slot array antennas at v-band based on inverted microstrip...

Thesis for the Degree of Licentiate of Engineering

Slot Array Antennas at V-band based onInverted Microstrip Gap Waveguide

Jinlin Liu

Department of Signals and SystemsChalmers University of Technology

Göteborg, Sweden 2017

Slot Array Antennas at V-band based on Inverted Microstrip Gap Waveg-

uide

Jinlin Liu

c© Jinlin Liu, 2017.

Technical report number: 2017/2017ISSN 1403-266X

Department of Signals and SystemsDivision of Communications and Antenna SystemsChalmers University of Technology

SE�412 96 GöteborgSwedenTelephone: +46 (0)31 � 772 1000Email: [email protected]

Typeset by the author using LATEX.

Chalmers ReproserviceGöteborg, Sweden 2017

To my family

"Look deep into nature, and then you will understand everything better"-Albert Einstein

1

Abstract

Recently, gap waveguide technology is introduced as a proper guiding structure formillimeter-systems. The conception of gap waveguide technology can be modeled fortheoretical analysis by two parallel plates, a top perfect electric conductor layer and abottom perfect magnetic conductor layer. This structure stops all modes propagatingin all directions except for a quasi-TEM mode when the gap between perfect electricconductor and perfect magnetic conductor plates is smaller than quarter wavelengthat an operating frequency. Until now there are already four di�erent visions of thisnovel concept�groove, ridge, inverted microstrip and microstrip ridge gap waveg-uides. Among those four structures, the inverted microstrip gap waveguide has someobvious advantages. First of all, it has a uniform bed of nails while the others donot. This uniform pin structure makes the fabrication much easier and cheaper. Sec-ondly, fabrication of microstrip circuitry on PCB by etching is accurate and verylow cost. In addition, theories and design principles of microstrip technologies arevery well-developed. Therefore, my work in this Lic. thesis is focusing on the theoryof inverted microstrip gap waveguide and its applications on millimeter wave arrayantenna design.

Keywords: metallic pins, perfect magnetic conductor, inverted microstrip gap waveg-uide, slots array and variational method.

i

Preface

This thesis is in partial ful�llment for the degree of Licentiate of Engineering atChalmers University of Technology.

The work that has resulted in this thesis was carried out between September 2014and April 2017 and has been performed within the Division of Antenna Systems atthe Department of Signals and Systems, Chalmers University of Technology. Prof.Dr.Jian Yang has been the examiner and main supervisor, and Associate Prof. AshrafUz Zaman has been the co-supervisor.

This work is �nancially supported by the Swedish Governmental Agency for Inno-vation Systems VINNOVA via a project within the VINN Excellence center CHASEand the European Research Council (ERC) under 7th Framework Program ERCgrant number 3222804.

iii

Acknowledgments

First of all, the great appreciation and the thanks I would like to give to Prof.Dr.Per-Simon Kildal for his talented idea of gap waveguide structures. His leaving is irre-versibly loss in the antenna world. Then I would like to thank Prof.Dr.MariannaIvashina and Prof.Dr.Jian Yang for their kind guidance to work on challengingand relevant research topics. I also would like to thank my supervisor AssistantProf.Dr.Ashraf Uz Zaman for his selection working in the group and kind supervisionof the project. His knowledges in gap waveguide and array antennas I admire verymuch. I would like to express my appreciation to Associate Prof.Dr.Rob Maaskantand Assistant Prof.Dr.Andreas Alayon Glazunov for their encouragements in researchand study in �elds theory of guided waves and wireless communications during theseyears. In the end I thank to Prof.Dr.Eva Rajo-Iglesias for her time to come to myLic. seminar.

Furthermore, I would like to appreciate every member in antenna group for theperfect research and work environment. First of all, I am very grateful for my of-�cemate Abbas Vosoogh, who is not only a microwave and antenna scientist andengineer, but also an artist for his creative ideas and highly e�cient work in the�eld of gap waveguide technology. It makes research simple and highly e�cient tocollaborate with him. Then I would like to thank Carlo Bencivenni for his kind helpand encouragement in the group. He has instructed lots of knowledge about antennaarray synthesis at the beginning and this is very bene�t for the following work. Manythanks to Dr.Aidin Razavi for his helpful advices in research and study in the group.Then I am very grateful to Sadegh Mansouri Moghaddam for his kind discussionin antennas. Then I appreciate Dr.Astrid Algaba Brazalez for her many years hardwork and promising achievements on the transition design of inverted microstrip gapwaveguide. Then I would like to thank Madeleine Schilliger Kildal, Artem Roev,Oleg Iupikov, Parastoo Taghikhani, Navid Amani, Pegah Takook, Samar Hossein-zadegan, Tomas Rydholm and Cristina Rigato for their getting along with in thegroup. Many thanks to Markus Froehle for his helpful advices in the thesis. Then Iwould like to thank Dr.Xuezhi Zeng, Dr.Simon He, Dr.Wei Yang, Li Yan, Dr.YixiaoYun, Chao Fang, Xinglin Zhang, Dr.Yinan Yu, Dr.Wanlu Sun, Prof.Dr.XiaomingChen, Prof.Dr.Kin Cheong Sou, Zhixing Chen, Dr.Yujiao Song, Xinxin Yang, SiningAn, Dr.Lei Shi from Chinese Department of Aerospace, Dr.Bin Dong from Chinese

v

Acknowledgments

Institute of Academy and Dr. Fangfang Fan from Xidian University. In addition Ialso appreciate my Iranian friends Ali at Kerman University and Davoud at KashanUniversity for their unreserved discussions on array antennas.

My special thanks go to all the former and current colleagues of the Signals andSystems Department for creating a nice and enjoyable working environment. We'vehad a lot of fun and enjoyable moments both at work and afterwork time.

Jinlin Liu

vi

List of Publications

This thesis is based on the work contained in the following appended papers:

Paper 1

J. L. Liu, A. Vosoogh, A. U. Zaman, and P. S. Kildal, �Design of a Cavity-backed SlotArray Unit Cell on Inverted Microstrip Gap Waveguide�, in International Symposiumon Antennas and Propagation, ISAP 2015, Hobart, Tasmania, Australia, November9-12th, 2015.

Paper 2

J. L. Liu, A. U. Zaman, and P. S. Kildal, �Optimizing the numerical port for invertedmicrostrip gap waveguide in full-wave simulators�, in 10th European Conference onAntennas and Propagation, EuCAP 2016, Davos, Switzerland, April 10-15th, 2016.

Paper 3

J. L. Liu, A. U. Zaman, and P. S. Kildal, �Design of transition fromWR-15 to invertedmicrostrip gap waveguide�, in Global Symposium on Millimetre-Wave Technology andApplications, GSMM 2016, Espoo, Finland, June 6-8th, 2016.

Paper 4

J. L. Liu, A. Vosoogh, A. U. Zaman, and P. S. Kildal, �Design of 8 × 8 Slot ArrayAntenna based on Inverted Microstrip Gap Waveguide�, in International Symposiumon Antennas and Propagation, ISAP 2016, Okinawa, Japan, October 24-28th, 2016.

Paper 5

J. L. Liu, A. Vosoogh, A. U. Zaman, and Jian Yang, �Design and Fabrication ofa High Gain 60-GHz Cavity-backed Slot Antenna Array fed by Inverted MicrostripGap Waveguide�, IEEE Transactions on Antennas and Propagation, vol. 65, no. 04,pp.2117-2122, April, 2017.

Paper 6

J. L. Liu, Jian Yang, and A. U. Zaman, �Analytical Solutions towards Inverted Mi-crostrip Gap Waveguide for characteristic Impedance and Losses based on variationalMethod�, submitted to IEEE Transactions on Antennas and Propagation,

vii

List of Publications

viii

Contents

Abstract i

Preface iii

Acknowledgments v

List of Publications vii

Contents ix

I Introductory Chapters

1 Introduction 1

1.1 Goal and outline of the thesis . . . . . . . . . . . . . . . . . . . . . . 7

2 High Gain 60-GHz array antenna based on Gap Waveguide 9

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2 Design for Bed of Nails . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Design for Antenna Unit Cell . . . . . . . . . . . . . . . . . . . . . . 12

2.4 Transition from WR-15 to Inverted Microstrip Gap Waveguide . . . . 15

2.5 Design of Feeding Distribution Networks . . . . . . . . . . . . . . . . 17

2.5.1 Design of T-junction Power Divider . . . . . . . . . . . . . . . 18

2.5.2 Design of Impedance Transformer . . . . . . . . . . . . . . . . 19

2.6 Comparison between Simulated and experimental results . . . . . . . 21

2.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3 Future Work 27

References 29

ix

Contents

II Included Papers

Paper 1 Design of a Cavity-backed Slot Array Unit Cell on Inverted

Microstrip Gap Waveguide 37

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2 Antenna Con�guration . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3 Simulated Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

References 45

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

Paper 2 Optimizing the numerical port for inverted microstrip gap

waveguide in full-wave simulators 49

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2 The Waveguide Port Details for inverted Microstrip Gap Waveguide . 50

3 Numerical Models and Numerical Simulations . . . . . . . . . . . . . 53

3.1 Simulation of Straight Inverted Microstrip Gap Waveguide . . 53

3.2 T-Junction Power Divider and 1:4 Distribution Networks . . . 55

4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

References 59

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Paper 3 Design of transition from WR-15 to inverted microstrip gap

waveguide 63

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

2 Non-symmetric Transition from WR-15 to Inverted Microstrip GapWaveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3 Symmetric Transition from WR-15 to Inverted Microstrip Gap Waveg-uide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

References 71

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Paper 4 Design of 8 × 8 Slot Array Antenna based on Inverted Mi-

crostrip Gap Waveguide 75

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

2 Antenna Con�guration . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3 Simulated Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

x

Contents

References 81

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Paper 5 Design and Fabrication of a High Gain 60-GHz Cavity-backed

Slot Antenna Array fed by Inverted Microstrip Gap Waveguide 85

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 852 Design for 2 × 2 Sub-array . . . . . . . . . . . . . . . . . . . . . . . . 863 Design of Feeding Distribution Network . . . . . . . . . . . . . . . . . 884 Simulated and experimental Results . . . . . . . . . . . . . . . . . . . 925 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

References 97

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Paper 6 Analytical Solutions towards Inverted Microstrip GapWaveg-

uide for Characteristic Impedance and Losses Based on Variational

Method 101

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1012 Fundamental Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

2.1 Solutions by spectral Domain Method . . . . . . . . . . . . . . 1032.2 Characteristic Impedance of the IMGW . . . . . . . . . . . . 1072.3 Attenuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

3 Theoretical and Simulated Results . . . . . . . . . . . . . . . . . . . . 1083.1 Theoretical and simulated characteristic Impedances . . . . . 1093.2 Theoretical and simulated Attenuations . . . . . . . . . . . . . 112

4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

References 117

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

xi

Part I

Introductory Chapters

Chapter 1

Introduction

Currently, considerable attention has been paid to millimeter and sub-millimeter wavecommunications [1]. In commercial applications, such as high-speed wireless accessand high streaming multimedia transmission, millimeter wave systems are able tosupply 100 times higher data than present WLAN and Wi-Fi technologies [2]. How-ever, wireless communications at such frequency bands are easily a�ected by thepropagation loss and strong atmospheric absorption according to fundamental prin-ciples of electromagnetic �eld theory [3]. Therefore, ultra-low loss materials and highgain antennas are required for such kind of wireless systems.

c03TransmissionLinesandWaveguides Pozar July 29, 2011 20:41

3.8 Microstrip Line 147

We see that the results are in reasonable agreement with the closed-form equa-tions of (3.179) and the results from a commercial CAD package, particularly forwider strips where the charge density is closer to uniform. Better results could beobtained if more sophisticated estimates were used for the charge density. ■

3.8 MICROSTRIP LINE

Microstrip line is one of the most popular types of planar transmission lines primarilybecause it can be fabricated by photolithographic processes and is easily miniaturized andintegrated with both passive and active microwave devices. The geometry of a microstripline is shown in Figure 3.25a. A conductor of width W is printed on a thin, groundeddielectric substrate of thickness d and relative permittivity εr ; a sketch of the field lines isshown in Figure 3.25b.

If the dielectric substrate were not present (εr = 1), we would have a two-wire lineconsisting of a flat strip conductor over a ground plane, embedded in a homogeneousmedium (air). This would constitute a simple TEM transmission line with phase veloc-ity vp = c and propagation constant β = k0.

The presence of the dielectric, particularly the fact that the dielectric does not fill theregion above the strip (y > d), complicates the behavior and analysis of microstrip line.Unlike stripline, where all the fields are contained within a homogeneous dielectric region,microstrip has some (usually most) of its field lines in the dielectric region between the stripconductor and the ground plane and some fraction in the air region above the substrate. Forthis reason microstrip line cannot support a pure TEM wave since the phase velocity ofTEM fields in the dielectric region would be c/

√εr , while the phase velocity of TEM fields

in the air region would be c, so a phase-matching condition at the dielectric–air interfacewould be impossible to enforce.

In actuality, the exact fields of a microstrip line constitute a hybrid TM-TE wave andrequire more advanced analysis techniques than we are prepared to deal with here. In mostpractical applications, however, the dielectric substrate is electrically very thin (d � λ),and so the fields are quasi-TEM. In other words, the fields are essentially the same as thoseof the static (DC) case. Thus, good approximations for the phase velocity, propagation con-stant, and characteristic impedance can be obtained from static, or quasi-static, solutions.Then the phase velocity and propagation constant can be expressed as

vp = c√εe

, (3.193)

β = k0√

εe, (3.194)

y

x

d�r

z

W

Ground planeE

H

(a) (b)

FIGURE 3.25 Microstrip transmission line. (a) Geometry. (b) Electric and magnetic field lines.Figure 1.1: Microstrip Transmission Line.

As is well-known, transmission lines are frequently utilized for traditional com-munications systems. Transmission lines are specialized cable structures which carryalternate current of radio frequency. In reality, transmission lines are used with thepurposes such as connected circuits for transmitter, receiver and antennas, distributedtelevision cable and high speed bus system in a computer. The most common types oftransmission lines are microstrip line and stripline. A microstrip line is the most pop-ular transmission line, as illustrated in Figure 1.1. A good conductor which is usuallycopper of Width W is printed on a thin, grounded dielectric substrate of thickness

1

Chapter 1. Introduction

d and relative permittivity εr. A regular sketch of the corresponding E- and H-�elds


3.7 Stripline 141

y

x

b�r

z

W

Ground plane

Groundplane

E

H

(a) (b)

FIGURE 3.22 Stripline transmission line. (a) Geometry. (b) Electric and magnetic field lines.

3.7 STRIPLINE

Stripline is a planar type of transmission line that lends itself well to microwave integratedcircuitry, miniaturization, and photolithographic fabrication. The geometry of stripline isshown in Figure 3.22a. A thin conducting strip of width W is centered between two wideconducting ground planes of separation b, and the region between the ground planes isfilled with a dielectric material. In practice stripline is usually constructed by etching thecenter conductor on a grounded dielectric substrate of thickness b/2 and then coveringwith another grounded substrate. Variations of the basic geometry of Figure 3.22a includestripline with differing dielectric substrate thicknesses (asymmetric stripline) or differentdielectric constants (inhomogeneous stripline). Air dielectric is sometimes used when it isnecessary to minimize loss. An example of a stripline circuit is shown in Figure 3.23.

Because stripline has two conductors and a homogeneous dielectric, it supports a TEMwave, and this is the usual mode of operation. Like parallel plate guide and coaxial line,however, stripline can also support higher order waveguide modes. These can usually beavoided in practice by restricting both the ground plane spacing and the sidewall widthto less than λd /2. Shorting vias between the ground planes are often used to enforce thiscondition relative to the sidewall width. Shorting vias should also be used to eliminatehigher order modes that can be generated when an asymmetry is introduced between theground planes (e.g., when a surface-mounted coaxial transition is used).

Intuitively, one can think of stripline as a sort of “flattened-out” coax—both have acenter conductor completely enclosed by an outer conductor and are uniformly filled witha dielectric medium. A sketch of the field lines for stripline is shown in Figure 3.22b.

The geometry of stripline does not lend itself to the simple analyses that were usedfor previously treated transmission lines and waveguides. Because we will be concernedprimarily with the TEM mode of stripline, an electrostatic analysis is sufficient to give thepropagation constant and characteristic impedance. An exact solution of Laplace’s equa-tion is possible by a conformal mapping approach [6], but the procedure and results arecumbersome. Instead, we will present closed-form expressions that give good approxima-tions to the exact results and then discuss an approximate numerical technique for solvingLaplace’s equation for a geometry similar to stripline.

Formulas for Propagation Constant, Characteristic Impedance,and Attenuation

From Section 3.1 we know that the phase velocity of a TEM mode is given by

vp = 1/√

µ0ε0εr = c/√

εr , (3.176)

Figure 1.2: Stripline Transmission Line.

is also shown in the �gure. Similarly, the geometry of a stripline transmission line isdepicted in Figure 1.2. A thin conducting strip of width W is centered between twowide conducting ground planes of separation b, the area between the ground planes is�lled with a dielectric material. In reality stripline is usually constructed by etchingthe center conductor on a grounded dielectric substrate of thickness b/2 and thencovering with another grounded substrate.

Generally, the total loss energy in a RF system consists of dielectric loss andconducting loss. Considering that those two guiding structures su�er from dielectricsubstrate, the dielectric loss is unavoidable in them. The stripline and the microstripline are typical applied topologies based on parallel-plate transmission line. Theoret-ically, the dielectric loss can be expressed as the multiplication of the frequency andloss tangent of the materials. Therefore, the corresponding dielectric loss squarelyincreases against the frequency. The high dielectric loss is the main existing problemin transmission lines at millimeter wave frequency band.

The waveguide structure usually refers to the rectangular waveguide, circularwaveguide and even optical �ber. A typical geometry of rectangular waveguide isdepicted in Figure 1.3. Usually, there is an obvious di�erence among these threestructures.The key point again focuses on the dielectric substrate. The optical �beras a main transmission component employs dielectric substrate of silicon. The puresilicon, namely glass is normally �lled in it. However, rectangular and circular waveg-uide usually does not contain any substrate. However, the manufacture and thefabrication cost will also be considered for millimeter wave frequency band. Untilnow we have several methods to fabricate waveguide structures, such as Computer-ized Numerical Control machining and Electric Discharging Machining. Generally,the waveguide structures are typically manufactured in split-blocks and then be con-nected by screwing, di�usion bonding or deep-brazing techniques. In millimeter waveband the split-blocks are very small so that the manufacture outcomes usually arenot accurate and perfect.

2


3.3 Rectangular Waveguide 111

FIGURE 3.6 Photograph of Ka-band (WR-28) rectangular waveguide components. Clockwisefrom top: a variable attenuator, an E-H (magic) tee junction, a directional coupler,an adaptor to ridge waveguide, an E-plane swept bend, an adjustable short, and asliding matched load.

and substituting into (3.73) to obtain

1

X

d2 X

dx2+ 1

Y

d2Y

dy2+ k2

c = 0. (3.75)

Then, by the usual separation-of-variables argument (see Section 1.5), each of the terms in(3.75) must be equal to a constant, so we define separation constants kx and ky such that

d2 X

dx2+ k2

x X = 0, (3.76a)

d2Y

dy2+ k2

yY = 0, (3.76b)

y

x

z

�, �

b

0a

FIGURE 3.7 Geometry of a rectangular waveguide.Figure 1.3: The geometry of a rectangular waveguide.

Substrate integrated waveguide (SIW) [4] has shown big advantages than bothstandard rectangular waveguide and printed circuit based transmission lines in mil-limeter waves. Geometrically, SIW is a compact planar printed circuit in which tworows of metallic via holes are embedded within a substrate material between twometallic plates, as illustrated in Figure 1.4. The electromagnetic behaviors of SIWis similar to those of rectangular waveguides with �lled dielectrics. The di�erenceexisting is that the electromagnetic wave propagates between two rows of metallic via68 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 1, JANUARY 2005

Fig. 3. Configuration of an SIW structure synthesized using metallic via-holearrays.

Since is a diagonal matrix, the eigenvalues of aresimply the diagonal elements of the matrix. This is usedto derive the unknown SIW propagation constants

(6)

where is the eigenvalue of and is the difference ofthe two SIW lines of different length. Each mode is associatedwith two opposite propagation constants and a pair of inverseeigenvalues. Since the SIW transmission line is an open peri-odic structure, we can easily extract the propagation constantsaccording to the attenuation constant of each mode.

The FDFD method we proposed and developed for modelingthe guided-wave properties in [7] is an algorithm that can modelperiodic structures of complicated geometry and anisotropy.The computational domain is restricted to a single period. Theguided-wave problem can be converted into an eigenvalueproblem as follows:

(7)

where isacomplexpropagation constant.Thealgorithmhasad-vantages to handle a periodic guided-wave problem quickly andaccurately, however, a very tedious programming job is required.

IV. PROPAGATION CONSTANT AND CUTOFF FREQUENCY

Fig. 3 shows a typical SIW structure that is synthesizedwith linear arrays of metallic via-holes on a low-loss substrate.Fig. 4 presents multimode calibration and simulation results ofa -mode propagation constant compared with measuredresults, as well as calculated results based on its equivalentrectangular waveguide. As shown in Fig. 3, the sizes of theSIW are selected as mm, mm,

mm, and mm. Excellent agreement betweenthe measured and calibrated results has verified the proposedmultimode calibration method. Experiments and simulationshave proven that dispersion characteristics of the SIW are thesame as those of its equivalent rectangular waveguide. Theequivalent width of the SIW is between and with avery good approximate equation [5]

(8)

provided that is sufficiently small.

Fig. 4. Comparison of aTE -mode propagation constant between calculatedresults using the numerical multimode calibration method and measured results,as well as calculated results of an equivalent rectangular waveguide.

Fig. 5. Comparison of a TE -mode propagation constant between an SIW(� = 2:33; d = 0:8 mm, s = 2:0 mm, w = 7:2 mm, h = 0:508 mm) and anequivalent rectangular waveguide (� = 2:33) whose width w is obtainedfrom (8).

Actually, is decided by three parameters, namely,and . However, the modified term in (8) does not include theeffect of . When increases, the small error will appear, asshown in Fig. 5. A more accurate empirical equation is proposedhere as follows:

(9)

When is smaller than three and is smaller than 1/5, theempirical equation is very accurate. Fig. 6 shows the comparisonof propagation constants between the same SIW used as in Fig. 5and the rectangular waveguide whose equivalent width iscalculated from (9).

For high-order modes of the SIW, the dispersion characteris-tics are also the same as its equivalent rectangular counterpart.However, there is a little difference in the equivalent widthbetween the high-order modes and the fundamental mode [5].

Figure 1.4: The geometry of a rectangular waveguide.

holes instead of metallic walls in rectangular waveguide. Moreover, SIW has an out-standing pro�le which facilities its easy integration with active RF components, suchlow noise ampli�er, power ampli�er and mixer.Nevertheless, SIW still has dielectricloss like normal microstrip lines due to the utilization of the substrate. Applying lowloss substrate materials is a choice to fabricate the SIW structure, but the dielectricloss still exists and its cost might increase. Another critical point to the overall loss inSIW is the leakage energy through the gaps between metallic via holes when these are

3


not properly organized. Thereby, the dimensions of metallic via holes, the periodicspace and the contact between two plates might increase the design complexity.

Multilayer technology [5] presents practical advantages in millimeter wave fre-quency band. The main advantage of multilayer technology is focusing on design ofprinted antenna array at millimeter wave frequency band. The multilayer technologymainly considers the transition and interconnections between several di�erent layers,which is very practical in millimeter wave antenna arrays and integrated microwavecomponents. Taking a simple two-layer microstrip circuit with glass Te�on substratesfor both layers for example, it will be essential to take into account a proper transi-tion technique to couple energy between transmission lines. This coupling mechanismcan be achieved using di�erent devices, depending on whether it is applied betweenmicrostrip lines or between microstrip lines and antennas. Di�erent options can bede�ned as follows: coaxial transition between lines, aperture coupled patch antennato couple energy between line and antenna and slot transition between lines with oneor two outputs. According to the fundamental theory, the substrate thickness mustbe low compared to the wavelength in order to achieve proper e�ciency for millime-ter wave antennas. For instance, thickness often equals 0.1 or 0.2 mm between 30and 100 GHz. Therefore, the printed circuits are very thin and �exible. Then, itbecomes useful to apply a thick ground plane to rigidify the antenna. Additionally,this thick metallic support allows the active components to be placed more easily.For slot transition and aperture coupled patch antenna, the coupling slot will beengraved in the support. It will then be essential to take into account the fact thata thick ground plane has been added. Hence, it will be necessary to increase the slotlength or to change the slot shape to permit the coupling between layers. At lowfrequencies (several gigahertz), a ground plane is often very thin (≤ 0.001λ). It isthen possible to consider this slot as in�nitely thin. On the contrary, at millimeterwaves, this parameter becomes more in�uential. For instance, if we consider only a0.2 mm-thick slot, it corresponds to 0.05λ at 77 GHz. The impact could be strongon the re�ection coe�cient and on the coupling between lines or between line andpatch. Several research institutes have already achieved a great deal of outcomes in

4.2 PHYSICAL DESCRIPTION OF MEMS CAPACITIVE SHUNT

SWITCHES

A MEMS shunt capacitive switch is shown in Fig. 4.1. The switch geometryfollows the same definitions as in Chapter 2. The switch is suspended at aheight g above the dielectric layer on the t-line, and the dielectric thickness is tdwith a dielectric constant er. The switch is L mm long, w mm wide, t mm thick.The width of the t-line is W mm. The substrate can be silicon, GaAs, alumina,LTCC, or a quartz dielectric.

The MEMS shunt switch can be integrated in a coplanar-waveguide (CPW)or in a microstrip topology. In a CPW configuration, the anchors of theMEMS switch are connected to the CPW ground planes. In a microstrip con-figuration, one anchor is connected to quarter-wave open stub that results in ashort circuit at the bridge. The second anchor of the bridge is left unconnectedor, is connected to the bias resistor (see Chapter 8).

A DC voltage is applied between the MEMS bridge and the microwave line.This results in an electrostatic force that causes the MEMS bridge to collapseon the dielectric layer, largely increasing the bridge capacitance by a factor of30–100. This capacitance connects the t-line to the ground and acts a short

Figure 4.1. Illustration of a typical MEMS shunt switch shown in cross section and planview. The equivalent circuit is also shown [6] (Copyright IEEE).

88 4 ELECTROMAGNETIC MODELING OF MEMS SWITCHES

Figure 1.5: The geometry of a typical RF MEMS switch.

4

the �elds of antenna and passive circuits. Nevertheless, due to the use of substratethe multilayer technology still face the dielectric loss.

MEMS, which is short for micro-electrical-mechanical-system, is also being devel-opment for wireless communications [6]. A typical MEMS switch geometry is illus-trated in Figure 1.5. As is well-known, the simplest devices in circuits and systems,such as switches, inductors, resistors and capacitors are crucial in wireless systemsbecause people are requiring high performance and functionality with the dimen-sions reducing. Thereby, these requirements in decreasing dimensions and meanwhilehigher functionality consequently increase the design complexity, manufacturing costand corresponding weight. In microwave frequency band RF MEMS is a good can-didate because it enables the design of new products with good functionality, lowinsertion loss, high isolation and reduced power consumption. Recently, RF MEMSdevices have opened up a wide range of technological approaches to enhance re-con�gurable antenna systems. Furthermore, this technology might even enable newantenna concepts previously not practically usable. Particularly in terms of reduc-tion in losses and power consumption, MEMS switches have demonstrated betterperformance compared with traditional ones. Up to now there are several di�erentapproaches to actuate RF MEMS switches. Magnetic, thermal, electrostatic and

Figure 1.6: Four realized di�erent gap waveguide geometries. (a) Ridge Gap Waveguide. (b) GrooveGap Waveguide. (c) Inverted Microstrip Gap Waveguide. (d) Microstrip-Ridged Gap Waveguide.

piezoelectric actuation methods have been applied. Among those all technologies,electrostatic actuation is the most commonly utilized approach. However, as the fre-

5


quency of the RF MEMS switches increasing, the dimension of corresponding deviceis supposed to be smaller and smaller so that the manufacturing cost rapidly increase.Compare with CMOS technology, it does not have big competitiveness at millimeterwave frequency in the �elds of fabrications cost and functionality. Especially, whenthe dimension of RF MEMS goes into the nanometers, the so-called nano-electrical-mechanical-systems requires very high manufacturing cost.

The recently introduced gap waveguide technology [7] constitutes a new type ofwave guiding structure which presents lots of potential to overcome the problemsexisting in conventional technologies mentioned before. The newly proposed gapwaveguide technology is based on the research results of soft- and hard- surfaces [8],which states the cuto� of electromagnetic �elds when a metal plate is placed parallelto a textured arti�cial magnetic conductor (AMC) and their distance is smaller thanquarter wavelength. The AMC surface is able to establish a high impedance sur-face boundary condition that ensures the removal of any parallel-plate mode, cavitymode, surface waves within a certain frequency band called the stopband. Usuallythis AMC is realized by the periodic structure by metallic pins or mushrooms. Thenonly a local TEM mode is allowed to propagate con�ned within the air gap and alonga desired path de�ned by a metallic ridge, groove or microstrip embedded in the AMClayer. Therefore, the gap waveguide technology is able to control the wave propaga-tion in the desired paths, and forbids propagation of waves in undesired directions.Thereby, the gap waveguide technology is a promising wave guiding structure alter-native to counteract the limitations of conventional technologies mentioned beforein this report. So far there are four di�erent realized versions based on guiding-line,propagation characteristics and the band gap structure. Ridge gap waveguide, groovegap waveguide, inverted microstrip gap waveguide and microstrip-ridge gap waveg-uide are four di�erent varieties of gap waveguide technology, as depicted in Figure 1.6.Firstly, the ridge gap waveguide guides a TE mode along the metallic ridge surround-ing by metallic pins and no dielectrics is required in the structure. Then the invertedmicrostrip gap waveguide guides a quasi-TEM mode along a microstrip etched on aPrinted Circuited Broad (PCB). This PCB can be either supported by an AMC sur-face or AMC itself embedded in the substrate materials. In inverted microstrip gapwaveguide the �eld is mainly con�ned in the air gap. The last groove gap waveguidecan propagate a TE mode along the periodic pins surface. No substrate materialis involved in the geometry. This cuto� principle on which this new technology isbased, provides promising opportunities compared to the conventional approaches,such as microstrip, coplanar waveguide, and standard waveguides. The gap waveg-uide technology has interesting characteristics such as low loss, easy manufacturing,and cost-e�ectiveness at millimeter wave frequencies. The advantage compared withother candidates is low loss because the wave propagates in the air. Secondly, theridge and groove gap waveguide does not contain any dielectrics so that they cantotally avoid the dielectric loss. Furthermore, they are mechanically more �exible to

6

1.1. Goal and outline of the thesis

fabricate and assemble them than normal hollow waveguide. In addition, electricalcontact between the building blocks is not needed anymore in such kinds of novelstructures. Thereby, this advantage o�ers good opportunities for making millimeterwave antennas and corporate feed networks. And most importantly, gap waveguidesgeometries can be manufactured by the usage of low cost fabrication techniques suchas injection molding, die pressing, plastic hot embossing or electrical discharging ma-chining.

Another useful advantage of gap waveguide technology is that the metallic pinsare able to supply PMC boundary condition. This boundary condition is able toavoid the surface current which is the origin for the metallic loss. This huge advan-tage can be utilized to package the integrated circuits [9] and passive elements [10].Microstrips and coplanar waveguide transmission lines are open structures and the�nal products need to be protected from interference and physical damages. The tra-ditional method is based on using metallic shielding boxes. As we discussed before,the metallic shielding boxes produce the surface current based on fundamental elec-tromagnetic boundary condition. In addition, this method allows easy appearance ofcavity resonance modes when two of the dimensions of the box are larger than halfwavelength. It is possible to suppress these resonances by adding absorber materials,which introduces additional losses. The new gap waveguide technology can avoid allsuch problems depicted in traditional method.

1.1 Goal and outline of the thesis

In this thesis, some of issues of the traditional technologies and challenges in the mil-limeter wave communications in the future have been already discussed very detailed.There exists a big gap between the planar transmission lines such as microstrips,coplanar waveguide, SIW, multilayer technology, RF MEMS and traditional hollowwaveguide. One of the main current research challenges is to �nd a new guidingstructure with �exible, low cost manufacture and low loss at the same time. Takingthe millimeter wave antennas design as examples, RF MEMS and hollow waveguideare able to realize a high e�ciency antennas, but the manufacture cost are veryhigh. Microstrip, SIW and multilayer technology have low cost and easy manufac-ture, but they su�er from high loss and low e�ciency. It is very di�cult to combineall advantages together at the same time. However, it is possible to utilize gapwaveguide technology to cover all advantages together. In addition, gap waveguideconcerns electromagnetic packaging aspects of this new approach and design of mil-limeter wave transitions. This technology also shows e�ective package advantage,particularly applied to microstrip circuits. Furthermore, in order to achieve highintegration between passive components, active components and antennas together,the gap waveguide technology is able to supply good integration ability with mono-

7


lithic microwave integrated circuits. The transitions [11] from gap waveguide to otherconventional structures has showed that it is very suitable to integrate other compo-nents. In the next chapter, the high-gain high-e�ciency array antenna based on theinverted microstrip gap waveguide technology will be detailedly introduced.

8

Chapter 2

High Gain 60-GHz array antenna

based on Gap Waveguide

This chapter deals with the design of high gain array antennas based on gap waveg-uide. Compared with the other technologies introduced in chapter 1, gap waveguidedecreases cost and complexity of fabrication process without the strict requirementof electric contact among di�erent layers. In this chapter a high gain array antennabased on inverted microstrip gap waveguide and ridge gap waveguide will be detailedintroduced. The �rst designed whole structure based on inverted microstrip gapwaveguide consists of radiating slots, groove gap cavity layer, distribution feedingnetwork and a transition from standard WR-15 waveguide to inverted microstrip gapwaveguide [11]. The complete antenna array is designed and fabricated using Elec-trical Discharging Machining (EDM) technology. The measurement shows that theantenna has 16.95% bandwidth covering 54-64 GHz frequency range. The measuredgain of the antenna is more than 28 dBi with the e�ciency higher than 40% covering54-64 GHz frequency range.

2.1 Introduction

The inverted microstrip gap waveguide technology is based on the presence of a thinsubstrate that lies over a periodic pin pattern that composes the bed of nails. Thisbed of nails constitutes an AMC material and the combination with the upper metallid prohibits any wave propagation within the air gap, also in the presence of thedielectric layer. Only local waves are allowed to propagate along strips etched on thissubstrate. Figure 2.1 shows the basic layout of the inverted microstrip gap waveguide.As sketched in Figure 2.1, the inverted microstrip gap waveguide technology is basedon the use of a thin substrate which is applied for feeding network and lies over aperiodic pin pattern. This periodic metallic pin layer constitutes an AMC surfaceand in combination with the upper metallic lid prohibits any wave propagation within

9

Chapter 2. High Gain 60-GHz array antenna based on Gap Waveguide

Top metallic plate

Microstrip

Substrate

Periodic Pins

Bottom

Metallic plate

Figure 2.1: Brief geometry of the inverted microstrip gap waveguide.

the air gap. Furthermore, a local quasi-TEM mode is allowed to propagate along themetallic strip. The main motivation and advantage of this inverted microstrip gapwaveguide antenna lies to the fact that the pin plate with uniform pin period canbe easily fabricated by metal sawing or wire-cut technique and this will reduce thecost of the overall antenna. Also, the feeding network will be printed on a PCBwhich can be also low cost. In this chapter, we will systematically present a 16×16slot antenna array designed with corporate feeding networks including an interfaceto WR-15 rectangular waveguide. The brief design idea of the complete 16×16 slotantenna array is shown as a �ow chart in Figure 2.2.

2.2 Design for Bed of Nails

As mentioned in previous section, gap waveguide uses a parallel-plate stopband overa speci�c frequency range. The pin dimensions of bed of nails should be chosen cor-rectly to achieve a parallel plate stopband which covers as much as 60-GHz frequencyband. The basic idea is numerical parametric analysis of the inverted microstrip gapwaveguide whose structure is illustrated in Figure 2.3. The PEC, periodic and PECboundary conditions are added for the structure in x-, y- and z-axis, respectively.The geometrical parameters which e�ect the stopband of inverted microstrip gapwaveguide are: the gap height hg, the period p of pins, the width a of pins, thepin height hp of pins and the thickness of substrate hs. Here the shape of pins inXOY plane is square while dispersion diagrams metallic strip are supposed to beidentical in the both propagation directions x and y. The starting point [12] for theparametric analysis is based on the following rules: the height of the air gap hgmust be smaller than λ/4 in order to stop the propagation of all parallel-plate modes.Secondly, the height of metallic pins hp is supposed to be approximately equal to λ/4so that highest surface impedance is achieved. The ratio between the width of metal-lic pins and period a/p has been chosen as 0.5. The considered substrate material

10

2.2. Design for Bed of Nails

Start

Evaluation of

dimensions of pins

Design of

Antenna Unit Cell

Design of Transition from

WR15 to Microstrip

Design of

Distribution Networks

Assemblage of

Components

Optimization of

whole Structure

End

Figure 2.2: The �ow chart for design the whole structure in this thesis.

PEC Boundary

PEC Boundary

Periodic Boundary

xy

z

p

a

ℎ𝑔

ℎ𝑠

ℎ𝑝

Figure 2.3: Geometrical interpretation of gap waveguide microstrip line. Along the y-axis Peri-odic Boundary Condition is set up and the structure is simulated in CST Microwave Studio usingEigenmode Solver.

Table 2.1: Geometrical Parameters of the Structure in Figure 2.3hs hg hp a p

Geometrical Parameters 0.2 mm 0.25 mm 1.2 mm 0.4 mm 0.8 mm

11


0 20 40 60 80 100 120 1400

20

40

60

80

100

120

140

160

180

Frequency [GHz]

Ph

ase

[d

egre

e]

7248

Unwanted Modes

Light LineSTOPBAND

Unwanted Modes

Figure 2.4: Dispersion diagram for the structure in Figure 2.2 and the blue curve crossing over thestopband represents the quasi-TEM mode.

is Rogers RO4003 with relative permittivity εr = 3.55, loss tangent tanδ = 0.0027(speci�cations are at 10 GHz according to Rogers material data sheet) and thicknesshs = 0.2 mm. It should be emphasized that the loss tangent value of the substratematerial Rogers RO4003 at 60-GHz frequency band is much higher than that at 10GHz in reality according to fundamental electromagnetic �eld theory. Therefore, wehave to set up the loss tangent value of Rogers RO4003 as 0.01 in CST MicrowaveStudio, which is almost 4 times higher than the value at 10 GHz. The motivationsto select RO4003 are that it has lower loss value than traditional PCB substrateFR4 and mechanically more rigid than other substrate materials. Correspondingly,the dispersion diagram of the structure is shown in Figure 2.4, which is obtainedby utilizing the eigenmode solver in CST Microwave Studio software. The obtainedstopband is from 48 to 72 GHz and only one mode propagates within the structure,as shown in Figure 2.4. The corresponding geometrical parameters are listed in Table2.1.

2.3 Design for Antenna Unit Cell

As mentioned before, a 2×2 element sub-array is �rstly designed using periodicboundary condition in order to evaluate the radiation pattern and directivity of wholearray antenna. Most importantly, the mutual coupling e�ect is taken into accountin this way so that the periodic boundary conditions in both x and y directions areplaced. Figure 2.5 shows exploded perspective view of the 2×2 element sub-array,which brie�y consists of radiating slot layer, cavity layer, PCB microstrip layer andbed of nails. Instead of normal hollow rectangular waveguide cavity [13], we have uti-

12

2.3. Design for Antenna Unit Cell

Metal Plate

with Pins

Substrate

Roger 4003

Inverted

Microstrip Line

Metallic Lid

Coupling Hole

Backed Cavity

Radiation Slots

xy

z

Figure 2.5: Detailed 3-D view of 2 × 2 slots sub-array.

x

yz

W

L

𝑑𝑦

𝑑𝑥

𝑊𝑠

𝐿𝑠

(a)

x

yz

W

L

𝑊𝑟1

𝐿𝑟1

𝑊𝑟2

𝐿𝑟2

(b)

x

yz

W

L

𝑊𝑐

𝐿𝑐

(c)

x

yz

W

L𝑊𝑚1

𝑊𝑚2

𝑊𝑚3

𝑊𝑚4

(d)

Figure 2.6: Geometrical parameters of a 2 × 2 slots array. (a) Top radiation slots layer. (b) Backedcavity layer. (c) Coupling hole layer. (d) Feed distribution networks layer.

13


lized groove gap waveguide cavity here because it is convenient to be manufactured.Here the groove gap waveguide cavity in the middle is partitioned into four spaces bytwo sets of metallic blocks extending in the x and y directions. The PCB microstriplayer feeds all the groove waveguide cavities with identical phase and amplitude by

57 58 59 60 61 62 63 64 65 66-40

-35

-30

-25

-20

-15

-10

-5

0

Frequency [GHz]

Ref

lect

ion

Coef

fici

ent

[dB

]

(a)

57 58 59 60 61 62 63 64 65 6631.5

32

32.5

33

33.5

34

Frequency [GHz]

Dir

ecti

vit

y [

dB

]

100% Aperture Efficiency



Simulated Directivity

100%

90%

80%

(b)

Figure 2.7: (a) Simulated re�ection coe�cient S11 of 2×2 slots sub-array. (b) Directivity of an arrayantenna of 16×16 slot aperture dimension in in�nite array environment.

-90 -60 -30 0 30 60 90

-40

-30

-20

-10

0

Angle [deg.]

Norm

ali

zed

Far

Fie

ld [

dB

]

E-Plane

57 GHz

61.5 GHz

66 GHz

(a)

-90 -60 -30 0 30 60 90

-40

-30

-20

-10

0

Angle [deg.]

No

rma

lize

d F

ar

Fie

ld [

dB

]

H-Plane

57 GHz

61.5 GHz

66 GHz

(b)

Figure 2.8: (a) Radiation pattern of 16×16 slot array antenna in E-Plane. (b) Radiation patternof 16×16 slot array antenna in H-Plane. Both simulation results are obtained by in�nite periodicapproach on 2×2 slot sub-array.

the middle coupling hole.As is well known, the slots in an antenna aperture ought to be uniformly spaced

in both x and y directions with spacing smaller than one wavelength in order to avoidgrating lobes in a large broadside array. The highest frequency of the antenna is cho-sen to be 66 GHz and the corresponding wavelength λ is about 4.5 mm. Therefore,

14

2.4. Transition from WR-15 to Inverted Microstrip Gap Waveguide

the slot space ds in this work we have chosen 4 mm. On the other hand, the valueW and L should be integer times of the pins period, namely W =Mp and L = Np.Given the above-mentioned considerations, we select W = L = 10p = 8 mm. Thedetailed geometrical demonstration of the antenna sub-array have been shown in Fig.6. First of all, the slot dimensions Ws and Ls as well as the cavity metallic blockdimensions Wr1, Lr1, Wr2 and Lr2 have been well optimized to achieve good radia-tion pattern. Secondly, Wc, Lc, Wm1, Wm2, Wm3 and Wm4 have been optimized toachieve minimum re�ection coe�cient. Figure 2.7 (a) shows corresponding re�ectioncoe�cient of sub-array and it has 14.5% impedance bandwidth (over 57-65.7 GHz)

Table 2.2: Geometrical Parameters of 2 × 2 Unit Cell the Structure in Figure 2.6W L dx dy Ws

Geometrical Parameters 8 mm 8 mm 4 mm 4 mm 1.75 mmLs Wc Lc Wr1 Lr1


with input re�ection coe�cient better than -15 dB. Figure 2.7 (b) also illustrates thesimulated directivity of 16×16 slot aperture array in in�nite array environment. Theoptimized sub-array achieves that expected design target for whole antenna array.The �nal dimensional parameters of sub-array are presented in Table 2.2. Here wehave utilized the CST Microwave Studio in�nite periodic approach along the x andy directions of 8 elements in order to estimate the radiation pattern of the wholestructure. Figure 2.8 illustrates the radiation patterns of E- and H-plane of 16×16slot array antenna according to in�nite periodic approach. We have observed thatthe �rst side-lobe levels in both E- and H-planes are around -13 dB and the gratinglobe levels (GL) in E- and H-planes are respectively below -19 dB and -25 dB.

2.4 Transition from WR-15 to Inverted Microstrip

Gap Waveguide

A vertical transition from standard V-band rectangular waveguide to inverted mi-crostrip gap waveguide is presented in this work. Since it is convenient to directlymeasure antenna array with rectangular waveguide excitation, millimeter wave highgain antennas are usually excited by a standard rectangular waveguide in reality. Astandard V-band rectangular waveguide (WR-15) thus works as the input port at thebottom of antenna structure. Obviously, the main challenge here is how to transferTE10 mode in rectangular waveguide to the quasi-TEM mode of inverted microstripgap waveguide e�ciently with simple con�gureation. Normally there are three typesof transitions in microwave technology: inline transitions, aperture coupled patchtransitions and vertical transitions. Here we choose the vertical transition.

As sketched in Figure 2.9, this transition is composed of three parts: WR-15

15


x

yz

𝑊𝑥2

𝑊𝑥1

WR15

Pin

(a)

Rectangular Waveguide WR15

Roger 4003 supported

by metallic pins

Inverted Microstrip Line

Air filled backshot cavity

Metallic Top Layer

(b)

Figure 2.9: (a) Top view transition geometry. In order to observe the microstrip and waveguideopen details the substrate is hidden. (b) Cross-sectional view for complete structure.

feeding waveguide, inverted microstrip gap waveguide and backshort cavity at topmetallic layer. The whole structure works as a three-port power divider that can bealso utilized for power division. First of all, a PCB is positioned over a bed of pins and

57 58 59 60 61 62 63 64 65 66-35

-30

-25

-20

-15

-10

-5

0

Frequency [GHz]

S-P

ara

met

ers

[dB

]

S11

S21

S31

-3.09

(a)

57 58 59 60 61 62 63 64 65 66

-150

-100

-50

0

50

100

150

Frequency [GHz]

Pha

se [

degr

ee]

S21S31

(b)

Figure 2.10: Simulated S-parameter results of designed transition structure. (a) Amplitude. (b)Phase.

it contains tapered section. These tapered-line sections act as an impedance trans-former. A parametric sweep of the position and impedance of this tapered sectionhas been carried out in order to achieve optimum return loss within the frequencyband of interest. The layout of the transition circuit is shown in Figure 2.9 (a). Onthe other hand, the whole transition is accomplished by adding a cavity backshort onthe top metallic lid, as shown in Figure 2.9 (b). The backshort is positioned opposite

16

2.5. Design of Feeding Distribution Networks

Table 2.3: Geometrical Parameters in Figure 2.9Wx1 Wx2 Lcbx Lcby Lcbz

Geometrical Parameters 0.815 mm 0.961 mm 3 mm 1.785 mm 0.375 mm

to the rectangular waveguide opening. Its dimensions are �rstly roughly evaluatedby impedance transformer and then optimized together with the tapered-line by fullwave simulation. The distance between the backshort cavity and the substrate isset as λ0/4 (λ0 = 4.95 mm) in order to compensate the reactance of two-steps mi-crostrips. Hereby, the backshort cavity together with the tapered microstrip lineessentially contributes in �eld matching as well as impedance matching over 57 - 66GHz. All signi�cant parameter values are speci�ed on Table 2.3 for this proposedtransition power divider. The simulated S-Parameters of the structure is shown inFigure 2.10. The function of simple section is actually equal to a single WR-15 toinverted microstrip gap waveguide transition and a T-junction power divider. Inaddition, we should notice that the phases of the output ports have 180 degree dif-ference, as shown in Figure 2.10 (b). Please observe that we will compensate thisdi�erence in design of distribution networks.

2.5 Design of Feeding Distribution Networks

Compared with groove and ridge gap waveguide structure, the feeding distributionnetworks based on inverted microstrip gap waveguide has some obvious advantages.First of all, the inverted microstrip gap waveguide has a uniform bed of nails whilethe other types of gap waveguide prototypes do not. This uniform pins make thefabrication much easier and cheaper. For instance, a uniform pins surface can besawed with parallel saw blades, whereas nonuniform pin locations and ridges mustbe milled with a thin milling tool. Secondly, theories and design principles of tradi-tional inverted microstrip technique are very maturate in the past decades so thatwe can directly utilize them with little modi�cation. For these reasons, the invertedmicrostrip gap waveguide is attractive in feeding networks for slot antenna arrays athigh frequency.

Despite its advantages, the inverted microstrip gap waveguide technology is stilla challenge in design of feeding distribution networks for slots array. In [14] a planarhorn array fed by inverted microstrip gap waveguide has been already expounded.Since metallic pins surface is able to supply a nearly PMC boundary condition, thedistribution networks in [14] has been �rst designed with an ideal PMC conditioninstead of metallic pins structure located at the bottom of the substrate. Neverthe-less, the corporate-feed networks design in this work di�ers from that in [14]. Mostimportant reason is that minute quantity of electric- and magnetic �elds still exist in-side the metallic pins structure in reality while a quasi-TEM mode propagates along

17


the top microstrip. However, electric- and magnetic �elds inside a PMC are bothnull. Therefore, assuming an ideal PMC condition to replace the metallic pins struc-ture may introduce signi�cant error in design of distribution networks. Until nowthe inverted microstrip gap waveguide technology has been merely applied for designbandpass �lter [15]. Given its complexity an antenna unit cell has been accomplishedwithout distribution networks in [16].

As introduced before, we have already designed a promising antenna unit cellwhich is fed by inverted microstrip gap waveguide. In this section, a new procedurefor design distribution networks based on inverted microstrip gap waveguide struc-ture will be presented. The feeding networks consists of several cascading T-junctionpower dividers and their impedance matching transformers between each other.

2.5.1 Design of T-junction Power Divider

Essentially a T-junction power divider is a simple three-port network that can be uti-lized for power division or combining. Thereby, the T-junction is a central componentin distribution networks for feeding antenna array. In this work we �rstly design a T-

Input Part

Output Part

Substrate

Roger4003

(a)

𝑊𝑡,1

𝑊𝑡,2

𝑊𝑡,3

𝑊𝑡,4𝑊𝑡,5

(b)

Figure 2.11: (a) Illustration for single T-junction power divider based on inverted microstrip gapwaveguide. (b) Geometrical description for single T-junction and the substrate is hidden in orderto observe the microstrip and bottom bed of nails.

junction power divider with metallic pins in CST Microwave Studio shown in Figure2.11 (a). In order to obtain correct transition performance an optimized numericalport [17] has been utilized during the entire design procedure. The T-junction thenhas been optimized with the dimensions of width of microstrips Wt,1, Wt,2, Wt,3, Wt,4

and Wt,5 and the �nal optimized geometrical parameters are listed in Table 2.4. Fig.12 shows S-parameters, where the re�ection coe�cient S11 is below -30 dB from 57to 66 GHz. The S21 and S31 are identical to -3.1 dB. Besides the lost energy in sub-

18

2.5. Design of Feeding Distribution Networks

57 58 59 60 61 62 63 64 65 66-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Frequency [GHz]

S-P

ara

met

ers

[dB

]

S11

S21

S31

-3.02

Figure 2.12: The simulated S-parameters of single T-junction.

Table 2.4: Geometrical Parameters in Figure 2.11Wt,1 Wt,2 Wt,3 Wt,4 Wt,5


strate RO4003, the rest of electromagnetic energy are identically split to output port2 and port 3. The simulated result also indicates that T-junction power divider haspromising abilities of power division and isolation for two output ports. The inputand output port impedances are calculated by CST and it is convenient to utilizethem for impedance transformer design in next subsection.

2.5.2 Design of Impedance Transformer

Impedance matching is a practical topic in microwave circuits. This fundamentalidea is that an impedance matching network placed between a load impedance and atransmission line. The re�ection e�ect will be eliminated on the distribution networksto the matching networks. The basic principle of impedance matching is shown inFig. 13 (a) and its implementation in this work is shown in Fig. 13 (b) as well.In this work we apply classical second order binomial impedance transformer forimpedance matching. All characteristic impedances and load impedances has beenobtained from optimized numerical ports introduced in [17]. Here we should notice

19


c05ImpedanceMatchingandTuning Pozar July 29, 2011 20:34

5.1 Matching with Lumped Elements (L Networks) 229

Z0Matchingnetwork

LoadZL

FIGURE 5.1 A lossless network matching an arbitrary load impedance to a transmission line.

� Implementation—Depending on the type of transmission line or waveguide being used,one type of matching network may be preferable to another. For example, tuningstubs are much easier to implement in waveguide than are multisection quarter-wavetransformers.� Adjustability—In some applications the matching network may require adjustment tomatch a variable load impedance. Some types of matching networks are more amenablethan others in this regard.

5.1 MATCHING WITH LUMPED ELEMENTS (L NETWORKS)

Probably the simplest type of matching network is the L-section, which uses two reac-tive elements to match an arbitrary load impedance to a transmission line. There are twopossible configurations for this network, as shown in Figure 5.2. If the normalized loadimpedance, zL = ZL/Z0, is inside the 1 + j x circle on the Smith chart, then the circuitof Figure 5.2a should be used. If the normalized load impedance is outside the 1 + j x cir-cle on the Smith chart, the circuit of Figure 5.2b should be used. The 1 + j x circle is theresistance circle on the impedance Smith chart for which r = 1.

In either of the configurations of Figure 5.2, the reactive elements may be either induc-tors or capacitors, depending on the load impedance. Thus, there are eight distinct possibil-ities for the matching circuit for various load impedances. If the frequency is low enoughand/or the circuit size is small enough, actual lumped-element capacitors and inductors canbe used. This may be feasible for frequencies up to about 1 GHz or so, although modernmicrowave integrated circuits may be small enough such that lumped elements can be usedat higher frequencies as well. There is, however, a large range of frequencies and circuitsizes where lumped elements may not be realizable. This is a limitation of the L-section

Z0

jX

ZL

(a) (b)

jB

jX

ZLjB

FIGURE 5.2 L-section matching networks. (a) Network for zL inside the 1 + j x circle. (b) Net-work for zL outside the 1 + j x circle.

(a)

Matching

Microstrip

between

T-junction

Matching

Micorstrip

from transition

to T-junction

1

2

34

(b)

57 58 59 60 61 62 63 64 65 66−35

−30

−25

−20

−15

−10

−5

0

Frequency [GHz]

S−

Par

amet

ers

[dB

]

S11

S21...S65,1

−18.9 dB

(c)

Figure 2.13: (a) Illustration for a network matching an arbitrary load impedance to a transmissionline. (b) Realized whole feeding networks and its matching parts in this work. (c) SimulatedS-Parameters in CST Microwave Studio.

20

2.6. Comparison between Simulated and experimental results

that part 1 of matching microstrip has been designed as shape of parallelogram inorder to remove its mutual coupling e�ect to the nearest coupling holes. In addition,the input port in CST is set up at the bottom of WR-15 and the output ports arebuilt at the output microstrip of last stage T-junction power divider. Finally, thewhole distribution network is optimized by genetic algorithm.

The �nal designed structure of the feeding distribution networks is shown in Fig.13 (b). The complete corporate-feed network consists of two 32-way power dividersconnected to the transition of WR-15 at the center. As described in section IV, thetransition power divider from WR-15 to inverted microstrip gap waveguide has 180degree phase di�erence. Thereby, the whole feeding network is mirrored in order tocompensate the phase di�erence. Fig. 13 (c) shows the corresponding S-parametersof the whole distribution networks. The re�ection coe�cient S11 is almost below -20dB over 57 - 66 GHz.

2.6 Comparison between Simulated and experimen-

tal results

Top radiating layer

Backed cavity layer

Coupling hole layer

Bottom bed of nails

Feeding microstrip

(a) (b)

Figure 2.14: (a) Numerical model in CST Microswave studio of proposed array antenna. In orderto observe the microstrip and waveguide open details the substrate is hidden. (b) Photogragh ofproposed 16×16 array antenna fabricated by EDM technology.

The numerical model and �nal manufactured prototype of the 16×16 slot arrayantenna discussed in this paper is shown in Fig. 14. The metallic parts of the arrayantenna is fabricated by Electrical Discharging Machining (EDM) Technology. Inthis manufacture technology, the designed prototype is etched by recurring electricdischarges between the workpiece and electrodes. The �nal designed array aperturedimension is 64 × 64 mm2 (8 mm×8 mm× 64 elements).

The simulated and measured input re�ection coe�cients of the proposed antenna

21


54 56 58 60 62 64 66-40

-35

-30

-25

-20

-15

-10

-5

0

Frequency [GHz]

Ref

lect

ion

Coe

ffic

ien

t [d

B]

Measured S11

Simulated S11

Figure 2.15: Comparison of simulated and measured re�ection coe�cient of the proposed 16 × 16slot array antenna.

Chapter 4. Gap Waveguide Technology for Millimeter Wave Applications

Bed of nails

Substrate

Metal strip

(a) Longitudinal variation along axis.

(b) Variation in transverse direction.

(c) Simultaneous transverse and longitudinal variation.

Figure 4.7: Modeled curved profiles with different type of variations (exag-gerated variation for illustration purpose).

cosine variation (longitudinal and transversal at the same time). These three

cases of variation are sketched in Fig. 4.7. For each type of variation, the

amplitude of the cosine and the number of periods have been controlled to

generate enough number of samples to extract relevant information about

the consequences of the bad contact between the bed of pins and the PCB.

Some conclusions that we can summarize from this study are:

1. If good contact between the pins and the planar substrate region that

contains the transition is forced, and longitudinal variation along the

52

Figure 2.16: Sketch of inverted microstrip gap waveguide with a bent substrate.

are shown in Fig. 15. The measured S11 is a bit higher than the simulation. How-ever, it is still below -10 dB from 54.5 GHz to 66 GHz (19.2% impedance bandwidth).There are some di�erences between the simulated and measured results. As abovediscussed in section II, the dispersion diagram of whole structure is a�ected by dimen-sions of metallic pins, the thickness of substrate and the height of air gap. Therefore,any manufacture tolerances of bed of nails and the height change of air gap will causeshift of parallel stopband. As reported in [18], there is always a frequency shift inre�ection coe�cient which drifts towards to lower or higher frequency. A consequenceof this is that the PCB may not remain rigidly supported over the bed of pins, andthere are some points in which the pins do not have a good contact with the substrate(see sketch presented in Fig. 16). Furthermore, these untouched gap between sub-strate and pins automatically creates capacitance e�ect. This small shunt capacitora�ects the dispersion diagram of inverted microstrip gap waveguide.

The radiation pattern of proposed antenna is measured in an anechoic chamber.The simulated and measured normalized radiation patterns in the E- and H-plane atfour di�erent frequencies 57, 60, 61, 66 GHz are shown in Fig. 17 and Fig. 18. Themeasured Co-polarization radiation patterns show a very good agreement with thesimulated results. The simulated and measured radiation patterns are symmetrical,and the �rst side-lobe levels in both E- and H-planes are around -13 dB. The mea-sured grating lobes of the fabricated array in both E- and H-planes are below -20 dB

22

2.6. Comparison between Simulated and experimental results

-80 -60 -40 -20 0 20 40 60 80-80

-70

-60

-50

-40

-30

-20

-10

0

Angle [degree]

Rel

ati

ve

Am

pli

tud

e [d

B]

Sim.Co-pol.

Mea.Co-pol.

Mea.Cross-pol.

(a)

-80 -60 -40 -20 0 20 40 60 80-80

-70

-60

-50

-40

-30

-20

-10

0

Angle [degree]

Rel

ati

ve

Am

pli

tud

e [d

B]

Sim.Co-pol.

Mea.Co-pol.

Mea.Cross-pol.

(b)

-80 -60 -40 -20 0 20 40 60 80-80

-70

-60

-50

-40

-30

-20

-10

0

Angle [degree]

Rel

ati

ve

Am

pli

tud

e [d

B]

Sim.Co-pol.

Mea.Co-pol.

Mea.Cross-pol.

(c)

-80 -60 -40 -20 0 20 40 60 80-80

-70

-60

-50

-40

-30

-20

-10

0

Angle [degree]

Rel

ati

ve

Am

pli

tud

e [d

B]

Sim.Co-pol.

Mea.Co-pol.

Mea.Cross-pol.

(d)

Figure 2.17: Measured and simulated radiation pattern of proposed array antenna on E-plane. (a)57 GHz. (b) 60 GHz. (c) 61 GHz. (d) 66 GHz.

-80 -60 -40 -20 0 20 40 60 80-80

-70

-60

-50

-40

-30

-20

-10

0

Angle [degree]

Rel

ati

ve

Am

pli

tud

e [d

B]

Sim.Co-pol.

Mea.Co-pol.

Mea.Cross-pol.

(a)

-80 -60 -40 -20 0 20 40 60 80-80

-70

-60

-50

-40

-30

-20

-10

0

Angle [degree]

Rel

ati

ve

Am

pli

tud

e [d

B]

Sim.Co-pol.

Mea.Co-pol.

Mea.Cross-pol.

(b)

-80 -60 -40 -20 0 20 40 60 80-80

-70

-60

-50

-40

-30

-20

-10

0

Angle [degree]

Rel

ati

ve

Am

pli

tud

e [d

B]

Sim.Co-pol.

Mea.Co-pol.

Mea.Cross-pol.

(c)

-80 -60 -40 -20 0 20 40 60 80-80

-70

-60

-50

-40

-30

-20

-10

0

Angle [degree]

Rel

ati

ve

Am

pli

tud

e [d

B]

Sim.Co-pol.

Mea.Co-pol.

Mea.Cross-pol.

(d)

Figure 2.18: Measured and simulated radiation pattern of proposed array antenna on H-plane. (a)57 GHz. (b) 60 GHz. (c) 61 GHz. (d) 66 GHz.

23


over the desired frequency band. The cross-polarization values are below -40 dB atall frequencies.

The simulated directivity and gain of proposed antenna are shown in Fig. 19. Thered solid line, which stand for simulated directivity, is above 80% aperture e�ciency(64×64mm2). The pink dash line in Fig. 19 indicates the simulated gain after settingup the modi�ed loss tangent of substrate. This method help us accurately predict thereal gain after manufacturing. The blue dash-dot line in Fig. 19 shows the measured

53 54 55 56 57 58 59 60 61 62 63 64 65 6620

21.5

23

24.5

26

27.5

29

30.5

32

33.5

35

Frequency [GHz]

Dir

ecti

vit

y &

Gain

[d

Bi]





Measured Gain

Simulated Directivity

Simulated Gain

100%

60%

50%

40%

Figure 2.19: Measured gain and simulated directivity of present 16 × 16 slot array antenna.

gain, illustrating above 40% aperture e�ciency over the frequency band 54-64 GHz.What we should notice in Fig. 19 is that the measured gain drops very rapidly at thestart of 64 GHz, yet our design target is 57-66 GHz. The probable explanation forreducing of antenna gain of proposed array antenna is that the true loss tangent ofsubstrate is actually unknown in reality. The value of tangent loss is probably evenhigher than 0.01 at higher frequency band. The other possible reason for the gainreduction is that the antenna is made of steel. The top radiating layer is too thin tobe deformed by the force. The analogues phenomenons also appear in [19] and [20].

In the following we will summarize several structural characteristics and perfor-mances of reported 60-GHz high-gain antenna arrays accompanied with our workin Table 2.5. Compared with the designs in [19] and [20], our work exhibits wideimpedance bandwidth, higher aperture e�ciency and low cost on fabrication. How-ever, because of the ohmic loss in dielectrics of feed distribution networks, the realizedgain of our work is lower than those reported in [13], [21] and [22]. Thereby, thereare still some work to do for the further improvements. As illustrated in Fig. 16,the untouched gap between pins and substrate is most important issue because itproduces negative e�ect on wave propagation of the structure. How to solve thisproblem is an important issue for this technology.

24

2.7. Conclusion

Table 2.5: COMPARISON BETWEEN THE PROPOSED AND REPORTED 60-GHz PLANAR ANTENNA ARRAYS

Performance Ref.[19] Ref.[20] Present Work

Technology SIW/Microstrip SIW/Microstrip IMGW

Size [cm] 6.8 × 6.8 12 × 12 6.4 × 6.4

Number of Elements 256 256 256

Frequency Band [GHz] 57-63 58.5-64.5 54.5-64

Bandwidth 10% 10% 17%

Max Gain [dBi] 30 34 30.5

Min E�ciency 47% 25% 40%

2.7 Conclusion

A high gain and wide bandwidth slot array antenna based on inverted microstrip gapwaveguide at 60-GHz has been presented in this work. The proposed antenna consistsof four unconnected layers without any electric contact between them. The designedprototype is manufactured by EDM technology. In this paper, we �rstly used weused a new corporate feed network based on the inverted microstrip gap waveguidetechnology. A transition power divider between WR-15 and inverted microstrip gapwaveguide have been designed in order to provide a simple excitation of the antenna.The simulated and measured results of the whole antenna structure shows very goodagreements in radiation patterns in both E- and H-plane. The measured realizedgain is higher than 29 dBi over the entire operation bandwidth from 54.5 to 64GHz, corresponding to e�ciency larger than 45%. This work shows that the invertedmicrostrip gap waveguide technology is an excellent candidate for array antennas inmillimeter wave communication.

25

Chapter 3

Future Work

A single layer high gain high e�ciency array antenna based on ridge gap waveguidewill be designed in the coming years. As is well known, millimeter wave array in-troduced before are all based on three layers, namely slot array layer, backed cavitylayer and feed networks layer. Obviously the manufacture price is lower if we onlyhave feed networks and slot array. At the same time this new topology still preservethe properties of high gain, high e�ciency, promising radiation pattern and widebandwidth. Secondly, bandpass �lters and diplexers based on ridge gap waveguidewill be developed in the future work. In addition, the package technology of activecomponents by gap waveguide technology will also be researched in the future work.

27

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