MICROSTRIP AND PRINTED ANTENNAS - Startseite · 10.2.1 Antenna Design 311 10.2.2 Parametric Study...
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MICROSTRIP AND PRINTED ANTENNAS NEW TRENDS, TECHNIQUES AND APPLICATIONS Editors Debatosh Guha Institute of Radio Physics and Electronics, University of Calcutta, India Yahia M.M. Antar Royal Military College, Canada
Transcript of MICROSTRIP AND PRINTED ANTENNAS - Startseite · 10.2.1 Antenna Design 311 10.2.2 Parametric Study...
MICROSTRIP ANDPRINTED ANTENNASNEW TRENDS, TECHNIQUESAND APPLICATIONS
Editors
Debatosh GuhaInstitute of Radio Physics and Electronics, University of Calcutta, India
Yahia M.M. AntarRoyal Military College, Canada
MICROSTRIP ANDPRINTED ANTENNAS
MICROSTRIP ANDPRINTED ANTENNASNEW TRENDS, TECHNIQUESAND APPLICATIONS
Editors
Debatosh GuhaInstitute of Radio Physics and Electronics, University of Calcutta, India
Yahia M.M. AntarRoyal Military College, Canada
This edition first published 2011
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Library of Congress Cataloging-in-Publication Data
Microstrip and printed antennas : new trends, techniques, and applications /
edited by Debatosh Guha, Yahia M.M. Antar.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-68192-3 (cloth)
1. Microstrip antennas--Design. 2. Polarization (Electricity) I. Guha,
Debatosh. II. Antar, Yahia.
TK7871.67.M5M53 2011
621.382’4–dc22
2010022377
A catalogue record for this book is available from the British Library.
Print ISBN: 9780470681923 (hb)
ePDF ISBN: 9780470973387
oBook ISBN: 9780470973370
Set in 10/12 pts Times New Roman by Thomson Digital, Noida, India
Contents
Preface xiii
List of Contributors xix
Acknowledgments xxi
1 Numerical Analysis Techniques 1
Ramesh Garg
1.1 Introduction 1
1.2 Standard (Yee’s) FDTD Method 3
1.3 Numerical Dispersion of FDTD and Hybrid Schemes 5
1.3.1 Effect of Non-Cubic Cells on Numerical Dispersion 6
1.3.2 Numerical Dispersion Control 7
1.4 Stability of Algorithms 11
1.5 Absorbing Boundary Conditions 12
1.5.1 Analytical Absorbing Boundary Conditions 13
1.5.1.1 Liao’s ABC 14
1.5.2 Material-Absorbing Boundary Conditions 17
1.5.3 Perfectly Matched Layer ABC 19
1.5.4 Uniaxial PML 19
1.6 LOD-FDTD Algorithm 22
1.6.1 PML Absorbing Boundary Condition for LOD-FDTD 28
1.7 Robustness of Printed Patch Antennas 29
1.8 Thin Dielectric Approximation 29
1.9 Modeling of PEC and PMC for Irregular Geometries 30
References 32
2 Computer Aided Design of Microstrip Antennas 35Debatosh Guha and Jawad Y. Siddiqui
2.1 Introduction 35
2.2 Microstrip Patch as Cavity Resonator 36
2.3 Resonant Frequency of Circular Microstrip Patch (CMP) 37
2.3.1 Suspended Substrate with Variable Air Gap 38
2.3.2 Inverted Microstrip Circular Patch (IMCP) 42
2.3.3 IMCP Enclosed in a Cylindrical Cavity 44
2.3.4 Superstrate Loaded Circular Microstrip Patch (SL-CMP) 45
2.4 Resonant Frequency of Rectangular Microstrip Patch (RMP)
with Variable Air Gap 47
2.5 Resonant Frequency of Equilateral Triangular Microstrip
Patch (ETMP) with Variable Air Gap 50
2.6 Input Impedance of a Microstrip Patch 51
2.6.1 Input Impedance of CMP 53
2.6.2 Input Impedance of IMCP 55
2.6.3 Input Impedance of RMP 56
2.6.4 Input Impedance of an ETMP 57
2.7 Feed Reactance of a Probe-Fed Microstrip Patch 59
2.8 Radiation Characteristics 59
2.8.1 Rectangular Microstrip Patch 60
2.8.2 Circular Microstrip Patch 61
2.9 Radiation Efficiency 61
2.10 Bandwidth 62
2.11 Conclusion 62
References 62
3 Generalized Scattering Matrix Approach for MultilayerPatch Arrays 65
Arun K. Bhattacharyya
3.1 Introduction 65
3.2 Outline of the GSM Approach 67
3.2.1 The GSM 67
3.3 Mutual Coupling Formulation 68
3.3.1 Mutual Impedance 69
3.4 Finite Array: Active Impedance and Radiation Patterns 71
3.5 Numerical Example 72
3.6 Conclusion 76
References 76
4 Optimization Techniques for Planar Antennas 79
Rabindra K. Mishra
4.1 Introduction 79
4.2 Basic Optimization Concepts 79
4.2.1 Cost (Fitness) Function 79
4.2.2 Design Parameters and Space 80
4.2.3 Global and Local Minima 80
4.3 Real Coded Genetic Algorithm (RCGA) 80
4.3.1 Genetic Algorithm 80
4.3.1.1 RCGA Design 83
4.3.1.2 Genetic Operators 83
4.3.1.3 Heuristic Crossover and Adewuya Mating (Quadratic
Crossover) 85
vi Contents
4.3.2 Sierpinski Gasket Fractal Microstrip Antenna Design 85
4.3.2.1 RCGS Strategy for SGMA 86
4.4 Neurospectral Design of Rectangular Patch Antenna 91
4.4.1 Model Development 93
4.4.1.1 Spectral Domain Formation 93
4.4.1.2 Artificial Neural Network Solution Technique 96
4.4.1.3 Closed Form Expressions for Integration 97
4.4.1.4 Data Generation and Pre-processing 98
4.4.2 Model Implementation 99
4.4.2.1 Simple Patch Antenna 99
4.4.2.2 Feeding Considerations 101
4.4.2.3 Any Other Arbitrary Shape 104
4.4.2.4 Points to Note 104
4.5 Inset-fed Patch Antenna Design Using Particle Swarm
Optimization 106
4.5.1 Explanation of PSO Terms 106
4.5.2 Inset-fed Patch Antenna Design 107
4.6 Conclusion 109
References 110
5 Microstrip Reflectarray Antennas 113
Jafar Shaker and Reza Chaharmir
5.1 Introduction 113
5.2 General Review of Reflectarrays: Mathematical Formulation and
General Trends 114
5.2.1 Mathematical Formulation 114
5.2.2 General Trends 118
5.3 Comparison of Reflectarray and Conventional Parabolic
Reflector 120
5.3.1 Illumination Efficiency 121
5.3.2 Spill-over Efficiency 122
5.3.3 Polarization Efficiency 122
5.3.4 Phase Efficiency 123
5.3.5 Blockage Efficiency 123
5.4 Cell Elements and Specific Applications: A General Survey 124
5.5 Wideband Techniques for Reflectarrays 133
5.5.1 Phase Response of Reflectarrays 136
5.5.2 Verification of the Optimization Method 144
5.6 Development of Novel Loop-Based Cell Elements 149
5.6.1 Motivation 149
5.6.2 Square Ring Cell Element 151
5.6.3 Cross-Ring Cell Element 153
5.6.4 Hybrid Cell Element 153
5.7 Conclusion 157
References 157
Contents vii
6 Reconfigurable Microstrip Antennas 161
Jennifer T. Bernhard
6.1 Introduction 161
6.2 Substrate Modification for Reconfigurability 162
6.3 Conductor Modification for Reconfigurability 163
6.3.1 Frequency Reconfigurability 163
6.3.2 Pattern Reconfigurability 167
6.3.3 Polarization Reconfigurability 170
6.4 Enabling Reconfigurability: Considerations for Reconfiguration
Mechanisms 175
6.5 Future Trends in Reconfigurable Microstrip Antenna Research
and Development 178
References 179
7 Wearable Antennas for Body Area Networks 183
Peter S. Hall and Yang Hao
7.1 Introduction 183
7.1.1 Overview 183
7.1.2 Domains of Operation 184
7.1.3 Antenna Parameters 184
7.2 Sources on the Human Body 185
7.2.1 Electrical Properties of the Human Body 185
7.2.2 Sources and Waves on the Body 186
7.3 Narrowband Antennas 187
7.3.1 Performance Changes Due to Body Proximity 187
7.3.2 Antenna Types 188
7.4 Fabric Antennas 194
7.4.1 Fabric Materials 194
7.4.2 Antenna Types 195
7.5 Ultra Wideband Antennas 197
7.5.1 Antenna Types 199
7.5.2 Antenna On-body and Off-body Performance 199
7.5.3 Antenna Fidelity and Transient Analysis 205
7.6 Multiple Antenna Systems 209
7.6.1 Diversity 209
7.6.2 MIMO 209
7.7 Conclusion 210
References 210
8 Printed Antennas for Wireless Communications 215
Satish K. Sharma and Lotfollah Shafai
8.1 Introduction 215
8.2 Broadband Microstrip Patch Antennas 215
8.2.1 Single Layer Broadband Patch Antennas 216
8.2.2 Feed Mechanism Modification for Broadband Patch Antennas 218
viii Contents
8.2.3 Artificial Magnetic Ground Planes for Broadband
Patch Antennas 221
8.3 Patch Antennas for Multiband Wireless Communications 225
8.4 Enhanced Gain Patch Antennas 229
8.5 Wideband Compact Patch Antennas 232
8.6 Microstrip Slot Antennas 234
8.6.1 Principle of Radiation and Limitations 234
8.6.2 Wideband Microstrip Slot Antennas and Size Reduction 235
8.6.3 Ultra-Wide Bandwidth (UWB) Slot Antennas 238
8.6.4 Multiband Slot Antennas 242
8.6.5 Differential Dual-Frequency Slot Antennas 249
8.7 Microstrip Planar Monopole Antenna 252
References 260
9 UHF Passive RFID Tag Antennas 263
Daniel Deavours and Daniel Dobkin
9.1 Introduction 263
9.2 Application Requirements 264
9.2.1 Electrically Small 264
9.2.2 Variable and Uncontrollable Dielectric Environment 265
9.2.3 Variable Orientation 266
9.2.4 Tag IC Requirements 267
9.2.5 Cost Pressures 268
9.3 Approaches 269
9.3.1 Meander Dipole 271
9.3.2 Tip Loading 274
9.3.3 Combined Meander and Load 274
9.3.4 Fat Dipole 276
9.3.5 Slot Antennas for Tags 278
9.3.6 Dual Dipole Antennas 279
9.3.7 Matching: A Case Study 280
9.3.8 Microstrip Patch Antennas 288
9.4 Fabrication 294
9.4.1 Antenna 295
9.4.1.1 Plating and Etching 295
9.4.1.2 Silver Ink Screen Printing 295
9.4.1.3 Vapor Deposition 296
9.4.1.4 Deposition and Laser Ablation 297
9.4.1.5 Printing and Plating 297
9.4.1.6 Electroless (Chemical) Deposition 297
9.4.1.7 Die Cut 297
9.4.2 Assembly 299
9.4.2.1 Bondwires 299
9.4.2.2 Flip-Chip and Anisotropic Conductive Adhesives 299
9.4.2.3 Straps 299
9.4.2.4 Fluidic Self-Assembly 300
Contents ix
9.5 Conclusion 302
Acknowledgments 302
References 302
10 Printed UWB Antennas 305Zhi Ning Chen, Xianming Qing and Shie Ping See
10.1 Introduction 305
10.2 “Swan” Antenna with Reduced Ground Plane Effect 309
10.2.1 Antenna Design 311
10.2.2 Parametric Study 313
10.3 Slim UWB Antenna 315
10.3.1 Antenna Design 315
10.3.2 Parametric Study 318
10.4 Diversity Antenna 319
10.4.1 Antenna Design 320
10.5 Printed Slot UWB Antenna and Band-Notched Solutions 325
10.5.1 Wide-Slot UWB Antenna 326
10.5.2 Monopole-Like Slot UWB Antenna 330
10.5.3 Band-Notched UWB Antennas 331
References 340
11 Metamaterial Antennas and Radiative Systems 345Christophe Caloz
11.1 Introduction
11.2 Fundamentals of Metamaterials 345
11.2.1 Resonant Particle (RP) Metamaterials 346
11.2.2 Transmission Line (TL) Metamaterials 346
11.2.3 Relation between RP and TL Metamaterials 348
11.3 Leaky-Wave Antennas 353
11.3.1 Fundamentals 354
11.3.2 Leaky-Wave Properties of CRLH Metamaterials 354
11.3.3 Fan Beam 355
11.3.4 Conical Beam 355
11.3.5 Pencil Beam 358
11.3.6 Efficiency Enhancement by Power Recycling 358
11.3.7 Active Beam Shaping 359
11.4 Resonant Antennas 361
11.4.1 Fundamentals 361
11.4.2 Resonant Properties of CRLH Metamaterials 363
11.4.3 Multi-Band 363
11.4.4 Zeroth Order Resonance 364
11.4.5 High Directivity 367
11.4.6 Electric/Magnetic Monopoles 367
11.5 Exotic Radiative Systems 370
11.5.1 Magnetic Resonance Imaging Coils 370
11.5.2 Uniform Ferrite CRLH Leaky-Wave Antenna 371
x Contents
11.5.3 Uniform Ferrite CRLH Integrated Antenna-Duplexer 373
11.5.4 Direction of Arrival (DOA) Estimator 376
11.5.5 Real-Time Spectrum Analyzer (RTSA) 376
11.5.6 Talbot Spatial Power Combiner 382
References 383
12 Defected Ground Structure for Microstrip Antennas 387
Debatosh Guha, Sujoy Biswas, and Yahia M. M. Antar
12.1 Introduction 387
12.2 Fundamentals of DGS 387
12.2.1 Evolution 387
12.2.2 Definition and Basic Geometries 388
12.2.2.1 Unit Cell DGS 390
12.2.2.2 Periodic DGS 395
12.2.3 Modeling of DGS 397
12.2.4 Popular Applications to Printed Circuits 404
12.3 DGS for Controlling Microstrip Antenna Feeds and Front-End
Characteristics 408
12.3.1 Basic Idea 408
12.3.2 Harmonic Control in Active Microstrip Antennas 409
12.3.3 Isolation at Microstrip Antenna Front-Ends 412
12.3.4 Impedance Matching for Microstrip Feed Design 414
12.4 DGS to Control/Improve Radiation Properties of Microstrip
Patch Antennas 414
12.4.1 Basic Idea 414
12.4.2 Suppression of Cross-Polarized Radiations from Microstrip
Patches 415
12.5 DGS for Reduced Mutual Coupling Between Microstrip Array
Elements and Associated Improvements 420
12.5.1 Basic Idea 420
12.5.2 Ring-Shaped DGS for Circular Patch Array 424
12.5.3 Dumbbell-Shaped DGS for Rectangular Patch Array 425
12.5.4 Elimination of Scan Blindness of Microstrip Phased Array 427
12.6 Conclusion 429
Appendix: A Brief DGS Chronology 430
References 431
13 Printed Leaky Wave Antennas 435Samir F. Mahmoud and Yahia M.M. Antar
13.1 Introduction 435
13.2 The Leaky Wave as a Complex Plane Wave 436
13.3 Radiation Pattern of a Leaky Wave 437
13.3.1 Unidirectional Leaky Wave 437
13.3.2 Bidirectional Radiation Pattern 440
13.4 Examples of Leaky Mode Supporting Structures 441
13.4.1 A Two Parallel Plate Leaky Waveguide 441
Contents xi
13.4.2 A Two-Layer Leaky Wave Structure 444
13.5 The Excitation Problem 447
13.5.1 Radiation Field in Terms of the Leaky Mode Pole 449
13.5.2 A Numerical Example 449
13.6 Two-Dimensional Leaky Waves 451
13.6.1 Leaky Wave Antennas with Periodic Screen 451
13.6.1.1 Boundary Conditions 453
13.6.1.2 Radiated Power and Surface Wave Power 454
13.6.2 Characterization of the Periodic Screen as an EBG Structure 456
13.7 Further Advances on a Class of Periodic Leaky Wave Antennas 457
13.7.1 Broadside Radiation 459
13.7.2 Frequency Scanning 459
13.7.3 Cylindrical Leaky Wave Antenna Design 460
References 461
Appendix I Preliminary Ideas: PTFE-Based Microwave Laminates and Making
Prototypes 463
Appendix II Preliminary Ideas: Microwave Connectors for Printed
Circuits and Antennas 469
Index 477
xii Contents
Preface
Microstrip technology has been popular for microwave andmillimeter wave applications since
the 1970s and recently has taken off, with the tremendous growth in communications, wireless,
as well as space-borne/airborne applications, although the concept dates back to 1952 [1]. The
basic microstrip configuration is very similar to a printed circuit board (PCB) used for low
frequency electronic circuits. It constitutes a low-loss thin substrate, both sides being coated
with copper film. Printed transmission lines, patches, etc. are etched out on one side of the
microstrip board and the other copper-clad surface is used as the ground plane. In between the
ground plane and the microstrip structure, a quasi-TEM electromagnetic wave is launched and
allowed to spread.
Such a structure offers some unique basic advantages such as low profile, low cost, light
weight, ease of fabrication, suitability to conform on curved surface, etc. All these have made
microstrip technology attractive since the early phase of its development.
Within a year of the pioneering article “Microstrip – a new transmission technology for the
kilomegacycle range” appearing [1], Deschamps [2] had conceived of microstrip as
“microwave antenna.” But its practical application started nearly two decades later. Howell [3]
and Munson [4] may be regarded as the pioneer architects of microstrip antenna engineering.
These early developments immediately attracted some potential research groups and the
following studies were mainly concerned with theoretical analysis of different patch geome-
tries and experimental verifications [5–12]. A parallel trend also developed very quickly and
some researchers tried to implement conventional antennas such as dipole, wire, aperture, etc.
in planar form [13–16]. They are commonly referred to as printed circuit antennas or simply
printed antennas. Their operations and characteristics are completely different from those due
to microstrip patches, although microstrip patch antennas, in many papers, are casually called
printed circuit antennas. The topic printed antenna had acquired tremendous importance by the
late 1970s and a three-day workshop held at New Mexico State University in Las Crises in
October, 1979 was dedicated to Printed Circuit Antenna Technology.
The developments inmicrostrip antennas that occurred up to the late1970swere documented
by Bahl and Bhartia in their famous book [17], published in 1980. The analysis and design
aspects were addressed in another book by James, Hall and Wood [18], published in 1981. A
contemporary article by Carver andMink [19] discussed the fundamental aspects of microstrip
antennas and this is still regarded as a good review paper for a beginner.
More activities in the area grew gradually and many applications were realized. The
suitability of deploying such lightweight low profile antennas in airborne and space-borne
systems initiated major developments in microstrip array technology.With the development of
mobile and wireless communications, microstrip and other printed antennas attained a new
focus to serve in different technology from themobile handset to base station antennas. General
information, gathered from journals, symposia and conference articles, reveals that about 50%
of the whole antenna community has been active in microstrip or printed antenna practice for
the past two or three decades.
The first handbook [20] was published in 1989, nearly a decade after the first book by Bahl
and Bhartia [17]. Within another five years, microstrip antenna research had attained a level of
maturity as is reflected in the title and topics of the microstrip antenna books published around
the middle of 1990s [21–23]. The edited volume by Pozar and Shaubert [21] contains some
published articles bearing the results of contemporary interests, such as bandwidth enhance-
ment approaches, analysis and design techniques, aperture coupling and other feeding
methods, active integrated antennas, conformal and phased arrays, etc. Narrow impedance
bandwidth appears an inherent limitation of the microstrip element. The research and
consequent developments in bandwidth enhancement were documented in [22]. Lee and
Chen [23] covered some key areas of advances reported up to 1997.
The growing need and interest in microstrip antenna designs are reflected in three design
handbooks [24–26] published at close interval from 2001 to 2004. Compacting, along with
bandwidth widening of printed antennas, has attracted worldwide interest to support new
wireless technology since the beginning of this century and its importance was reflected in
titles [27–32] which appeared between 2002 and 2007.
The book edited by Lee andChen [23] was a timely effort to incorporatemajor technological
developments that had occurred up to1997, under the same cover. Since then, more than a
decade has passed during which many new trends, techniques and applications in planar
antenna technology have been developed. For example,RFID (Radio Frequency Identification)
is an ideal example to showcase the need to this day. This application needs low cost antennas,
printed on paper or very thin substrate. Another example is printed antenna using unconven-
tional and new innovations, such as using metamaterials and defected ground structures
(DGSs). Replacing a large parabolic dish with a flat microstrip array with a special feeding
mechanism is also a new area of activity. The design of small ultrawideband (UWB) antennas
with good performance is a challenging area. Antenna for the body area network is another
interesting new topic.
From our long experience in teaching andmentoring doctoral and post-doctoral students and
working with practicing engineers, we certainly feel there is a need for a book that is to address
more recent topics of microstrip and printed antennas. We have chosen some topics that have
recently been developed or have considerably advanced during the past decade and at the same
time appear to be important to the new generation of researchers, developers and application
engineers. We shared the ideas with some of our colleagues and friends who are the real
technical experts and potential developers in those selected topics. They fully agreed with our
views, gave valuable suggestions and delivered on their promise to contribute. Our collabora-
tive efforts have finally culminated in the present title.
As indicated by the title, the focus is on the New Trends, Techniques and Applications of
Microstrip and Printed Antennas. The chapters are organized as follows: Chapters 1–4 address
advances in design, analysis, and optimization techniques, Chapters 5–10 focus on some
important new techniques and applications, Chapters 11 and 12 deal with engineered materials
xiv Preface
applied to printed antenna designs, and finally Chapter 13 addresses advanced methods and
designs of printed leaky wave antenna.
Chapter 1 deals with numerical techniques, which are essential in analyzing and designing
planar antennas of any arbitrary geometry. A brief overview of the commonly usedmethods are
discussed and the finite difference time domain (FDTD) technique is elaborated on, with
special emphasis on the recent developments that occurred after 2003. Chapter 2 presents the
advances in computer aided designs (CAD) of microstrip antennas reported during 2001 and
onwards. The aim of this chapter is to provide accurate closed form expressions, which can be
reliably used to compute essential design parameters such as operating frequency, input
impedance and matched feed-location for a given antenna involving single or multiple
dielectric layers. Chapter 3 embodies the Generalized Scattering Matrix (GSM) approach to
analyzing the multilayer finite printed array structures. The methodology is demonstrated
through examples. Chapter 4 deals with antenna optimization techniques. Optimization in
terms of performance, size and cost is discussed and the basic concept of stochastic
optimization techniques is demonstrated.
Chapter 5 describes microstrip reflectarray technology, its general principle, design,
operation, and applications. Microstrip’s inherent demerit of narrow bandwidth is dealt with
in terms of spatial and frequency dispersions and some of the techniques to suppress these
factors are presented. Chapter 6 deals with Reconfigurable Microstrip Antennas, which use
switches, tunable materials, or control circuitry to give additional degrees of operational
freedom or to make a single element operative in multiple frequencies. A wide variety of
reconfigurability is discussed. The emerging trends and directions for future research have also
been indicated.
Chapter 7 describes wearable antennas for body area networks. The properties of the human
body in terms of electromagnetic radiations and the performance of multiple antenna systems
in presence of the human body are described. Chapter 8 presents printed wireless antennas.
These include three primary configurations: microstrip patch, slot, and monopole showing
multiband, wideband, or ultra wideband performances. Significant developments reported
since 2000 are addressed in this chapter. Chapter 9 deals with printed antennas for RFID tags.
An RFID systemmay be one of the following types: active, passive, or in between of these two,
based on the nature of the devices used and also any of LF, HF, or UHF type based on the
frequency of operations. Passive tags operating at UHF place several specialized requirements
on the associated antenna structures and these are described in this chapter. Chapter 10 deals
with printed antennas for ultra-wideband (UWB) applications. This incorporates the innovative
technologies to minimize ground plane effects on the performance of small printed antennas.
Chapter 11 presents applications of metamaterials to planar antenna and radiative system
designs. Both leaky wave and resonant metamaterial antennas are discussed with special
emphasis on their recent and somewhat exotic applications. Chapter 12 deals with defected
ground structures (DGS) applied to microstrip antennas. This is a recently developed topic and
all the major developments that have occurred after 2002 are discussed, indicating the future
scope of development. This is probably addressed here as an exclusive book chapter for the first
time. Chapter 13 concludes with printed leakywave antennas. It includes both theory and some
applications based on recent advances in technology.
Each chapter is designed to cover the range from fundamental concepts to the state-of-the-art
developments.Wehave tried to satisfy awide cross-section of readers.A student or a researcher
may consider this a guide book to understanding the strength and weaknesses of the
Preface xv
contemporary topics. To a practicing engineer, we hope that the book will be a ready reference
tomany new areas of applications. To an educator, the book appears as a comprehensive review
and a source of up-to-date information.
Our sincere efforts and exercise will be successful if our readers appreciate and find it useful
for their respective purposes.
Debatosh Guha
Yahia M. M. Antar
References
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of microstrip antennas,” IEEE Trans. Antennas Propagat., vol. 27, no. 2, pp. 267–270, 1979.
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Letters, vol. 14, no. 24, pp. 767–769, 1978.
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Conference, 1979, pp. 687–691, 1979.
16. A.Mulyanto, and R. Vernon, “AV-shaped log-periodic printed-circuit antenna array for the 1 to 10 GHz frequency
range,” Antennas and Propagation Society Intl. Symp., 1979, vol. 17, pp. 392–395.
17. I. J. Bahl and P. Bhartia, Microstrip Antennas, Artech House, Dedham, MA, 1980.
18. J. R. James, P. S. Hall and C. Wood,Microstrip Antennas: Theory and Design, Peter Peregrinus, London, 1981.
19. K. Carver and J.Mink, “Microstrip antenna technology,” IEEE Trans. Antennas Propagat., vol. 29, pp. 2–24, Jan.
1981.
20. J. R. James and P. S. Hall, Handbook of Microstrip Antennas, Peter Peregrinus, London, 1989.
21. D. M. Pozar and D. H. Schaubert, Microstrip Antennas, IEEE Press, New York, 1995.
22. J. F. Z€urcher and F. E. Gardiol, Broadband Patch Antennas, Artech House, Boston, 1995.
23. K. F. Lee andW. Chen, Advances in Microstrip and Printed Antennas, JohnWiley & Sons, Inc., NewYork, 1997.
24. R. Garg et al., Microstrip Antenna Design Handbook, Artech House, Boston, 2001.
25. R. Waterhouse, Microstrip Patch Antennas: A Designer’s Guide, Springer, Berlin, 2003.
26. R. Bancroft, Microstrip and Printed Antenna Design, Noble Publishing, 2004.
27. Kin-Lu Wong, Compact and Broadband Microstrip Antennas, John Wiley & Sons, Inc., New York, 2002.
xvi Preface
28. G. Kumar and K. P. Ray, Broadband Microstrip Antennas, Artech House, Boston, 2002.
29. Kin-Lu Wong, Planar Antennas for Wireless Communications, John Wiley & Sons, Inc., New York, 2003.
30. Zhi NingChen andMichael YanWahChia,Broadband Planar Antennas: Design and Applications, JohnWiley&
Sons, Inc., New York, 2006.
31. Peter S. Hall and Yang Hao, Antennas and Propagation for Body-Centric Wireless Communications, Artech
House, Boston, 2006.
32. Zhi Ning Chen (eds.), Antennas for Portable Devices, John Wiley & Sons, Inc., New York, 2007.
Preface xvii
List of Contributors
Yahia M. M. Antar, Royal Military College, Canada
Jennifer T. Bernhard, University of Illinois at Urbana-Champaign, USA
Arun K. Bhattacharyya, Northrop Grumman Corporation, USA
Sujoy Biswas, Institute of Technology and Marine Engineering, India
Christophe Caloz, Ecole Polytechnique, Montreal, Canada
Reza Chaharmir, Communication Research Centre Canada, Ottawa, Canada
Zhi Ning Chen, Institute for Infocomm Research, Singapore
Daniel Deavours, University of Kansas, USA
Daniel Dobkin, Enigmatics, USA
Ramesh Garg, Indian Institute of Technology, Kharagpur, India
Debatosh Guha, Institute of Radio Physics and Electronics, University of Calcutta, India
Peter S. Hall, University of Birmingham, UK
Yang Hao, Queen Mary College, University of London, UK
Samir F. Mahmoud, University of Kuwait, Kuwait
Rabindra K. Mishra, Electronic Science Department, Berhampur University, India
Xianming Qing, Institute for Infocomm Research, Singapore
Shie Ping Terence See, Institute for Infocomm Research, Singapore
Lotfollah Shafai, University of Manitoba, Canada
Jafar Shaker, Communication Research Centre Canada, Ottawa, Canada
Satish K. Sharma, San Diego State University, USA
Jawad Y. Siddiqui, Institute of Radio Physics and Electronics, University of Calcutta, India
Acknowledgments
Editing a book, like this, is a rare experience involving both liberty and responsibility.We came
upwith this idea in 2008 and started consulting with the experts who could be potential authors
for different chapters of this book. The idea has turned into reality only due to the unstinted
cooperation of the authors, who could dedicate time from their extremely busy schedules and
contribute to different topics. We are grateful to all of them for their spontaneous help and
support.
We would also like to express our thanks to a number of our colleagues, researchers and
students who helped with many tasks throughout the process. Mr. Sujoy Biswas of Institute
of Technology and Marine Engineering, India, Dr. Jawad Y. Siddiqui of the University of
Calcutta, India (currently associated with the Royal Military College, Canada), Mr.
Chandrakanta Kumar of the Indian Space Research Organization, and Mr. Anjan Kundu of
University of Calcutta have extended their constant help and technical support throughout the
whole process. We have also received help from some of our students: Sudipto Chattopadhyay
of Siliguri Institute of Technology, India, Symon Podilchak of Queen’s University and the
RoyalMilitaryCollege,Canada, andMr.DavidLee ofCRC inOttawa.Dr. SomnathMukherjee
of RBTechnology, USA, helped us tremendously in resolving the organization of the book.We
have received constant help and support from Sarah Tilley, Anna Smart, and GennaManaog of
Wiley, which made our job easy. We are extremely grateful to all of them.
We cannot but acknowledge the ungrudging support and cooperation received from our
families and from our respective Institutions: the University of Calcutta and the RoyalMilitary
College of Canada. It is always challenging to bring so many people from different parts of the
world to work together on one task at the same time. We express our indebtedness to all
members of this team for contributing to this volume in their different capacities.
1
Numerical Analysis Techniques
Ramesh GargIndian Institute of Technology, Kharagpur, India
1.1 Introduction
Microstrip and other printed antennas are constituted of, in general, patches, strips, slots,
packaged semiconductor devices, radome, feed, etc. in a nonhomogeneous dielectric medium.
Finite substrate and ground plane size are the norm. The dielectric used is very thin compared to
the other dimensions of the antenna. The design of these antennas based on models such as
transmission linemodel or cavitymodel is approximate. Besides, these designs fit regular-shaped
geometries (rectangular, circular, etc.) only, whereas most of the useful antenna geometries are
complex and do not conform to these restrictions [1]. The effect of surface waves, mutual
coupling, finitegroundplane size, anisotropic substrate, etc. is difficult to include in these types of
design. The numerical techniques, on the other hand, can be used to analyze any complex antenna
geometry including irregular shape, finite dielectric and ground plane size, anisotropic dielectric,
radome, etc. The popular numerical techniques for antenna analysis includemethod ofmoments
(MoM), finite element method (FEM), and finite difference time domainmethod (FDTD).MoM
analysis technique, though efficient, is not versatile because of its dependence on Green’s
function. FEM and FDTD are the most suitable numerical analysis techniques for printed
antennas. FDTD is found to be versatile because any embedded semiconductor device in the
antenna can be included in the analysis at the device-field interaction level. This leads to an
accurate analysis of active antennas. Maxwell’s equations are solved as such in FDTD, without
analytical pre-processing, unlike the other numerical techniques. Therefore, almost any antenna
geometry can be analyzed. However, this technique is numerically intensive, and therefore
require careful programming to reduce computation cost. We shall describe the advances in
FDTD. Our reference in this respect is the classic book on FDTD by Taflove and Hagness [2].
A large number of FDTD algorithms have been developed. These can be classified as
conditionally stable and unconditionally stable. The conditionally stable schemes include the
original or Yee’s FDTD also called FDTD (2,2), FDTD (2,4), sampling bi-orthogonal time-
domain (SBTD) and their variants; and the unconditionally stable schemes include ADI
Microstrip and Printed Antennas: New Trends, Techniques and Applications. Edited by Debatosh Guha
and Yahia M.M. Antar
� 2011 John Wiley & Sons, Ltd
(Alternate Direction Implicit), CN (CrankNicolson), CNSS (CrankNicolson Split Step), LOD
(Local One-Dimensional) and their variants. The updating of fields in conditionally stable
schemes does not require a solution of matrix equation as an intermediate step, and are
therefore fully explicit. However, these schemes have a limit on themaximumvalue of the time
step, which is governed by theminimum value of the space step through the Courant-Friedrich-
Levy (CFL) condition.
c:DtCFL � 1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1=Dx2þ1=Dy2þ1=Dz2
p ð1:1Þ
Due to the heterogeneous nature of the dielectric in the printed antennas, the wave velocity is
less than c and may vary from cell to cell and from one frequency to another. We therefore
introduce a safetymargin and chooseDt ¼ ð1=2ÞDtCFL uniformly to simplify coding and avoid
instability. Defining the Courant number q as
q ¼ Dt=DtCFL ð1:2Þ
implies that q¼ 1/2 and the wave takes 2Dt time to travel to the next node.
The value ofDtCFL puts a severe computational constraint on the structures as they have fine
geometrical features such as narrow strips or slots or thin dielectric sheets. Since the simulation
time of an antenna is independent of space and time steps, the number of updates of fields
increases linearly with the decrease in the time step. This results in an increase in processor
time. The limitation on DtCFL is removed in some of the FDTD algorithms and these are
therefore called unconditionally stable schemes. In these schemes one can use the same value
of the time step over the whole geometry even if fine geometrical features exist without
significantly affecting the accuracy of simulation results. Updating fields in unconditionally
stable schemes is carried out in stages called time splitting and involves solving a set of
simultaneous equations before going on to the next stage. These schemes therefore are more
computationally intensive. However, their accuracy is similar to that of conditionally stable
FDTD schemes.
The FDTD analysis of open region problems such as antennas necessitates the truncation
of the domain to conserve computer resources. The truncation of the physical domain of the
antenna is achieved through absorbing boundary conditions, either analytical ABC or
material ABC. Material ABC in the form of PML can achieve a substantial truncation of
domain with very low reflection. The design of PML should be compatible with the FDTD
scheme employed for the rest of the antenna. A number of PML formulations are available.
These are split-field and non split-field PML. Non split-field types are convenient for coding
and are therefore preferred. Of the various PML formulations available now, uniaxial PML
looks promising.
All the FDTD algorithms suffer from computational error, and the amount of error is related
to the space and time step sizes employed. The error is quantified in the form of numerical
dispersion. The goal of various FDTD schemes is to analyze multi-wavelength long complex
geometries, efficiently and accurately. The complexity of the geometry may be in the form of
fine geometrical dimensions, anisotropic dispersive medium, embedded packged semicon-
ductor device, feed, mounting structure, etc. The efficient FDTD algorithms try to achieve this
2 Microstrip and Printed Antennas
aim by increasing the permissible space step size without increasing dispersion, by an increase
in the time step size compatible with fine geometrical features, the applicability of the
algorithm to anisotropic and dispersivemedium and reduced reflection from the PMLmedium.
The presence of thin strips/slotsmakes uniform discretization an inefficient approach. New and
efficient solutions are being tested in the form of a sub-cell approach, quasi-static approxima-
tion, etc. The treatment of PEC and PMC boundary conditions presented by irregular
geometries is receiving due attention, while the interface conditions interior to the device
are somewhat difficult to implement accurately. Modeling of fast variation of fields in metal,
and analysis of curved geometries is being attempted. We shall now discuss the advances in
FDTD analysis since 2003.
Yee’s algorithm is outlined first in order to define the grid structure and the placement of
electric andmagnetic field components on the Yee cell. This grid will be used as a reference for
other FDTD algorithms.
1.2 Standard (Yee’s) FDTD Method
The FDTD method was first proposed by Yee in 1966 [3] and has been used by many
investigators because of its host of advantages. However, computer memory and processing
time for FDTD have to be huge to deal with the problems which can be analyzed using
techniques based on the analytical pre-processing ofMaxwell’s equations such asMoM,mode
matching, method of lines, FEM, etc. Therefore, the emphasis in the development of FDTD
technique is to reduce the requirement for computer resources so that this technique can be used
to analyze electrically large complex electromagnetic problems.
To determine time-varying electromagnetic fields in any linear, isotropic media with
constants e, m, s Maxwell’s curl equations are sufficient; the curl equations are
r�H ¼ sEþe@E
@tð1:3aÞ
�r � E ¼ m@E
@tð1:3bÞ
The partial differential equations (1.3) are solved subject to the conditions that: (i) the fields are
zero at all nodes in the device at t¼ 0 except at the plane of excitation; (ii) the tangential
components of E andHon the boundary of the domain of the antennamust be given for all t> 0.
For computer implementation of Equation (1.3), the partial derivatives are implemented as
finite difference approximations, and are partly responsible for the inaccuracy of the solution.
For better accuracy, the central difference approximation is used in FDTD and is defined as,
@F
@u
�����uo
¼F uoþDu
2
� ��F uo�Du
2
� �Du
�����Du! 0
þOðDuÞ2 ð1:4Þ
where O(�) stands for the order of. Use of Equation (1.4) converts Equation (1.3) into the
following form:
Numerical Analysis Techniques 3
Enþ1x ðiþ1
2 ; j; kÞ ¼ e�sDt=2eþsDt=2
0@
1AEn
xðiþ1
2; j; kÞ
þ Dt=DyeþsDt=2
Hnþ1=2z ðiþ1
2; jþ1
2; kÞ�Hnþ1=2
z ðiþ1
2; j�1
2; kÞ
� �
� Dt=DzeþsDt=2
Hnþ1=2y ðiþ1
2; j; kþ1
2Þ�Hnþ1=2
y ðiþ1
2; j; k�1
2Þ
� �ð1:5aÞ
Enþ1y ði; jþ1
2 ; kÞ ¼ e�sDt=2eþsDt=2
0@
1AEn
yði; jþ1
2; kÞ
þ Dt=DzeþsDt=2
Hnþ1=2x ði; jþ1
2; kþ1
2Þ�Hnþ1=2
x ði; jþ1
2; k�1
2Þ
� �
� Dt=DxeþsDt=2
Hnþ1=2z ðiþ1
2; jþ1
2; kÞ�Hnþ1=2
z ði�1
2; jþ1
2; kÞ
� �ð1:5bÞ
Enþ1z ði; j; kþ1
2 Þ ¼ e�sDt=2eþsDt=2
0@
1AEn
z
�i; j; kþ1
2
�
þ Dt=DxeþsDt=2
Hnþ1=2y ðiþ1
2; j; kþ1
2Þ�Hnþ1=2
y ði�1
2; j; kþ1
2Þ
� �
� Dt=DyeþsDt=2
Hnþ1=2x ði; jþ1
2; kþ1
2Þ�Hnþ1=2
x ði; j�1
2; kþ1
2Þ
� �ð1:5cÞ
Hnþ1
2
xði; jþ1
2; kþ1
2Þ ¼ H
n�12
x ði; jþ1
2; kþ1
2Þ� Dt
mDyEnzði; j; kþ1
2Þ�En
zði; j�1; kþ1
2Þ
� �
þ DtmDz
Enyði; jþ1
2; k�En
yði; jþ1
2; k�1Þ
� �ð1:5dÞ
Hnþ1
2
yðiþ1
2; j; kþ1
2Þ ¼ H
n�12
y ðiþ1
2; j; kþ1
2Þ� Dt
mDzEnxðiþ1
2; j; k�En
xðiþ1
2; j; k�1Þ
� �
þ DtmDx
Enzði; j; kþ1
2Þ�En
zði�1; j; kþ1
2Þ
� �ð1:5eÞ
Hnþ1
2
zðiþ1
2; jþ1
2; kÞ ¼ H
n�12
z ðiþ1
2; jþ1
2; k� Dt
mDxEnyði; jþ1
2; k�En
yði�1; jþ1
2; kÞ
� �
þ DtmDy
Enxðiþ1
2; j; k�En
xðiþ1
2; j�1; kÞ
� �ð1:5fÞ
4 Microstrip and Printed Antennas
Theindices i, j, andkdefinethepositionofthefieldnodes, suchthatx ¼ iDx; y ¼ jDy; z ¼ kDz.The time instant is defined by t ¼ nDt. To implement the finite difference scheme in three
dimensions, theantenna isdividedintoanumberofcells,calledYeecells,ofdimensionDxDyDz.One such cell is shown inFigure 1.1.Remarkably the positions of different components ofE and
H on the cell satisfy the differential and integral forms of Maxwell’s equations. One may note
fromFigure1.1 that theplacements of theEandHnodes areoffset in spacebyhalf a space step; it
is called staggeredgrid.Wenote fromEquation (1.5) that the time instantswhen theEandHfield
componentsarecalculatedareoffsetbyhalf a timestep, that is, componentsofEarecalculatedat
nDt and components ofHare calculated at (n þ 1/2)Dt. The alternate update ofE andHfields is
called leap frog and saves computer processing time.
1.3 Numerical Dispersion of FDTD and Hybrid Schemes
The finite difference form of derivative (1.4) has an error term OðDuÞ2. As a result,
Equations (1.5 a–f) are second-order accurate, resulting in an approximate solution of the
problem. The first sign of this approximation appears in the phase velocity vph for the numerical
wave being different from that in the continuous case. This phenomenon is called numerical
dispersion. The amount of dispersion depends on the wavelength, the direction of propagation
in the grid, time step Dt and the discretization size Du. The above algorithm is second-order
accurate in space and time, and is therefore called FDTD(2,2). The numerical dispersion for
plane wave propagation may be determined from the following expression
Ey
Ey
Ey
Ey
Ex
Ex
Ex
Ex
x
y
z
Ez
Ez
Ez
Δh
Ez
Hz
Hz
Hy Hy
Hx
Hx
Figure 1.1 Geometry of Yee’s cell used in FDTD analysis
Numerical Analysis Techniques 5
sinðoDt=2ÞcDt
0@
1A
2
¼ sinð�k sin y cos jDx=2ÞDx
0@
1A
2
þ sinð�k sin y sinjDy=2ÞDy
0@
1A
2
þ sinð�k cos yDz=2ÞDz
0@
1A
2ð1:6Þ
where �k is thewave number for the numerical wave. The phase velocity�v ¼ o=�k is determined
by solving Equation (1.6) as a function of discretizationsDx;Dy;Dz;Dt and propagation angley;f. The phase velocity is found to be maximum and close to the velocity of light for
propagation along the diagonals and minimum for waves propagating along the axis.
1.3.1 Effect of Non-Cubic Cells on Numerical Dispersion
Devices with high aspect ratio may be analyzed by using uniform or non-uniform cell size. An
alternative is to employ non-square or non-cubic cells. The influence of the aspect ratio of the
unit cell on the numerical dispersion of FDTD(2,2) has been reported by Zhao [4]. It is found
that the dispersion error ðc��vÞ=c increases with the increase in aspect ratio of the cell but
reaches an upper limit for aspect ratios greater than 10. For N (number of cells per wavelength,
l=D)¼ 10, the maximum dispersion error for non-cubic cells is 1.6%which decreases to 0.4%
for N¼ 20, showing second-order accuracy. In general, the maximum error for non-cubic cells
is about 1.5 times that of the corresponding error for cubic cells. For the non-square cells, this
ratio is twice that of square cells [4]. For guidance, the minimum mesh resolution required to
achieve a desired phase velocity error is plotted in Figure 1.2 for the cubic and non-cubic cells.
Figure 1.2 Comparison of minimum mesh resolution required for a given accuracy of phase velocity
when non-cubic (with high aspect ratio) or cubic unit cells are employed. Reproduced by permission of
�2004 IEEE, Figure 8 of [4]
6 Microstrip and Printed Antennas
