Yahia M.M. Antar Royal Military College, Canada

MICROSTRIP AND PRINTED ANTENNAS

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

This edition first published 2011 Ó 2011 John Wiley & Sons Ltd. Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. 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

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List of Contributors

xix

Acknowledgments

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1

2

Numerical Analysis Techniques Ramesh Garg 1.1 Introduction 1.2 Standard (Yee’s) FDTD Method 1.3 Numerical Dispersion of FDTD and Hybrid Schemes 1.3.1 Effect of Non-Cubic Cells on Numerical Dispersion 1.3.2 Numerical Dispersion Control 1.4 Stability of Algorithms 1.5 Absorbing Boundary Conditions 1.5.1 Analytical Absorbing Boundary Conditions 1.5.1.1 Liao’s ABC 1.5.2 Material-Absorbing Boundary Conditions 1.5.3 Perfectly Matched Layer ABC 1.5.4 Uniaxial PML 1.6 LOD-FDTD Algorithm 1.6.1 PML Absorbing Boundary Condition for LOD-FDTD 1.7 Robustness of Printed Patch Antennas 1.8 Thin Dielectric Approximation 1.9 Modeling of PEC and PMC for Irregular Geometries References Computer Aided Design of Microstrip Antennas Debatosh Guha and Jawad Y. Siddiqui 2.1 Introduction 2.2 Microstrip Patch as Cavity Resonator 2.3 Resonant Frequency of Circular Microstrip Patch (CMP) 2.3.1 Suspended Substrate with Variable Air Gap 2.3.2 Inverted Microstrip Circular Patch (IMCP)

1 1 3 5 6 7 11 12 13 14 17 19 19 22 28 29 29 30 32 35 35 36 37 38 42

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2.3.3 IMCP Enclosed in a Cylindrical Cavity 2.3.4 Superstrate Loaded Circular Microstrip Patch (SL-CMP) 2.4 Resonant Frequency of Rectangular Microstrip Patch (RMP) with Variable Air Gap 2.5 Resonant Frequency of Equilateral Triangular Microstrip Patch (ETMP) with Variable Air Gap 2.6 Input Impedance of a Microstrip Patch 2.6.1 Input Impedance of CMP 2.6.2 Input Impedance of IMCP 2.6.3 Input Impedance of RMP 2.6.4 Input Impedance of an ETMP 2.7 Feed Reactance of a Probe-Fed Microstrip Patch 2.8 Radiation Characteristics 2.8.1 Rectangular Microstrip Patch 2.8.2 Circular Microstrip Patch 2.9 Radiation Efficiency 2.10 Bandwidth 2.11 Conclusion References 3

4

Generalized Scattering Matrix Approach for Multilayer Patch Arrays Arun K. Bhattacharyya 3.1 Introduction 3.2 Outline of the GSM Approach 3.2.1 The GSM 3.3 Mutual Coupling Formulation 3.3.1 Mutual Impedance 3.4 Finite Array: Active Impedance and Radiation Patterns 3.5 Numerical Example 3.6 Conclusion References Optimization Techniques for Planar Antennas Rabindra K. Mishra 4.1 Introduction 4.2 Basic Optimization Concepts 4.2.1 Cost (Fitness) Function 4.2.2 Design Parameters and Space 4.2.3 Global and Local Minima 4.3 Real Coded Genetic Algorithm (RCGA) 4.3.1 Genetic Algorithm 4.3.1.1 RCGA Design 4.3.1.2 Genetic Operators 4.3.1.3 Heuristic Crossover and Adewuya Mating (Quadratic Crossover)

44 45 47 50 51 53 55 56 57 59 59 60 61 61 62 62 62

65 65 67 67 68 69 71 72 76 76 79 79 79 79 80 80 80 80 83 83 85

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4.3.2

5

Sierpinski Gasket Fractal Microstrip Antenna Design 4.3.2.1 RCGS Strategy for SGMA 4.4 Neurospectral Design of Rectangular Patch Antenna 4.4.1 Model Development 4.4.1.1 Spectral Domain Formation 4.4.1.2 Artificial Neural Network Solution Technique 4.4.1.3 Closed Form Expressions for Integration 4.4.1.4 Data Generation and Pre-processing 4.4.2 Model Implementation 4.4.2.1 Simple Patch Antenna 4.4.2.2 Feeding Considerations 4.4.2.3 Any Other Arbitrary Shape 4.4.2.4 Points to Note 4.5 Inset-fed Patch Antenna Design Using Particle Swarm Optimization 4.5.1 Explanation of PSO Terms 4.5.2 Inset-fed Patch Antenna Design 4.6 Conclusion References

85 86 91 93 93 96 97 98 99 99 101 104 104

Microstrip Reflectarray Antennas Jafar Shaker and Reza Chaharmir 5.1 Introduction 5.2 General Review of Reflectarrays: Mathematical Formulation and General Trends 5.2.1 Mathematical Formulation 5.2.2 General Trends 5.3 Comparison of Reflectarray and Conventional Parabolic Reflector 5.3.1 Illumination Efficiency 5.3.2 Spill-over Efficiency 5.3.3 Polarization Efficiency 5.3.4 Phase Efficiency 5.3.5 Blockage Efficiency 5.4 Cell Elements and Specific Applications: A General Survey 5.5 Wideband Techniques for Reflectarrays 5.5.1 Phase Response of Reflectarrays 5.5.2 Verification of the Optimization Method 5.6 Development of Novel Loop-Based Cell Elements 5.6.1 Motivation 5.6.2 Square Ring Cell Element 5.6.3 Cross-Ring Cell Element 5.6.4 Hybrid Cell Element 5.7 Conclusion References

113

106 106 107 109 110

113 114 114 118 120 121 122 122 123 123 124 133 136 144 149 149 151 153 153 157 157

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6

7

8

Reconfigurable Microstrip Antennas Jennifer T. Bernhard 6.1 Introduction 6.2 Substrate Modification for Reconfigurability 6.3 Conductor Modification for Reconfigurability 6.3.1 Frequency Reconfigurability 6.3.2 Pattern Reconfigurability 6.3.3 Polarization Reconfigurability 6.4 Enabling Reconfigurability: Considerations for Reconfiguration Mechanisms 6.5 Future Trends in Reconfigurable Microstrip Antenna Research and Development References

161

Wearable Antennas for Body Area Networks Peter S. Hall and Yang Hao 7.1 Introduction 7.1.1 Overview 7.1.2 Domains of Operation 7.1.3 Antenna Parameters 7.2 Sources on the Human Body 7.2.1 Electrical Properties of the Human Body 7.2.2 Sources and Waves on the Body 7.3 Narrowband Antennas 7.3.1 Performance Changes Due to Body Proximity 7.3.2 Antenna Types 7.4 Fabric Antennas 7.4.1 Fabric Materials 7.4.2 Antenna Types 7.5 Ultra Wideband Antennas 7.5.1 Antenna Types 7.5.2 Antenna On-body and Off-body Performance 7.5.3 Antenna Fidelity and Transient Analysis 7.6 Multiple Antenna Systems 7.6.1 Diversity 7.6.2 MIMO 7.7 Conclusion References

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Printed Antennas for Wireless Communications Satish K. Sharma and Lotfollah Shafai 8.1 Introduction 8.2 Broadband Microstrip Patch Antennas 8.2.1 Single Layer Broadband Patch Antennas 8.2.2 Feed Mechanism Modification for Broadband Patch Antennas

161 162 163 163 167 170 175 178 179

183 183 184 184 185 185 186 187 187 188 194 194 195 197 199 199 205 209 209 209 210 210 215 215 215 216 218

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8.2.3

Artificial Magnetic Ground Planes for Broadband Patch Antennas 8.3 Patch Antennas for Multiband Wireless Communications 8.4 Enhanced Gain Patch Antennas 8.5 Wideband Compact Patch Antennas 8.6 Microstrip Slot Antennas 8.6.1 Principle of Radiation and Limitations 8.6.2 Wideband Microstrip Slot Antennas and Size Reduction 8.6.3 Ultra-Wide Bandwidth (UWB) Slot Antennas 8.6.4 Multiband Slot Antennas 8.6.5 Differential Dual-Frequency Slot Antennas 8.7 Microstrip Planar Monopole Antenna References 9

UHF Passive RFID Tag Antennas Daniel Deavours and Daniel Dobkin 9.1 Introduction 9.2 Application Requirements 9.2.1 Electrically Small 9.2.2 Variable and Uncontrollable Dielectric Environment 9.2.3 Variable Orientation 9.2.4 Tag IC Requirements 9.2.5 Cost Pressures 9.3 Approaches 9.3.1 Meander Dipole 9.3.2 Tip Loading 9.3.3 Combined Meander and Load 9.3.4 Fat Dipole 9.3.5 Slot Antennas for Tags 9.3.6 Dual Dipole Antennas 9.3.7 Matching: A Case Study 9.3.8 Microstrip Patch Antennas 9.4 Fabrication 9.4.1 Antenna 9.4.1.1 Plating and Etching 9.4.1.2 Silver Ink Screen Printing 9.4.1.3 Vapor Deposition 9.4.1.4 Deposition and Laser Ablation 9.4.1.5 Printing and Plating 9.4.1.6 Electroless (Chemical) Deposition 9.4.1.7 Die Cut 9.4.2 Assembly 9.4.2.1 Bondwires 9.4.2.2 Flip-Chip and Anisotropic Conductive Adhesives 9.4.2.3 Straps 9.4.2.4 Fluidic Self-Assembly

221 225 229 232 234 234 235 238 242 249 252 260 263 263 264 264 265 266 267 268 269 271 274 274 276 278 279 280 288 294 295 295 295 296 297 297 297 297 299 299 299 299 300

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10

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9.5 Conclusion Acknowledgments References

302 302 302

Printed UWB Antennas Zhi Ning Chen, Xianming Qing and Shie Ping See 10.1 Introduction 10.2 “Swan” Antenna with Reduced Ground Plane Effect 10.2.1 Antenna Design 10.2.2 Parametric Study 10.3 Slim UWB Antenna 10.3.1 Antenna Design 10.3.2 Parametric Study 10.4 Diversity Antenna 10.4.1 Antenna Design 10.5 Printed Slot UWB Antenna and Band-Notched Solutions 10.5.1 Wide-Slot UWB Antenna 10.5.2 Monopole-Like Slot UWB Antenna 10.5.3 Band-Notched UWB Antennas References

305

Metamaterial Antennas and Radiative Systems Christophe Caloz 11.1 Introduction 11.2 Fundamentals of Metamaterials 11.2.1 Resonant Particle (RP) Metamaterials 11.2.2 Transmission Line (TL) Metamaterials 11.2.3 Relation between RP and TL Metamaterials 11.3 Leaky-Wave Antennas 11.3.1 Fundamentals 11.3.2 Leaky-Wave Properties of CRLH Metamaterials 11.3.3 Fan Beam 11.3.4 Conical Beam 11.3.5 Pencil Beam 11.3.6 Efficiency Enhancement by Power Recycling 11.3.7 Active Beam Shaping 11.4 Resonant Antennas 11.4.1 Fundamentals 11.4.2 Resonant Properties of CRLH Metamaterials 11.4.3 Multi-Band 11.4.4 Zeroth Order Resonance 11.4.5 High Directivity 11.4.6 Electric/Magnetic Monopoles 11.5 Exotic Radiative Systems 11.5.1 Magnetic Resonance Imaging Coils 11.5.2 Uniform Ferrite CRLH Leaky-Wave Antenna

305 309 311 313 315 315 318 319 320 325 326 330 331 340 345

345 346 346 348 353 354 354 355 355 358 358 359 361 361 363 363 364 367 367 370 370 371

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11.5.3 11.5.4 11.5.5 11.5.6 References 12

13

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Uniform Ferrite CRLH Integrated Antenna-Duplexer Direction of Arrival (DOA) Estimator Real-Time Spectrum Analyzer (RTSA) Talbot Spatial Power Combiner

Defected Ground Structure for Microstrip Antennas Debatosh Guha, Sujoy Biswas, and Yahia M. M. Antar 12.1 Introduction 12.2 Fundamentals of DGS 12.2.1 Evolution 12.2.2 Definition and Basic Geometries 12.2.2.1 Unit Cell DGS 12.2.2.2 Periodic DGS 12.2.3 Modeling of DGS 12.2.4 Popular Applications to Printed Circuits 12.3 DGS for Controlling Microstrip Antenna Feeds and Front-End Characteristics 12.3.1 Basic Idea 12.3.2 Harmonic Control in Active Microstrip Antennas 12.3.3 Isolation at Microstrip Antenna Front-Ends 12.3.4 Impedance Matching for Microstrip Feed Design 12.4 DGS to Control/Improve Radiation Properties of Microstrip Patch Antennas 12.4.1 Basic Idea 12.4.2 Suppression of Cross-Polarized Radiations from Microstrip Patches 12.5 DGS for Reduced Mutual Coupling Between Microstrip Array Elements and Associated Improvements 12.5.1 Basic Idea 12.5.2 Ring-Shaped DGS for Circular Patch Array 12.5.3 Dumbbell-Shaped DGS for Rectangular Patch Array 12.5.4 Elimination of Scan Blindness of Microstrip Phased Array 12.6 Conclusion Appendix: A Brief DGS Chronology References Printed Leaky Wave Antennas Samir F. Mahmoud and Yahia M.M. Antar 13.1 Introduction 13.2 The Leaky Wave as a Complex Plane Wave 13.3 Radiation Pattern of a Leaky Wave 13.3.1 Unidirectional Leaky Wave 13.3.2 Bidirectional Radiation Pattern 13.4 Examples of Leaky Mode Supporting Structures 13.4.1 A Two Parallel Plate Leaky Waveguide

373 376 376 382 383 387 387 387 387 388 390 395 397 404 408 408 409 412 414 414 414 415 420 420 424 425 427 429 430 431 435 435 436 437 437 440 441 441

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13.4.2 A Two-Layer Leaky Wave Structure 13.5 The Excitation Problem 13.5.1 Radiation Field in Terms of the Leaky Mode Pole 13.5.2 A Numerical Example 13.6 Two-Dimensional Leaky Waves 13.6.1 Leaky Wave Antennas with Periodic Screen 13.6.1.1 Boundary Conditions 13.6.1.2 Radiated Power and Surface Wave Power 13.6.2 Characterization of the Periodic Screen as an EBG Structure 13.7 Further Advances on a Class of Periodic Leaky Wave Antennas 13.7.1 Broadside Radiation 13.7.2 Frequency Scanning 13.7.3 Cylindrical Leaky Wave Antenna Design References Appendix I Preliminary Ideas: PTFE-Based Microwave Laminates and Making Prototypes Appendix II Preliminary Ideas: Microwave Connectors for Printed Circuits and Antennas Index

444 447 449 449 451 451 453 454 456 457 459 459 460 461

463 469 477

Preface Microstrip technology has been popular for microwave and millimeter 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 geometries 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 in microstrip antennas that occurred up to the late1970s were 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 and Mink [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

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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 the mobile 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 enhancement 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 and Chen [23] was a timely effort to incorporate major 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 unconventional 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 and mentoring 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 collaborative 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

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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 used methods 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 system may 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 leaky wave 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. We have tried to satisfy a wide cross-section of readers. A student or a researcher may consider this a guide book to understanding the strength and weaknesses of the

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contemporary topics. To a practicing engineer, we hope that the book will be a ready reference to many 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 1. D. D. Greig and H. F. Engleman, “Microstrip – a new transmission technology for the kilomegacycle range,” Proc. IRE, vol. 40, pp. 1644–1650, 1952. 2. G. A. Deschamps, “Microstrip microwave antennas,” presented at the 3rd USAF Symp. on Antennas, 1953. 3. J. Q. Howell, “Microstrip antennas,” Dig. IEEE Int. Symp. Antennas Propagat., pp. 177–180, Dec. 1972. 4. R. E. Munson, “Conformal microstrip antennas and microstrip phased arrays,” IEEE Trans. Antennas Propagat., vol. 22, pp. 74–78, 1974. 5. T. Itoh and R. Mittra, “Analysis of microstrip disk resonator,” Arch. Elek. Ubertagung, vol. 21, pp. 456–458, Nov. 1973. 6. T. Itoh, “Analysis of microstrip resonator,” IEEE Trans. Microwave Theory Tech., vol. 22, pp. 946–952, Nov. 1974. 7. A. Derneryd, “Linearly polarized microstrip antennas,” IEEE Trans. Antennas Propagat., vol. 24, no. 6, pp. 846–851, 1976. 8. G. Dubost, M. Nicolas and H. Havot, “Theory and applications of broadband microstrip antennas,” Proc. 6th European Microwave Conference, pp. 275–279, 1976. 9. P. Agrawal and M. Bailey, “An analysis technique for microstrip antennas,” IEEE Trans. Antennas Propagat., vol. 25, no. 6, pp. 756–759, 1977. 10. W.F. Richards, Y.T. Lo and D. D. Harrison, “Improved theory for microstrip antennas,” Electronics Letters, vol. 15, no. 2, pp. 42–44, 1979. 11. Y.T. Lo, D. Solomon and W. Richards, “Theory and experiment on microstrip antennas,” IEEE Trans. Antennas Propagat., vol. 27, no. 2, pp. 137–145, 1979. 12. P. Hammer, D. Van Bouchaute, D. Verschraeven and A. Van de Capelle, “A model for calculating the radiation field of microstrip antennas,” IEEE Trans. Antennas Propagat., vol. 27, no. 2, pp. 267–270, 1979. 13. K. Keen, “A planar log-periodic antenna,” IEEE Trans. Antennas Propagat., vol. 22, no. 3, pp. 489–490, 1974. 14. D.T. Shahani and Bharathi Bhat, “Network model for strip-fed cavity-backed printed slot antenna,” Electronics Letters, vol. 14, no. 24, pp. 767–769, 1978. 15. Inam E. Rana and N. G. Alexopoulos, “On the theory of printed wire antennas,” 9th European Microwave 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 and W. Chen, Advances in Microstrip and Printed Antennas, John Wiley & Sons, Inc., New York, 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.

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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 Ning Chen and Michael Yan Wah Chia, Broadband Planar Antennas: Design and Applications, John Wiley & 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.

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, E´cole 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 up with 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 Royal Military College, Canada, and Mr. David Lee of CRC in Ottawa. Dr. Somnath Mukherjee of RB Technology, USA, helped us tremendously in resolving the organization of the book. We have received constant help and support from Sarah Tilley, Anna Smart, and Genna Manaog 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 Royal Military 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 Garg Indian 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 line model or cavity model 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, finite ground plane 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 include method of moments (MoM), finite element method (FEM), and finite difference time domain method (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 timedomain (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 Ó 2011 John Wiley & Sons, Ltd

Microstrip and Printed Antennas

2

(Alternate Direction Implicit), CN (Crank Nicolson), CNSS (Crank Nicolson 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 the maximum value of the time step, which is governed by the minimum value of the space step through the Courant-FriedrichLevy (CFL) condition. 1 c:DtCFL pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 1=Dx þ1=Dy2 þ1=Dz2

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 safety margin and choose Dt ¼ ð1=2ÞDtCFL uniformly to simplify coding and avoid instability. Defining the Courant number q as q ¼ Dt=DtCFL

ð1:2Þ

implies that q ¼ 1/2 and the wave takes 2Dt time to travel to the next node. The value of DtCFL 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 semiconductor device, feed, mounting structure, etc. The efficient FDTD algorithms try to achieve this

Numerical Analysis Techniques

3

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 dispersive medium and reduced reflection from the PML medium. The presence of thin strips/slots makes uniform discretization an inefficient approach. New and efficient solutions are being tested in the form of a sub-cell approach, quasi-static approximation, 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 and magnetic 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 of Maxwell’s equations such as MoM, 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 r E ¼ m

@E @t

ð1:3aÞ

@E @t

ð1:3bÞ

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 t ¼ 0 except at the plane of excitation; (ii) the tangential components of E and H on the boundary of the domain of the antenna must 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, Du Du F uo þ F uo @F 2 2 þOðDuÞ2 ð1:4Þ ¼ Du @u uo

Du ! 0

where O() stands for the order of. Use of Equation (1.4) converts Equation (1.3) into the following form:

Microstrip and Printed Antennas

4

0

Exnþ1 ðiþ12 ; j; kÞ

1 esDt=2 AEn ðiþ1; j; kÞ ¼@ 2 eþsDt=2 x

Dt=Dy Hznþ1=2 ðiþ12 ; jþ12 ; kÞHznþ1=2 ðiþ12 ; j12; kÞ eþsDt=2 Dt=Dz nþ1=2 1 1 nþ1=2 1 1 Hy ðiþ2 ; j; kþ2 ÞHy ðiþ2 ; j; k2Þ eþsDt=2 0 1 Eynþ1 ði; jþ12 ; kÞ ¼ @esDt=2AEn ði; jþ1; kÞ 2 eþsDt=2 y

ð1:5aÞ

Dt=Dz nþ1=2 1 1 nþ1=2 1 1 Hx þ ði; jþ2 ; kþ2 ÞHx ði; jþ2 ; k2Þ eþsDt=2 Dt=Dx Hznþ1=2 ðiþ12 ; jþ12 ; kÞHznþ1=2 ði12 ; jþ12; kÞ eþsDt=2 0 1 esDt=2 1 nþ1 Ez ði; j; kþ2 Þ ¼ @ AEn i; j; kþ1 z 2 eþsDt=2

ð1:5bÞ

þ

Dt=Dx Hynþ1=2 ðiþ12 ; j; kþ12 ÞHynþ1=2 ði12 ; j; kþ12Þ eþsDt=2 Dt=Dy nþ1=2 nþ1=2 1 1 1 1 Hx ði; jþ2 ; kþ2 ÞHx ði; j2 ; kþ2Þ eþsDt=2

þ

nþ12

Hx

nþ12

Hy

nþ12

Hz

Dt Ezn ði; j; kþ12 ÞEzn ði; j1; kþ12Þ mDy Dt þ Eyn ði; jþ12 ; kÞEyn ði; jþ12; k1Þ mDz

ð1:5cÞ

n12

ði; jþ12 ; kþ12Þ ¼ Hx ði; jþ12 ; kþ12Þ

Dt Exn ðiþ12 ; j; kÞExn ðiþ12; j; k1Þ mDz Dt Ezn ði; j; kþ12 ÞEzn ði1; j; kþ12Þ þ mDx

ð1:5dÞ

n12

ðiþ12 ; j; kþ12Þ ¼ Hy ðiþ12 ; j; kþ12Þ

Dt n n 1 1 Ey ði; jþ2 ; kÞEy ði1; jþ2; kÞ ðiþ ; jþ ; kÞ ¼ Hz ðiþ ; jþ ; kÞ mDx Dt Exn ðiþ12 ; j; kÞExn ðiþ12; j1; kÞ þ mDy 1 2

1 2

n12

1 2

ð1:5eÞ

1 2

ð1:5fÞ

Numerical Analysis Techniques

5

The indices i, j, and k definethe position of the field nodes, such that x 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, the antenna is divided into a number of cells, called Yee cells, of dimension DxDyDz. One such cell is shown in Figure 1.1. Remarkably the positions of different components of E and H on the cell satisfy the differential and integral forms of Maxwell’s equations. One may note from Figure 1.1 that the placements of the E and H nodes are offset in space by half a space step; it is called staggered grid. We note from Equation (1.5) that the time instants when the E and H field components are calculated are offset by half a time step, that is, components of E are calculated at nDt and components of H are calculated at (n þ 1/2)Dt. The alternate update of E and H fields is called leap frog and saves computer processing time. Ey

Hx

Ez

Ez

Ex

Ex

Hz Ey Hy

Hy

Hz

Ex

Ex

Ey

Hx

Ez

Ez Δh

x z

Ey y

Figure 1.1

1.3

Geometry of Yee’s cell used in FDTD analysis

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

Microstrip and Printed Antennas

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0

12 0 12 0 12 sin y cos jDx=2Þ sin y sin jDy=2Þ sinðoDt=2Þ sinð k sinð k @ A¼ @ A þ@ A cDt Dx Dy 0

12 sinðk cos yDz=2ÞA þ@ Dz

ð1:6Þ

is the wave number for the numerical wave. The phase velocity v ¼ o=k is determined where k by solving Equation (1.6) as a function of discretizations Dx; Dy; Dz; Dt and propagation angle y; 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 ðcvÞ=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 N ¼ 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 Ó2004 IEEE, Figure 8 of [4]