiation efficiency, impedance bandwidth, axial ratio beamwidth and bandwidth. The effects of finite ground planes on radiation patterns was also investigated using Uniform Theory of Diffraction (UTD). Also, the effects of dieiectric covers was investigated. Finally, sorne analytical design relations and performance predictors are given and used in conjunction with the experimental data to evaluate the potential of these antennas for "personal communications".

ACKNO WLEDGMENT

This thesis is the culmination of more than one persons efforts or one persons ideas. The scope of an engineering postgraduate thesis demands the marshaling of numerous resources and acceptance of al1 forrns of assistance.

In this context 1 wish to M y , thank my thesis advisor, Dr. Yahia M.M. Antar for his support, guidance, gentleness and patience. Without, his unwavering confidence and his genuine persona1 interest in me, 1 am sure I would never have completed this thesis. 1 wamily thank Dr. Fan for shanng his knowledge with me and in always making time for my often times repetitive questions. For RMC and particularly the Engineering Department 1 acknowledge your generous support particularly fiom the administration and technical support staff. Without Martine Simard 1 would of been totalIy out of touch while researching in Ottawa at CRC.

To Dr. Apisak Ittipiboon thanks for helping me focus on the topic of rny thesis and for your guidance and help with the theoretical portions of this work. 1 also offer my appreciation to Dr. Aldo Petosa, for always making time to assist me and to intently listen and offer insight into my problems. For the technical staff that provided both material and technical support 1 am most grateful especially to Shaun Sarazin, who is a cheerfl kindred spirit and a fiiend who helped me tremendously.

More personalIy, 1 wish to thank my fiend Major Luc Lafieniere for prodding cajoling and supporting me throughout this whole process. There were times when 1 needed a gentle (firm) push to keep me going.

Finally, and most irnportanly, for Anne - two years with a new baby, long weeks and months alone in Ottawa, and a scared sometimes overwhelmed husband - your sacrifice which was far greater than mine made this work possible. thanks.

Dedicated to my wife and best friend, Anne You most of a l , made this possible.

Graydon, Dad wiu no longer be in Kingston.

TABLE OF CONTENTS

Chapter 1 .............................................................................................. 1

Introduction ...................................................................................................... 1 ................................................................................................... 1.1 Overview I ........................................... ................................................ 1.2 Objective .. 2

1.3 Goal and Scope of Research .................... ... .................... .. ........................ 3 ............................................................. 1.4 Organization .... ....................... 5

Chapter 2 .............................................................................................. 7

Microstrip Patch Antennas for Personal Communications ............................... 7 .......................................................................... 2.1 Overview .................... ..- 7

2.2 Polarkation ............................................................................................... 7 2.2.1 Polarkation States .................................................................................. 8 2.2.2 Circular Polarized Antemas ............................................................... 1 1

....................................................................... 2.3 Microstrip Patch Antemas 1 1

...................................................................... 2.3.1 Circular Polarized MPAs 13 2.4 Summary o f MPA's for Persona1 Communications ................................... 15

Chapter 3 ........................................................................................... 16

....................................................................................... Dielectric Resonators 16 3.1 Overview ................................................................................................. 16

....................................................... 3.2 Introduction to Dielectric Resonators 16 .............................................. 3.2.1 Dielectric Resonators as Circuit Elements 17

......................................................... 3.2.2 Dielectric Resonators as Antennas 18 ..................................................................... 3.2.3 Linear Polarized Antennas 19 ................................................................... 3.2.4 Circular Polarized Antemas 21 ................................................................... 3.3 CP DRA Mode1 Development 26

3.3.1 Method ................................................................................................. 26 ............................................ 3.3.2 Microwave Dielectric Resonators - General 26

................................................................................. 3.3.3 Simple DR Mode1 3 2 ................................................................ 3.3.4 Models for Cylindncal DR'S 36 .................................................................. 3.3.5 Models for Rectangular DRs 37

......... 3.3.6 Modined Dielectric Waveguide Mode1 with Mked Magnetic W a b 39 ............................................................................. 3.3.7 CP Design Relations -48 .......................................................................... 3.4 Fzed S ystem and Fields 51

............................................................................................ 3.4.1 Structure 51 ..................................................................................... 3.4.2 Microstrip Line 52

....................................................................................... 3 .4.3 Aperture Feed 53 ............................................................ 3 .4.4 Aperture DRA Matching ... . . . 55

.................................................................................... 3.5 Radiation Models 5 6 ............................................ 3.5.1 Far Fields ftom Crossed Magnetic Dipoles 5 7

Chapter 4 ............................................................................................ 65

................................................................... Material. Design and Fabrication 65 ................................................................................................ 4.1 Overview 6 5

........................................................................................ 4.2 Elernent Design 65 .......................................................................................... 4.3 Aperture Feed 69

Chapter 5 ............................................................................................ 72

................... .......~............................ Experimental and Theoretical Results .. 72 ................................................................................................. 5.1 Overview 72

........................................................................ 5.2 Measurement Techniques -73 5.2.1 Radiation Pattern and Polarization ................................................ 7 3 5.2.2 Measurement Equipment and Measurement Error .................................. -75

.............................................................................. 5.3 Antenna Performance 7 7 .. 5.3.1 Multiple Coupling Positions ................................................................... 78

.............................................................................. 5.3.2 Resonant Frequency 78 .......................................................... 5.3.3 Q-Factor (Irnpedance Bandwidth) 81

................................................................................. 5.3.4 Radiation Patterns 82 * *

........................................................................................... 5.3.5 Directivity 87 5.3.6 Gain ..................................................................................................... 88

........................................................................... 5.3.5 Radiation Efnciency -90 ................................................................... 5.4 F'ite Ground Plane Effects 9 2

............................................................................................. 5.4.1 Overview 9 2 5.4.2 DRAs on Finite Ground Planes ............................................................. 94

............................................................. 5.4.3 Uniform Theory of Dfiaction 100 5.5 Dielectric Covers ................................................................................. 104

Chapter 6 ........................................................................................... 109

................................................................ Conclusion and Recommendations 109 6.1 Introduction ........................................................................................... 109

........... 6.3 Design Procedure .. ................................................................... 1 1 1 6.4 CP DRA Performance versus Printed Technology .................................. 112

......................... 6.5 Conclusions of Results ..- ......................................... 114 .......................................................................................... 6.6 Future Work 116

Annex A ............................................................................................. 118

Loss Tangent ................................................................................................. 118

Annex B ............................................................................................. 119

............................... Resonant Frequency and Q-Factor Prediction Program 119

Annex C ............................................................................................. 121

............................................. DRA Return Loss (SII) and Smith Chart Plots 121

......................................................................................... Annex D J 4 7

. .............................*............................. Radiation Patterns Spinning Linear 147

Crossed Dipote Radiation Pattern Prediction Program .........................O...... 160 ............................................................................................. Annex F 161

Linear Radiation Plots of Orthogonal Fields ............................................. 161

Annex G ............................................................................................ 173

............................. Large and Smatl Ground Plane Axial Ratio Cornparison 173

............................................................................................ Annex H 180

........................................................................ UTD Diffraction Coefficients 180

Annex I .............................................................................................. 182

UTD Program .............................................................................................. 182 ..................... 1.1 Matlab UTD Program for Rectangular Finite Ground Planes 182

... 1.2 Matlab UTD Wedge Dfiaction Subrouthe ....................................... 190 1.3 MatIab UTD Transition Function ............................................................ 192

............................................................................................. Annex J 193 ........................................ Measured and Predicted (Normalized) UTD Plots 193

REFERENCES .............................................................................................. 199

LIST OF FIGURES

Nurnber Page .............................................................. Figure 2-1 Polarkation Examples 8

Figure 2-2 Basic Microstrip Patch Antenna Configuration ............................. 12 ...................................................... Figure 2-3 MPA's for Circular Polarization 14

Figure 2-3 MPA's for Circular Polarization ................................................. 14 Figure 3-1 Sub- Array of Chopped Corner DRA .............................................. 22

................................................... Figure 3-2 Active Quarter-Wavelength Array 23 Figure 3-3 Slot-Fed Cruciforrn Antenna ............................................................ 23 Figure 3-4 Cylindrical Ring DRA with Dual Probes .......................................... 24 Figure 3-5 Rectangular CP DRA with Single Slot Feed ...................................... 25 Figure 3-6 Parallel Resonant Circuit and Normalized Response ..................... 27 Figure 3-7 Dissimilar Media Interface with Incident Plane Wave ..................... 28 Figure 3-8 Infinite Rectangular Dielectric Waveguide ................................... 39 Figure 3-9 Transverse E & H Fields in a Rectangular DR ............................... 40 Figure 3-10 Truncated Dual Mode DR with End Wall Approximations ........... 45

.................................. Figure 3-11 Ideal SI1 Response of Dual Mode CP DRA 49 .................. Figure 3-12 Cross-section of a Microstrip Line (Quasi TEM mode) 52

........................................................... Figure 3-13 Equivalent Magnetic Dipole 54 ................................... ..................... Figure 3-14 Crossed Magnetic Dipoles .. 58

............................................. Figure 3-15 Crossed Magnetic Dipoles and Image 6 2 .......................................................... Figure 4-1 Aperture Feed Configuration 7 0

................................................ Figure 5-1 Theoretical Field Patterns at Phi = 0 83 ... Figure 5-2 Measured Orthogonal Polarized Fields from DR4 (mid coupling) 84

........... Figure 5-3 DRA Axial Ratio with Frequency on a Large Ground Plane 85 Figure 5-4 Wheeler Cap Antenna Measurement Setup ..................................... 90

.............. Figure 5-5 DRA Axial Ratio with Frequency on Finite Ground Planes 95 Figure 5-6 DRA on Finite Ground Plane Geometry for Calculating UTD Rays101

Figure C-1 Return Loss Plot of DR1 Upper Linear Mode .............................. 121 Figure C-2 Smith Cjart Plot of DR1 Upper Linear Mode ................... ...... 121 Figure C-3 Return Loss Plot of DR1 Upper Linear Mode (Kydex) ................. 122

................. Figure C-4 Smith Chart Plot of DR1 Upper Linear Mode (Kydex) 122 ............................... Figure C-5 Return Loss Plot of DR1 Lower Linear Mode 123 .............................. Figure C-6 Smith Chart Plot of DR1 Lower Linear Mode 123

.............. Figure C-7 Return Loss Plot of DR1 Lower & Upper Linear Modes 124

.............. Figure C-8 Smith Chart Plot of DR1 Lower & Upper Linear Modes 124 ................. Figure C-9 Return Loss Plot of DR1 Lower Linear Mode (Kydex) 125 ............... Figure C-10 Smith Chart Plot of DR1 Lower Linear Mode (Kydex) 125

Figure C-11 Return Loss Plot of DR1 CP Mode .............................................. 126 .............................................. Figure C-12 Smith Chart Plot of DR1 CP Mode 126

................................ Figure C-13 Return Loss Plot of DR1 CP Mode (Kydex) 127

................................ Figure C- 14 Smith Chart Plot of DR1 CP Mode (Kydex) 127 ............................. Figure C-15 Return Loss Plot of DR4 Upper Linear Mode 128 ............................. Figure C-16 Smith Chart Plot of DR4 Upper Linear Mode 128 ............................. Figure C-17 Retum Loss Plot of DR4 Lower Linear Mode 129 ............................. Figure C-18 Smith Chart Plot of DR4 Lower Linear Mode 129

............. Figure C-19 Return Loss Plot of DR4 Upper & Lower Linear Modes 130 ............ Figure C-20 Smith Chart Plot of DR4 Upper & Lower Linear Modes 130

............... Figure C-21 Return Loss Plot of DR4 Upper Linear Mode (Kydex) 131

............... Figure C-22 Smith Chart Plot of DR4 Upper Linear Mode (Kydex) 131

............... Figure C-23 Return Loss Plot of DR4 Lower Linear Mode (Kydex) 132

............... Figure C-24 Smith Chart Plot of DR4 Lower Linear Mode (Kydex) 132 Figure C-25 Return Loss Plot of DR4 Upper & Lower Linear Modes (Kydex) 133 Figure C-26 Smith Chart Plot of DR4 Upper & Lower Linear Modes (Kydex) 133

........................................ Figure C-27 Return Loss Plot of DR4(M) C P Mode 134 ....................................... Figure C-28 Smith Chart Plot of DR4(M) CP Mode 134

.......................... Figure C-29 Return Loss Plot of DR4(M) C P Mode (Kydex) 135

.......................... Figure C-30 Smith Chart Plot of DR4(M) CP Mode (Kydex) 135

Figure C-31 Return Loss Plot of DR4 (U) CP Mode ....................................... 136 Figure C-30 Smith Chart Plot of DR4 (U) CP Mode ....................................... 136 Figure C-33 Return Loss Plot of DR4 (U) CP Mode (Kydex) .......................... 137 Figure C-34 Smith Chart Plot of DR4 (U) CP Mode (Kydex) ......................... 137 Figure C-35 Retum Loss Plot of DR4 (L) CP Mode ...................................... 138 Figure C-36 Smith Chart Plot of DR4 (L) CP Mode ........................................ 138 Figure C-37 Return Loss Plot of DR4 (L) CP Mode (Kydex) .......................... 139 Figure C-38 Smith Chart Plot of DR4 (L) CP Mode (Kydex) ............. ....... 139 Figure C-39 R e t u n Loss Plot of DR5 Lower Linear Mode ........................... 140 Figure C-40 Smith Chart Plot of DR5 Lower Linear Mode ............................. 140 Figure C-41 Return L o s Plot of DR5 Upper Linear Mode ............................. 141 Figure C-42 Smith Chart Plot of DR5 Upper Linear Mode ............................. 141 Figure C-43 Return Loss Plot of DR5 Upper & Lower Linear Modes ............. 142 Figure C-44 Smith Chart Plot of DR5 Upper & Lower Linear Modes ............ 142 Figure C-45 Return Loss Plot of DR5 Lower Linear Mode (Kydex) ............... 143 Figure C-46 Smith Chart Plot of DR5 Lower Linear Mode (Kydex) ............... 143 Figure C-47 Return Loss Plot of DR5 Upper Linear Mode (Kydex) ............... 144 Figure C-48 Smith Chart Plot of DR5 Upper Linear Mode (Kydex) ............... 144 Figure C-49 Return Loss Plot of DR5 CP Mode ........................................... 145

.............................................. Figure C-50 Smith Chart Plot of DR5 CP Mode 145 Figure C-51 Return Loss Plot of DR5 CP Mode (Kydex) ............................... 146 Figure C-52 Smith Chart Plot of DR5 CP Mode (Kydex) ................................ 146

............................ Figure D-l Measured CP Pattern for DR1 on SLot 8 (LGP) 147 ............. Figure D-2 Measured CP Pattern for DR1 on Slot 8 ( L W & Kydex) 147

............................. Figure D-3 Measured CP Pattern for DR1 on Slot 8 (SGP) 148 ............. Figure D-4 Measured CP Pattern for DR1 on Slot 8 (SGP & Kydex) 148

........................ Figure D-5 Measured CP Pattern of DR4 (U) on Slot 2 (LGP) 149 ....... Figure D-6 Measured CP Pattern for DR4 (U) on Slot 2 (LGP & Kydex) 149

Figure D-7 Measured CP Pattern for DR4 (U) on Slot 2 (SGP) ............... .... 150 Figure D-8 Measured CP Pattern for DR4 (U) on SIot 2 (SGP & Kydex) ....... 150

Figure D-9 Measured CP Pattern for DR4 (M) on Slot 2 (LGP) ..................... 151 Figure D-IO Measured CP Pattern of DR4 (M) on Slot 2 (LGP & Kydex) ...... 151 Figure D-11 Measured CP Pattern for DR4 (M) on Slot 2 (SGP) .................... 152 Figure D-12 Measured CP Pattern for DR4 (M) on Slot 2 (SGP & Kydex) .... 152 Figure D-13 Measured CP Pattern for DR4 (L) on Slot 2 (LGP) ..................... 153 Figure D-14 Measured CP Pattern for DR4 (L) on Slot 2 (LGP & Kydex) ..... 153 Figure D-15 Measured CP Pattern for DR4 (L) on Slot 2 (EGP) ..................... 154 FIgure D-16 Measured CP Pattern for DR4 (L) on SIot 2 (SGP & Kydex) ..... 154 Figure D-17 Measured CP Pattern for DR4 (L) on Slot 2 (VSGP) .................. 155 Figure D-18 Measured CP Pattern for DR4 (L) on Slot 2 (VSGP & Kydex) ... 155 Figure Da19 Measured CP Pattern for DR4 on Slot 2 (SqSGP) .............. ......... 156 Figure D-20 Measured CP Pattern for DR4 (L) on Slot 2 (SqSGP & Kydex) . 156 Figure D-21 Measured CP Pattern for DR4 (L) on Slot 2 (VvSGP) ................ 157 Figure D-22 Measured CP Pattern for DR4 (L) on Slot 2 (VvSGP & Kydex) . 157 Figure D-23 Measured CP Pattern for DR5 on Slot 4 (LGP) ............................ 158 Figure D-24 Measured CP Pattern for DR5 on Slot 4 (LGP & Kydex) ........... 158 Figure D-25 Measured CP Pattern for DR5 on Slot 4 (SGP) ........................... 159 Figure D-25 Measured CF Pattern for DR5 on Slot 4 (SGP & Kydex) ............ 159

............ Figure D-26 Measured CP Pattern for DR5 on Slot 4 (SGP & Kydex) 159 Figure F-1 Dual Orthogonal Plots of DR1 on Slot 8 (LGP) ............................. 161

.............. Figure F-2 Dual Orthogonal Plots of DR1 on Slot 8 (LGP & Kydex) 161 Figure F-3 Dual Orthogonal Plots of DR1 on Slot 8 (SGP) .............................. 162

.............. Figure F-4 Dual Orthogonal Plots of DR1 on Slot 8 (SGP & Kydex) 162 Figure F-5 Dual Orthogonal Plots DR4 (U) on Slot 2 (LGP) ........................... 163

........ Figure F-6 Dual Orthogonal Plots of DR4 (U) on Slot 2 (LGP & Kydex) 163 Figure F-7 Dual Orthogonal Plots of DR4 (U) on SIot 2 (SGP) ....................... 164 Figure F-8 Dual Orthogonal Plots of DR4 (U) on Slot 2 (SGP & Kydex) ........ 164 Figure F-9 Dual Orthogonal Plots of DR4 (M) on Slot 2 (LGP) ...................... 165 Figure F-10 Dual Orthogonal Plots of DR4 (M) on Slot 2 (LGP & Kydex) ..... 165 Figure F - l l Dual Orthogonal Plots of DR4 (M) on Slot 2 (SGP) ..................... 166

xii

Figure F-12 Dual Orthogonal Plots of DR4 (M) on Slot 2 (SGP & Kydex) ..... 166 Figure F-13 Dual Orthogonal Plots of DR4 (L) on Slot 2 (LGP) ..................... 167 Figure F-14 Dual Orthogonal Plots of DR4 (L) on Slot 2 (LGP & Kydex) ....... 167 Figure F- 15 Dual Orthogonal Plots of DR4 (L) on Slot 2 (SGP) .................. ... 168 Figure F-16 Dual Orthogonal Plots of DR4 (L) on Slot 2 (SGP & Kydex) ...... 168 Figure F-17 Dual Orthogonal Plots of DR4 (L) on Slot 2 (VSGP) ................... 169 Figure F-18 Dual Orthogonal Plots of DR4 (L) on Slot 2 (VSGP & Kydex) .... 169 Figure F- 19 Dual Orthogonal Plots of DR4 (L) on Slot 2 (SqSGP) .................. 170 Figure F-20 Dual Orthogonal Plots of DR4 (L) on Slot 2 (SqSGP & Kydex) .. 170 Figure F-21 Dual Orthogonal Plots of DR4 (L) on Slot 2 (VvSGP) ................. 171 Figure F-22 Dual Orthogonal Plots of DR4 (L) on Slot 2 (VvSGP & Kydex) .. 17 1 Figure F-23 Dual Orthogonal Plots of DR5 on Slot 4 (LGP) ........................... 172 Figure F-24 Dual Orthogonal Plots of DR5 on Slot 4 (LGP & Kydex) ............ 172

............. ...................... Figure G-1 Axial Ratio versus Frequency of DR1 ... 173 Figure G-2 Axial Ratio versus Frequency of DR4 (M) .................................... 174 Figure G-3 Axial Ratio versus Frequency of DR4 (U) ..................................... 175 Figure G-4 Axial Ratio versus Frequency of DR4 (L) Part A .......................... 176 Figure 6 - 5 Axial Ratio versus Frequency of DR4 (L) Part B .......................... 177

............................................ Figure G-6 Axial Ratio versus Frequency of DR5 178 Figure J-1 Predicted and Measured Orthogonal Fields of DR1 LGP .............. 193

............... Figure 5-2 Predicted and Measured Orthogonal Fields of DR1 SGP 193 ............ Figure 5-3 Predicted and Measured Orthogonal Field of DR4M LGP 194 ........... Figure 5-4 Predicted and Measured Orthogonal Fields of DR4M SGP 194 ............ Figure J-5 Predicted and Measured Orthogonal Fields of DR4U LGP 195 ............ Figure 5-6 Predicted and Measured Orthogonal Fields of DR4U SGP 195 ............ Figure 5-7 Predicted and Measured Orthogonal Fields of DR4L LGP 196

Figure 5-8 Predicted and Measured Orthogonal Fields of DR4L SGP ............ 196 ......... Figure J-9 Predicted and Measured Orthogonal Fileds of DR4L VSGP 197

Figure J-10 Predicted and Measured Orthogonal Fields of DR4L SqSGP ...... 197 Figure J-11 Predicted and Measured Orthogonal Fields of DR4L VvSGP ...... 198

Figure 5-12 Predicted and Measured Orthogonal Fields of DR5 L W ............ 198

LIST OF TABLES

Number Table 2-1 Table 3-1 Table 4-1 Table 4-2 Table 4-3 Table 4-4 Table 5-1 Table 5-2 Table 5-3 Table 5-4 Table 5-5 Table 5-6 Table 5-7 Table 5-8

Page

Special Polarkation States .......................................................... 9 Summary of Results for Parallel Resonators .................................... 28

CP DRA Elernents Fabricated ................... .... ............................ 67 Physical and Mechanical Properties of DRA Material ...................... 68 Microstrip Line to Aperture Dimensions ........................................... 71 Electrical Properties of RTfDuroid 6010 ............................................ 71 Polarization Measurement Methods .................................................. 73 Measured Resonant Frequencies (GHz) and Magnitudes (dB) ......... 79 Error Table of Predicted Frequencies to Measured Values (GHz) .... 80 Measured 3 dB Impedance Bandwidths venus Predicted ................. 82 Measured Axial Ratio Bandwidth and Beamwidth ........................... 86 Approximate Directivity Estimated from System Dimensions ........... 88 Measured and Corrected Gains of Antennas on Boresight ................. 89 Estimated DRA Efficiencies usin Wheeler Cap Method .................... 92

Table 5-9 Axial Ratio Bandwidth and Beam width for finite Ground Planes .... 95 Table 5-10 Percentage Change in Characteristics due to Firite Ground Planes 96 Table 5-11 Gain and Directivity with Finite Ground Planes ............................. 98 Table 5-12 Dielectric Cover Specifications .................................................. 104

........................................ Table 5-13 DRA Characteristics with Kydex Cover 105 Table 5-14 Cornparison of DRA Characteristics (Cover vs . No Cover) ........... 106 Table 6-1 Summary of Circularlp Polarized MPAs ......................................... 113 Table G-1 DRA System Characteristics versus Size of Ground Plane ............. 179

ABBREVIATIONS

AR AUT

BW CP CRC dB dBi dB ic DR

DRA

DWGM GHz

GPS GTD

IMW LP

MIC

MMW MoM MPA

PEC PMC RMC UTD

VSWR

Axial Ratio Antenna Under Test Bandwidth Circular Po larization Communications Research Centre Decibels Decibels (referenced to an isotropic source) Decibels (referenced to a circularly polarized isotropic source) Dielectric Resonator Dielectric Resonator Antenna

Dielecmc Waveguide Model Gigahertz ( 1 O' hertz)

Global Positioning S ystem Geometrical Theory of Diffraction Imperfect Magnetic Wall Linear Polarizatio n Microwave Integrated Circuit

Mixed Magnetic WaUs Method of Moments Microstrip Patch Antenna

Perfect Elecmc Conductor Perfect Magnetic Conductor Royal Military College of Canada Uniform Theory of Diffraction Voltage Standing Wave Ratio

xvi

C h a p t e r I

Introduction

1.1 Overview

The demand for "Personal Communications Systems (PCS)", which includes: Global Positioning Systerns (GPS); indoor and outdoor 'wireless' communications; terrestrial and satellite ceilular telephones; and a host of medical, military and poce data, voice and video communications is increasing rapidly. AU of these applications require highly efficient, srnail, low profile antennas, capable of operating over a large bandwidth (3% or greater). Most of these applications employ portable devices that are required to transmit high speed data (9600 baud or greater) either terrestrally or extraterresmally using a variety of polarization's (linear & circular) to achieve low bit error rates. The criteria required to enable the portability, high data rates and polarization diversity are - high efficiency >958 ; large bandwidth (>3%) to enable high data rate transmission, and the ability to operate with either a linear or circular polarized wave. Consequently there is an increasing demand for low cost, Light weight and efficient antenna systerns that will conform to the obvious requirement of portability, yet remain stable, reliable and reproducible.

Another advantage, is that the antema's design process be fkequency scaleable. This stems Born the fact, the above communication applications currently operate in the L-band (1-2 GHz), however, due to forecasted congestion, other bands in the WKa specmirn (20/30 GHz) have k e n allocated specifically for use in civilian satellite communications. A further advantage, is that these antennas ( E s ) are capable of producing both linear and circularly polarized waves.

Such antenna technology exists in the form of Microstnp Patch Antennas (MPAs), which have seen considerable research into there application for the above communications requirements. They have also demonstrated a lirnited ability to operate in the K/Ka bands."' However, sorne disadvantages of single patch antennas

are their relatively narrow 3 dB axial ratio bandwidth (-1 to 1.5% for simple geometry's) and their low radiation efficiency (-80%). The low efficiency is due to high inherent conductor and surface wave losses. The surface wave losses aiso become worse with higher fiequencies because of stronger excitation of surface waves. The surface waves also have a distorting effect on the radiation patterns. Some research has been aimed at improving impedance bandwidths and at compensating for conductor losses for higher gain, by using stacked or coplanar parasitic sub-array configurations, as well as using active devices. ri.z.3.41

Recently, research into Dielectric Resonator Antemas (DRAs) has shcwn they may have some potential for use in persona1 communication systemsrS1 suice DRAs in cornparison to MP As offer higher radiation efficiencies (-98 %) , wider bandwidths (>3% for simple geometry's) and no excitation of surface waves. To date the effort has mainly k e n into the characterizhg of iinear polarized antennas, with simple geometry's, within the fiequency range of 4 to 40 GHz using various feed systerns. However, some recent papers have shown that a simple single feed mechanism can produce circular polarization at frequencies of 4 to 6 GHZ? This thesis will investigate the characteristics of single aperture fed CP DRA'S within the L and S bands in order to demonstrate there use as a possible alternative to MPA's for persona1 communication systerns.

1.2 Objective

The objective of this research was to investigate and develop a design process for rectangular circularly polarized dielectric resonator structures for possible use in persona1 communication systems. These devices were to then be characterized and compared to previous results rom similar geometry's for MPA's in order to demonstrate the$ ability as an alternative system Some possible applications for these DRA antennas are GPS, satellite cellular systems or indoor/outdoor cornputer networks. For most of these applications it is desirable to have a circularly polarked

antenna, hence the bulk of the issues to be addressed wiU be to optimize the design for CP operation.

The research undertaken was focused on the performance and characterization of CP rectangular DRA'S, exarnining such properties as far-field radiation patterns, losses, polarization ability, radiation efficiency, effects of finite ground planes and effects of dielectric covers. The intent was to characterize a practical antenna system packaged for use in any one of the applications mentioned above, and to present a simple design methodology that could produce stable, reliable and reproducible results.

1.3 Goal and Scope of Research

Given the above objective, the goal of this thesis was to develop a simple design methodology that would enable the design of simple single feed low profile circular polarized rectangular dielecnic resonator antennas that wo uld out-perform the state of the art MPA devices currently available. In so doing the validity of the first order design and engineering models used to develop and gain insight into the behaviour of these antennas would be demonstrated by cornparison to experimental results. The emphasis, was therefore, placed on designing and measuring the performance of several antennas of various shapes and permittivities. The secondary goal was to investigate sorne of the effects on the DRA'S performance when employed in a pseudo 'practical' package. This investigation was accomplished by operating the DRA'S produced above under differing configurations of finite ground planes and with a dielectic cover.

The state of the art for MPA's of sirnilar simple design and feed systems was First found, through a literature search (surnrnary provided in Table 6-1). Given these results, and the fact that to date most PCS devices operate in the L and S bands led to the setting of some broad design goals for this thesis. Sirnply stated these were to design a range of devices that would operate within a fiequency band of 2.1 to 2.4 GHz. This range is used for GPS, some celiular applications, and it is also used in

some 'wireless' Intranet applications. To ensure stable high data rate communications (9600 baud or greater) for portable applications, circular poiarization operation was chosen, with axial ratio bandwidths of 3 6 or greater. In a radical departure fiom MPA's, this bandwidth was to be measured at the 3 dB points, not 6 dB as is the n o m for MPA's, since the current research to date indicates the DRA would be capable of this more exacting standard. Finally, since the devices were to dernonstrate portable utility, with the inherent restrictions on power, size and weight, the DRA'S were to: have efficiencies >96%, such that as Little power as possible was wasted to any loss modes; be as small as possible to reduce their profde and weight.

The research for this thesis was primarily empixicai in nature, since the author had access to excellent research and test facilities. By reviewing this empincal research, the general reader, should gain useful information about the design process, fabrication and characterizatio n of the operation of such an antenna under closely approximated real world conditions. It would have been equally valid to explore a numerical investigation of the characteristics of a CP rectangular DRA. However, the scope of the research would have been more involved analytically, concentrating mostly on the properties of the DRA element, with less information about the effects of a practical implementation. Thus Little t h e would of k e n left. within the tirne fiame available, to investigate antenna fabrication, finite ground planes and dielectric cover effects.

This thesis work is complementary to an earlier introductory investigation of CP rectangular DKAs lq at 4 to 6 GHz. Taken together the significant property of fiequency scalability of DRA design is demonstrated, by cornparison of the more basic properties - resonant frequency, Q-factor, radiation pattern, efficiency and the axial ratio beamwidth and bandwidth. However, the work undertaken for this thesis expands on these basic properties and investigates the characteristics of not only the DRA element but also, its behaviour as a practical antema system including the fhite ground plane and dielectric cover effects. This thesis work was carried out to lay a

foundation for future, more rigorous research delving more deeply into the optirnization of CP DRA elements.

1.4 O rganization

This thesis is presented in a number of chapters. Chapter 1 provides a generaI ovewiew of the thesis, its approach, scope and a prcis of the goal. Chapter 2 contains a review of polarization, particularly circular polarization. It continues with a general discussion of Microstrip Patch h t e ~ a s . Next it provides a general introduction and then a rapid review of some of the work done to date on circularly polarized MPA's. The major design characteristics are presented and an identification of the advantages and disadvantages of this technology are introduced.

Chapter 3, contains a similarly structured review of dielectric resonator antennas. It continues with the analytical mode1 development, which includes a discussion on field configurations, modes of operation and first order design equations. It also, contains a brief overview of the aperture feed mechanism and a prfcis of the design tools and their use. to provide impedance matching of the aperture to the DRA for CP. Chapter 4 discusses the material specifications and the methods of design and fabrication of the systems used. It also, includes a bnef summary of the feed systerns.

AU the experimental results are presented in Chapter 5. First a description of the measurement techniques, equipment and errors are discussed. Next, the experimental and theoretical results are presented and any pertinent observations are made. All of the initial presentations are based on the k i n g on a large ground plane. The final two sections review all of the same constituent parameters (resonant fiequency, Q-factor, radiation pattern, efficiency and the axial ratio beamwidth and bandwidth) of the on the large ground plane, except the effects of finite ground planes and dielectnc covers are shown.

Finally, chapter 6 compares the results of this work with results of previous work. From this cornparison, some concIusions as to the rectangular DRA'S performance will be given. Also, the applicability of this configuration will be explored. After presenting the final CO nclusions based on the experimental and theoretical work some recornrnendations will be made for areas requing further research.

C h a p t e r 2

Microstrip Patch Antennas for Personal Communications

2.1 Overview

This chapter provides an introduction into polarization in general, and circular polarization in particular. Next, a general review of the research and development of MPA technology is given. The review begins with MPAs in general, but quickiy focuses on methods for producing circular polarized antennas. The intent is to outline sorne of the major advantages and disadvantages of this technology. In so doing the stage will be set, to introduce the DRA as an alternative to overcome some of the weaknesses of this existing and maturing technology.

2.2 Polanzation

Before reviewing the body of work concerning the employment of MPAs as circularly polarized elements it is prudent to provide a summary of definitions and requirements for polarized Es and circular polarization in particular.

The polarization of a wave is sirnply a description of the motion of the tip of the instantaneous electic field vector with tirne, at a fmed point in spacei7'. This electric field vector can then be decomposed into two orthogonal linear polarizatio ns, usually taken to be horizontal and vertical. The relative amplitudes and phases of these cornponents determine polarization of the wave. In the most general case, the horizontal and vertical components can have any amplitude and any relative phase, thus the resultant locus forrns an ellipse.

If the electric field vector only varies in amplitude, but is always oriented in one plane (spatially invariant), the field is linearly polarized. Most E s used today are linearly polarized, such as dipoles, monopoles, horns, MPAs, and DRAs. An is said to be circularly polarized when the electric field vector has constant amplitude, but rotates spatiaiIy at a constant rate. Examples of these three types of polarization are given in figure 2- 1.

I (a) Ellipcical Polanzation (b) Cirailu P o f ~ o n (c) Linear PoIanPtion

Figure 2- 1 Polarization Examples

Circularly polarized waves have some advantages in some applications. For example a CP wave operates better in rain and heavy fog with more consistent behaviour than LP, which is important in establishing a communication Iink. Also, since the instantaneous magnitude is invariant, a CP does not require spatial orientation for maximum power transfer, like an LP does. Another advantage of CP 's occurs with satellite to terrestrial Links. Here the receiver remain unaffected by the effect of Faraday Rotation as the signal passes through the ionosphere, uniike linearly polarized waves[*'.

2.2.1 Polarization States

The instantaneous electric field of a generally plane wave traveling in the +z direction can be decomposed into its x and y components as shown below:

where E, , E, = amplitudes of instantaneous electric field in x, y directions [V / m] o = radian fresuency = 21r f (rad / s)

2 0 = phase constant = - (rad / m) A

6 = phase by which the y component leads the x component

Each component represents a linear polarized wave. The resultant elecmc field, is the vector combination of these two components at any instant in time:

The t h e varying field which corresponds to this at z 4, is the same for ail points along the z axis. Therefore the resultant vector is:

( t ) = XE, c o s ( u t ) + FE2 cos(wt + 6 ) (2-4)

The length of this vector traces out an ellipse as a function of time, making one revolution every penod (T = l/f). As can be seen i5om table 2-1 there are a number of special cases, of polarization.

1 PARAMETER 1 POLARIZATION STATE

1 1 ato=O.rJZ (~=o)=B, and ( t = ~ / 4 ) = - j ~ * 6 = 0

6 = 90" LUiear Polarization 6 t h tilt angle r = tan*' EJEl Left Hand Circular Polarized (t) = XE, cos(ot) - j E , sin(wt)

I ( Tilt angle depends on the value of 6 Table 2-1 Special Polarization States

El = O

E2 = O

Linear PoIarization nominally dong y-mis Tilt angle depends on the value of 6 Linear Polarkation nominally dong x-mis

In the more general case we can show that the electric field actuaily describes an ellipse. Using the mgonometric identity below equation (2.4) becomes:

Using

c o s ( a f p ) = c o s a c o s p T s i n a s i n p E , ( t ) = E , ( C O S W ~ C O S ~ - s i n o t s i n 6 )

and substituting these hto independent of any tirne variation:

= Ji-(E, /E,I2

equation(2.5) we get the following result that is

This is an equation of an ellipse when Ex and E, are treated as x and y positions in a rectangular graph. They can easily be transformed to Ee and E+ for a spherical graph. The polarization can have any shape (axial ratio) and orientation (tilt angle) or sense of rotation ('handedness').

A usefl neasure, comrnonly used, for the quality of CP is the axial ratio, which, as indicated above, is the ratio of the two orthogonal field components. The components are either rneasured in the two principle planes, or as the ratio of the magnitudes of the major and minor axis, of the polarization ellipse (figure 2-la).

Axial Ratio (AR) = (2-7)

AR = 1, is by definition perfect circular polarization, although no such antenna exists. The purity of polarization usually deteriorates as observations move away

kom boresight (extent and magnitude can be dependent on inite ground plane effects). The polarization emanated from a practical CP is generaily eiliptical, with varying degrees of ellipicity throughout the pattern.

2.2.2 CircuIar Polarized Antennas

The are two general methods to create CP. Type 1 CP antemas produce CP by virtue of their unique structure. Examples of type 1 E s are h e h and spirals. The sense of polarization is determined by the sense of the winding of the helix or spiral.

Type 2 CP Es produce CP as a result of a special feed structure or some mode degeneracy characteristics. These E s must be able, by virtue of the two previously rnentioned mechanisms, explicitly generate spatialiy orthogonal components in phase quadrature and of equal amplitude. The Es under study in this thesis are ail of the type 2 variety and thus must be able to meet these three requirements for CP:

a. Each field component must be of equal amplitude;

b. There must be spatial orthogonality between each field component; and

c. There must be tirne quadrature between each field component.

A more detailed discussion of polarization is available kom either Harold ~ o t t ' s ' ~ ' or Warren ~tutzrnan's'~' book.

2.3 Microstrip Patch Antennas

In its sirnplest form the MPA is composed of some arbitrarily shaped radiating patch separated fiom a ground plane by a dielectric substrate as shown in figure 2-2. The radiating patch may be a simple resonant circular or rectangular shape, a resonant dipole, slotted patch or some other construction. Since the early work by Munson in the mid 1970's ['O' MPAs have seen rapid development. Most of this development has focused on irnproving upon, or compensating for, some inherent limiting factors.

These include narrow band performance (1 - 6 %), and low radiation efficiency due to high conductor losses ?om the rnetallic patch and surface wave excitation - which distorts the far-field radiation pattern and causes extra power loss, and thus less radiation efficiency. These limiting factors become dramaticaily worse at millimeter frequencies where there is stronger excitation of surface waves and thus greater distortion. Also, the conductor losses are greater, thereby further reducing radiation

Radiating Patch

Dielechic S u b e

d Plane

Figure 2-2 Basic Microstrip Patch Antenna Configuration

Despite these Limititions a large body of work with MPAs has produced some weil proven configurations and designs['3114*151 . Also, extensive current research has been airned at compensating for conductor loss (for high gain), and for irnproving bandwidths by using active de~ices''*~'. Other approaches include: parasitic resonators or thicker substrates to irnprove bandwidth; or different patch sizes or spur iine fiiters to permit multiband operation [16.17,13.181 . Ali these achieve greater performance but at the cost of eiiminating the MPAs' prime advantages of king simple, small, low cost and conforma1 in nature. Also, the thicker substrates cause increased surface wave excitation[191, and increasing the conductor size or using multiple patches increases conduction oss ses,['^^ both of which reduce the radiation efficiency.

One very cornmon analysis method for analyzing the MPA is to consider the patch and ground plane as forming the upper and lower surfaces of a resonant cavity.

The side walls (in the dielectric) are then considered to be perfect magnetic wails (PMC), while the metal surfaces are considered as perfect electric w a h (PEC)'~**"'. It is this approach that wiU be followed as it has direct application to the theoretical developrnent of this thesis.

2,3.1 Circular Polarized MPAs

MPAs are inherently linearly polarized (when driven in the fundamental mode). therefore, to produce CP radiation fiom these s requires the use of simultaneous multiple modes or multiple feeds on a single element, or multiple elernents. Thus these Es are classed as type 2 CP 's. A variety of designs using multiple orthogonal radiators or using various feed mechanisms (hybrids or phase shifter/power dividers) have k e n shown in the literature. However, such designs are cornplicated and relatively large in comparison to single element designs and, hence, become unwieldy when size is limited in area or thickness.

In order to provide for later comparison to the single feed single element DRA the rest of this summary will be restncted to discussing the designs employing single elements. The single patch can have single or multiple feeds. Double feed MPAs achieve the required mode orthogonality by the use of hybnd or quarter-wave delay l i n e ~ [ ~ ? Whe reas, the single feed MPAs excite two nearly degenerate modes by using a perturbation segment. If adjusted properly, the boresight axial ratio WU be extremely srnall, theoretically approaching unit y.

For square or nearly square patches, this perturbation can be achieved by truncating corners, introducing inductive or capacitive discontinuities (slots or notches) or by feeding the nearly square patch nom a corner [alUv26J. Figue 2-3 presents a selection of some proven configurations. While these E s are shown as edge fed they may be equally excited by using other techniques such as dots, probes, or proximity coupling.

Most of the results pubiished for the configurations shown in figure 2-3 are quite limited. The bandwidths are normaUy reported as between 1% to 3% for axial ratios not greater than 6 dB for those E s operating in the L and S bands. Also, for this 6 dB axial ratio. beamwidths ranged from 1.5% for the eiliptical LEIn' to about 60% for diagonal slot loaded lEi2? One of the more recent studies was of a simple rectangular patch structure that was proximity fed, offset fiom the centre of the patch operating at 1.575 GHz. It reported a 10 dB irnpedance bandwidth of 3.54. and a 120 degree bearnwidth with Iess than 2 dB axial ratio. However, the bandwidth reported was only 0.55% at this same axial ratior1? Although no reference was made to the radiation efficiency this suffers from the same conductive losses inherent in all MPAs and thus it would be expected to be about 80 - 85%.

Offset Feed Slot Loaded Nearly Square Ellip tical

Figure 2-3 MPA's for Circular Polarization

These results, and those from the slot Ioaded patch are excellent representatives of the abilities of simple MPAs within the L and S bands, and are singled out sirnply for Iater cornparison to the simple slot fed DRA proposed in this thesis.

2.4 Summary of MPA's for Personal Communications

This chapter has reviewed polarization, particularly the requirements for the creation of circular polarization fiom inherently linear polarized elements. Also, a review was presented of the various architectures proposed for enhancing, eliminating, or compensating for the inherent Limitations of narrow bandwidth, low gain, and low radiation efficiency. Next, a subset of simple MPAs designed to produce circular polarization was presented, giving some quantification as to there relative performance. Fiiially, a particularly recent and simple design that is similar in construction, and operation to the proposed DRA was discussed as a particular example for future cornparison. This chapter was not intended to be a thorough review, but merely an introduction into the large body of research into CP MPAs and there relative 0verai.I performance levels. In doing so, the foundation has been laid fi-om which to introduce a new and a frarnework introduced fkom which to asses its relative perfomance.

C h a p t e r 3

Dielectric Resonators

3.1 Overview

This chapter firstly, will provide a brief historieal background into the research into dielectic resonators. From this foundation, the historical employment of DR's as circuit elements, and the research undertaken in this area wiU be surnrnarized. Continuing on this theme the research and employment of DR's as hear ly and circularly polarized elements will be presented. Next, the development of the mode1 used in this thesis will be presented ending with an analytical description of the fields at the periphery of the element. From this development, a design relation for establishg LP and CP resonant fiequencies, as they relate to the physical dimensions of an isolated DRA wiU be derived. FinaIly, a brief description of the feed mechanism wll be given.

3.2 Introduction to Dietectric Remnators

Diefectrics as resonators were first proposed by Richtmyer in 1939r?81 however it was not until the 1960's when suitable dielectric rnatenals were available for any applications. A typical dielectric resonator (DR) is arbitrarily shaped, and made of low-loss, high permittivity, temperature stable material of resonant dimensions at its frequency of operation (i.e. the dimensions are proportional to the operating wavelength).

Early research was into the use of DR's as microwave components, such as waveguide filters or oscillators. As better materials appeared, more progress was made into employing DR's as rnicrowave circuit elements. A significant step occurred when C O M [ ~ ~ ' demonstrated in 1968 that a Titanium Qxide DR filter could be made, that was 3 to 5 percent srnalier in volume, to an equivalent waveguide filter. As interest grew so did the amount of theoretical and analytical research. This research

demonsnated the advantages of DR's as srnaii, iight, low cost, microwave elements that could easily be integrated with WC's.

However, to fuUy employ these new devices more research was required that could classify more of their circuit properties like: resonant fiequency, modes, coupling to other microwave circuits and Q-factors. Some significant papers were published by ~ee"", who examined the natural resonant frequencies and modes of DR's. Karp et af3" offered sorne experirnental data on circuit properties of DR's. In the 1970's Van Bladel conducted significant theoretical work on the modal resonance behaviour of lossless, very high permittivity re~onators '~~* '~~. Further work with ~ e r p l a n k e n [ ~ * ~ ' exarnined resonance's in ring resonators and developed the Quality (Q) factor. As the analytical modeling progressed, more accurate predictions of circuit properties were possible. The use of the variational technique used by Konishi et al'"] to investigate the resonant frequencies of a cylindncal dielectric resonator was

[37,38] further developed in the late 70 s and early 80's"~'. AU these models used variations of the Dielectric Waveguide Model (DWM) developed through the work of Okaya & Barash and ~arcatili"?

Increasingly, with the development of cornputers, numerical analysis of many shapes of DR's have been solved for their resonant fkequency and Q-factors. Tsuji et ali4'' using an approximate mode matching method were able to predict, quite accurately, the complex resonant fiequency and Q-factor of a cylindrical disk. Various other authors have carried out analysis's of DR'S using a variety of numerical techniques; Boundary Elernent rnethod, Conjugate-Gradient Fast Fourier Transform rnethod, Method of Moments etc. An excellent guide and overview of the analytical and numerical techniques used with DR's was provided by a monograph in the book "Dielectric Resonators" edited by Kajfez and ~uillon''?

3.2.1 Dielectric Resonators as Circuit Elements

As already mentioned the early use of DR'S was as microwave circuit elements. Toward this goal DR research concentrated on concerns of coupling,

frequency tuning and other properties usehl in describing the effect a DR would have in a microwave circuit. A good surnmary of the of this work up to 198 1 was provided by Plourde and en'^^'.

3.2.2 Dielectric Resonators as Antennas

Although flrst suggested by Richtmyer in 1939, that a DR must radiate, they were not even considered as elements until 1968, when Sager and si'^' proposed using thern as such. The first reported use of DRs as elements however, was not until 198 1, when Birand and ~els thorpe[~ '~ reponed the construction of a iinearly polarized array of dielectric elements.

The idea of DRs as elements is intuitively clear when they are compared to a metallic resonator. In a metallic resonator, low losses exist in the conducting walis, but because of these electric wall boundaries no radiation loss can occur. However, since the DR wails are not conductors, there is a loss mode which is not present in metallic cavity resonators; radiative losses. It is this lors mode that is exploited when the DR is operated as an element.

DRAs have many features that rnake them attractive as a substitute for MPAs. Since they are non-metallic, they are free of conduction Iosses, and dielectric Iosses are usually very small. They have an inherently wider bandwidth (5 - 15%) than MPAs and are easily integrated with MIC's. There bandwidth is controUable by the perrnittivity as are its dimensions, which are much smaller than its metal equivalent.

Finally, as there is no metaVdielectric interface, as with the MPA, the surface wave phenomena is avoided. Given this and the fact there are no conducive losses the DRA is a much more efficient radiator.

Since this thesis is prirnarily about the use of L and S band circularly polarized DRA's only a brief review of the previous research into iinear polarized 's wiU be given. However, it should be emphasized that this thesis is largely based on previous research into DRA's, both linear and circular polarized.

As mentioned above the f is t employment of dielectrics as elements was by Birand and Gelsthorpe. Their array was designed to operate at 35.5 GHz. The design although using simple anay theory with the assumption of loose coupling gave good agreement with measured data. Their design employed a dielectric waveguide placed on a ground plane that proximity fed the non-resonant dielectric elements.

Cvlindrical. Rectangular and Hemis~hencal with h o be Work was carried out by Long and McAUister et a1[as47*48' using probe feeds for the elements mentioned. at fkequencies of 8 to 12 GHz with elements of E, = 15.2, 8.9, 6.6 and 4.5. Their initial theoretical analysis of the cylindncal element, assumed a cornplete rnagnetic wall approximation (PMC). However, this approximation did not work well with the rectangular shape. In order to better predict the resonant frequencies. the model was adjusted by considering the DRA as existing inside a below-cutofF waveguide with PMC w a k - the Dielectric waveguide model (DWM). A signincant conclusion from this research was that these 's could be easily scaled to millimetre bands.

Cvlindncal DRA on micros tri^ Feed Line Here, Kranenburg & Long in 1988, excited the cylindrical rescnator using an open circuited microstrip h e . Various aspect ratios and permittivities (E, = 8.1 to 20.8) were used. Also, the amount of overlap of the element over the feed line was varied. It was found that the maximum coupling occurred when the feed line was about !A of a dielectic wavelength fkom the cylinders leading edge. However the feed h e radiation and the interaction at the interface of the two dielecmcs had unpredictable effects on the radiation pattern and return loss.

Half-Sdit DRA with Probe Feed Dr. ~ o n ~ i a ' ' ~ ' tested two different heights of E, = 12 elernents placed on a ground plane. Again they exhibited the typical wide impedance bandwidths and he was able to confkm that the half-split DRA radiated

like a rnagnetic dipole, a characteristic of the TEois mode. Mongia et continued this work by using an aperture feed in place of the probe. A characteristic of both systems was a broad beam radiation pattern. It was also, observed that the slot length (while remaining non-resonant) had little effect on the resonance of the system.

Stacked Cvlindrical DRA with Probe Feed In chapter 1, it was mentioned that stacked MPA's were employed to increase the bandwidth of the . Therefore, Kishk, Ahn and ~ajfez'~' ' , using a probe fed DRA with a srnalier cyhder placed on top, were able to obtain an impedance bandwidth at VSWR < 2 of 25%. This was better than double that for the single element. The dimensions of the large DRA were such that is was tuned to 10 GHz while the srnaller DRA was tuned to 12 GHz. Both elements were fabricated with material of permittivity of 10.5.

Cvlindrical DRA with Aperture Feed St.-Martin in his Masters ~hesis["' conducted a mainiy experimental examination of a design procedure for this type of configuration at 14 GHz. Unlike most of the studies, which were carried out at the

fundamental mode, this study was done using the hybrid HEMlls mode. (Modal structures and labeling wilI be discussed later but are weIl defined in [42].) Various parameters were varied to analyze their effect on the performance of the . DRA aspect ratio was altered, as were the tuning stub length and aperture dimensions. Kishk et al'"] Further quantified the perforn-ance of this configuration. The most significant fmding was that the slot length selection was critical to the excitation of desired modes.

A variation on the cylindrical DRA, was a coplanar waveguide feed which was presented by Kranenburg et al in 1991["'. Again this demonstrated wide band performance and further cemented the ability of DRA'S to be coupled easily to almost any type of MIC feed.

Cviindrical Ring DRA excited bv Coaxial Probe A dielectric ring resonator which was shown to radiate Like an elecuic monopole was reported by Mongia et alrss1

in 1993. They used a high permittivity element (e, = 36.2), thereby reducing the height of the resonator. Thus, they were able to show that high permittivity matenal aUowed for the use of very low profile DRA's. This work was carried out at 7.7 GHz and showed that even with high permittivity matenals, a careful selection of the aspect ratio could produce bandwidths of approximately 3%.

Trianeular and Rectangular DRA with Aperture C o u ~ h r : Ittipiboon et alLs6' continuing there work on DRAs, investigated the above shapes which were far easier to fabricate. Again, the DRAs demonstrated wide bandwidth, broad beam and very high radiation efficiency properties.

G.D. ~ o o s ' ~ ' continued invesiigating rectangular DRA's and developed a fairly comprehensive study on the design procedure for this configuration. A four element

square sub-array operating at 7 GHz was produced and a study of mutual c o u p h g was completed. The m a y produced gains of 11.3 dBi at boresight and possessed a large bandwidth of approximately 18%.

3.2.4 Circular Polarized Antennas

Interestingly there are very few pubiished articles concerning CP DRAs. This is not surpnsing since DRA's are a fairly new area of study. To date there have been five difXerent element configurations published and these wiIl be summarized below.

Choooed Corner DRA Arrav This was an X band anay composed of a pair of CP DRA's presented by Haneishi and Takazawa in 1985~"'. A DRA pair-unit was constructed with a pair of CP DRA's. Each element of the pair was fed unifonnly in power from orthogonal feed points with a 90 degree phase shift. The sub-ar-ray was then formed by two of these pair units in an attempt ro increase the eUipicity bandwidth. They were able to achieve a 2 dB ellipicity bandwidth of 3% for a single element and 15% for the sub-array. The material used had a permittivity of 9.4 and

the fkequency of operation was around 10 GHz. The feed network however, was very cornplex and for their 4 x 4 array they experienced considerable feed losses. Figure 3- 1 provides a plan view of the configuration of the DRA sub-array.

/ Feed ~o in td

Figure 3-1 Sub-Array of Chopped Corner DRA

Active Ouarter-Wavelength Arrav Ng, Yam and ~arn''~' presented a four

element active CP array of slow wave u4 radiators in 199 1. This system was designed to operate at 0.48 GHz, for possible use as a Doppler detector. Figure 3-2, shows the configuration of the elements. DR's A and B are fed in-phase and DR's C and D are fed in phase, shifted 90 degrees from the feed to A and B. but with the same amplitude. The coaxial centre conductor feeds power to each element and is short circuited to the outer conductor at the end of each element. The interconnection between A,B and C,D through the phase shifter is done using the outer conductors on the sides. The DR in this is actuaUy used as a phase shifter. A cornplicated feed system and power divider along with a transistor is used to boost the transmit and receive gains. This is not the typical form of resonating that is king explored in this thesis yet it remains one of a few CP dielectric E s .

Coaxial Conductor DR A

DR D

Figure 3-2 Active Quarter-Wavelength Array

Cross DRA on a Single A~erture Ittipiboon, Roscoe, Mongia and ~uhaci'"', developed a cmciform shaped DRA for CP at 11.2. The consists of basically two linear DR elements, (of E, = 10.8) of slightly different lengths, piaced diagonaily over the slot feed. The length of

Dielecrric Cross

Figure 3-3 Slot-Fed Cruciform Antenna

each arm was experimentaily selected to produce equal amplitude radiated fields with phase and space quadrature. They obtained 3 dB axial ratio bandwidths of 4 8 and beam widths of over 100 degrees. The system was also quite tolerant to fabrication errors and positioning, with Little degradation of performance.

C~iindncal Ring DRA with Dual Feed A second configuration for CP demonstrated by Mongia, Ittipiboon and Roscoe was a ring DRA wi:h two probe f e e d ~ ' ~ ~ ' . The , shown in figure 3-4 consisted of a ring resonator, of er = 36.2 operating at 4.56 GHz, placed on a ground plane and fed by two probes which excite two mutualiy orthogonal HElla modes. Measured result showed that the axial ratio of less than 3 dB over a beam width of 100 degrees.

had an

Figure 3-4 Cylindrical Ring DRA with Dual Probes

Rectaneular DRA with a Single Feed M.B. 01iver'~' developed a novel CP rectangula. DRA using both single probe and aperture feeds, in 1995. The configuration used is shown in figure 3-5. By properly choosing the two base dimensions, and matching the feed mechanism to equally excite two orthogonal linear polarized modes, circular polarization was achieved. A number of difTerent elements were tested using both feed systems in order to characterize the 's performance. Ushg elements of permittivity 10.8, 20, and 40 and operating at frequencies of 4 to 6

GHz, 3 dB axkl ratio bandwidths of 1.9 to 6.6%, and beam widths of 110 to 140 degrees respectively were achieved along with radiation efficiencies of 92 to 98%. A simple design relation was also proposed for this dual mode CP along with a modfed DWM using Mixed Magnetic walis to describe the field distributions. Finally, as part of this extensive analytical and experhental characterization of this new type of , he proposed a simple circuit mode1 using simple lumped elements as a desigr! tool for this type of configuration.

Figure 3-5 Rectangular CP DRA with Single Slot Feed

It was fiom this background, on which the remainder of this thesis is based. The work undertaken and presented in the following sections was to first ver@ the design relations of M.B. Oliver's work and their scalability down to the L and S bands. Next was the experimental characterization of this type of 's operation in regards to a 'reai world' environrnent, and in attempting to irnprove upon its performance. This involved investigating various coupling techniques, and the employment of a more systematic approach to irnpedance matching the feed to the radiating DR element. Also, an investigation and characterization of the effects of finite ground planes and dielectic covers on the far-field radiation pattern was undertaken to simulate this 'real world' environrnent and the actual configuration of such an system.

3.3 CP DRA Mode1 Developrnent

3.3.1 Method

The development of the rectangular CP DRA model in this thesis follows a classical approach. Starting with statement by ~ichtrn~er"' in 1939 ". . . that suitably shaped O bjects of dielectric rnaterial can function as electrical resonators.. ." a literature review concerning the descnption of this resonance phenornena was undertaken, including a review of basic resonator properties. From this review, a summary of the evolution of an analytical mode1 for DRs, particularly the rectangular DR is presented. As part of this process, it is necessary to give a bref descnption of the modes of operation, and field distributions of DRs and their accepted labeling methods.

This information is then used to develop the model for the rectangular CP DRA, as proposed by M.B. ~liver'? With some modifications, this model was used to develop some design relations for isolated elements. These design relations provided suitable dimensions for the fabrication of L and S band rectangular CP DRA elements.

3.3.2 Microwave Dielectric Resonators - General

As mentioned, in section 3.2.2 there is a definite paralle1 between the DR and metailic waveguide cavity resonators. In the case of the metallic waveguide cavity resonator, the fields are completely confined within it walis. Therefore, it acts as an efficient storage device, where the Q-factor is a direct measure of this efficiency. The Q-factor is defined as:

energy stored Q = per cycle energy dissipated

In the case of the cavity, with perfectly conducting wails, the Q-factor can become extremely large (- 10'). If, however, this metal cavity is fiUed with a dielectric it becomes a dieIectric waveguide cavity.

Van Bladel demonstrated in 1971t611 that an aperture resonant cavity may be modeled as a paraiiel resonant circuit. Therefore, a quick review of the properties of a parallel RLC lumped-element circuit is prudent. A typical parauel resonant circuit and its response are shown in figure 3-6.

Figure 3-6 Parallel Resonant Circuit and Normalized Response

This reso nator can be characterized by two quantities; the resonant fkequenc y and the unloaded Q-factor. Externd loading of the resonator can be included by moddjmg the Q-factor accordingly. It is important to note that energy is stored equally in the inductor, as a magnetic field, and in the capacitor, as an electric field. At resonance impedance of the reactive components cancel and only the resistive component is seen as the circuit impedance. Also, the phase angle between the voltage and curent is such that it is positive below resonance, transitionhg through zero at resonance and finally, becorning negative above resonance. The denvation of these and other properties of this circuit are provided by most texts on the subject

and hence, will not be repeated here. Table 3-1 provides a summary of these

Quantiy Paraltel Resonator Input Admittance 1 1 Yin = R+ jmC - j -

oL.

Power Loss

S tored Magnetic Energy

S tored Electric Energy

Resonant Frequenc y

Unloaded Q

Extemal Q R L Q , = - o 0 L L

Table 3-1 Summary of Results for Parallel Resonators

Unlike a closed metal cavity, the dielectric waveguide interfaces form a 'leaky' boundary, and a signincant portion of the resonator energy is lost to radiation. The following section will explore this through an examination of the boundary conditions.

Boundarv Conditions at an Interface With a dielectric we essentially have two media with two sets of constitutive parameters. These parameters are; conductivity (a), permittivity (E), and perrneability (p) which cm be defined as constants or as functions of any combination of frequency, position or direction.

- - -

Figure 3-7 Dissimilar Media Interface with Incident Plane wave At the boundary of these two non-conducting media the electromagnetic relations at the interface are given as:

Where: M. is the surface magnetic current distribution, J, is the surface current distribution, os is the electric surface charge density, n2 is the normal at the interface into medium 2.

If M, = I, = O (source free), and the regions are both non-conducting. the tangential components of both E and H field must be continuous across the boundary. If the media are also isotropic, then the electric flux density and rnagnetic flux density may be related to their respective fields by:

Next we must consider two special boundary conditions that are fkequently used in electromagnetic analysis. One occurs when one medium is considered to be a perfect electric conductor (PEC), or waL1, and is used to represent ideaily conducting metal surfaces. Since no fields exist within a perfect conductor, any incident E-field must become let medium 2

a surface current and/or a surface charge distribution. For our purposes, be the PEC.

The dual of the PEC is a perfect magnetic conductor (PMC). Although strictly not a physically realisable quantity, it is often used to approximate certain boundaries

as magnetic wails. Since it is defined that no fields exist within a PMC, the incident H-field must become a magnetic surface current density (M,), and/or a rnagnetic surface charge density (0,'). Let medium 2 be the PMC:

Wave Behaviour at an Interface To gain a better grasp of the concept of a PMC, consider a uniform plane wave norrnally incident upon a plane boundary between an ideal dielectric (i.e. loss fiee) (medium 1) and air (medium 2). The dielectrics' constitutive parameters pi=pa, EL= areo and al=O; while air is described b y:

pz = = 4sx IO-' H/m EZ = EO = 8 .854~ 10-l2 F/m (3-6) 0 2 = O

In general, the intrinsic impedance of any medium is given by:

The wave impedance at the interface must be continuous which means:

Which is finally expressed in t e m of the intrinsic impedance of each region (q) and the reflection coefficient (r). Solving for the reflection coefficient we get:

In this case, where o = O for both media, these quantities equate to:

Substituting the above equation for both regions, into equation (3.9) we get:

The mechanism by which a dielectric resonator stores energy internally can be made clearer if in equation (3.1 l), 1, is allowed to approach infnity. Then the limiting case for I: as this occurs is:

lim r = &,-' -

Thus, the implications

high perrnittivity, most of the of equation (3.12) are that for a dielectric medium of incident energy of a normal uniform plane wave at the

dielectric/air boundary wiU be reflected back, with only a smali amount of energy transrnitting into the air. As the permittivity of the dielectric increases to uifinity the amount of energy reflected back at the interface increases until total interna1 reflection occurs.

This can be conceptualised as an ideal electric short circuit, although the fields and their corresponding reflections propagating within the DR boundaries, are much more complex than a simple plane wave normaiiy incident upon the interface. The notion of the dielectric/air interface as a short circuit boundary condition is important if one considers that any propagating field can be considered as a summation of plane waves, with a range of ali possible angles of incidence at the boundary. One can draw from elementary physical optics, or various treatments of oblique incidence for electromagnetic plane wave propagation'63*M', that at angles of incidence O ther than 'normal' the reflection coefficient r wiU be at least as high, and in most cases higher, than that of normal incidence.

Thus, for a region of dielectric with a sufficiently large value of permittivity the interface with air can be considered a short circuit. For the ideal case, this corresponds to the PMC boundary condition.

3.3.3 Simple DR Mode1

In attempting to form any model, one attempts to find a method of accurately representing the properties of the device. In this case, we wish to represent the properties of a rectangular DR, in order to predict its behaviour. Some of the parameters of interest in formulating this model include, resonant frequency, input impedance, Q-factor (related to bandwidth), the field or mode structure and its c o u p h g behaviour.

Field Structures ~ a r r i n g t o n , [ ~ ~ ' showed that a rnicrowave cavity resonator could, in theory, siippon an infinite number of resonant modes. For the DR each of these modes will posses a distinct field distribution dependent upon the properties of the DR. Essentially there are two types of modes for DR'S, which are grouped as E and H modes. An H-mode is characterized as having a large normal (perpendicular) component of the rnagnetic field at boundary surfaces. An E-mode, however, is characterized as not having a large normal of magnetic fields at boundary surfaces. The lowest order H-mode resembbs a magnetic dipole in both field structure and radiation pattern, whereas, the E-mode resembles an electric d i p ~ l e ' ~ ~ ] .

For a rectangular DR, we are primarily interested with the H-mode, or 'rnagnetic dipole mode', since it is the fundamental mode of operation. There are, however, three linearly independent orientations of the H-mode, each corresponding to one of the three rectangular axes'"'.

Mode Labelinp. Okaya and ~ a r a s P ~ I established a convention for labeling modes in 1962 (which will be explained later in conjunction with the rectangular DRA), however, this was later rnodifed by ~ee[ '* ' in 1965. Using this convention, the modes of a rectangular DR can be divided h t o two families: transverse magnetic

( TM - old H-mode) and transverse electric (TE - old E-mode). In addition to these designations, there are three subscripts (e-g. TMh) which indicate the number of field extrema that are within the DR in each of the three ordinal directions. A superscript is used for rectangular DRs to indicate the direction to which the given mode is transverse. The fundamental mode for a rectangular DR can thus, be iabeled, TElilx, T E ~ I ~ ~ , or T E ~ ~ I * depending on which modes is excited.

Resonant Freauency There are no exact analytical techniques for detefinining the resonant fiequency of DR which do not have axial symmetry. Consequently, either an approxirnate analytical or numencal technique is required to estimate this quantity. Cylindrical shaped DRs have seen wide use in microwave circuits and as a consequence, there have been many published approximate analysis techniques that provide good results. Rectangular DRs, however, have seen much less use and hence very Lirtle has been published about them.

O-Factor and Bandwidth As defined in section 3.3.2 the quality factor compares the energy lost per cycle to the energy stored per cycle for the time varying fields inside the resonator.

m a x i m u m e n e r g y stored Q = 21c p e r cyc le average energy d i ss ipated

- -

2zw, ooWo -- -

PT P

Where Wo is the stored energy, P is the power dissipated, is the resonant frequency, and T is the period. In our model, of a dielectric filled cavity, we wiU assume that the walls are imperfect to aIlow for radiation. We can now express the total power dissipated as a sum the various loss factors:

where Pd = power dissipated in dielectric

P, = power dissipated in any conducting material

Pr = power lost to radiation, and

Pen = power coupled to an external circuit.

Equation (3.14) can be substituted into equation 3.13 to give an expression for the unloaded and loaded Q-factor:

For resonators, with no loading, the unloaded Q will be determined simply by the dielectric and conduction losses. Metal boundaries, thicker than the skin depth will preclude the radiation of energy. Given this situation, the Q for unloaded resonators can become very high. On the other hand if a low value of dielectric constant is used for an unshielded DR, radiation will become the dominant loss term for some of the DR'S lowest order modes. This is exactly what is needed for applications where one wants to efficiently radiate power. In this situation where the

dielectric and conduction losses are very low the unloaded Q can be considered approxirnately equal to Q,.

A hrther relation to the Q-factor is the bandwidth of the resonator at the half power point.

It can also be shown, that the dielectric constant has a direct effect on the Q-factor. The dielectnc Q-factor for a homogeneous dielecmc filliig a cavity, is given by Kajfez and ~ u i l I o n [ ~ ~ '

1 Qd =--- - O tan 6

T where 6 = tan-' - the dielectric loss tangent (definition in Annex A).

%Er

For a rectangular open DR, there are published works on evaluating Q-factors. However, Mongia et al'"', derived a closed form expression for the radiation Q factor of a rectangular DRA. The DR was represented as an equivalent volume curent source, and a simple closed form solution for the radiation Q-factor was found nom expressions for radiated power and stored energy.

Firstly, as wiU be discussed at length later, the fields in the DRA must be found. Next. as Van lade el'^^' showed, a homogeneous dielectric body in ftee space radiates like a volume electric current of density, I,.

Using the conclusions of the asyrnptotic theory of Van lade el''^', that for an arbitrarily shaped DR of high dielectric constant, the principle electric field inside the resonator is tangential to the surface. A DR, therefore, radiates like a magnetic dipole of moment, p,, given by:

where R is a vector from the ongin of the DR coordinate system, used to describe the fields. Substituting in the appropnate electric field expressions, into equation (3.19), for the appropriate mode of operation, and using equation (3.20) wiU lead to a closed form solution for p,, fkom which the radiated power can be found fiom the standard equation taken from S tutzman & hiel le^"':

As discussed earlier for the isolated, or unbounded DR, the primary loss mode is through radiation. Aowever, there is some energy that is stored and this must be found. Most of the stored energy Lies in the DR due to its high dielectric constant. Frorn ~ a r r i n ~ t o n [ ~ ~ ' the stored electric energy can be computed fkom the fields Liside the DR.

This tirne averaged electric stored energy represents half the total stored energy, since the other half is stored as magnetic energy. Substituthg this into equation (3.1 3) where Wo = 2 W,:

The accuracy of this method depends on the accuracy of the model used to describe the DRs field structure. However, this does provide a physical hsight into the radiation mechanism, and it has been sho wn to give very reasonable values for the radiation Q-factor for a rectangular DR, operating in the fundamental mode. This process will be employed later during the actual design of the CP DRA elements, after a description for the fields has been developed.

3.3.4 Modeis for Cylindrical DR'S

Since, this shape of DR has been employed quite extensively, as microwave filters and oscillators, there has consequently, been a number of theoretical developments in terms of predictors for resonant fiequency, modes and fields. Much of this work is sumrnarized by Kajfez & ~ u i l l o n ' ~ ~ ' , however, a very brief sumrnary will be presented below.

~ee"", developed an approximate model for calculating the natural resonant frequencies of cylindrical DRs, assuming the sides were PMCs and rnatching tangential fields at the cylinder ends. This was valid for DRs of high permittivity

(ep279), achieving relatively good (within 10%) agreement with experimental results.

Van Bladel '"* 331, showed, using asymptotic theory that the modes of an arbitrarily shaped DR of high permittivity, approaching uinnity, were of the non- confined type. He also, showed that radiation fiom the lowest order of this mode was like that of a magnetic dipole. For shapes with axial symrnetry, confined modes would be supported, that could be characterized as behaving like electric dipoles. Drawing on this work, ~ o n ~ i a ' ~ ~ ' has demonstrated that the fundamental mode of a rectangular DR behaves as a magnetic dipole and is therefore, a non-confined mode.

Various other approaches have been used to calculate resonant fiequencies, including: the variational rneth~d"~', where the surface irnpedance is varied fiom an infinite value; and an approximate mode-matching rneth~d'~'"~', where an approximate field of the resonator is expanded h to a truncated series of solutions to the Helmholtz wave equation in spherical coordinates.

3.3.5 Modeis for Rectangular DRs

The basis for most of the analysis of rectangular DRs is the infinite dielectric rectangular wav