Design of Nonplanar Microstrip Antennas and Transmission Lines
Kin-Lu Wong
Copyright  1999 John Wiley & Sons, Inc.
Print ISBN 0-471-18244-3 Online ISBN 0-471-20066-2

Design of Nonplanar
Microstrip
Antennas
and Transmission
Lines


Design of Nonplanar
Microstrip Antennas
and Transmission lines
KIN-LU
National

WONG
Sun Yat-Sen University

A WILEY-INTERSCIENCE
JOHN
NEW

WILEY
YORK

/

PUBLICATION

& SONS,
CHICHESTER

INC.
/

WEINHEIM

/

BRISBANE

/

SINGAPORE

/

TORONTO


Copyright  1999 by John Wiley & Sons, Inc. All rights reserved.
No part of this publication may be reproduced, stored in a retrieval system or transmitted in
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services of a competent professional person should be sought.
ISBN 0-471-20066-2.
This title is also available in print as ISBN 0-471-18244-3
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Library of Congress Cataloging-in-Publication Data:
Wong, Kin-Lu.
Design of nonplanar microstrip antennas and transmission lines /
Kin-Lu Wong.
p. cm. — (Wiley series in microwave and optical engineering)
“A Wiley-Interscience publication.”
Includes bibliographical references and index.
ISBN 0-471-18244-3 (cloth: alk. paper)
1. Strip transmission lines–Design and construction.
2. Microstrip antennas–Design and construction. I. Title.
II. Series.
TK7876.W65 1999
98-35003
621.3810 331 — dc21
Printed in the United States of America.
10 9 8 7 6 5 4 3 2 1


Contents

ix

PREFACE

1

Introduction

1

and Overview

1.1 Introduction
1.2 Cylindrical Microstrip Antennas
1.2.1 Full-Wave Analysis
1.2.2 Cavity-Model
Analysis
1.2.3 Generalized Transmission-Line
1.3 Spherical Microstrip Antennas
1.4 Conical Microstrip Antennas
1S Conformal Microstrip Arrays
1.6 Conformal Microstrip Transmission
References
2

Resonance Problem

of Cylindrical

Model Theory

Lines

Microstrip


Patches

2.1 Introduction
2.2 Cylindrical Rectangular Microstrip Patch with a Superstrate
2.2.1 Theoretical Formulation
2.2.2 Galerkin’s Moment-Method Formulation
2.2.3 Complex Resonant Frequency Results
2.3 Cylindrical Rectangular Microstrip Patch with a Spaced
Superstrate
2.3.1 Theoretical Formulation
2.3.2 Resonance and Radiation Characteristics
2.4 Cylindrical Rectangular Microstrip Patch with an Air Gap
2.4.1 Complex Resonant Frequency Results

1
2
5
6
7
8
10
11
12
14
16
16
17
17
24

26
30
30
32
35
36


vi

CONTENTS

2.5 Cylindrical

Rectangular Microstrip

Patch with a Coupling

Slot

39
43

2.5.1 Theoretical Formulation
2.5.2 Resonance Characteristics
2.6 Cylindrical

Triangular

Microstrip


44

Patch

44
48

2.6.1 Theoretical Formulation
2.6.2 Complex Resonant Frequency Results
2.7 Cylindrical

Wraparound

Microstrip

50

Patch

51
54

2.7.1 Theoretical Formulation
2.7.2 Complex Resonant Frequency Results
References
3

Resonance


54
Problem

of Spherical

3.1 Introduction
3.2 Spherical Circular

Microstrip

Microstrip

Patches

Patch on a Uniaxial

Substrate

3.2.1 Fundamental Wave Equations in a Uniaxial Medium
3.2.2 Spherical Wave Functions in a Uniaxial Medium
3.2.3 Full-Wave Formulation for a Spherical Circular
Microstrip Structure
3.2.4 Galerkin’s Moment-Method Formulation
3.2.5 Basis Functions for Excited Patch Surface Current
3.2.6 Resonance Characteristics
3.2.7 Radiation Characteristics
3.2.8 Scattering Characteristics
3.3 Spherical Annular-Ring

Microstrip


Patch

3.3.1 Theoretical Formulation
3.3.2 Complex Resonant Frequency Results
3.4 Spherical Microstrip

Patch with a Superstrate

3.4.1 Circular Microstrip Patch
3.4.2 Annular-Ring Microstrip Patch
3.5 Spherical Microstrip

Patch with an Air Gap

4.1
4.2

57
59
64
68
69
70
73
75
77
78
83
83


94
94
96

References
Characteristics

56
56
56

83
89

3.5.1 Circular Microstrip Patch
3.5.2 Annular-Ring Microstrip Patch

4

37

101
of Cylindrical

Introduction
Probe-Fed Case: Full-Wave
4.2.1 Rectangular Patch
4.2.2 Triangular Patch


Microstrip

Solution

Antennas

103
103
103
108
112


CONTENTS

Probe-Fed Case: Cavity-Model
Solution
4.3.1 Rectangular Patch
4.3.2 Triangular Patch
4.3.3 Circular Patch
4.3.4 Annular-Ring Patch
4.4 Probe-Fed Case: Generalized Transmission-Line
Solution
4.4.1 Rectangular Patch
4.4.2 Circular Patch
4.4.3 Annular-Ring Patch
4.5 Slot-Coupled Case: Full-Wave Solution
4.5.1 Printed Slot as a Radiator
4.5.2 Rectangular Patch with a Coupling Slot
4.6 Slot-Coupled Case: Cavity-Model

Solution
4.6.1 Rectangular Patch
4.6.2 Circular Patch
4.7 Slot-Coupled Case: GTLM Solution
4.7.1 Rectangular Patch
4.7.2 Circular Patch
4.8 Microstrip-Line-Fed
Case
4.9 Cylindrical Wraparound Patch Antenna
4.10 Circular Polarization Characteristics
4.11 Cross-Polarization
Characteristics
4.11.1 Rectangular Patch
4.11.2 Triangular Patch
References

113
118
121
124
129

4.3

5

Characteristics

of Spherical


and Conical

Microstrip

Model
133
133
144
147
153
155
165
168
170
176
180
180
183
184
189
191
196
196
199
202
Antennas

Coupling

between


Conformal

Microstrip

205
205
205
206
219
230
234
239

5.1 Introduction
5.2 Spherical Microstrip Antennas
5.2.1 Full-Wave Solution
5.2.2 Cavity-Model
Solution
5.2.3 GTLM Solution
5.3 Conical Microstrip Antennas
References
6

vii

Antennas

6.1 Introduction
6.2 Mutual Coupling of Cylindrical Microstrip Antennas

6.2.1 Full-Wave Solution of Rectangular Patches
6.2.2 Full-Wave Solution of Triangular Patches

241
241
241
241
246


...
VIII

7

CONTENTS

6.2.3 Cavity-Model
Solution of Rectangular Patches
6.2.4 Cavity-Model
Solution of Circular Patches
6.25 GTLM Solution of Rectangular Patches
6.2.6 GTLM Solution of Circular Patches
6.3 Cylindrical Microstrip Antennas with Parasitic Patches
6.4 Coupling between Concentric Spherical Microstrip Antennas
6.4.1 Annular-Ring Patch as a Parasitic Patch
6.4.2 Circular Patch as a Parasitic Patch
References

251


Conformal

286

Microstrip

Arrays

7.1 Introduction
7.2 Cylindrical Microstrip Arrays
7.3 Spherical and Conical Microstrip
References
8

Cylindrical

Microstrip

Waveguides

8.1 Introduction
8.2 Cylindrical Microstrip Lines
8.2.1 Quasistatic Solution
8.2.2 Full-Wave Solution
8.3 Coupled Cylindrical Microstrip Lines
8.4 Slot-Coupled Double-Sided Cylindrical Microstrip
8.5 Cylindrical Microstrip Discontinuities
8.5.1 Microstrip Open-End Discontinuity
8.5.2 Microstrip Gap Discontinuity

8.6 Cylindrical Coplanar Waveguides
8.6.1 Quasistatic Solution
8.6.2 Full-Wave Solution
References
Appendix

A

294
294
294
295
299

Lines

308
315
324
324
330
335
336
342
353

Curve-Fitting
Formula for Complex Resonant
Frequencies of a Rectangular Microstrip
Patch with

a Superstrate

356
361

Appendix

B

Modified

Appendix

C

Curve-Fitting
Frequencies
Superstrate

Index

284

286
286
290
293

Arrays


lines and Coplanar

257
264
268
272
280
280
283

Spherical

Bessel Function

Formula for Complex
of a Circular Microstrip

Resonant
Patch with a
363

369


Preface

Due to their conformal capability, research on nonplanar microstrip antennas and
transmission lines has received much attention. Many studies have been reported
in the last decade in which canonical nonplanar structures such as cylindrical,
spherical, and conical microstrip antennas and cylindrical microstrip transmission

lines have been analyzed extensively using various theoretical techniques. These
results are of great importance because from the research results of such curved
microstrip structures, the characteristics of general nonplanar microstrip antennas
and circuits can be deduced. The information can provide a useful reference for
working engineers and scientists in the design and analysis of microstrip antennas
and circuits to be installed on curved surfaces. Since the results are scattered in
papers in many technical journals, it is our intention in this book to organize the
research results on nonplanar microstrip antennas and circuits and provide an
up-to-date overview of this area of technology.
The book is organized in eight chapters. In Chapter 1 we present an
introduction and overview of recent progress in research on nonplanar microstrip
antennas and transmission lines and give readers a quick guided tour of subjects
treated in subsequent chapters.
In Chapters 2 and 3 we discuss, respectively, resonance problems inherent in
cylindrical and spherical microstrip patches. In addition to study of single-layer
microstrip patches of various shapes, structures related to microstrip patches with
an air gap for bandwidth enhancement or a spaced superstrate for gain improvement are analyzed based on a full-wave formulation incorporating moment-method
calculations. From the formulation, the complex resonant frequencies of a curved
microstrip patches are solved whose real and imaginary parts give, respectively,
information on resonant frequency and radiation loss of a curved microstrip
structure. By comparison with results calculated from curve-fitting formulas for
complex resonant frequencies of planar rectangular and circular microstrip
patches, basic curvature effects on the characteristics
of curved microstrip
structures can be characterized. In addition to the resonance problems discussed,
ix


X


PREFACE

electromagnetic scattering from spherical circular microstrip patches is formulated
and analyzed. Uniaxial anisotropy in the substrate of a spherical microstrip
structure is included in the investigation.
Practical cylindrical
microstrip patch antennas fed by coax or through a
coupling slot in the ground plane of a cylindrical microstrip feed line are analyzed
in Chapter 4. Various theoretical techniques, including the full-wave approach,
cavity-model analysis, and generalized transmission-line
model (GTLM) theory,
are discussed in detail, and expressions of the input impedance and far-zone
radiated fields are presented and numerical results are shown. Experiments are also
conducted and measured data are shown for comparison. Circular polarization and
cross-polarization characteristics of microstrip antennas due to curvature variation
are also analyzed.
The results for microstrip antennas mounted on spherical or conical surfaces are
discussed in Chapter 5. For spherical microstrip antennas, formulations using the
different theoretical approaches of full-wave analysis, the cavity-model method,
and GTLM theory are described in detail. Both input impedance and radiation
characteristics
due to the curvature variation are characterized. For conical
microstrip antennas, available studies are based primarily on the cavity-model
method. Related published results for nearly rectangular and circular wraparound
patches on conical surfaces are described and summarized.
Chapter 6 is devoted to coupling problems with cylindrical
and spherical
microstrip array antennas. Mutual coupling coefficients between two microstrip
antennas mounted on cylindrical
or spherical surfaces are formulated and

calculated. Bandwidth-enhancement
problems of cylindrical and spherical microstrip antennas using gap-coupled parasitic patches are also discussed in this
chapter.
Conformal microstrip arrays are discussed in Chapter 7. A one-dimensional or
wraparound microstrip array mounted on a cylindrical body for use in omnidirectional radiation is studied first. The curvature effect on the radiation patterns of
two-dimensional microstrip arrays is then formulated and investigated. A design in
the feed network to compensate for curvature effects on radiation patterns is also
shown. Several specific applications of spherical and conical microstrip arrays are
described.
Finally,
in Chapter 8, characteristics
of cylindrical
microstrip
lines are
discussed. Both quasistatic and full-wave
solutions of the effective relative
permittivity
and characteristic
impedance of inside and outside cylindrical
microstrip lines are shown. Coupled coplanar cylindrical
microstrip lines and
slot-coupled double-sided cylindrical microstrip lines are also studied. Cylindrical
microstrip open-end and gap discontinuities are formulated, and equivalent circuits
describing the microstrip discontinuities
are presented. The characteristics of
cylindrical coplanar waveguides (CPWs) are solved using a quasistatic method
based on conformal mapping and a dynamic model based on a full-wave
formulation. Inside CPWs, outside CPWs, and CPWs in substrate-superstrate
structures are investigated.
The information contained in this book is largely the result of many years of



PREFACE

xi

research at National Sun Yat-Sen University, and I would like to thank my many
former graduate students who took part in the studies. This book was designed to
provide information on the basic characteristics of conformal microstrip antennas
and microstrip transmission lines and to serve as a useful reference for those who
are interested in the analysis and design of nonplanar microstrip antennas and
circuits.
KIN-LU
Kaohsiung,

Taiwan

WONG


Design of Nonplanar Microstrip Antennas and Transmission Lines
Kin-Lu Wong
Copyright  1999 John Wiley & Sons, Inc.
Print ISBN 0-471-18244-3 Online ISBN 0-471-20066-2

Index

Air gap:
cylindrical rectangularmicrostrip structure,
35

sphericalmicrostrip structure
annular-ringpatch,96
circular patch,94
Annular-ring microstripantenna:
conical,seeConical microstrip antenna
cylindrical, seeCylindrical annular-ring
microstrip antenna
spherical,seeSphericalannular-ringmicrostrip
antenna
Annular-ring-segmentmicrostripantenna,
conical,seeConical microstripantenna
Antennaarray:
conical,seeConical microstriparray
cylindrical, seeCylindrical microstrip array
spherical,seeSphericalmicrostriparray
Aperturecoupling,seeSlot-coupled
Cavity-modelanalysis:
conicalmicrostrip structure,236
cylindrical microstrip structure:
annular-ringpatch, 129
circular patch, 124
rectangularpatch, 118
triangularpatch, 12I
wraparoundpatch, 189
mutual coupling:
cylindrical circular patches,257
cylindrical rectangularpatches,251
sphericalmicrostrip structure:

annular-ringpatch,228

circular patch,2 19
Characteristicimpedance,299,301,305,345
Circular microstripantenna:
conical,seeConical microstripantenna
cylindrical, seeCylindrical circular microstip
antenna
spherical,seeSphericalcircular microstrip
antenna
Circular polarization, 191
Complexresonantfrequency:
cylindrical microstripstructure:
rectangularpatch,26,36
triangularpatch,48
wraparoundpatch,54
curve-fitting formula:
circular patch,363
rectangularpatch,356
sphericalmicrostrip structure:
annular-ringpatch,9 l-93,98-99
circular patch,70, 86,95
Conformalmapping,336-339
Conformalmicrostrip antenna:
conical,seeConical microstrip antenna
cylindrical, seeCylindrical microstripantenna
spherical,seeSphericalmicrostripantenna
Conical microstriparray,290
Conical microstripantenna:
annular-ringpatch, 11,236
annular-ring-segment
patch, 11,237

circular patch, 11,235
Coupling coefficient,320
369


370

INDEX

Cross-polarizationcharacteristics:
cylindrical microstrip structure:
rectangularpatch, 196
triangular patch, 199
sphericalmicroship structure:
annular-ringpatch,2 15-217
circular patch,2 12-2 13
Cylindrical annular-ringmicrostrip antenna:
cavity-model analysis, 129
GTLM analysis, 147
Cylindrical circular microstrip antenna:
cavity-model analysis, 124, 176
GTLM analysis, 144, 183
mutual coupling:
cavity-model analysis,257
GTLM analysis,268
probe-fed:
cavity-model analysis, 124
GTLM analysis, 144
slot-coupled:
cavity-model analysis, 176

GTLM analysis, 183
Cylindrical coplanarwaveguide:
characteristicimpedance,342,345
conformal mapping,336-339
effective relative permittivity, 339,345
full-wave solution, 342
inside, 345
outside,342
quasistaticsolution, 336
substrate-super&atestructure,351
Cylindrical microstrip antenna:
annular-ringpatch,seeCylindrical annularring microstrip antenna
cavity-model analysis, 113, 168
circular patch,seeCylindrical circular
microstrip antenna
full-wave analysis, 103, 153
GTLM theory, 133, 180
parasiticpatches,272
probe-fed, 103, 113, 133
rectangularpatch,seeCylindrical rectangular
microstrip antenna
slot-coupled,153, 168, 180
triangular patch,seeCylindrical triangular
microstrip antenna
wraparoundpatch,seeCylindrical wraparound
microstrip antenna
Cylindrical microstrip array:
wraparoundarray, 287
side lobe level (SLL), 290
Cylindrical microstrip lines:

characteristicimpedance,298,301,305
coupled,308

effective propagationconstant,301
effective relative permittivity, 298, 301
full-wave solution, 299
gap discontinuity, 330
gap capacitance,332
gap conductance,332
inside, 295,299
open-enddiscontinuity, 324
open-endcapacitance,327
open-endconductance,327
outside,295,303
quasistaticsolution, 295
slot-coupleddouble-sided,3 15
Cylindrical printed slot, 155
Cylindrical rectangularmicrostrip antenna:
circular polarization characteristics,191
cross-polarizationcharacteristics,196
mutual coupling:
cavity-modelanalysis,251
full-wave analysis,241
GTLM analysis,264
probe-fed:
cavity-modelanalysis,118
full-wave analysis,108
GTLM analysis,133
slot-coupled:
cavity-modelanalysis,170

full-wave analysis,165
GTLM analysis,180
Cylindrical rectangularmicrostrip structure:
air gap, 35
spacedsuper&ate, 30
superstrate-loaded,
17
Cylindrical triangular microstrip antenna:
cavity-modelanalysis,121
cross-polarizationcharacteristics,199
full-wave analysis,44, 112
mutual coupling, 246
Cylindrical wraparoundmicrostrip antenna:
array, 286
cavity-modelanalysis, 189
complexresonantfrequency,54
full-wave analysis,5 1
Curve-fitting formula:
circular patch,363
rectangularpatch,356
Curvilinear coefficient, 298
Dielectric superstrate:
cylindrical microstrip antenna:
rectangularpatch, 17,30
wraparoundpatch,50
planarmicrostrip antenna:
circular patch, 363


INDEX

rectangular patch, 356
spherical microstrip antenna:
annular-ring patch, 89
circular patch, 83
Directivity, 32
Dyadic Green’s functions, 2 1
Effective loss tangent, 118
Effective propagation constant, 301
Effective relative permittivity, 298,301
Equivalence principle, 40
Equivalent circuit:
probe-fed cylindrical microstrip antenna:
annular-ring patch, 151
circular patch, 145,274
rectangular patch, 137,272
slot-coupled cylindrical microstrip antenna:
circular patch, 184
rectangular patch, 182
spherical microstrip antenna:
annular-ring patch, 233
circular patch, 23 1
Equivalent magnetic current, 40
Equivalent series impedance, 160
Full-wave analysis:
coplanar waveguide:
inside cylindrical, 345
outside cylindrical, 342
substrate-superstratestructure, 35 1
cylindrical microstrip antenna:
rectangular patch, 108, 165

triangular patch, 112
wraparound patch, 189
cylindrical microstrip line:
coupled, 308
gap discontinuity, 330
open-end discontinuity, 324
slot-coupled double-sided, 3 15
mutual coupling:
cylindrical circular patches, 257,268
cylindrical rectangular patches, 24!,25 1,
264
cylindrical triangular patches, 246
spherical microstrip antenna:
annular-ring patch, 206,2 13
circular patch, 206,2 11
Galerkin’s moment-method formulation, 24
Generalized transmission-line mode! (GTLM):
mutual coupling:
cylindrical circular patches, 268
cylindrical rectangular patches, 264
probe-fed cylindrical microstrip antenna:

371

annular-ring patch, 147
circular patch, 144
rectangular patch, 133
slot-coupled cylindrical microstrip antenna:
circular patch, 183
rectangular patch, 180

spherical annular-ring patch, 232
spherical circular patch, 230
Half-power bandwidth:
cylindrical rectangular microstrip structure, 26,
33,39
spherical circular microstrip structure, 70,
87
Impedance matrix, 6
Input impedance, 118, 120,124, 129, 131, 141,
147,153,!68,!74,!91
Isotropic, 78
Magnetic wall, 114
Modified spherical function, 62,361
Moment method, 24
Mutual admittance, 180
Mutual coupling:
cavity-mode! analysis:
cylindrical circular patches, 257
cylindrical rectangular patches, 25 1
full-wave analysis:
cylindrical rectangular patches, 241
cylindrical triangular patches, 246
GTLM analysis:
cylindrical circular patches, 268
cylindrical rectangular patches, 264
Mutual impedance, 243
Patch surface current distribution:
spherical annular-ring patch, 2 18
spherical circular patch, 2 11
Parasitic patch(es):

cylindrical microstrip antenna, 272
spherical microstrip antenna, 280
Parseval’s theorem, 68
Port impedance matrix, 242
Printed slot:
coupling, 165
radiating, 155
Probe-fed cylindrical microstrip antenna:
annular-ring patch:
cavity-mode! analysis, I29
GTLM analysis, 147
circular patch:
cavity-mode! analysis, 124
GTLM analysis, 144


372

INDEX

Probe-fedcylindrical microstrip antenna
(continued)

rectangularpatch:
cavity-modelanalysis,118
full-wave analysis,108
GTLM analysis,133
triangularpatch:
cavity-modelanalysis,121
full-wave analysis,112

wraparoundpatch:
cavity-modelanalysis,189
full-wave analysis,50
Probe-fedsphericalmicrostripantenna:
annular-ringpatch:
cavity-modelanalysis,228
full-wave analysis,2 13
GTLM analysis,232
circular patch:
cavity-modelanalysis,2 19
lull-wave analysis,206
GTLM analysis,230
Quality factor:
cylindrical microstrip structure:
rectangularpatch,29
triangularpatch,49
sphericalannular-ringmicrostrip structure,81
Quasistaticsolution:
cylindrical microstrip line, 295
cylindrical coplanarwaveguide,336
Radarcrosssection(RCS), 76
Reciprocityanalysis,155
Reflectioncoefficient, 158
Scatteringcharacteristics,75
Slot-coupleddouble-sidedmicrostrip lines, 308
Slot-coupled:
circular microstrip antenna:
cavity-modelanalysis,176
GTLM analysis,183
rectangularmicrostripantenna:


cavity-modelanalysis,170
full-wave analysis,153
GTLM analysis,180
S-parameters,320
Sphericalannular-ringmicrostripantenna:
cavity-modelanalysis,228
full-wave analysis,2 13
GTLM theory,230
patchsurfacecurrentdistribution,2 I8
Sphericalcircular microstripantenna:
cavity-modelanalysis,2 19
cross-polarizedfield, 2 10
full-wave analysis,206
GTLM theory,230
patchsurfacecurrentdistribution, 2 11
radarcrosssection(RCS),76
scatteringcharacteristics,75
uniaxial substrate,57
Sphericalmicrostripantenna:
annular-ringpatch,seeSphericalannular-ring
microstripantenna
circular patch,seeSphericalcircular microstrip
antenna
Sphericalmicrostriparray,287
Sphericalwave function, 59
Storedenergyin cavity:
electric field, 117
magneticfield, 117
Substrate:

spaced,35
uniaxial, 57
Superstrate,seeDielectric superstrate
Transmissioncoefficient, 158
Transmissionline model (TLM), 7
Triangularmicrostripantenna,seeCylindrical
triangularmicrostripantenna
Tuning stub, 160
Two-port network,243
Uniaxial substrate,57


Design of Nonplanar Microstrip Antennas and Transmission Lines
Kin-Lu Wong
Copyright  1999 John Wiley & Sons, Inc.
Print ISBN 0-471-18244-3 Online ISBN 0-471-20066-2

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ELECTRICAL MACHINES,
AND PROPULSION
SYSTEMS l A. R. Iha
OPTICAL COMPUTING:

AN INTRODUCTION
l M. A. Karim
and A. S. S. Awwal
INTRODUCTION
TO ELECTROMAGNETIC
AND MICROWAVE
ENGINEERING
l
Paul R. Karmel,
Gabriel D. Colef, and Raymond
L. Camisa
MILLIMETER
WAVE OPTICAL DIELECTRIC INTEGRATED
GUIDES AND CIRCUITS l
Shiban K. Koul
MICROWAVE
DEVICES, CIRCUITS AND THEIR INTERACTION
l Charles
A. Lee and
C. Conrad Da/man
ADVANCES
IN MICROSTRIP
AND PRINTED ANTENNAS
l Kai-Fang
Lee and Wei Chen (eds.)
OPTICAL FILTER DESIGN AND
C. K. Madsen and 1. H. Zhao
OPTOELECTRONIC

PACKAGING


ANALYSIS:
l

A SIGNAL

A. R. Mickelson,

PROCESSING
N. R. Basavanhally,

APPROACH

l

and Y. C. Lee (eds.)


ANTENNAS
Harold Mott

FOR RADAR

INTEGRATED

AND

COMMUNICATIONS:

ACTIVE ANTENNAS


AND

A POLARIMETRIC

SPATIAL

POWER

APPROACH

COMBINING

l

.

julio A. Navarro

and

Kai Chang

FREQUENCY
SOLAR

CONTROL

CELLS AND


ANALYSIS

OF SEMICONDUCTOR

THEIR APPLICATIONS

OF MULTICONDUCTOR

TO ELECTROMAGNETIC

INTRODUCTION

TO HIGH-SPEED
IN MEDICAL

ELECTROMAGNETIC

LINES

l

COMPATIBILITY

ELECTRONICS

AND

Ohtsu

(ed.)


l

Clayton

R. Paul

Clayton

R. Paul

OPTOELECTRONICS

NONLINEAR

OPTICS
MATERIALS

and

Hasegawa

Hideki

DEVICE TECHNOLOGY

PROPAGATION

InP-BASED


l

l

DEVICES:
MICROSTRIP

FREQUENCY

SELECTIVE SURFACE
QUASI-OPTICAL

A. York

and

Rosen

RANDOM

and

MEDIA

Hare/ Rosen
Harrison

l

(eds.)

E. Rowe

PHYSICS

AND TECHNOLOGY

l

Osamu

Wada

(eds.)

ACTIVE

AND

Arye

l

IN MULTI-MODE

E. C. Sauter

AND

DESIGN OF NONPLANAR
LINES l Kin-Lu Wong


Zoya

AND

ARRAYS

B. PopoviC

OPTICAL SIGNAL PROCESSING,
Suganda lutamulia

and

Motoichi

M. Riaziat

NEW FRONTIERS

Robert

l

D. Partain (ed.)

TRANSMISSION

INTRODUCTION
Leonard


LASERS
Larry

l

ANTENNAS
GRID

ARRAY

AND
l

FOR SOLID-STATE

TRANSMISSION

T. K. Wu (ed.)
POWER

COMBINING

.

(eds.)

COMPUTING

AND


NEURAL

NETWORKS

l

Francis

T. 5. Yu


Design of Nonplanar Microstrip Antennas and Transmission Lines
Kin-Lu Wong
Copyright  1999 John Wiley & Sons, Inc.
Print ISBN 0-471-18244-3 Online ISBN 0-471-20066-2

CHAPTER

ONE

Introduction

1 .l

and Overview

INTRODUCTION

The microstrip antenna concept was first proposed in the 1950s. Due to the

development of printed-circuit
technology, many practical applications of microstrip antennas mounted on missiles and aircraft were demonstrated in the early
1970s. Since then, the study of microstrip antennas has boomed, giving birth to a
new antenna industry. Figure 1.l shows the basic geometry of a microstrip
antenna: a metallic patch printed on a grounded dielectric substrate. The metallic
patch can be of any shape, but in practical applications, rectangular and circular
patches are most common, although annular and triangular patches are also
common. Because of its simple geometry, the microstrip antenna offers many
attractive advantages, such as low profile, light weight, easy fabrication, integrability with microwave and millimeter-wave
integrated circuits, and conformabiliis the most
ty to curved surfaces. Among these advantages, conformability

dielectric substrate

FIGURE

1.1

Geometry of a microstrip

conducting patch of
arbitrary shape

antenna with an arbitrary patch shape.
1


2

INTRODUCTION


AND

OVERVIEW

important to future applications of microstrip antennas. For example, by using
conformal microstrip antennas as a substitute for conventional antennas, such as
parabolic reflector antennas and wire antennas, environmental beauty can be
maintained, which is a great impetus for the deployment of conformal antennas.
After over two decades of research, the development of planar microstrip
antennas has now reached maturity. However, the progress of research on
conformal or nonplanar microstrip antennas lags far behind that for planar
microstrip antennas. This situation has been improved in the last decade, in which
many theoretical works on microstrip antennas conformal to nonplanar surfaces,
such as those on cylindrical, spherical, and conical bodies, have been reported. In
addition to research on nonplanar microstrip antennas, printed transmission lines
mounted on cylindrical surfaces have also received much attention. In this book
we reorganize and review these recent publications on the theoretical modeling
and experimental investigation of nonplanar microstrip antennas and transmission
lines.

1.2

CYLINDRICAL

MICROSTRIP

ANTENNAS

The basic structures of cylindrical microstrip antennas excited through a probe

feed are depicted in Figure 1.2, where various patch shapes are shown: rectangle,
disk, annular ring, triangle, and wraparound. The probe-fed design provides no
stray radiation from the probe current and is the simplest in geometry for
theoretical analysis and practical manufacturing. Among the patch shapes, the
wraparound patch can provide omnidirectional radiation in the roll plane of the
cylindrical host, and the rectangular and circular patches are the most commonly
used for general applications. Figure 1.3 shows the configurations
of the
rectangular and circular microstrip antennas excited through a coupling slot. Slot
coupling is another commonly used feeding mechanism, in addition to the

ground
/

\
FIGURE 1.2

substrate

cylinder

triangular
patch
\

wraparound
patch
\

\

/
probe feed

Basic structures of probe-fed cylindrical

microstrip antennas.


CYLINDRICAL

FIGURE 1.3
antennas.

Configurations

of slot-coupled cylindrical

MICROSTRIP

ANTENNAS

3

rectangular and circular microstrip

probe-fed case. The slot-coupling method involves two substrates separated by a
ground plane; one substrate contains the radiating patch and the other contains the
feeding network. Electromagnetic energy is coupled from the microstrip feed line
to the microstrip patch through a coupling slot in the ground plane. A feeding
mechanism using slot coupling offers the following advantages:

1. No spurious radiation from the feed network can interfere with the radiation
pattern and polarization purity of the patch antenna, since a ground plane
separates the feed network and the microstrip patch.
2. No direct contact with the radiating microstrip patch through the substrate is
required, and the problem of a large self-reactance for a probe feed, which is
critical at millimeter-wave
frequencies, is avoided.
3. More degrees of freedom, such as slot size, slot position relative to the
patch, feed-substrate parameters, and microstrip-feed-line
parameters, are
allowed in the feed design. Impedance matching can be achieved by
adjusting the size of the coupling slot and the open-circuited tuning stub of
the microstrip feed line. By choosing a suitable coupling slot size and
adjusting its relative position to the radiating patch, a much larger antenna
bandwidth can be obtained than when using a coax feed.
4. The configuration is well suited for monolithic phased-array antennas by
integrating radiating patches on the low-permittivity
substrate and the feed
network,
phase shifters, bias, and other circuitry in the high-permittivity
gallium arsenide on a single monolithic chip.


4

INTRODUCTION

AND

OVERVIEW


Besides its advantages, slot-coupled feed is relatively costly and complex in
antenna design compared to the probe-fed case. Another popular choice of feeding
arrangement is feeding the microstrip patch directly through a coplanar microstrip
line, which is especially suited for microstrip array design. Figure 1.4 shows two
kinds of arrangements for a cylindrical rectangular microstrip antenna fed by a
microstrip line. Since the input impedance at the patch edge is usually on the order
of 100 to 200 R (for higher-permittivity
substrates, the patch-edge input impedance can be greater than 200 a), an inset patch or quarter-wavelength impedance
transformer is commonly used for impedance matching to a 50-a microstrip feed
line.
Other feeding arrangements, using coplanar-waveguide
(CPW) feed [ 11, buried
microstrip line feed [2], and others, have also been demonstrated. CPW feed has
the advantages of no via holes, easy integration with active devices, small stray
radiation from the feed, and convenience in etching antenna and feed line in one
step. However, CPW-feed design has less freedom in a large feed network design
for antenna arrays. Buried microstrip line feed, on the other hand, provides
flexibility
in patch and microstrip line designs. However, this feed design has
difficulty in integration with active devices.

inset-fed structure
(a)

edge-fed structure with quarter-wavelength
impedance transformer
(b)
Two kinds of arrangements for the cylindrical rectangular microstrip antenna
fed by a microstrip line: (a) inset-fed case; (b) edge-fed with h/4 impedance transformer.

FIGURE

1.4


CYLINDRICAL

MICROSTRIP

ANTENNAS

5

For the analysis and design of cylindrical microstrip antennas, a number of
theoretical techniques, including the full-wave approach, cavity-model analysis,
and generalized transmission-line
model (GTLM) theory, have been reported.
Among these models, the full-wave approach is computationally inefficient, and
careful programming is usually required. Calculation of a full-wave solution may
become difficult for a cylindrical microstrip antenna with a large cylinder radius
(i.e., small-curvature case). However, full-wave solutions are more accurate and
applicable to thick-substrate conditions. As for cavity-model analysis and GTLM
theory, the theory and numerical computation are much simpler than with the
full-wave approach. However, these two simple approaches are suitable only for
the analysis of thin-substrate cases.

1.2.1

Full-Wave


Approach

The full-wave approach for a probe-fed case is described briefly here in terms of
the geometry shown in Figure 1.2. To begin with, the metallic ground cylinder and
patch are assumed to be perfect conductors, and the thickness is neglected since it
is much less than that of the operating wavelength. Based on the assumption, the
patch can be replaced by a surface current distribution, which is unknown and
needs to be solved. By noting that the radius of the feeding coax is usually a very
small fraction of the operating wavelength, the probe can be treated as a line
source with unit amplitude. To solve the unknown patch surface current density,
the boundary condition that the total electric field tangential to the patch surface
must be zero is applied; that is, on the patch,

6X[ED@,
z>+ E’(qb,
z)]= o,

(1.1)

where E”(qb, z) is the electric field due to the patch current and E’(c$, z) is the
electric field due to the probe with the patch being absent. For deriving E”(+, z),
the theoretical formulation technique in [3] can be applied, and it gives

dk, ej’zz&q,

k,)

J,(q,
kZ)
[ 1


(1.2)

J,(q,

k,)

’

where &q, k,) is the dyadic Green’s function in the spectral domain for the
cylindrical grounded substrate &q, k,) and is the Fourier transform of the current
density on the patch; the tilde denotes a Fourier transform. The subscripts 4 and z
denote, respectively, the field components in the 4 and z directions.
For EP(+, z), the field expression due to a point source in a layered medium
needs to be derived first. Then, by imposing the boundary conditions at the
cylindrical ground plane and the substrate-air interface, and after some straightforward manipulation, summing up all the field contributions from point sources
along the input line-current source, an expression of EP(+, z) can be derived which


6

INTRODUCTION

AND

OVERVIEW

has the form of an integral equation [3]. Next, by substituting (1.2) and the derived
E’(+, z) into (1.1) and applying Galerkin’s moment method to solve the resulting
integral equation, a matrix equation can be obtained:


expressions of the matrix elements are described in subsequent chapters. By
solving (1.3), the unknown patch surface currents Z4n and ZZMare obtained, and the
input impedance, radiation pattern, and other information of interest can be
calculated.
To obtain full-wave solutions, numerical convergence for the moment-method
calculation needs to be tested. The numerical convergence depends strongly on the
basis function chosen for the expansion of the patch surface current density. A
good choice of the basis functions used in moment-method calculation are the
sinusoidal basis functions satisfying the edge condition that the normal component
of the patch surface current must vanish at the patch edge. Details of the results are
covered in Chapter 2.
1.2.2

Cavity-Model

Analysis

The cavity-model analysis proposed by Lo et al. [4] offers both simplicity and
physical insight into the operation of microstrip antennas. This model is valid
when the substrate thickness is much smaller than the operating wavelength and is
based on the following observations:
1. The close proximity between the patch and the ground plane suggests that
for a cylindrical
microstrip
structure, the electric field has only a 6
component, and the magnetic field has only 4 and i components in the
region bounded by the patch and the ground cylinder.
2. The field in the above-mentioned region is independent of the p coordinate
for the frequency of interest.

3. The electric current on the microstrip patch must have no component normal
to the edge at any point on the edge, implying a negligible component of
magnetic field along the edge.
The region between the patch and the ground cylinder can therefore be treated as a
cavity bounded by electric walls on the top and bottom and a magnetic wall
around the perimeter of the cavity. Based on this cavity approximation, resonant
frequencies of the TM,, mode for cylindrical rectangular and circular microstrip
antennas are given as follows: For the rectangular patch,


CYLINDRICAL

and for the circular

MICROSTRIP

ANTENNAS

7

patch,

(1.5)
where c is the speed of light and or is the relative permittivity of the substrate; 2L
and 2W are, respectively, the length and width of the rectangular patch; k,,
satisfies JL(k,,a) = 0, where J,(X) is a Bessel function of the first kind with order
m, a is the radius of the circular patch, and the prime denotes a derivative.
The fields inside the cavity can then be expressed in terms of discrete modes
individually satisfying the appropriate boundary conditions. Once the fields inside
the cavity are known, the radiating field can be obtained from the effective

magnetic current source flowing on the magnetic wall. After the cavity and
radiated fields are determined, the radiation pattern, total radiated power, and input
impedance can be calculated.

1.2.3

Generalized

Transmission-line

Model

Theory

Theoretical treatment based on the transmission-line model (TLM) is the first and
simplest method applied for the analysis and design of microstrip antennas.
Although the TLM method is relatively simple, the accuracy of TLM analysis can
be made comparable to that of other more complicated methods [5]. For an
analysis of mutual coupling between rectangular microstrip antennas, the TLM
method can also be calculated in a fairly accurate and efficient way. However, the
TLM method in its original form is applicable only for planar rectangular or
square microstrip antennas. To cope with this problem, generalized transmissionline model (GTLM) theory is proposed [6], where the line parameters are the
electromagnetic fields under the patch. In this case, as long as the separation of
variables is possible for the wave equation expressed in that particular coordinate
system, GTLM theory is applicable to microstrip antennas of any patch shape. The
extension of GTLM theory to microstrip antennas with thick substrates is also
possible. In the TLM method, the corresponding line parameters are the characteristic impedance and effective propagation constant. The equivalent circuits of a
planar probe-fed rectangular microstrip antenna derived based on the TLM and
GTLM methods are shown in Figure 1.5 for comparison. For GTLM theory, the
rectangular patch is considered as a transmission line in the direction joining the

radiating apertures of the patch. The effect of other apertures is considered as
leakage of the transmission line. The transmission line can be further separated
into two sections by the feed position, and each section of the transmission line
can be replaced by an equivalent network and loaded with a wall admittance y,, at
the radiating apertures; y, denotes the mutual admittance between two radiating
apertures. When expressions are derived for these circuit elements, the input
impedance of the patch antenna seen at the feed position can readily be obtained.


8

INTRODUCTION

AND

OVERVIEW

section of transmission line
transmission line parameters (Z,, “I): Z, = characteristic impedance
y = effective propagation constant
(a)

radiating aperture

Y,(u9

radiating aperture

section of transmission line
transmission line parameters (E, H): E = electric field under the patch

H = magnetic field under the patch
(b)

FIGURE 1.5 Equivalent circuits derived based on TLM and GTLM theory: (a) TLM
model and (b) GTLM model of a planar probe-fed rectangular microstrip antenna at the
TM,, mode.

1.3

SPHERICAL

MICROSTRIP

ANTENNAS

The spherical microstrip antenna is another canonical structure of conformal
microstrip antennas, which can overcome the scanning problems involved with
planar patch antennas at low elevations. Figure 1.6 shows the basic structures of
spherical microstrip antennas with circular and annular-ring patches. The cavitymodel theory has been used in the theoretical analysis of such spherical microstrip
antennas [7,8], in which the curvature effects on the characteristics of microstrip
patches mounted on a spherical body are analyzed. Reports on use of the full-wave


SPHERICAL

MICROSTRIP

ANTENNAS

9


(a)

az

rI

lb)

Basic structures of spherical microstrip antennas with (a) a circular patch
and (b) an annular-ring patch.

FIGURE 1.6

approach and GTLM theory for analysis of spherical microstrip antennas have also
been published. In full-wave analysis, the Green’s function in the spectral domain
for the grounded spherical substrate is formulated and Gale&in’s moment method
is used for the numerical calculation [9- 111. In many related reports based on the
full-wave approach, the resonance problem, input impedance, radiation pattern,
cross-polarization
radiation, electromagnetic scattering, and surface current distribution on patches have been studied extensively [ 12- 161. Several modified
spherical microstrip antenna structures, including a patch loaded with a superstrate
layer, a microstrip structure with an air gap, and a patch with parasitic elements,
have also been investigated [ 17- 191.
GTLM theory has also been used in the analysis of spherical microstrip
antennas [20,21]. According to the theory, the microstrip patches can be treated as
a transmission line, taken in the direction of 0, loaded with a wall admittance
evaluated at the radiation apertures. The equivalent transmission line can then be
replaced by a 7~ network. Figure 1.7 shows the corresponding equivalent circuits
for circular and annular-ring patches. For a circular patch, the network of the

circuit elements, YA, YB, and Yc, represents the transmission-line
section between
the feed position and the radiation aperture at the patch edge. The shorted
transmission-line section between the feed position and the patch center is replaced
by an equivalent admittance, y,. For an annular-ring patch, there are two sections