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Advances in Microstrip and Printed Antennas Edited by




This text is printed on acid-free 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 10158-0012.

Library of Congre11 Cataloging--in-Publication 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 Wilcy-lntcrscience publication." Includes bibliographical references (p. ). ISBN 0-471-04421-0 (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 96-39032

Printed in the United States of America 109876543






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

I.I 1.2

Introduction Full-Wave Analysis of Multilayer Multipatch Microstrip Antennas 1.2.1 Introductory Remarks 1.2.2 Conventions and Definitions 1.2.3 Basic Formulations 1.2.4 Green's Functions 1.3 Spectral Domain Full-Wave Analysis of Probe-Fed Rectangular Microstrip Antennas 1.3.1 Formulation 1.3.2 Basis Functions 1.3.3 Multiple Feeds and Shorting Pins 1.3.4 Attachment Modes 1.4 Representative Numerical and Experimental Results 1.4.1 Single Patch 1.4.2 Single Patch in Multidielectric Media 1.4.3 Coplanar Parasitic Subarray 1.4.4 Two-Layer Stacked Patches 1.5 Rectangular Patch with a U-Shaped Slot 1.6 Concluding Remarks References

1 4 4 5 7 13 19 19 23 24 26 35 36 42 50 53 63 68 68 V

vi 2



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


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 Dual-Patch Microstrip Antennas 2.4.4 Two-Layer Microstrip Antennas with Stacked Parasitic Patches 2.5 Infinite Arrays of Aperture-Coupled Multilayer Microstrip Antennas 2.5.1 Skewed Periodic Structure and Floquet Modes 2.5.2 Infinite Array of Microstrip Antennas with Air Gaps 2.5.3 Infinite Array of Dual-Patch Microstrip An tennas 2.6 Conclusions Appendix: Fourier Transforms of Expansion and Test Functions Acknowledgments References


109 109 113 114 118 120 121 121

Microstrip Arrays: Analysis, Design, and Applications


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 Full-Wave Moment Method Analysis 3.2.3 Calculation of Mutual Coupling 3.2.4 Infinite Array Analysis 3.2.5 The Active Element Pattern 3.2.6 Waveguide Simulators 3.3 Design Methodology 3.3.1 Array Configuration Design 3.3.2 Patch Element Design 3.3.3 Power Division Transmission Line Design 3.3.4 Microstrip Reflectarray Design 3.4 Applications 3.4.1 Military Applications 3.4.2 Space Applications 3.4.3 Commercial Applications

123 124 125 126 128 132 134 135 137 138 143 144 148 152 152 154 157





3.5 Summary and Conclusion References

159 159

Dual and Circularly Po larized Microstrip Antennas P. S. Hall and J. S. Dahele


4.1 Introduction 4.2 Polarization in Antenna Systems 4.3 Generation of Orthogonal Polarizations 4.4 Circularly Polarized Patches 4.4.1 Orthogonal Patches 4.4.2 Multipoint Feeds 4.4.3 Single-Point Feeds 4.5 D ual Polarized Patches 4.5.1 Triangular Patch with Right- and Left-Hand Circular Polarization 4.6 Microstrip Spirals 4.6.1 Operation of the Spiral Antenna 4.7 Special Substrates and Active Antennas 4.8 Dual and Circularly Polarized Arrays 4.8.1 Patch Arrays 4.8.2 Microstrip Line Arrays 4.8.3 Sequentially Rotated Arrays 4.9 Conclusions References

163 164 165 167 169 170 177 183 184 184 185 186 188 188 188 190 217 217

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


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 Surface-Wave and Space-Wave Q Factors 5.4.3 Space-Wave Quality Factor 5.5 CAD Formula for Bandwidth 5.5.1 CAD Formula 5.5.2 Results 5.6 CAD Formula fo r Radiation Efficiency

235 237 242 243 243 246




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


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 High-Temperature Superconductors 7.2.3 Characteristics of High-Temperature Superconductors

276 276 286 294 302 307 308 312 312 315 317 317 325

325 326 327 329 333


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 Diode-Integrated Active Microwave Antennas 8.4 Transistor-Integrated 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 Far-Field Computation Feeding Techniques Characteristics of TSA 9.7.1 Radiation Characteristics 9.7.2 Impedance Characteristics 9.7.3 Bandwidth Characteristics 9.7.4 Field Distributions Tapered Slot Antenna Arrays Active Tapered Slot Antenna Array


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




9.10 Conclusion References

510 510

Efficient Modeling of Microstrip Antennas Using the Finite-Difference Time-Domain Method


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 Two-Layer Stacked Patch Antenna 10.7 Design of a Compact Broadband Antenna 10.8 Conclusions References 10.1 10.2 10.3 10.4


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 Aperture-Coupled Hemispherical DR Antenna 11.2.1 Problem Formulation 11.2.2 Moment Method Solution 11.2.3 Derivation of DR Antenna Green's Function G~ 11.2.4 Evaluation of Y:U. ' 11.2.5 Single-Cavity-Mode Approximation 11.2.6 Single-Cavity-Mode Radiation Field of the DR Antenna

553 555 556 557 560 566 567 568


11.2.7 Results and Discussions 11.2.8 Summary 11.3 FDTD Analysis of Probe-Fed 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 Far-Field Calculations 11.3.6 Results and Discussions 11.3.7 Summary References Index


568 573 573 574 576 578 579 580 582 589 589 593


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


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



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 16802-2705 U.S.A.

J. R. James School of Engineering and Applied Science Royal Military College of Science Cranfield University Shrivenham, Wilts SN6 8LA England K. F. Lee Department of Electrical Engineering University of Missouri-Columbia Columbia, MO 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


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.


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




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 two-volume handbook was published. The contributors are all active researchers and well known in the field. Chapters 1-4 deal with recent advances in conventional topics. These include accounts on recent results on probe-fed microstrip antennas and 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 computer-aided 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 finite-difference time-domain method of analysis which is becoming popular due to its ability to handle complex configurations and to generate the characteristics of the patch over a broad band of frequencies with a single simulation. The book ends with a chapter xvii



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


Probe-Fed Microstrip Antennas K. F. LEE, W. CHEN, and R. Q, LEE



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 three-layer configuration of Figure 1.3b results. Figure 1.3c shows a one-superstrate two-substrate geometry, as, for example, when an air gap is introduced between the substrate and the ground plane to alter the resonant frequency of the antenna. Figure 1.4 shows the two-layer stacked geometry consisting of one fed patch and a parasitic patch on another layer. These stacked patches are popular for providing wide bandwidth characteristics. Another wideband microstrip antenna is the rectangular patch with a U-shaped slot (Figure 1.5). In recent years, the various linearly polarized probe-fed microstrip antennas depicted above have been extensively studied. It is the purpose of

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




Conducting patch


Ground plane Coax feed (b)

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

this chapter to give a coherent account of recent work in this area. The materials to be presented are based mainly on the authors' research. Related work by others will be referenced but not described in detail. We shall be concerned with rectangular patches only. However, the methods of 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 full-wave analysis of multilayer multipatch microstrip antennas is presented. The application of the analysis to probe-fed rectangular microstrip antennas is described in Section 1.3. Representative numerical and experimental results for configurations 1.1 - 1.4 are given in Section 1.4. Experimental results of the U-slot patch are described in Section 1.5. The chapter ends with some concluding remarks.


□GQ. ., LJ;:;ches


Parasitic patch

Fed patch



'>. \ / Substrate I -----1 ,__ICoax feed (bl


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

Superstrate Substrate




~ LJ

Superstrate 1


Superstrate 2



Coax feed

Coax feed

Coax feed




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.



Superstrate /Parasitic patch Substrate

Fed patch

71"""" Coax feed


Geometry of two-layer stacked patches.


t n ~


U S ~ !al




Air or foam ---------""



E(l,)·1, dV


(JJJ,> = - H(l,)·M,dV (M,,M,)= -



(i, ,7,> = E,·1,dV







Basic Formulations

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






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






Thus, the magnetic current excitation over the aperture(s) is expressed by (1.17)



Conducting plane


Conducting plane (bl


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:



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


j =l

k= l

L C;E(l)+ L y,E(M,);:,O




or N


I c/f(J),,, - I y.£(M,l

J: l


Testing the above equation using



J,, we obtain (1.21)

or N




I c/J,,1) = - I y.(J,,iJ,>


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






I c)f(l)+ I y,E(iJJ,,,z. I c);

1f C;


Jy, fE(MJ-1,ds= z,, J c f1;·J;ds J C;(Y,)) JY,(J;,M,) = J C fJ,-1,ds

E(l;)·J;ds +







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



k= 1

H,"' L C,H,(},) + L y,H,(MJ




Testing it using

it, we get

or N



k =I

( MmJi,) = L C/ Mm,J)+ L Y,(Mm,M,)


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


= [(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 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)



Conducting planes


Conducting planes


Conducting planes



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





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


x ,land

M~ = £~xi. nis the inward normal.




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



n= l


L C)=- L 1!- ( f/,M!- >+ L r! 1



11 "" 1


Mt - !

= L CJ+ L 1:- 1

j= 1





- ,,1 L r!

na: 1

m= 1


+d(J,,.,,,J;,".,",>+ L b,(M,, J;.""·"')=0



nl = 1,2, .. . ,N H


n= 1



L a.(J,,,"'·'J,m,z>+ L Cm=O



ml=l,2, ... ,M N



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


.~o '



cos-(y' +b/2)•-,-c,,-'=~=~-~= b • (k~ -Z 2)[k;-(mt/b) 2 ]


S1, = Z cos Zx/sin Za/2


C 1 , = jZ sin Zx/ cosZa/2





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)


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(n-x)(-I)"= _::cosa(n-x)





i..,, m=o

-a 2

m2 -a2


• sman

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

!) " .


A(u) = (





2 el•,•12


Note that


-fe;,,;, '





· { - j(xk,

+ yk,)k;;' e 1



.... _:,":.":.-



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 1-35. 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 half-power beam widths in the x-z (H) plane were 59° at 812 MHz and 57° at 1.1 GHz, whereas in the y-z (E) plane they were 65° at 812 MHz and 70° at 1.1 GHz. The beamwidths are narrower than those of the rectangular patch without the slot:







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.




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 U-slot rectangular patches with center frequencies around 4.5 GHz. Their measurements included crosspolarization patterns and gain characteristics. They confirmed the wideband behavior of the structure and investigated the effects of various parameters on the antenna performance. It was found that the antenna can be designed to have either wideband or dual-frequency characteristics. The gain of the U-slot patch is about 7 dBi. Lee et al. [41] also studied a two-element array of U-slot patches. The array had an impedance bandwidth of 29.5%, centered around 4.5 Ghz, with good pattern characteristics. The U-slot rectangular patch is an example of realizing wideband or 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 dual-frequency response characteristic. The slot also appears to introduce a capacitive reactance which counteracts the inductive reactance of the probe. The moment method analysis described in this chapter and in the references, with



"' 3::


----------------------- ---------1.5

1.0 0.8





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.



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 U-slot patch of Huynh and Lee (Figure 1.39) for h = 1.06 inch using the moment method-based 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 U-slot patch antenna is confirmed theoretically. Further confirmation using Finite Difference Time Domain (FDTD) analysis has also been obtained [ 42]. 1-6


This chapter presents a coherent account of recent work on probe-fed linearly polarized microstrip antennas, based mainly on the authors' research. This includes a spectral domain full-wave 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 two-layer stacked patches. In addition, the results of a recent wideband design in the form of a rectangular patch with a U-shaped slot have also been presented. REFERENCES [1] A. G. Demeryd, "A Theoretical Investigation or the Rectangular Microstrip Antenna," IEEE Trans. Antennas Propagat., Vol. AP-26, 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. AP-29, pp. 38-46, 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 Coaxially-Fed 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. AP-27, No. 2, pp. 137-145, 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. 424--432, 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. AP-30, No. 6, pp. 1191-1196, 1982.



[10] J. T. Aberle and D. M. Pozar, "Analysis of Infinite Arrays of Probe-Fed Rectangular Microstrip Patches Using a Rigorous Feed Model," IEE Proc., Vol. 136, Pt. H, No. 2, pp. 110-119, 1989. [11] J. T. Aberle and D. M. Pozar, "Accurate and Versatile Solutions for Probe-Fed Microstrip Patch Antennas and Arrays," Electromagnetic,, Vol.11, No. I, pp. 1-19, 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 Probe-Fed MicrostripDisk Antenna," IEE Proc., Vol. 138, Pt. H, pp. 185-191, 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. AP-27, No. 6, pp. 677-682, 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. AP-30, pp. 314-318, 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. 254-257, 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 Millimeter-Wave Computer-Aided Engg., Vol. 3, No. 4, pp. 340-349, 1993. [21] K. F. Lee, K. Y. Ho, and J. S. Dahele, 'Circular-Disc Microstrip Antenna with an Air Gap," IEEE Trans. Antennas Propagat., Vol. AP-32, pp. 880-884, 1984. [22] K. F. Lee, W. Chen, K. M. Luk, K. F. Tong. and R. Q. Lee, "Microstrip Antennas in Multi-Dielectric Media," Microwave Opt. Techno. Lett., Vol. 9, pp. 149-153, 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 AP-S Inter. Symp. Dig., pp. 397-400, 1985. [25] C. K. Aanandan, P. Mohanabm, and K. G. Nair, "Broad-Band Gap Coupled Antenna," IEEE Trans. Antennas Propagat., Vol. AP-38, pp. 1581-1586, 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. 835-837, 1987.



[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 AP-S Int. Symp. Dig., pp. 878-881, 1989. [29] M. R. Staker, J.C. MacKinchan, and J. S. Dahele, "Synthesis ofln-Line Parasitically








[37] [38] [39) [ 40]

[ 41]

[ 42]

Coupled Rectangular Microstrip Patch Antenna Subarrays," 18th Eur. Microwave Conf. Proc., Stockholm, Sweden, pp. 1069-1073, 1988. P. A Miller, J.C. MacKinchan, M. R. Staker, and J. S. Dahele, "A Wide Bandwidth, Low Sidelobe, Low Profile Microstrip Array Antenna for Communication Applications," Proc. ISAP'89, pp. 525-528. W. Chen, K . F. Lee and R. Q. Lee, "Spectral-Domain Moment-Method Analysis of Coplanar Microstrip Parasitic Subarrays," Microwave Optical Technol. Lett., Vol. 6, No. 3, pp. 157-163, 1993. R. Q. Lee, K. F. Lee, and J. Bobinchak, "Characteristics of a Two-Layer Electromag• netically Coupled Rectangular Patch Antenna," Electron. Lett. , Vol. 23, pp. 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. AP-38, 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 Probe-fed Stacked Circular Microstrip Antennas," IEEE Trans. Antennas Propagat., Vol. AP-39, 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. AP-39, pp. 12471251, 1991. Z. Fan and K. F. Lee, "Analysis of Electromagnetically Coupled Patch Antennas," Microwave Opt. Technol. Lett., Vol. 6, pp. 436-441, 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. 212-215, 1995. T. Huynh and K. F. Lee, "Single-Layer Single-Patch Wideband Microstrip Antenna," Electron. Lett., Vol. 31, No. 16, pp. 1310-1312, 1995. K. F. Lee, K. M. Luk, Y. L. Yung. K. F. Tong, and T. Huynh, "Experimental Study of the Rectangular Patch with a U-Shaped Slot," IEEE-APS Inter. Symp. Dig., pp. 10-13, 1996. K. F. Lee, K. M. Luk, K. F. Tong, Y. L. Yung, and T . Huynh, "Experimental Study of a Two-Element Array of U-Slot Patches," Electron. Lett., Vol. 32, No. 5, pp. 418-420, 1996. K. F . Lee, K. M. Luk, T. Huynh, K. F. Tong, and R. Q. Lee, "U-Slot Patch Wideband Microstrip Antenna," Proceedings of the 1996 WR! International Symposium, Plenum Press, New York, 1996.


Aperture-Coupled Multilayer Microstrip Antennas K. M. LUK, T. M. AU, K. F. TONG, and K. F. LEE



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, the coaxially fed microstrip antenna has an impedance bandwidth of 2-3%. By using parasitic elements to create dual or multiple resonances, the bandwidth can be improved to 10-20% but seldom exceeds 20% [1-9]. 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 0-471-04421-0 © 1997 John Wiley & Sons, lnc.






(k X' kY, z) =

f +rof+ro -,:o


(x I y I z)e -i,,l dx dy




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


d2 dz 2 F + k 2F = 0 where Im(k) e • 40"

Id) 9 • 40"





0 .9




0.7 \ 0.6



f; 0 .5






0.2 0.1


0 . 0 + - - - ~ - - - - -...... 2.0








2 .5

Frequency (GHz)






Frequency (GHz)

lb)8=50" 1.0..-------------,







0 .7

0.7 \

0 .6

0 .6


!: 0.5





0.2 0.1

0.2 ••.. ·




0.0+---~--~--...... 2.0

8• 50°





Frequency 1GHz)

(cl 0=60"



0.0+---~--~---1 2.0



3 .5 4 .0



Frequency (GHz) (f)



Scan characteristics of an infinite array of dual-patch 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








0.7 0.6

5 0.5 0.4





0 .2

0.1 ______ • . ··-:-::.-:., o.o.._ .....;c.:,...--l 2.0



3 .5 4.0




•· ,/.,.;!/

, ·_'>C.7 ':::_..j_1

0.0-1-------....a.-',-......./ 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Frequency (GHz)

Frequency (GHz) (a) 8= 40.,


(d)8 • 40" I.Or---------~

0 .9


0 .8





0 .6


!; 0.5




0.3 0 .2

/ . \ ..)v-....-·--·




0 . 0 + - - - - - - - - ' - - -....... 2.0 2.5 3.0 3.5 4.0 4.5 5.0



0 .0+-~~~·Yv_ .• ..a_.~ ·-_..:~ _ _ ,


2.5 3.0


4 .0



Frequency (GH2:)

Frequency (GHz)

Cb> 0. so• I.Or-----------,

8 • so• I.Or---------~



0 .8



0.7 0 .6

!: 0.5 0.4 0.3 0.2 0.1

• ..:,;

\ .:

0.0 -----------2.0


3 .0


4.0 4.5

Frequency (GHz) le) 8 =60°




2.5 3.0



4.5 5.0

Frequency (GHz)

(f) 8s60"

Scan characteristics of an infinite array of offset dual-patch microstrip

antenna with rectangular and triangular grids against frequency for different 0 scan volumes, x 1 = 1.0mm. (a- c) Rectangular grid. (d- f) Triangular grid. - - Broadside; - - - E plane; ---- D plane; - - - H plane. 116




Scan-Bandwidth(%) Rectangular Grid ({ = 90°)

o· 40•

so· 60°

Triangular Grid ((

= 60°)

Without Offset

With Offset

Without Offset

With Offset

59 49 42 27


59 50 43 37

61 53 49 40

50 43 29

frequency-independent matching networks were necessary to be inserted between the array elements and the feedlines. It is not easy to implement the desired dielectric constant of the upper layer, and frequency-independent matching networds are difficult to design over wide operating frequencies. It will be seen in the results that follow that the above disadvantages can be overcome by using an infinite array of dual-patch microstrip antennas with an air gap between the substrates supporting the patches. After selecting a set of element spacings of U. and U, and the scan angle (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 air-gap spacing between two patch substrates are 4.5 mm. The resonant lengths of the lower and upper patches are 19.8 mm and 20.2mm, 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 scan-bandwidth is obtained at higher scan angle 0. For this configur• ation, the scan-bandwidth is increased slightly if the patches are offset. The scan-bandwidths(%) of the configuration in different scan volumes IJ are tabulated in Table 2.12. We can conclude that the scan-bandwidth of an array can be optimized with appropriate a,. 2 , s,x 1, and U•.,·



1.0.,.-----------------.55 0.9 0.8




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


Reflection coefficient magnitude against frequency for an aperture-

coupled dual-patch 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 aperture-coupled dual-patch 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.


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



Green's functions. Piecewise simusoidal modes have been chosen as expansion and testing functions. The unknown reflection coefficient in the microstrip feedline has been formulated by using the reciprocity theorem. Different special cases of multilayer patch antennas have been examined. The tunable characteristic of an aperture-coupled patch antenna with an air gap between the antenna substrate and the ground plane has been investigated. The resonant frequency and the front-to-back ratio of this patch antenna increase, while the maximum input resistance and the E plane beamwidth decrease with increasing air gap width. The SWR bandwidth and far-field radiation patterns of coplanar microstrip subarrays have been studied. The parasitic elements are gap-coupled to the nonradiating edges of the fed patch. The parasitic elements can improve the antenna bandwidth and directivity, but high backlobe and cross-polarization levels have been found. Nevertheless, the maximum level of E plane cross-polarization is below - 30 dB across the passband. A microstrip subarray with a planar reflector has also been examined. In addition to the reduction in backlobe level, the bandwidth is also enhanced with a suitable distance between the reflector and the feed substrate. The radiation patterns do not vary significantly. The characteristics of an aperture-coupled dual-patch antenna have been evaluated. Maximum bandwidth is attained by choosing appropriate resonant lengths for the patches, substrate spacing, and offset displacement. The crosspolarization levels increase with offset displacements. The maximum level of cross-polarization at the E plane is about - 40dB. Beam squint has been observed in the E plane. Two versions of aperture-coupled two-layer microstrip antenna with stacked parasitic patches have been presented. For the five-patch design, large SWR bandwidth and narrow beamwidth can be obtained by using relatively large values of x 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 three-patch design, the effects of the positions and dimensions of two stacked parasitic elements on the input impedance, SWR bandwidth, and radiation patterns have been examined. A wideband design procedure is demonstrated. A full-wave analysis of infinite arrays of aperture-coupled patch antennas has been carried out. If a large scan volume is required, the element spacings in both oblique directions should be around 0.4-lo.. It is also found that an array with a triangular grid has the wider scan angle in the E plane. Computed results have been compared with experimental data for patch antennas with an air gap, a coplanar subarray, an offset dual-patch antenna, and an infinite array of dual-patch antennas. Reasonable agreement between theory and measurement has been obtained. The developed computer code can be used to generate design data for different structures at different operating frequency bands. Further work will be focused on the design of aperture-coupled multilayer CP microstrip antennas and arrays.


..., 0

APPENDIX: FOURIER TRANSFORMS OF EXPANSION AND TEST FUNCTIONS The one-dimensional Fourier transforms of the following expansion or test function modes are as follows:

{.!__ 2a




Edge condition

for lx-x0 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~(x-x 0 +a)

for lx - x0 l~a


for lx-x 0 1;;. a


sin k"a e- itx"°

for lx-x 0 1.;;a



na Ja' ,}x-x 0) 2 Traveling wave





k, is the effective wavenumber of the PWS mode. JO is the zeroth-order Bessel function oflirst kind.

for lx -x0 l"s• for lx-x0 1;;.a

k,a k:

coskxh- cosk)i e-lkx:ro

1- cosk,h


(mn:)2(- 1re-Jbo - e+Jt:.11 e-Jb%0


(2k.J 2 -(mn)2




J 0(k,a)e " 1''"'


2nb(k, + /J,)





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 Two-Layer Electromagnetically Coupled Rectangular Patch Antenna," Electron. Lett., Vol. 23, pp. 10701073, 1989; see also IEEE Trans. Antennas Propagat., Vol. AP-38, pp. 1298-1302, 1987. [2] R. Q. Lee and K. F. Lee, "Gain Enhancement of Microstrip Antennas with Overlaying Parasitic Directors," Electron. Lett., Vol. 24, pp. 656- 658, 1988. [3] 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. 163-170, 1990. [ 4] L. Barlatey, J. R. Mosig and T. Sphicopoulos, "Analysis of Stacked Microstrip Patches with a Mixed Potential Integral Equation," IEEE Trans. Antennas Propagat., Vol. AP-38, pp. 608-615, 1990. [5] P. S. Bhatnagar, J. P. Daniel, K. Mandjoubi, and C. Terrel, "Displaced Multilayer Triangular Elements Widen Antenna Bandwidth," Electron. Lett, Vol. 24, pp. 962-964, 1988. [6] G. Kumar and K. C. Gupta, "Nonradiating Edges and Four Edges Gap-Coupled Multiple Broad-Band Microstrip Antenna," IEEE Trans. Antennas Propagat., Vol. AP-33, pp.173-178, 1985. [7] W. Chen, K. F. Lee, and R. Q. Lee, "Spectral Domain Moment-Method Analysis of Coplanar Microstrip Parasitic Subarrays," Microwave Opt. Technol. Lett., Vol. 6, No. 3, pp.157-163, 1993. [8] K. F. Lee, W. Chen, and R. Q. Lee, "Studies of Stacked Electromagnetically Coupled Patch Antennas," Microwave Opt. Technology Lett., Vol. 8,No.4,pp.212-215, 1995. [9] A. N. Tulintsett, S. M. Ali, and J. A. Kong, "Input Impedance ola Probe-Fed Stacked Circular Microstrip Antenna," IEEE Trans. Ante1111as Propagat., AP-39, pp. 12471251, 1991. [!OJ D. M. Pozar, "Microstrip Antenna Aperture-Coupled 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 AP-S Int. Symp. Dig., pp. 878-881, 1989. [12] F. Croq, and D. M. Pozar, "Millimeter-Wave Design of Wide-Band ApertureCoupled Stacked Microstrip Antenna," IEEE Trans. Antennas Propagat., Vol. AP-39, pp. 1770-1776, 1991. [13] D. M. Pozar, "A Reciprocity Method of Analysis for Printed Slot and Slot-Coupled Microstrip Antennas," IEEE Trans. Antennas Propagat., AP-34, pp. 1439- 1446, 1986.



[14] D. M. Pozar," Analysis ofao Infinite Phased array of Aperture-Coupled Microstrip Patches," IEEE Trans. Antennas Propagat., AP-37, 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, "Full-Wave Analysis ofMicrostrip Open-End and Gap Discontinuities", IEEE Trans. Microwave Theory Techniques, Vol. MTT-33,

pp. 1036- 1042, 1985. [17] D. M. Pozar, "Input Impedance and Mutual Coupling of Rectangular Microstrip Antenna," IEEE Trans. Antennas Propagat., AP-30, 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, McGraw-Hill, New York, 1985. [20] Z. fan and K. F. Lee, "Spectral Domain Analysis of Rectangular Microstrip Antennas with an Air gap," Microwave Opt. Technol. Lett., Vol. 5, No. 7, pp. 315-318, 1992. [21] H. Legay and L. Shafai, "New Stacked Microstrip Antenna with Large Bandwidth and High Gain;' IEE Proc. Microwave Antennas Propagat., Vol. 141 , No. 3, pp. 199-204, 1994. (22] A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering, Prentice-Hall, New York, 1991. (23] J. 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. AP-39, pp.1247-1251 , 1991. [25] T. M . Au, K. F. Tong, and K. M. Luk, "Analysis of Offset Dual-Patch Microstrip Antenna," IEE Proc. Microwave Antennas Propagat., Vol. 141, No. 6, pp. 523-526,

1994. [26] Y. Lubin and A. Hessel, "Wide-Band, Wide-Angle Microstrip Stacked-PatchElemeot Phased Arrays, IEEE Trans. Antennas Propagat., Vol. AP-39, pp. 10621070, 1991. [27] J. T. Aberle, D. M. Pozar, and J. Manges, "Phased Arrays of Probe-Fed Stacked Microstrip Patches," IEEE Trans. Antennas Propagat., Vol. AP--42, pp. 920--927, 1994.


Microstrip Arrays: Analysis, Design, and Applications JOHN HUANG and DAVID M. POZAR



In many microstrip antenna applications, systems requirements can be met with a single patch element. In other cases, however, systems require higher antenna gains while maintaining a low-profile structure, which calls for the development of microstrip arrays. This chapter explores the analysis techniques, design methodology, and applications of microstrip array antennas for current and future advanced systems. Microstrip arrays, due to their extremely thin profiles (0.01-0.05 free-space wavelength), offer three outstanding advantages relative to other types of antennas [1-3]: 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 high-gain 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 power-handling capability. To minimize these effects, accurate analysis techniques, optimum design methods, and innovative array concepts are imperative to the successful development of a microstrip array antenna. For example, accurate analysis and a correct design approach can often overcome deficiencies in such performance factors as mutual coupling, beam Advances in Microstrip and Printed Antennas, Edited by Kai Fong Lee and Wei Chen. © 1997 John Wiley & Sons, Inc

ISBN 0-471-04421.0




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

3.2 ANALYSIS TECHNIQUES FOR MICROSTRIP ARRAYS Accurate, flexible, and computationally efficient analysis techniques are important for antenna design primarily to reduce costly and time-consuming experimental cut-and-try design cycles. Analysis can also provide a more complete understanding of the operation of an antenna and can aid in optimizing its performance or determining limitations in its performance. As discussed in reference [ 4], micros trip elements can often be successfully designed with little or no computer-aided design (CAD) support, but the increased complexity of microstrip arrays is more often facilitated by the availability of robust CAD tools. Another factor in the evaluation of the current state of the art in microstrip antennas analysis and associated CAD software is that there is a very wide variety of element geometries, feeding methods, and substrate configurations for practical microstrip antennas and arrays. The majority of microstrip arrays are designed as fixed-beam broadside antennas, often with the feed network located coplanar with the array elements for purposes of simplicity and economics. In this case, the design procedure can be broken into the fairly disparate steps of element design, array layout and spacing, and feed design. The design of the radiating element involves considerations such as the bandwidth and polarization specifications. The grid layout, the number, and the spacing of the array elements are determined by the required principal plane beamwidths, or the gain, of the array. The feed network is a function of the amplitude tapers required for the sidelobe specification, impedance matching to the elements, and the array bandwidth and may take the form of a series feed or a corporate feed. Fortunately, mutual coupling can often be ignored for 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 millimeter-wave frequencies (higher than about 20 GHz) (5]. In these cases, loss



and tolerance effects may accumulate sufficiently to cause severe performance degradation, and it becomes critical to have CAD design tools based on solid analysis. Such tools are only partially available at the present time. The design and analysis of scanning phased microstrip arrays is another situation that typically requires rigorous and versatile CAD software. The primary driver for this requirement is the fact that such antennas are very expensive because of the phase shifter or T /R module cost per element, so it is critical that antenna performance be analyzed and optimized accurately and thoroughly-. Experimental trials using small arrays, active element patterns, and waveguide simulators can play an important role in the design process, but accurate CAD models can provide much more information about important effects such as scan blindness, impedance mismatch, losses, random errors, sidelobe levels, and cross-polarization as a function of any design parameter. Unlike the case for fixed beam arrays, scanning arrays usually do require the inclusion of mutual coupling effects, as well as the effect of the feed network, for a complete characterization of the array. This is a very difficult problem in general, especially for arrays that have more than a few elements (so that coupling effects are important) but are too small to apply the infinite array approximation . .In the following sections we will present a brief review of several analysis techniques for microstrip arrays and then concentrate on full-wave moment method techniques for single elements, mutual coupling between elements, and infinite array analysis. We will also discuss the use of the active element pattern and waveguide simulators in array design.

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



as providing an intuitive explanation for the operation of the microstrip element. Generally they give good results for antennas on thin, low-dielectric constant substrates. While originally developed for probe-fed and line-fed elements, models of this type have also been proposed for more complicated structures such as the aperture coupled patch element [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

Full-Wave Moment Method Analysis

Microstrip antenna models that account for the dielectric substrate in a rigorous manner are referred to as full-wave solutions. Thus "full-wave" may be used to describe FDTD or finite element solutions, but most of the full-wave analyses of microstrip antennas have been moment method solutions using the exact Green's function for the dielectric substrate. This techniques enforces the boundary conditions at tbe air-dielectric 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 full-wave moment method procedure here. The equivalence theorem is used to replace conducting patch elements with equivalent electric surface currents, and slot elements are replaced with equivalent magnetic currents. A moment method solution is then derived from the enforcement of the continuity of electric or magnetic fields at the patch or slot elements. The fields from these current elements are found using the exact Green's function for the substrate geometry, which can be derived in closed form for a wide variety of multilayer substrates consisting of isotropic, anisotropic, ferrite, or chiral materials [3, 11]. The key calculation in this procedure then becomes the evaluation



of impedance matrix elements having the general form


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 full-wave 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


F,(k,,k,) ·G(k,,k,) ·F;(k,,k,)dad{J


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 self-impedance terms because it eliminates the need for special treatment of the source singularity. There is still a surface wave pole associated with the TM 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



FIGURE 3.1 Measured and calculated input impedance of an aperture-coupled 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,