241 153 272MB
English Pages 618 Year 1997
Advances in Microstrip and Printed Antennas Edited by
KAI FONG LEE WEI CHEN
A WILEYINTERSCIENCE PUBLICATION
JOHN WILEY & SONS, INC. NEWYORK/CHICHESTER/WEINHEIM/ BRISBANE/SINGAPORE/ TORONTO
This text is printed on acidfree paper. Copyright © 1997 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. Reproduction or translation of any part of this work beyond that permitted by Section 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful. Requests for permission or further information should be addressed to the Perrnis.sions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 101580012.
Library of Congre11 CataloginginPublication Data Advances in microstrip and printed antennas / edited by Kai Fong Lee and Wei Chen. p. cm.   (Wiley series in microwave and optical engineering) "A Wilcylntcrscience publication." Includes bibliographical references (p. ). ISBN 0471044210 (alk. paper) 1. Microstrip antennas. 2. Printed circuits. I. Lee, Kai Fong. II. Chen, Wei, 1959III. Series. TK7871.6.A394 1997 621.381 '33 1 dc20 9639032
Printed in the United States of America 109876543
Contents
Contributors
xiii
Preface
xvii
ProbeFed Microstrip Antennas K. F. Lee, W. Chen, and R. Q. Lee
I.I 1.2
Introduction FullWave Analysis of Multilayer Multipatch Microstrip Antennas 1.2.1 Introductory Remarks 1.2.2 Conventions and Definitions 1.2.3 Basic Formulations 1.2.4 Green's Functions 1.3 Spectral Domain FullWave Analysis of ProbeFed Rectangular Microstrip Antennas 1.3.1 Formulation 1.3.2 Basis Functions 1.3.3 Multiple Feeds and Shorting Pins 1.3.4 Attachment Modes 1.4 Representative Numerical and Experimental Results 1.4.1 Single Patch 1.4.2 Single Patch in Multidielectric Media 1.4.3 Coplanar Parasitic Subarray 1.4.4 TwoLayer Stacked Patches 1.5 Rectangular Patch with a UShaped Slot 1.6 Concluding Remarks References
1 4 4 5 7 13 19 19 23 24 26 35 36 42 50 53 63 68 68 V
vi 2
3
CONTENTS
ApertureCoupled Multilayer Microstrip Antennas K. M. Luk, T. M. Au, K . F. Tong, and K. F. Lee
71
2.1 In trod uctio n 2.2 Green's Function Formulation 2.2.1 Field Components 2.2.2 Boundary Conditions 2.3 Galerkin's Method 2.4 Illustrative Results 2.4.1 Microstrip Antenna with an Air Gap 2.4.2 Coplanar Microstrip Subarrays 2.4.3 Offset DualPatch Microstrip Antennas 2.4.4 TwoLayer Microstrip Antennas with Stacked Parasitic Patches 2.5 Infinite Arrays of ApertureCoupled Multilayer Microstrip Antennas 2.5.1 Skewed Periodic Structure and Floquet Modes 2.5.2 Infinite Array of Microstrip Antennas with Air Gaps 2.5.3 Infinite Array of DualPatch Microstrip An tennas 2.6 Conclusions Appendix: Fourier Transforms of Expansion and Test Functions Acknowledgments References
71
109 109 113 114 118 120 121 121
Microstrip Arrays: Analysis, Design, and Applications
123
73 74 76 78 81 82 83 93 97
John Huang and David M. Pozar
3.1 Introduction 3.2 Analysis Techniques for Microstrip Arrays 3.2.1 Review of Micros trip Antenna Analysis Techniques 3.2.2 FullWave Moment Method Analysis 3.2.3 Calculation of Mutual Coupling 3.2.4 Infinite Array Analysis 3.2.5 The Active Element Pattern 3.2.6 Waveguide Simulators 3.3 Design Methodology 3.3.1 Array Configuration Design 3.3.2 Patch Element Design 3.3.3 Power Division Transmission Line Design 3.3.4 Microstrip Reflectarray Design 3.4 Applications 3.4.1 Military Applications 3.4.2 Space Applications 3.4.3 Commercial Applications
123 124 125 126 128 132 134 135 137 138 143 144 148 152 152 154 157
CONTENTS
4
5
vii
3.5 Summary and Conclusion References
159 159
Dual and Circularly Po larized Microstrip Antennas P. S. Hall and J. S. Dahele
163
4.1 Introduction 4.2 Polarization in Antenna Systems 4.3 Generation of Orthogonal Polarizations 4.4 Circularly Polarized Patches 4.4.1 Orthogonal Patches 4.4.2 Multipoint Feeds 4.4.3 SinglePoint Feeds 4.5 D ual Polarized Patches 4.5.1 Triangular Patch with Right and LeftHand Circular Polarization 4.6 Microstrip Spirals 4.6.1 Operation of the Spiral Antenna 4.7 Special Substrates and Active Antennas 4.8 Dual and Circularly Polarized Arrays 4.8.1 Patch Arrays 4.8.2 Microstrip Line Arrays 4.8.3 Sequentially Rotated Arrays 4.9 Conclusions References
163 164 165 167 169 170 177 183 184 184 185 186 188 188 188 190 217 217
ComputerAided Design of Rectangular Microstrip Antennas David R. Jackson, Stuart A . Long, Jeffery T. Williams, and Vickie B. Davis
223
5.1 5.2 5.3 5.4
223 224 231 234 234
Introduction CAD Model for Rectangular Patch Antenna CAD Form ulas for Resonance Frequency CAD Formulas for the Q Factors 5.4.1 Dielectric and Conductor Q Factors 5.4.2 Relation Between SurfaceWave and SpaceWave Q Factors 5.4.3 SpaceWave Quality Factor 5.5 CAD Formula for Bandwidth 5.5.1 CAD Formula 5.5.2 Results 5.6 CAD Formula fo r Radiation Efficiency
235 237 242 243 243 246
viii
6
CONTEN TS
5.6.1 CAD Formula 5.6.2 Results 5.7 CAD Formula for Input Resistance 5.8 CAD Formula for Probe Reactance 5.9 Results for Input Impedance 5.10 Radiation Patterns 5. I 0.1 Infinite Substrate 5.10.2 Truncated Substrate 5.11 CAD Formula for Directivity 5.12 Conclusions Appendix A: Derivation of the p Factor Appendix B: Radiation Formulas for HED and HMD References
246 247 248 252 254 256 256 260 263 265 266 269 270
Multifunction Printed Antennas J. R. James and G. Andrasic
273
6.1 Introduction 6.2 Printed Antenna Design Freedom 6.3 Multifunction Antenna Design Opportunities and Recent Advances 6.3.1 Choice of Substrate Materials and Their Design Potential 6.3.2 Innovative Use of Superstrates 6.3.3 Printed Conductor Topology 6.3.4 Quest for Feeder Simplicity 6.3.5 Conformality 6.3.6 Integration of Antennas and Circuits 6.4 Possible Future Developments 6.4.1 Impact of New Materials 6.4.2 The Application Drivers 6.5 Conclusions References
273 274
7 Superconducting Microstrip Antennas Jeffery T. Williams, Jarrett D. Morrow, David R. Jackson, and Stuart A. Long
7.1 Introduction 7.2 Basics of Superconductivity 7.2.1 General Properties of Superconductors 7.2.2 HighTemperature Superconductors 7.2.3 Characteristics of HighTemperature Superconductors
276 276 286 294 302 307 308 312 312 315 317 317 325
325 326 327 329 333
CONTEN TS
7.3 HTS Micros trip Transmission Lines and Antennas 7.3.1 Superconducting Transmission Lines and Feed Networks 7.3.2 Superconducting Microstrip Patch Antennas 7.4 Design Considerations 7.5 Experimental Results 7.6 Summary Appendix References 8 Active Microstrip Antennas Julio A. Navarro and Kai Chang
8.1 Introduction 8.2 The Early History of Integrated Antennas 8.3 DiodeIntegrated Active Microwave Antennas 8.4 TransistorIntegrated Active Microstrip Antennas 8.5 Diode Arrays for Spatial Power Combining 8.6 Transistor Arrays for Spatial Power Combining 8.7 System Applications 8.8 Conclusions and Future Trends Acknowledgments References 9 Tapered Slot Antenna Richard Q. Lee and Rainee N. Simons
9.1 9.2 9.3 9.4 9.5
9.6 9.7
9.8 9.9
Introduction Basic Geometries Design Considerations Fundamentals Analytical Methods 9.5.1 Analysis of Uniform Slotline by the Spectral Domain Approach 9.5.2 FarField Computation Feeding Techniques Characteristics of TSA 9.7.1 Radiation Characteristics 9.7.2 Impedance Characteristics 9.7.3 Bandwidth Characteristics 9.7.4 Field Distributions Tapered Slot Antenna Arrays Active Tapered Slot Antenna Array
ix
338 339 347 354 356 365 365 367 371
371 374 376 390 409 422 428 431 432 432 443
443 444 447 447 453 455 459 461 476 476 487 494 495 498 502
X
10
CONTENTS
9.10 Conclusion References
510 510
Efficient Modeling of Microstrip Antennas Using the FiniteDifference TimeDomain Method
515
Siva Chebolu, Supriyo Dey, Raj Mittra, and John Svige/j
Introduction A Comparison of Various CAD Approaches The Basic FDTD Algorithm Efficient FDTD Modeling of Microstrip Antennas 10.4.1 Spatial Discretization 10.4.2 Source Excitation 10.4.3 Phased Array Ex.citation 10.4.4 Extrapolation Techniques 10.4.5 Impedance 10.4.6 Absorbing Boundaries 10.4.7 Radiation Pattern 10.4.8 Distributed Computing 10.4.9 Dielectric Loss Tangent 10.5 Single Patch Modeling 10.5.1 Impedance of a Patch Antenna Mounted on a Moderately Thick Substrate 10.5.2 Impedance ofa Patch Antenna Mounted on a Thick Substrate 10.5.3 Effect of a Finite Ground Plane on Impedance and Radiation Pattern 10.6 Analysis of a TwoLayer Stacked Patch Antenna 10.7 Design of a Compact Broadband Antenna 10.8 Conclusions References 10.1 10.2 10.3 10.4
11
Analysis of Dielectric Resonator Antennas
515 516 519 522 522 526 526 526 530 531 532 533 534 534 535 536 538 538 543 547 548 553
K. M. Luk, K. W Leung, and S. M. Shum 11.l Introduction 11.2 Analysis of ApertureCoupled Hemispherical DR Antenna 11.2.1 Problem Formulation 11.2.2 Moment Method Solution 11.2.3 Derivation of DR Antenna Green's Function G~ 11.2.4 Evaluation of Y:U. ' 11.2.5 SingleCavityMode Approximation 11.2.6 SingleCavityMode Radiation Field of the DR Antenna
553 555 556 557 560 566 567 568
CONTENTS
11.2.7 Results and Discussions 11.2.8 Summary 11.3 FDTD Analysis of ProbeFed Cylindrical DR Antenna 11.3.1 TheFDTDMethod I 1.3.2 Antenna Feed Modeling 11.3.3 Absorbing Boundary Condition 11.3.4 Input Impedance Calculation 11.3.5 FarField Calculations 11.3.6 Results and Discussions 11.3.7 Summary References Index
xi
568 573 573 574 576 578 579 580 582 589 589 593
Contributors
G. Andrasic
J. S. Dahele
School of Engineering and Applied Science Royal Military College of Science Cranfield University Shrivenham, Wilts SN6 8LA England
School of Engineering and Applied Science Royal Military College of Science Shrivenham WiltsSN6 8LA England
T.M.Au
Vickie B. Davis Department of Electrical and Computer Engineering University of Houston Houston, TX 77204 U.S.A.
Center of Wireless Communications National University of Singapore Singapore
Kai Chang Department of Electrical Engineering Texas A&M University College Station, TX 77843 U.S.A.
Siva Chebolu Celwave Division of Radio Frequency Systems, Inc. Phoenix, AZ 85034 U.S.A.
W.Chen Cooper Energy Services Mount Verson, OH 43050 U.S.A.
Supriyo Dey Electromagnetic Communication Laboratory University of Illinois, UrbanaChampaign Urbana, IL 61801 U.S.A.
P. S. Hall School of Electronic and Electrical Engineering University of Birmingham Edgbaston, Birmingham B15 2TT England xiii
xiv
CONTRIBUTORS
John Huang Jet Propulsion Laboratory California Institute of Technology Pasadena, CA 91109 U.S.A.
K.M. Luk Department of Electronic Engineering City University of Hong Kong Kowloon Hong Kong
David R. Jackson Department of Electrical and Computer Engineering University of Houston Houston, TX 77204 U.S.A.
Raj Mittra Depanment of Electrical Engineering Pennsylvania State University University Park, PA 168022705 U.S.A.
J. R. James School of Engineering and Applied Science Royal Military College of Science Cranfield University Shrivenham, Wilts SN6 8LA England K. F. Lee Department of Electrical Engineering University of MissouriColumbia Columbia, MO 65211 U.S.A. Richard Q. Lee NASA Lewis Research Center 21000 Brookpark Road Cleveland, OH 44135 U.S.A. K. W. Leung Depanment of Electronic Engineering City University of Hong Kong Kowloon Hong Kong Stuart A. Long Department of Electrical and Computer Engineering University of Houston Houston, TX 77204
U.S.A.
Jarrett D. Morrow Department of Electrical and Computer Engineering University of Houston Houston, TX 77204 U.S.A. Julio A. Navarro Boeing Defense and Space Group Seattle, WA 98124 U.S.A. David M. Pozar Depanment of Electrical and Computer Engineering University of Massachusetts, Amherst Amherst, MA 01003 U.S.A. S.M. Shum Depanment of Electronic Engineering City University of Hong Kong Kowloon Hong Kong Rainee N. Simons NASA Lewis Research Center 21000 Brookpark Road Cleveland, OH 44135 U.S.A. John Svigelj Texas Instruments, Inc. 2501 University Drive MS 8019 McKinney, TX 75070 U.S.A.
CONTRIBUTORS
K.F. Tong
Jeffery T. Williams
Department of Electronic Engineering City University of Hong Kong Kowloon Hong Kong
Department of Electrical and Computer Engineering University of Houston Houston, TX 77204
U.S.A.
xv
Preface
Since the late 1970s, the international antenna community has devoted much effort to the theoretical and experimental research on microstrip and printed antennas, which offer the advantages oflow profile, compatibility with integrated circuit technology, and conformability to a shaped surface. The results of this research have contributed to the success of these antennas not only in military applications such as aircraft, missiles, and rockets but also in commercial areas such as mobile satellite communications, the direct broadcast satellite (DBS) system, global positioning system (GPS), remote sensing, and byperthermia. While many of the results of the late 1970s and 1980s were summarized in the Handbook of Microstrip Antennas, edited by J. R. James and P. S. Hall in 1989, the research on microstrip and printed antennas bas continued unabated in the 1990s. In addition to advances in conventional topics, there have been new research areas. The purpose of this book is to update and to present new information on microstrip and printed antennas since the twovolume handbook was published. The contributors are all active researchers and well known in the field. Chapters 14 deal with recent advances in conventional topics. These include accounts on recent results on probefed microstrip antennas and aperturecoupled microstrip antennas; analysis, design, and applications of microsfrip · arrays including the recently developed configuration known as microstrip reflectarray; and dual and circularly polarized planar aniennas. Most of the topics in Chapters 5 11 are relatively new. They were not covered in the 1989 Handbook. These include the development of computeraided design (CAD) formulas for the rectangular patch; the concept, development, and future possibilities of multifunction printed antennas; microstrip antennas made of hightemperature superconducting materials; active microstrip antennas; and tapered slot printed antennas. Chapter 10 discusses the finitedifference timedomain method of analysis which is becoming popular due to its ability to handle complex configurations and to generate the characteristics of the patch over a broad band of frequencies with a single simulation. The book ends with a chapter xvii
xviii
PREFACE
on dielectric resonator antennas. These antennas have potential advantages over microstrip antennas at extremely high frequencies because of reduced copper loss. Although different in physical appearance, dielectric resonator antennas and microstrip antennas have much in common in analysis methods and design concepts. Because of page limitation, it is not possible to include all topics which represent advances in this field in the 1990s. It is hoped, however, that antenna researchers and practicing engineers will find much useful information in the coverage of the topics selected. KAI FONG LEE WEI CHEN
CHAPTER ONE
ProbeFed Microstrip Antennas K. F. LEE, W. CHEN, and R. Q, LEE
1.1
INTRODUCTION
One of the common methods of feeding a microstrip antenna is by means of a coaxial probe. The basic configuration is shown in Figure I.I, where a single metallic patch is printed on a grounded substrate. A number of designs have evolved from the basic configuration. Figure 1.2 shows a design in which a fed patch is surrounded by closely spaced parasitic patches, which can have the effect of improving the impedance bandwidth and the gain of the antenna. Such a configuration is referred to as a coplanar parasitic subarray. Figure 1.3 .shows cases where the metallic patch is embedded in a multilayered dielectric media. In Figure 1.3a, a superstrate or dielectric cover is used to protect the patch against environmental hazards. If a naturally occurring dielectric layer such as ice is formed on top of the cover, the threelayer configuration of Figure 1.3b results. Figure 1.3c shows a onesuperstrate twosubstrate geometry, as, for example, when an air gap is introduced between the substrate and the ground plane to alter the resonant frequency of the antenna. Figure 1.4 shows the twolayer stacked geometry consisting of one fed patch and a parasitic patch on another layer. These stacked patches are popular for providing wide bandwidth characteristics. Another wideband microstrip antenna is the rectangular patch with a Ushaped slot (Figure 1.5). In recent years, the various linearly polarized probefed microstrip antennas depicted above have been extensively studied. It is the purpose of
Advances in Microstrip and Printed Antennas, Edited by Kai Fong Lee and Wei Chen. ISBN 0471044210 © 1997 John Wiley & Sons, Inc.
2
PROBEFED MICROSTRIP AN TENNAS
(a)
Conducting patch
Substrate
Ground plane Coax feed (b)
FIGURE 1.1 Basic configuration of the probefed microstrip antenna. (a) Top view, (b)side view.
this chapter to give a coherent account of recent work in this area. The materials to be presented are based mainly on the authors' research. Related work by others will be referenced but not described in detail. We shall be concerned with rectangular patches only. However, the methods of anal ysis can be extended to other geometrical shapes; and many qualitative features are not dependent on whether the patches are rectangular or circular, which are the two most commonly used shapes in practice. In Section 1.2, a general fullwave analysis of multilayer multipatch microstrip antennas is presented. The application of the analysis to probefed rectangular microstrip antennas is described in Section 1.3. Representative numerical and experimental results for configurations 1.1  1.4 are given in Section 1.4. Experimental results of the Uslot patch are described in Section 1.5. The chapter ends with some concluding remarks.
□
Fedpatch
□GQ. ., LJ;:;ches
(a)
Parasitic patch
Fed patch
Parasitic
patch
'>. \ / Substrate I 1 ,__ICoax feed (bl
FIGURE 1.2
Geometry of coplanar parasitic subarray. (a) Top view, (b) side view.
Superstrate Substrate
~~:
Patch
LJ
~ LJ
Superstrate 1
Superstrate
Superstrate 2
Substrate
l1F1F
Coax feed
Coax feed
Coax feed
(a)
(b)
(c)
FIGURE 1.3 Microstrip antenna in multidielectric media. {a) Patch with superstrate, (b) patch with two superstrates, (c) patch with one superstrate and two substrates.
4
PROBEFED MICROSTRIP ANTE NNAS
Superstrate /Parasitic patch Substrate
Fed patch
71"""" Coax feed
FIGURE 1.4
Geometry of twolayer stacked patches.
y
t n ~
Patch
U S ~ !al
•
t
/Patch
I
Air or foam ""
"j=
f
E(l,)·1, dV
I I
(JJJ,> =  H(l,)·M,dV (M,,M,)= 
H(M,)·M,dV
f
(i, ,7,> = E,·1,dV
(1.10)
(1.11)
(1.12)
(1.13)
(1.14)
1.2.3
Basic Formulations
In this section, we shall set up the basic formulation for general layered structures based on the electric field integral equations (EFIE).
1.2.3.1 Simple Region. We define a simple region as a region consisting of layered materials bounded by free space or metallic conducting surface(s) (Figure 1.6). It also contains radiating elements and feeding elements which are assumed to be approximately represented by a set of current expansions; that is, the current on the radiating elements and feeding elements is expanded into a set of basis functions: N
J""L
j=:l
cJ;
(1.15)
Yi
where are the basis functions and C1 are the corresponding coefficients. A simple region may connect to the outside through aperture coupling. For the aperture coupling case, the electrical field in the aperture(s) is expanded into basis functions, M
if,""
I:
y,if,
(1.16)
k=l
Thus, the magnetic current excitation over the aperture(s) is expressed by (1.17)
8
PROBEFED MICROSTRIP ANTEN NAS
Conducting plane
(al
Conducting plane (bl
(c)
FIGURE 1.6 Examples of simple regions. Conducting patches embedded in multilayer dielectric media bounded by (a) two conducting planes, (b) one conducting plane. In (c),
there are no conducting boundaries other than the patches.
where M, = E, x n and M, = E, x n. ,1 in the inward normal. Note that this expansion represents the magnetic current over all the aperture(s). If we assume all ·the metal sheets to be perfect conducts, the electric integral equation is established by forcing the total tangential electric field to vanish on all the metallic surfaces inside the region:
E(])+E(M,)=0
(1.18)
This is basically an integral equation. We will convert it to a set of linear equations using the Method of Moments. Using the current expansions, we have N
M
j =l
k= l
L C;E(l)+ L y,E(M,);:,O
(1.19)
MULTILAYER MUL TIPATCH MICROSTRIP ANTENNAS
9
or N
M
I c/f(J),,,  I y.£(M,l
J: l
,l:::::o
Testing the above equation using
(1.20)
l
J,, we obtain (1.21)
or N
M
j=l
.t•l
I c/J,,1) =  I y.(J,,iJ,>
(1.22)
This is one of the most important equations in our formulation. We call it fundamental equation one.
If the metal sheets are not perfect conducts, we have to apply the impedance boundary condition (1.23)
where z, is the surface impedance (fl/square meter). Equations (L19) (l.21) become N
M
N
}=1
k=l
j=l
I c)f(l)+ I y,E(iJJ,,,z. I c);
1f C;
(1.24)
Jy, fE(MJ1,ds= z,, J c f1;·J;ds J C;(Y,)) JY,(J;,M,) = J C fJ,1,ds
E(l;)·J;ds +
+
Z,1
1
(1.25)
1
(1.26)
Equation (1.26) is the generalization of fundamental equation one to nonperfect conductors. To define the problem completely, we also need the condition of continuity of tangential magnetic fields across the aperture. The total tangential magnetic field in the inner side of the aperture(s) is (1.27)
or N
M
[:aal
k= 1
H,"' L C,H,(},) + L y,H,(MJ
(1.28)
10
PROBEFED MICROSTRIP ANTENNAS
Testing it using
it, we get
or N
M
j=l
k =I
( MmJi,) = L C/ Mm,J)+ L Y,(Mm,M,)
(J.30)
We call this equation fundamental equation two. Note that to apply the fundamental equation two, we also need to know the total tangential magnetic field on the other side of the aperture which usually is done by applying the same equation to the region on the other side of the aperture. The two fundamental equations can also be written in matrix form. Define:
[Z] = [(},, } ) JN ,N
[QJ
= [(l,, M, ) ]N,M
(1.31) (1.32)
and (1.33)
The fundamental equation one becomes (1.34)
and the fundamental equation two is (1.35)
Combining the two equations, we have
1.2.3.2 Complex Region. A complex region is a region consisting of two or more simple regions coupled through apertures (Figure 1.7). Let us label the simple regions sequentially from top down starting with region 0. Region k is on the top of region k + I with a common boundary which we label as interface k. The electric field in the apertures on interface k can be expanded as (1.37)
11
MULTILAYER MUL TIPATCH M/CROSTRIP ANTENNAS
Conducting planes
(a)
Conducting planes
(b)
Conducting planes
(c)
FIGURE 1.7
Examples of complex regions.
On the side of region k, n= i, and the magnetic current over the apertures is M,
MCJ = L n= l
n
y:M:
(1.38)
n
where M0 =£.ix and M: = f! xi. is the inward normal. On the side of region k + I, n =  i, and the magnetic current over the apertures is M,
ii.=  L r;ii; n""l
where M11
=£
0
x ,land
M~ = £~xi. nis the inward normal.
(1.39)
12
PROBE FED MICROSTRIP ANTENNAS
Now, we can still write fundamental equations for each simple region: For region k, M
Mho
j=l
n= l
~
L C)= L 1! ( f/,M! >+ L r! 1
1
(1.4Dl
11 "" 1
N~
Mt  !
= L CJ+ L 1: 1
j= 1
11=
1
1
M,
 ,,1 L r!
na: 1
m= 1
L1
+d(J,,.,,,J;,".,",>+ L b,(M,, J;.""·"')=0
(1.114)
l:Q
nl = 1,2, .. . ,N H
M
n= 1
m"'l
(1.115)
L a.(J,,,"'·'J,m,z>+ L Cm=O
(1.116)
l=O
ml=l,2, ... ,M N
(1.117)
M
L a,+m::l L Cm ( f,mi.J.,.. ) +d ( J.,..,J.,.. )
n= l
(1.126) And the fundamental equation two can be written as
(H0,M0 ) r 0 (H0 ,M0 ) = +
[1 a, ([,,,"'·••Mo >
f Cm" g
•
b
.~o '
mt
(l)"eik,b/2_e1•,bt2
cos(y' +b/2)•,c,,'=~=~~= b • (k~ Z 2)[k;(mt/b) 2 ]
(1.162)
S1, = Z cos Zx/sin Za/2
(1.163)
C 1 , = jZ sin Zx/ cosZa/2
(l.164)
30
PROBEFED MICROSTRIP ANTENNAS
=
e j(W,+ k1y,k~x,> k2 k' ·{xk,k,[A(k.)  A(k,)] + y[k; A(k.) k; A(k,)]} y
•
(1.165) (1.166) (1.167)
(1.168)
lf x~ < a/2, S1 , and C 1 , decay exponentially. When x~ approaches a/2, these terms decay more slowly. However, unless the feed is at a corner of the patch, one can always avoid this problem by choosing the coordinates wisely. The last step in Eq. (1.165) is obtained using partial fraction expansion. From Eq. (1.153), we have ~ e.cosmx = ~ e.cosm(nx)(I)"= _::cosa(nx)
£....
m=O
m
2
i..,, m=o
a 2
m2 a2
a
• sman
•
(1.169) Hence, A(u) can be summed up in closed form:
!) " .
cos~(~n+::)
A(u) = (
_
u
b
smub
2 el•,•12
(1.170)
Note that
A(k,)=
fe;,,;, '
(1.171)
SPECTRAL DOMAIN FULLWAVE ANALYSIS
31
Hence
· {  j(xk,
+ yk,)k;;' e 1
(...
'\
'~
.... _:,":.":.
I
I I I
I 1.0
FIGURE 1.36 Impedance loci when a superstrate of thickness h 1 = 0.26 mm and relative permittivity e, 1 = 2.2 is added to the antenna of Figure 135. 1.0
...
\
. . A:::::
~ ...........,,,✓': 0.081. at 900MHz).
(b) Measured VSWR versus frequency for h = 1.06 inches.
the slot, in which a large inductive reactance is present for substrate thicknesses exceeding O.o3 I [15]. The radiation from the antenna is linearly polarized, with the E plane parallel to the vertical slots and the H plane parallel to the horizontal slot. The measured patterns in these planes at 900MHz are shown in Figures 1.41 a and 1.41 b. The patterns were found to be stable: The halfpower beam widths in the xz (H) plane were 59° at 812 MHz and 57° at 1.1 GHz, whereas in the yz (E) plane they were 65° at 812 MHz and 70° at 1.1 GHz. The beamwidths are narrower than those of the rectangular patch without the slot:
66
PROBEFED MICROSTRIP ANTENNAS
o·
150
150'
180'
(al
o·
180' (b)
(a) Measured pattern in the H (x z) plane at 900 MHz for h = 1.06 inches. (b) Measured pattern in the E (y z) plane at 900 MHz for h = 1.06 inches.
FIGURE 1.41
RECTANGULAR PATCH WITH AUSHAPED SLOT
67
Huynh and Lee also measured the impedance loci when the patch is 0.53 inches above the ground plane, other parameters remaining the same. This corresponds to h ,:; 0.044 .t at the new center frequency of 990 MHz. The VSWR = 2 bandwidth for this case was found to be about 12.4%, which is still considerably larger than the patch without the slot. The input impedance again does not have an appreciable inductive component. Following Huynh and Lee [39], Lee et al. [40] studied a variety of Uslot rectangular patches with center frequencies around 4.5 GHz. Their measurements included crosspolarization patterns and gain characteristics. They confirmed the wideband behavior of the structure and investigated the effects of various parameters on the antenna performance. It was found that the antenna can be designed to have either wideband or dualfrequency characteristics. The gain of the Uslot patch is about 7 dBi. Lee et al. [41] also studied a twoelement array of Uslot patches. The array had an impedance bandwidth of 29.5%, centered around 4.5 Ghz, with good pattern characteristics. The Uslot rectangular patch is an example of realizing wideband or dualfrequency behavior using a single patch on a single layer. It appears that the currents along the edges of the slot introduce an additional resonance, which, in conjunction with the resonance of the main patch, produce an overall broadband or dualfrequency response characteristic. The slot also appears to introduce a capacitive reactance which counteracts the inductive reactance of the probe. The moment method analysis described in this chapter and in the references, with
3.5,,
2.5
"' 3::
"'>
 1.5
1.0 0.8
0.9
1.0
1.1
1.2
Frequency (GHz) FIGURE 1.42 Theoretical VSWR versus frequency curve for the antenna of Figure 1.40
using the ENSEMBLE software developed by Boulder Microwave Technologies, Inc.
68
PROBEFED MICROSTRIP ANTENNAS
careful modeling of the currents around the slot, should be able to predict the performance of this antenna. Figure 1.42 shows the theoretical VSWR versus frequency curve obtained for the Uslot patch of Huynh and Lee (Figure 1.39) for h = 1.06 inch using the moment methodbased Ensemble software developed by Boulder Microwave Technologies, Inc. There is reasonable agreement with the measured results shown in Figure 1.40 b. Thus the wideband characteristic of the Uslot patch antenna is confirmed theoretically. Further confirmation using Finite Difference Time Domain (FDTD) analysis has also been obtained [ 42]. 16
CONCLUDING REMARKS
This chapter presents a coherent account of recent work on probefed linearly polarized microstrip antennas, based mainly on the authors' research. This includes a spectral domain fullwave analysis of multilayer multipatch microstrip antennas, representative numerical and experimental results on the single patch, single patch in multidielectric media, coplanar parasitic subarray, and the twolayer stacked patches. In addition, the results of a recent wideband design in the form of a rectangular patch with a Ushaped slot have also been presented. REFERENCES [1] A. G. Demeryd, "A Theoretical Investigation or the Rectangular Microstrip Antenna," IEEE Trans. Antennas Propagat., Vol. AP26, pp. 532 535, 1978. [2] W. F. Richards, Y. T. Lo, and D. Harrison, "An Improved Theory for Microstrip Antennas and Applications," IEEE Trans. Antennas Propagat. , Vol. AP29, pp. 3846, 1981. [3] K. F. Lee and J. S. Dahele, "Characteristics or Microstrip Antennas and Some Methods or improving frequency agility and Bandwidth," in Handbook of Microstrip Antennas, J. R. James and P. S. Hall, eds., Peter Peregrinus, London, 1989. [4] W. C. Chew, Waves in Inhomogeneous Media, Van Nostrand Reinhold, New York, 1990, Chapters 2 and 7. [5] W. Chen, K. F. Lee, and R. Q. Lee, "Spectral Domain Full Wave Analysis of the Input Impedance of CoaxiallyFed Rectangular Microstrip Antennas," J . Electromagn. Waves Appl., Vol. 8, No. 2, pp. 249 272, 1994. [6] Y. T. Lo, D. Solomon and W. F. Richards, ''Theory and Experiment on Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. AP27, No. 2, pp. 137145, 1979. [7] J. R. Mosig and F. E. Gardiol, "General Integral Equation Formulation for Microstrip Antennas and Scatters," IEE Proc., Vol. 132, Pt. H, No. 7, pp. 424432, 1985. [8] R. C. Hall and J. R. Mosig, "The Analysis of Coaxially Fed Micros trip Antennas with electrically thick substrates," Electromagnetics, Vol. 9, pp. 367 384, 1989. [9] D. M. Pozar, "Input Impedance and Mutual Coupling or Rectangular Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. AP30, No. 6, pp. 11911196, 1982.
REFERENCES
69
[10] J. T. Aberle and D. M. Pozar, "Analysis of Infinite Arrays of ProbeFed Rectangular Microstrip Patches Using a Rigorous Feed Model," IEE Proc., Vol. 136, Pt. H, No. 2, pp. 110119, 1989. [11] J. T. Aberle and D. M. Pozar, "Accurate and Versatile Solutions for ProbeFed Microstrip Patch Antennas and Arrays," Electromagnetic,, Vol.11, No. I, pp. 119, 1991. [12] D. Zheng and K. A. Michalski, "Aoalysis of Coaxially Fed Microstrip Antennas of Arbitrary Shape with Thick Substrate," J. Electromagn. Waves Appl., Vol. 5, No. 12, pp. 1303 1327, 1991. [13] W.C. Chew, Z. Nie, Q. H. Liu,and Y. T. Lo, "Analysis of ProbeFed MicrostripDisk Antenna," IEE Proc., Vol. 138, Pt. H, pp. 185191, 1991. [14] D. H. Schaubert, D. M. Pozar, and A. Adrain, "Effect of Microstrip Aotenna Substrate Thickness and Permittivity: Comparison of Theories with Experiment," IEEE Trans. Antennas Propagat., Vol. AP27, No. 6, pp. 677682, 1989. [15] W. Chen, K. F. Lee, and R. Q. Lee, "Input Impedance of Coaxially Fed Rectangular Microstrip antenna on Electrically Thick substratet Microwave Opt . Techno. Lett., Vol. 6, No. 6, pp. 387 390, 1993. [16] I. J. Bahl, P. Bhartia, and S. S. Stuchly, "Design of Microstrip Antennas Covered with a Dielectric Layer," IEEE Trans. AntennaPropagat, Vol. AP30, pp. 314318, 1982. [17] A. Bhattacharyya and T. Tralman, "Effect of Dielectric Superstrate on Patch Antennas," Electron. Lett., Vol. 24, pp. 356 358, 1988. [18] Z. Fan and K. F. Lee, "Input Impedance of Rectangular Microstrip Aotennas with a Dielectric Cover," Microwave Opt. Techno. Lett., Vol. 5, pp. 123 125, 1992. [19] 0. M. Ramshi and Y. T. Lo, "Superstrate Effect on the Resonant Frequency of Microstrip Antennas," Microwave Opt. Techno. Lett., Vol. 5, pp. 254257, 1992. [20] W. Chen, K. F. Lee, J. S. Dahele, and R. Q. Lee, "CAD Formulas for Resonant Frequencies of TM 01 and TM 10 Modes of Rectangular Patch Aotenna with Superstrate," Int. J. Microwave and MillimeterWave ComputerAided Engg., Vol. 3, No. 4, pp. 340349, 1993. [21] K. F. Lee, K. Y. Ho, and J. S. Dahele, 'CircularDisc Microstrip Antenna with an Air Gap," IEEE Trans. Antennas Propagat., Vol. AP32, pp. 880884, 1984. [22] K. F. Lee, W. Chen, K. M. Luk, K. F. Tong. and R. Q. Lee, "Microstrip Antennas in MultiDielectric Media," Microwave Opt. Techno. Lett., Vol. 9, pp. 149153, 1995. [23] C. Wood, "Improved Bandwidth of Micros trip Antennas Using Parasitic Elements," IEE Proc., Vol. 127, Pt. H, pp. 231  234, 1980. [24] J. Mosig and F. Gardiol, "The Effect of Parasitic Elements on Microstrip Aotennas," IEEE APS Inter. Symp. Dig., pp. 397400, 1985. [25] C. K. Aanandan, P. Mohanabm, and K. G. Nair, "BroadBand Gap Coupled Antenna," IEEE Trans. Antennas Propagat., Vol. AP38, pp. 15811586, 1990. [26] K. C. Gupta, "Multiport Network Approach for Modelling and Analysis of Microstrip Patch Antenna and Arrays," in J. R. James and P . S. Hall, eds., Handbook of Microstrip Antennas, Peter Peregrinus, London, 1989. [27] R. Q. Lee, R. Acosta, and K. F. Lee, "Radiation Characteristics of Micros trip Arrays with Parasitic Elements," Electron. Lett., Vol. 23, pp. 835837, 1987.
70
PROBEFED MICROSTRIP ANTENNAS
[28] J. C. MacKinchan, P. A. Miller, M. R. Staker, and J. S. Dahele, 'A Wide Bandwidth
Microstrip Subarray for Array Antenna Applications Fed Using Aperture Coupling," IEEE APS Int. Symp. Dig., pp. 878881, 1989. [29] M. R. Staker, J.C. MacKinchan, and J. S. Dahele, "Synthesis oflnLine Parasitically
[30]
[31]
[32]
[33)
[34)
[35]
[36]
[37] [38] [39) [ 40]
[ 41]
[ 42]
Coupled Rectangular Microstrip Patch Antenna Subarrays," 18th Eur. Microwave Conf. Proc., Stockholm, Sweden, pp. 10691073, 1988. P. A Miller, J.C. MacKinchan, M. R. Staker, and J. S. Dahele, "A Wide Bandwidth, Low Sidelobe, Low Profile Microstrip Array Antenna for Communication Applications," Proc. ISAP'89, pp. 525528. W. Chen, K . F. Lee and R. Q. Lee, "SpectralDomain MomentMethod Analysis of Coplanar Microstrip Parasitic Subarrays," Microwave Optical Technol. Lett., Vol. 6, No. 3, pp. 157163, 1993. R. Q. Lee, K. F. Lee, and J. Bobinchak, "Characteristics of a TwoLayer Electromag• netically Coupled Rectangular Patch Antenna," Electron. Lett. , Vol. 23, pp. 10701072, 1987. L. J. Barlately, J. R. Mosig, and T. Sphicopoulos, "Analysis of Stacked Microstrip Patches with a Mixed Potential Integral Equation," IEEE Trans. Antennas Propagat., Vol. AP38, pp. 608 615, 1990. J. P. Daminano, J. Benneguouche, and A. Papiernik, "Study of Multilayered Microstrip Antennas with Radiating Elements of Various Geometry," Proc. IEE, Vol. 137, Pt. H, pp. 163 170, 1990. A N. Tulintself, S. M. Ali, and J. A. Kong, "Input Impedance of a Probefed Stacked Circular Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. AP39, pp. 382 390, 1991. T. M. Au and K. M. Luk, "Effect of Parasitic Elements on the Characteristics of Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. AP39, pp. 12471251, 1991. Z. Fan and K. F. Lee, "Analysis of Electromagnetically Coupled Patch Antennas," Microwave Opt. Technol. Lett., Vol. 6, pp. 436441, 1994. K. F. Lee, W. Chen, and R. Q. Lee, "Studies of Stacked Electromagnetically Coupled Patch Antennas," Microwave Opt. Technol. Lett., Vol. 8, No. 4, pp. 212215, 1995. T. Huynh and K. F. Lee, "SingleLayer SinglePatch Wideband Microstrip Antenna," Electron. Lett., Vol. 31, No. 16, pp. 13101312, 1995. K. F. Lee, K. M. Luk, Y. L. Yung. K. F. Tong, and T. Huynh, "Experimental Study of the Rectangular Patch with a UShaped Slot," IEEEAPS Inter. Symp. Dig., pp. 1013, 1996. K. F. Lee, K. M. Luk, K. F. Tong, Y. L. Yung, and T . Huynh, "Experimental Study of a TwoElement Array of USlot Patches," Electron. Lett., Vol. 32, No. 5, pp. 418420, 1996. K. F . Lee, K. M. Luk, T. Huynh, K. F. Tong, and R. Q. Lee, "USlot Patch Wideband Microstrip Antenna," Proceedings of the 1996 WR! International Symposium, Plenum Press, New York, 1996.
CHAPTER TWO
ApertureCoupled Multilayer Microstrip Antennas K. M. LUK, T. M. AU, K. F. TONG, and K. F. LEE
2.1
INTRODUCTION
Microstrip antennas are commonly fed by one of three methods: (a) coaxial probe, (b) stripline connected directly to the edge of a patch, and (c) stripline coupled to the patch through an aperture. These are shown in Figure 2.1. Feeding by a coaxial probe has the advantages of ease in impedance matching and low spurious radiation and the disadvantage of having to physically connect the center conductor to the patch. In its basic form shown in Figure 2.la, the coaxially fed microstrip antenna has an impedance bandwidth of 23%. By using parasitic elements to create dual or multiple resonances, the bandwidth can be improved to 1020% but seldom exceeds 20% [19]. Coaxially fed microstrip antennas is the subject of Chapter I. The advantage of directly connecting a stripline to the edge of a patch is ease of fabrication. However, impedance matching is not as convenientas the probe feed case, and unwanted radiation from the feed line can be a problem. A method which has become very popular is to couple energy from the stripline through an aperture (slot) in the ground plane. This method, known as aperture coupling, was first proposed by Pozar [10]. Some of its advantages are as follows: (a) The feed network is isolated from the radiating element by the ground plane which prevents spurious radiation; (b) active devices can be fabricated in a feed substrate with high dielectric constant for size reduction; (c) there are more degrees of freedom for the designer. Aduances in Microstrip and Printed Antennas, Edited by Kai Fong Lee and Wei Chen. [SBN 0471044210 © 1997 John Wiley & Sons, lnc.
71
72
APERTURECOUPLED MULTILAYER MICROSTRIP ANTENNAS Conducting patch
~"'
X,)',Z
(k X' kY, z) =
f +rof+ro ,:o
X,)',I'
(x I y I z)e i,,l dx dy
(2.5)
co
(2.6)
The quantity in Eqs. (2.5) and (2.6) with the tilde (~)is the Fourier transform of the corresponding one without the tilde. Tranforming Eq. (2.4) into the spectral domain, we obtain the following ordinary differential equations:
d2 dz2A+k2A =0
(2.7)
d2 dz 2 F + k 2F = 0 where Im(k) e • 40"
Id) 9 • 40"
4.5
5.0
1.0~
1.0~
0 .9
0.9
0.8
0.8
0.7 \ 0.6
0.6
!:0.5
f; 0 .5
0.4
0.4
0.3
0.3
0.2
0.2 0.1
0.1
0 . 0 +    ~     ...... 2.0
2.5
3.0
3.5
4.0
4.5
2.0
5.0
2 .5
Frequency (GHz)
3.0
3.5
4.0
4.5
5.0
Frequency (GHz)
lb)8=50" 1.0..,
1.0..~,
0.9
0.9
0.8
0.8
(e)
0 .7
0.7 \
0 .6
0 .6
!:0.5
!: 0.5
0.4
0.4
0.3
0.3
0.2 0.1
0.2 ••.. ·
·.
.r
0.1
0.0+~~...... 2.0
8• 50°
2.5
3.0
3.5
4.0
Frequency 1GHz)
(cl 0=60"
4.5
5.0
0.0+~~1 2.0
2.5
3.0
3 .5 4 .0
4.5
5.0
Frequency (GHz) (f)
9=60°
FIGURE 2.30
Scan characteristics of an infinite array of dualpatch microstrip antenna with rectangular and triangular grids against frequency for different B scan volumes, x 1 =0.0mm. (a c) Rectangular grid. (d f) Triangular grid.   Broadside;   E plane;  D plane;  ·  H plane. 115
I.Or,
1.0.,..
0.9
0.9
,
0.8
0.8
0.7 0.6
5 0.5 0.4
0.4
0.3
0.3
0.2
0 .2
0.1 ______ • . ··:::.:., o.o.._ .....;c.:,...l 2.0
2.5
3.0
3 .5 4.0
4.5
5.0
0.1
•· ,/.,.;!/
, ·_'>C.7 ':::_..j_1
0.01....a.',......./ 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Frequency (GHz)
Frequency (GHz) (a) 8= 40.,
I.Or,
(d)8 • 40" I.Or~
0 .9
0.9
0 .8
0.8
0.7
0.7
0.6
0 .6
so
!; 0.5
0
0.4
0
0.3 0 .2
/ . \ ..)v....··
0
0.1
0.1
0 . 0 +         '   ....... 2.0 2.5 3.0 3.5 4.0 4.5 5.0
\"\
,,.,r..:,··
0 .0+~~~·Yv_ .• ..a_.~ ·_..:~ _ _ ,
2.0
2.5 3.0
3.5
4 .0
4.5
5.0
Frequency (GH2:)
Frequency (GHz)
Cb> 0. so• I.Or,
8 • so• I.Or~
0.9
0.9
0 .8
0.8
(e)
0.7 0 .6
!: 0.5 0.4 0.3 0.2 0.1
• ..:,;
\ .:
0.0 2.0
2.5
3 .0
3.5
4.0 4.5
Frequency (GHz) le) 8 =60°
FIGURE 2.31
5.0
a.a+2.0
2.5 3.0
3.5
4.0
4.5 5.0
Frequency (GHz)
(f) 8s60"
Scan characteristics of an infinite array of offset dualpatch microstrip
antenna with rectangular and triangular grids against frequency for different 0 scan volumes, x 1 = 1.0mm. (a c) Rectangular grid. (d f) Triangular grid.   Broadside;    E plane;  D plane;    H plane. 116
INFINITE ARRAYS
117
TABLE2.12
ScanBandwidth(%) Rectangular Grid ({ = 90°)
o· 40•
so· 60°
Triangular Grid ((
= 60°)
Without Offset
With Offset
Without Offset
With Offset
59 49 42 27
60
59 50 43 37
61 53 49 40
50 43 29
frequencyindependent matching networks were necessary to be inserted between the array elements and the feedlines. It is not easy to implement the desired dielectric constant of the upper layer, and frequencyindependent matching networds are difficult to design over wide operating frequencies. It will be seen in the results that follow that the above disadvantages can be overcome by using an infinite array of dualpatch microstrip antennas with an air gap between the substrates supporting the patches. After selecting a set of element spacings of U. and U, and the scan angle (IJ, q:, ), the element parameters are adjusted until a maximum bandwidth is obtained. An array with a triangular grid and with a scan angle of IJ = 60' in the H plane is selected. The calculated reflection coefficient magnitude against frequency for different scan angles at different scan planes are reported. Numerical results for reflection coefficient magnitude against frequency are obtained to compare with measurements from a waveguide simulator. The element spacings in two oblique directions are equal and are selected to be 30.0 mm. The parameters of the feed substrate are described in Section 2.4.3 and are repeated here: e,1 =2.32, d=l.6mm, w=4.6mm, and 11 =13.0mm The dimensions of the aperture are 1.0 mm x 24.0 mm. The thicknesses of the lower and upper dielectric layers are 3.2mm and 1.6mm, respectively. The relative permittivity of the patch substrates is 2.32. The airgap spacing between two patch substrates are 4.5 mm. The resonant lengths of the lower and upper patches are 19.8 mm and 20.2mm, respectively. The width of each metal patch is identical; that is, w 1 = w2 = 12.5 mm. The upper patch is centered above the aperture. Figures 2.30 and 2.31 show, respectively, the scan characteristics of the infinite array with a rectangular and triangular grids for different scan angles (0,q,). A larger scanbandwidth is obtained at higher scan angle 0. For this configur• ation, the scanbandwidth is increased slightly if the patches are offset. The scanbandwidths(%) of the configuration in different scan volumes IJ are tabulated in Table 2.12. We can conclude that the scanbandwidth of an array can be optimized with appropriate a,. 2 , s,x 1, and U•.,·
118
APERTURECOUPLED MULTILAYER MICROSTRIP ANTENNAS
1.0.,..55 0.9 0.8
50
0.7
0.6
f. 0.5 0.4 0.3 0.2 0.1 0.0+~~~~~..+30 3.0 4.0 5.0 Frequency (GHz)
Calculated • Measured      Scanangle
FIGURE 2.32
Reflection coefficient magnitude against frequency for an aperture
coupled dualpatch microstrip antenna, a 1 = 9.9mm, a 2 = 10.l mm, w1 = w1 = 12.5mm, x, =0.0mm,s=4.5mm, U,= U,=30.0mm, ,;=90°.
Figure 2.32 shows the active reflection coefficient magnitude against frequency for the waveguide simulator of an aperturecoupled dualpatch microstrip antenna. The simulated array is arranged in a rectangular grid ({ =90°). The lengths of unit cell in the x and y directions are equal; that is, U, = U, = 29.0 mm. The TE 10 waveguide mode is used to simulate scanning of the array in the H plane from an angle of 51.6° at 3.3 GHz to an angle of 31.9° at 4.9 GHz. The reference plane is selected at the center of the aperture. Qualitative agreement between theory and measurement is obtained. A 40 ° phase lag of the measured reflection coefficients is observed compared to that of the calculated result. The discrepancy between theory and measurement may be caused by the imperfect contact between the metal patches and the waveguide walls.
2.6 CONCLUSIONS
In this chapter, the method of moments has been employed to evaluate the characteristics of aperturecoupled multilayer rectangular microstrip antennas. The substrate effect has been taken into account with the use of spectral domain
CONCLUSIONS
119
Green's functions. Piecewise simusoidal modes have been chosen as expansion and testing functions. The unknown reflection coefficient in the microstrip feedline has been formulated by using the reciprocity theorem. Different special cases of multilayer patch antennas have been examined. The tunable characteristic of an aperturecoupled patch antenna with an air gap between the antenna substrate and the ground plane has been investigated. The resonant frequency and the fronttoback ratio of this patch antenna increase, while the maximum input resistance and the E plane beamwidth decrease with increasing air gap width. The SWR bandwidth and farfield radiation patterns of coplanar microstrip subarrays have been studied. The parasitic elements are gapcoupled to the nonradiating edges of the fed patch. The parasitic elements can improve the antenna bandwidth and directivity, but high backlobe and crosspolarization levels have been found. Nevertheless, the maximum level of E plane crosspolarization is below  30 dB across the passband. A microstrip subarray with a planar reflector has also been examined. In addition to the reduction in backlobe level, the bandwidth is also enhanced with a suitable distance between the reflector and the feed substrate. The radiation patterns do not vary significantly. The characteristics of an aperturecoupled dualpatch antenna have been evaluated. Maximum bandwidth is attained by choosing appropriate resonant lengths for the patches, substrate spacing, and offset displacement. The crosspolarization levels increase with offset displacements. The maximum level of crosspolarization at the E plane is about  40dB. Beam squint has been observed in the E plane. Two versions of aperturecoupled twolayer microstrip antenna with stacked parasitic patches have been presented. For the fivepatch design, large SWR bandwidth and narrow beamwidth can be obtained by using relatively large values of x 2, and y 2 ; x2 and y 2 are the displacements of the four parasitic patches. With the use of this kind of high gain micros trip antennas, the sizes of micros trip array may be reduced for a given gain. This advantage is very attractive for applications in satellite communications. For the threepatch design, the effects of the positions and dimensions of two stacked parasitic elements on the input impedance, SWR bandwidth, and radiation patterns have been examined. A wideband design procedure is demonstrated. A fullwave analysis of infinite arrays of aperturecoupled patch antennas has been carried out. If a large scan volume is required, the element spacings in both oblique directions should be around 0.4lo.. It is also found that an array with a triangular grid has the wider scan angle in the E plane. Computed results have been compared with experimental data for patch antennas with an air gap, a coplanar subarray, an offset dualpatch antenna, and an infinite array of dualpatch antennas. Reasonable agreement between theory and measurement has been obtained. The developed computer code can be used to generate design data for different structures at different operating frequency bands. Further work will be focused on the design of aperturecoupled multilayer CP microstrip antennas and arrays.

..., 0
APPENDIX: FOURIER TRANSFORMS OF EXPANSION AND TEST FUNCTIONS The onedimensional Fourier transforms of the following expansion or test function modes are as follows:
{.!__ 2a
Pulse
0 PWS
EB
Edge condition
for lxx0 1;;.a
k,sia k,{(h  Ix  x0 1) t I h 2(1  cos k,h) or x  xol "s 0 for lx x 01;;. h nm sin~(xx 0 +a)
for lx  x0 l~a
0
for lxx 0 1;;. a
4a
sin k"a e itx"°
for lxx 0 1.;;a
2a
I
na Ja' ,}xx 0) 2 Traveling wave
](k.J
J(x)
Function
e1,.x
k, is the effective wavenumber of the PWS mode. JO is the zerothorder Bessel function oflirst kind.
for lx x0 l"s• for lxx0 1;;.a
k,a k:
coskxh cosk)i elkx:ro
1 cosk,h
k;k;
(mn:)2( 1reJbo  e+Jt:.11 eJb%0
2
(2k.J 2 (mn)2
(2.76)
(2.77)
(2.78)
J 0(k,a)e " 1''"'
(2.79)
2nb(k, + /J,)
(2.80)
REFERENCES
121
ACKNOWLEDGMENTS
The authors are especially grateful to Dr. C. S. Leung, Dr. P. C. Ng, and Mr. W. W. Luk for their coordination in the moment method computation at the Chinese University of Hong Kong.
REFERENCES [I] R. Q. Lee, K. F. Lee, and J. Bobinchak, "Characteristics of a TwoLayer Electromagnetically Coupled Rectangular Patch Antenna," Electron. Lett., Vol. 23, pp. 10701073, 1989; see also IEEE Trans. Antennas Propagat., Vol. AP38, pp. 12981302, 1987. [2] R. Q. Lee and K. F. Lee, "Gain Enhancement of Microstrip Antennas with Overlaying Parasitic Directors," Electron. Lett., Vol. 24, pp. 656 658, 1988. [3] 1. P. Damiano,J. Bennegueouche, and A. Papiernik, "Study of Multilayer Microstrip Antennas with Radiation Elements of Various Geometery," JEE Proc. Microwave Antennas Propagat., pp. 163170, 1990. [ 4] L. Barlatey, J. R. Mosig and T. Sphicopoulos, "Analysis of Stacked Microstrip Patches with a Mixed Potential Integral Equation," IEEE Trans. Antennas Propagat., Vol. AP38, pp. 608615, 1990. [5] P. S. Bhatnagar, J. P. Daniel, K. Mandjoubi, and C. Terrel, "Displaced Multilayer Triangular Elements Widen Antenna Bandwidth," Electron. Lett, Vol. 24, pp. 962964, 1988. [6] G. Kumar and K. C. Gupta, "Nonradiating Edges and Four Edges GapCoupled Multiple BroadBand Microstrip Antenna," IEEE Trans. Antennas Propagat., Vol. AP33, pp.173178, 1985. [7] W. Chen, K. F. Lee, and R. Q. Lee, "Spectral Domain MomentMethod Analysis of Coplanar Microstrip Parasitic Subarrays," Microwave Opt. Technol. Lett., Vol. 6, No. 3, pp.157163, 1993. [8] K. F. Lee, W. Chen, and R. Q. Lee, "Studies of Stacked Electromagnetically Coupled Patch Antennas," Microwave Opt. Technology Lett., Vol. 8,No.4,pp.212215, 1995. [9] A. N. Tulintsett, S. M. Ali, and J. A. Kong, "Input Impedance ola ProbeFed Stacked Circular Microstrip Antenna," IEEE Trans. Ante1111as Propagat., AP39, pp. 12471251, 1991. [!OJ D. M. Pozar, "Microstrip Antenna ApertureCoupled to a Microstrip Line," Electron. Lett., Vol. 21, pp. 49 50, 1985. [11] 1. C. MacKinchan, P.A. Miller, M. R. Staker, and 1. S. Dahe!e," A Wide Bandwidth Microstrip Subarray for Array Antenna Applications Fed Using Aperture Coupling," IEEE APS Int. Symp. Dig., pp. 878881, 1989. [12] F. Croq, and D. M. Pozar, "MillimeterWave Design of WideBand ApertureCoupled Stacked Microstrip Antenna," IEEE Trans. Antennas Propagat., Vol. AP39, pp. 17701776, 1991. [13] D. M. Pozar, "A Reciprocity Method of Analysis for Printed Slot and SlotCoupled Microstrip Antennas," IEEE Trans. Antennas Propagat., AP34, pp. 1439 1446, 1986.
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APERTURECOUPLED MULTILAYER MICROSTRIP ANTENNAS
[14] D. M. Pozar," Analysis ofao Infinite Phased array of ApertureCoupled Microstrip Patches," IEEE Trans. Antennas Propagat., AP37, pp. 418 425, 1989. [15] C. A. Balanis, Advanced Engineering Electromagnetic, John Wiley & Sons, New York, 1989. [16] R. W. Jackson and D. M. Pozar, "FullWave Analysis ofMicrostrip OpenEnd and Gap Discontinuities", IEEE Trans. Microwave Theory Techniques, Vol. MTT33,
pp. 1036 1042, 1985. [17] D. M. Pozar, "Input Impedance and Mutual Coupling of Rectangular Microstrip Antenna," IEEE Trans. Antennas Propagat., AP30, pp. 1191  1196, 1982. [18] K. E. Atkinson, An Introduction to Numerical Analysis, John Wiley & Soos, New York, 2•• edition, 1978. [19] R. E. Collin, Antennas and Radiowave Propagation, McGrawHill, New York, 1985. [20] Z. fan and K. F. Lee, "Spectral Domain Analysis of Rectangular Microstrip Antennas with an Air gap," Microwave Opt. Technol. Lett., Vol. 5, No. 7, pp. 315318, 1992. [21] H. Legay and L. Shafai, "New Stacked Microstrip Antenna with Large Bandwidth and High Gain;' IEE Proc. Microwave Antennas Propagat., Vol. 141 , No. 3, pp. 199204, 1994. (22] A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering, PrenticeHall, New York, 1991. (23] J. I. H. Wang, Generalized Moment Methods in Electromagnetics: Formulation and Computer Solution of Integral Equations, John Wiley & Sons, New York, 1991. [24] T. M. Au and K . M. Luk, "Effect of Parasitic Element on the Characteristics of Microstrip Antenna," IEEE Trans. Antennas Propagat. Vol. AP39, pp.12471251 , 1991. [25] T. M . Au, K. F. Tong, and K. M. Luk, "Analysis of Offset DualPatch Microstrip Antenna," IEE Proc. Microwave Antennas Propagat., Vol. 141, No. 6, pp. 523526,
1994. [26] Y. Lubin and A. Hessel, "WideBand, WideAngle Microstrip StackedPatchElemeot Phased Arrays, IEEE Trans. Antennas Propagat., Vol. AP39, pp. 10621070, 1991. [27] J. T. Aberle, D. M. Pozar, and J. Manges, "Phased Arrays of ProbeFed Stacked Microstrip Patches," IEEE Trans. Antennas Propagat., Vol. AP42, pp. 920927, 1994.
CHAPTER THREE
Microstrip Arrays: Analysis, Design, and Applications JOHN HUANG and DAVID M. POZAR
3.1
INTRODUCTION
In many microstrip antenna applications, systems requirements can be met with a single patch element. In other cases, however, systems require higher antenna gains while maintaining a lowprofile structure, which calls for the development of microstrip arrays. This chapter explores the analysis techniques, design methodology, and applications of microstrip array antennas for current and future advanced systems. Microstrip arrays, due to their extremely thin profiles (0.010.05 freespace wavelength), offer three outstanding advantages relative to other types of antennas [13]: low weight, low profile with conformability, and low manufacturing cost. Because of these attractive features, many ntilitary, space, and commercial applications are employing microstrip arrays instead of conventional highgain antennas, such as arrays of horns, helices, slotted waveguides, or parabolic reflectors. However, advantages of the micros trip array can be offset by three inherent drawbacks: small bandwidth (generally less than 5%), relatively high feed line loss, and low powerhandling capability. To minimize these effects, accurate analysis techniques, optimum design methods, and innovative array concepts are imperative to the successful development of a microstrip array antenna. For example, accurate analysis and a correct design approach can often overcome deficiencies in such performance factors as mutual coupling, beam Advances in Microstrip and Printed Antennas, Edited by Kai Fong Lee and Wei Chen. © 1997 John Wiley & Sons, Inc
ISBN 047104421.0
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scanning effect, pattern shaping, power divider configuration, and impedance matching. In this chapter, several different techniques for analyzing microstrip arrays are briefly reviewed. One techniquethe full wave moment methodis presented in more detail because it is probably the most widely used technique due to its accuracy and reasonable computation time. In addition to analysis techniques, practical design approaches for microstrip arrays are presented, including patch elements and power division circuits. A recently developed array configuration, namely the microstrip reflectarray, is highlighted. Applications of microstrip arrays in the military, space, and commercial segments are also discussed.
3.2 ANALYSIS TECHNIQUES FOR MICROSTRIP ARRAYS Accurate, flexible, and computationally efficient analysis techniques are important for antenna design primarily to reduce costly and timeconsuming experimental cutandtry design cycles. Analysis can also provide a more complete understanding of the operation of an antenna and can aid in optimizing its performance or determining limitations in its performance. As discussed in reference [ 4], micros trip elements can often be successfully designed with little or no computeraided design (CAD) support, but the increased complexity of microstrip arrays is more often facilitated by the availability of robust CAD tools. Another factor in the evaluation of the current state of the art in microstrip antennas analysis and associated CAD software is that there is a very wide variety of element geometries, feeding methods, and substrate configurations for practical microstrip antennas and arrays. The majority of microstrip arrays are designed as fixedbeam broadside antennas, often with the feed network located coplanar with the array elements for purposes of simplicity and economics. In this case, the design procedure can be broken into the fairly disparate steps of element design, array layout and spacing, and feed design. The design of the radiating element involves considerations such as the bandwidth and polarization specifications. The grid layout, the number, and the spacing of the array elements are determined by the required principal plane beamwidths, or the gain, of the array. The feed network is a function of the amplitude tapers required for the sidelobe specification, impedance matching to the elements, and the array bandwidth and may take the form of a series feed or a corporate feed. Fortunately, mutual coupling can often be ignored for fixedbeam micros trip arrays, a fact which greatly simplifies the design procedure, since for purposes of design the elements and their excitations can be treated as if they were isolated. The feed network can then generally be simply designed with impedance matching networks and power divider circuits, possibly with the aid of a microwave circuit CAD tool. The situation is more complicated for arrays with high gain (more than about 30dB) [5], very low sidelobes (less than about 30dB) [6], or arrays operating at millimeterwave frequencies (higher than about 20 GHz) (5]. In these cases, loss
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and tolerance effects may accumulate sufficiently to cause severe performance degradation, and it becomes critical to have CAD design tools based on solid analysis. Such tools are only partially available at the present time. The design and analysis of scanning phased microstrip arrays is another situation that typically requires rigorous and versatile CAD software. The primary driver for this requirement is the fact that such antennas are very expensive because of the phase shifter or T /R module cost per element, so it is critical that antenna performance be analyzed and optimized accurately and thoroughly. Experimental trials using small arrays, active element patterns, and waveguide simulators can play an important role in the design process, but accurate CAD models can provide much more information about important effects such as scan blindness, impedance mismatch, losses, random errors, sidelobe levels, and crosspolarization as a function of any design parameter. Unlike the case for fixed beam arrays, scanning arrays usually do require the inclusion of mutual coupling effects, as well as the effect of the feed network, for a complete characterization of the array. This is a very difficult problem in general, especially for arrays that have more than a few elements (so that coupling effects are important) but are too small to apply the infinite array approximation . .In the following sections we will present a brief review of several analysis techniques for microstrip arrays and then concentrate on fullwave moment method techniques for single elements, mutual coupling between elements, and infinite array analysis. We will also discuss the use of the active element pattern and waveguide simulators in array design.
3.2.1 Review of Microstrip Antenna Analysis Techniques Compared to other types of antennas, microstrip antenna analysis is complicated by the presence of a dielectric inhomogeneity, a narrowband impedance characteristic, and a wide variety of patch, feed, and substrate configuration. Present microstrip antenna models invariably compromise their treatment of one or more of these features. Most theories to date can be categorized as either (a) simplified (or reduced) analyses that maintain simplicity at the expense of accuracy or versatility or (b) fullwave models that maintain accuracy and rigor at the expense of computational efficiency. There is no model or CAD package that can provide accurate results for a significant fraction of the microstrip antenna and array geometries that are of practical interest at this time. Reduced analyses refer to microstrip antenna models that introduce one or more simplifying assumptions to the problem. These thus include (a) the cavity model [3, 7, 8, 11 ], which uses a magnetic wall boundary condition around the periphery of the patch to form a closed resonant cavity, (b) the transmission line model [3, 9, 11], which models the element as a section of transmission line with load admittances to model the radiating edges of the antenna, and the multiport segmentation model [3, 10, 11], which generalizes the cavity model to treat arbitrarily shaped elements. These models were the first to be developed for microstrip antennas and have proven to be very useful for practical design as well
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as providing an intuitive explanation for the operation of the microstrip element. Generally they give good results for antennas on thin, lowdielectric constant substrates. While originally developed for probefed and linefed elements, models of this type have also been proposed for more complicated structures such as the aperture coupled patch element [12] and proximity coupled element [11], as well as for elements covered with radome layers [3, I 1]. Generally, however, the inclusion of multilayer substrates requires more rigorous modeling techniques. In recent years, because of the vast increase in computer power, finite element and finite difference time domain (FDTD) methods have begun to be applied to microstrip and other planar antenna problems [13]. Such methods offer what are probably the most versatile computational techniques presently available and are beginning to become available as commercial CAD packages. These methods are relatively "brute force" in nature, however, requiring considerable computational resources and offering little physical insight into the operation of the antenna. Such numerical models are already reducing the need for electromagnetic analysts, but it remains true that more analytically based solutions for particular geometries, such as cavity models or moment method solutions, can give more accurate results with less computational effort. 3.2.2
FullWave Moment Method Analysis
Microstrip antenna models that account for the dielectric substrate in a rigorous manner are referred to as fullwave solutions. Thus "fullwave" may be used to describe FDTD or finite element solutions, but most of the fullwave analyses of microstrip antennas have been moment method solutions using the exact Green's function for the dielectric substrate. This techniques enforces the boundary conditions at tbe airdielectric inter.face and treats the contributions of space waves, surface waves, dielectric loss, and coupling to external structures in an accurate manner. It is also possible to apply the method to a wide variety of patch and substrate geometries, including arrays, mutual coupling effects, multiple layers, stacked elements, and various feeding methods, and it can be easily extended to infinite arrays of microstrip antennas [3, 11]. It is probably the most popular analysis technique for microstrip antennas and arrays. While the reader is referred to the literature for details on the analysis of particular microstrip antenna geometries [3, 11 ], we can summarize some of the key features of the fullwave moment method procedure here. The equivalence theorem is used to replace conducting patch elements with equivalent electric surface currents, and slot elements are replaced with equivalent magnetic currents. A moment method solution is then derived from the enforcement of the continuity of electric or magnetic fields at the patch or slot elements. The fields from these current elements are found using the exact Green's function for the substrate geometry, which can be derived in closed form for a wide variety of multilayer substrates consisting of isotropic, anisotropic, ferrite, or chiral materials [3, 11]. The key calculation in this procedure then becomes the evaluation
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of impedance matrix elements having the general form
(3.1)
where J, and 1 1 are the expansion and test mode currents, and G is the dyadic Green's function for the substrate geometry. This sixfold integration involves surface wave poles, a slowly converging integrand, and singularities associated with the source point. The evaluation of this expression therefore requires considerable care and attention to details. The order of integration in Eq. (3.1) can be chosen in at least two ways, leading to solutions with somewhat different characteristics. In the fullwave spectral domain approach [3, 11, 15), the space integrations over the expansion and test mode coordinates x, y, x 0 , y 0 are done in closed form, which amounts to taking the Fourier transform of the expansion and test modes. Then the rectangular spectral variables k, and k, are transformed to polar coordinates, fJ and ex, where k, = fJ cos ex, k, = fJ sin ex. Then Eq. (3.1) reduces to Z,1 =
f~f2, 0
0
F,(k,,k,) ·G(k,,k,) ·F;(k,,k,)dad{J
(3.2)
which is in a convenient form for numerical evaluation. The source singularity that occurs in Eq. (3.1) when x = x 0 and y = y0 is eliminated in Eq. (3.2) by the smoothlng process of integrating over the expansion mode to form the Fourier transform F1• This is a convenient feature of the spectral domain method, especially for the evaluation of selfimpedance terms because it eliminates the need for special treatment of the source singularity. There is still a surface wave pole associated with the TM 0 surface wave, but this can be treated fairly easily [14). It is also convenient to use the residue of the surface wave pole to evaluate the surface wave power generated by the antenna, in contrast to the more cumbersome method of using a volume integral of the surface wave fields [15). Alternatively, the spectral variables in Eq. (3.1) can be transformed to polar form, and the ,x integration done in closed form, to yield
which is generally referred to as the space domain approach because of the remaining integrations over the space coordinates. The source singularity that remains in this formulation requires special consideration, but can be treated in a manner very similar to the treatment of the source singularity for wire antennas. The integration over fJ must be performed numerically, but there are several techniques for doing this efficiently [3, 16). Recent work in this area has focused
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FIGURE 3.1 Measured and calculated input impedance of an aperturecoupled stacked microstrip antenna. Substrate thickness (bottom layer)= 0.508 mm, (top layer) =0.7874mm, (feed layer)=0.508. Dielectric constant (bottom layer)=2.2, (top layer)= 2.33, (feed layer)= 2.2. Bottom patch length and width= 3.5 mm. Top patch length and width= 3.8mm. Slot length= 3.2mm, slot width =0.4mm. (From reference 18,