Antenna Theory and Microstrip Antennas

308 Pages·2009·5.56 MB·English

by  D. G. Fang

K10367_FM.indd 1 11/16/09 2:36:13 PM
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Library of Congress Cataloging‑in‑Publication Data
Fang, D. G.
Antenna theory and microstrip antennas / author, D.G. Fang.
p. cm.
“A CRC title.”
Includes bibliographical references and index.
ISBN 978-1-4398-0727-9 (hardcover : alk. paper)
1. Microstrip antennas. I. Title.
TK7871.67.M5F36 2010
621.382’4--dc22 2009031426
Visit the Taylor & Francis Web site at
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To the memory of my father and mother, and to my family.
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Contents
Preface................................................................................ix
About the Author...................................................................xi
Chapter 1 Basic Concepts of Antennas...........................................1
1.1 Introduction.....................................................................1
1.2 Radiation Mechanism............................................................2
1.3 Two Kinds of Linear Elementary Sources and Huygens’ Planar Element..........2
1.3.1 Radiation Fields Generated byan Infinitesimal Electric Dipole..................3
1.3.2 Radiation Fields Generated byan Infinitesimal Magnetic Dipole.................9
1.3.3 Radiation Fields Generated byHuygens’Planar Element......................11
1.4 Fundamental Parameters of Antennas...........................................14
1.4.1 Radiation Pattern..........................................................14
1.4.2 Directivity and Gain........................................................15
1.4.3 Polarization................................................................18
1.4.4 Characteristics and Parameters of an Antennain ReceivingMode..............24
1.4.5 Radar Equation and Friis Transmission Formula..............................28
Bibliography.........................................................................29
Problems............................................................................30
Chapter 2 Arrays and Array Synthesis..........................................33
2.1 Introduction....................................................................33
2.2 N-Element Linear Array: Uniform Amplitude and Spacing......................33
2.3 Phased (Scanning) Array, Grating Lobe and Sub-Array.........................34
2.4 N-Element Linear Array: Uniform Spacing, Nonuniform Amplitude.............38
2.4.1 Schelkunoff’sUnit Circle Representation (SUCR).............................38
2.4.2 Dolph-Tschebyscheff(DT) Distribution.......................................39
2.4.3 Taylor Distribution.........................................................43
2.4.4 Woodward-Lawson (WL) Method............................................49
2.4.5 Supergain Arrays...........................................................53
2.5 N-Element Linear Array: Uniform Amplitude, Nonuniform Spacing.............54
2.5.1 Density Taper-Deterministic.................................................54
2.5.2 Density Taper-Statistical....................................................56
2.6 Signal Processing Antenna Array...............................................57
2.6.1 Multi-Beam AntennaArray (Analog Beamforming) ...........................59
2.6.2 Angular Super-Resolution for Phased AntennaArray through Phase Weighting..61
2.6.3 Angular Super-Resolution for Conventional Antennathrough Angle Weighting...63
2.6.4 AdaptiveBeamforming AntennaArray.......................................64
2.7 Planar Arrays ..................................................................66
2.7.1 Array Factor...............................................................66
2.7.2 Taylor Patterns of Circular Aperture.........................................69
2.8 Array Synthesis through Genetic Algorithm (GA)...............................72
2.8.1 Introduction to Genetic Algorithms..........................................72
2.8.2 Optimized Design of Planar Array byUsing the Combination of GA and Fast
Fourier Transform (FFT)....................................................77
Bibliography.........................................................................80
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vi Contents
Problems............................................................................81
Chapter 3 Microstrip Patch Antennas...........................................85
3.1 Introduction....................................................................85
3.2 Cavity Model and Transmission Line Model.....................................85
3.2.1 Field Distribution from Cavity Model........................................85
3.2.2 Radiation Pattern..........................................................89
3.2.3 Radiation Conductance.....................................................90
3.2.4 InputImpedancefrom Cavity Model.........................................91
3.2.5 InputImpedancefrom Transmission Line Model..............................95
3.2.6 Bandwidth of InputImpedance,Efficiency and Directivity.....................96
3.2.7 Multiport Analysis.........................................................97
3.3 Improvement and Extension of the Cavity Model...............................98
3.3.1 Correction of Edge Effect by DCFringing Fields..............................98
3.3.2 Irregularly Shaped Patch as Perturbation of Regularly Shaped Patch..........101
3.4 Design Procedure of a Single Rectangular Microstrip Patch Antenna...........102
3.4.1 Choice of theMicrostrip Substrate..........................................103
3.4.2 Coarse Determination of the Dimensions for Initial Patch Design..............103
3.4.3 FeedingMethods..........................................................103
3.4.4 Matching Between thePatch and the Feed..................................104
3.4.5 Design Example...........................................................105
3.5 Example of LTCC Microstrip Patch Antenna..................................107
Bibliography........................................................................109
Problems...........................................................................110
Chapter 4 Spectral Domain Approach and Its Application to Microstrip
Antennas..............................................................111
4.1 Introduction...................................................................111
4.2 Basic Concept of Spectral Domain Approach...................................112
4.3 Some Useful Transform Relations..............................................114
4.4 Scalarization of Maxwell’s Equations...........................................116
4.5 Dyadic Green’s Function (DGF)...............................................119
4.6 Mixed Potential Representations...............................................122
4.7 Transmission-Line Green’s Functions ..........................................126
4.7.1 Parallel Current Source....................................................127
4.7.2 Series Voltage Source......................................................129
4.7.3 Example..................................................................130
4.8 Introduction to Complex Integration Techniques...............................133
4.8.1 Branch Points and Branch Cuts............................................133
4.8.2 Poles.....................................................................138
4.8.3 Integration Paths..........................................................140
4.9 Full Wave Discrete Image and Full Wave Analysis of Microstrip Antennas......144
4.9.1 Extraction of Quasi-Static Images..........................................144
4.9.2 Extraction of Surface Waves................................................146
4.9.3 Approximation for the Remaining Integrands................................148
4.9.4 Application of Full WaveDiscrete Image Method in Microstrip Structures......153
4.10 Asymptotic Integration Techniques and Their Applications...................153
4.10.1 The SaddlePoint Method.................................................154
4.10.2 The Steepest Descent Method.............................................155
4.10.3 The Stationary Phase Method.............................................156
4.10.4 Extensions of the AboveAsymptoticFormulas..............................156
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Contents vii
4.10.5 Radiation Patterns of Microstrip Antennas.................................157
Bibliography........................................................................161
Problems...........................................................................163
Chapter 5 Effective Methods in Using Commercial Software for Antenna
Design.................................................................167
5.1 Introduction...................................................................167
5.2 The Space Mapping (SM) Technique...........................................167
5.2.1 Original SpaceMapping Algorithm.........................................168
5.2.2 Aggressive SpaceMapping Algorithm (ASM)................................170
5.2.3 Using theClosed Form Created by theFull WaveSolveras a Coarse Model in
ASM.....................................................................172
5.2.4 Using theClosed Form Created by theCavity Model as a Coarse Model
in ASM...................................................................174
5.3 Extrapolation and Interpolation Methods......................................175
5.3.1 One-Dimensional AsymptoticWaveform Evaluation (AWE)...................175
5.3.2 Two-Dimensional AsymptoticWaveform Evaluation (AWE)...................179
5.4 Using the Model from Physical Insight to Create a Formula....................181
5.4.1 Mutual ImpedanceFormula Between Two AntennaElements.................181
5.4.2 Relationship Between Bailey’s Formula and That in Formula (5.4.4)...........185
5.4.3 Numerical Results.........................................................185
5.5 Using Models from the Artificial Neural Network (ANN) to Train Formula.....190
5.5.1 Concept of the Artificial Neural Network (ANN).............................190
5.5.2 Hybridof AWE and ANN..................................................195
5.5.3 Hybridof SMand ANN....................................................199
5.5.4 Hybridof SM/ANN and AdaptiveFrequencySampling (AFS)................202
5.6 Summary......................................................................203
Bibliography........................................................................204
Problems...........................................................................206
Chapter 6 Design of Conventional and DBF Microstrip Antenna Arrays ..207
6.1 Introduction...................................................................207
6.2 Feeding Architecture..........................................................208
6.2.1 Series Feed................................................................208
6.2.2 Parallel Feed..............................................................209
6.2.3 HybridSeries/Parallel Feed................................................210
6.2.4 Single-Layer or Multilayer Design and OtherConsiderations ..................210
6.3 Design of Power Divider and Transmission on the Transformer.................210
6.4 Design Examples of Microstrip Antenna Arrays................................215
6.4.1 Design of a 16GHz Compact Microstrip AntennaArray.......................215
6.4.2 Design of a Low SideLobe Level Microstrip AntennaArray...................219
6.4.3 Design of a Compact Single Layer Monopulse Microstrip AntennaArray With
Low SideLobe Levels .....................................................221
6.4.4 Design of an Integrated LTCC mm-WavePlanar AntennaArray ..............229
6.5 Mutual Coupling in Finite Microstrip Antenna Arrays.........................233
6.5.1 Mutual Coupling Effects and Analysis.......................................233
6.5.2 Mutual Coupling in a Linear Dipole Array of Finite Size......................234
6.5.3 Mutual Coupling in Finite Microstrip Patch Arrays..........................239
6.6 Introduction to a Digital Beamforming Receiving Microstrip Antenna Array...244
6.6.1 Description of theAntennaArray...........................................244
6.6.2 Mutual Coupling Reduction of theMicrostrip AntennaArray.................244
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viii Contents
6.6.3 AdaptiveNulling..........................................................246
Bibliography........................................................................248
Problems...........................................................................251
Chapter 7 High Frequency Methods and Their Applications to
Antennas..............................................................253
7.1 Introduction...................................................................253
7.2 Geometrical Optics............................................................253
7.3 Physical Optics................................................................257
7.4 Diffraction by a Conducting Half Plane With Normal Incidence................260
7.5 Diffraction by a Conducting Half Plane With Arbitrary Incidence..............265
7.6 Applications of Geometrical Theory of Diffraction in Antennas.................270
7.6.1 Radiation from a Slit Aperture.............................................270
7.6.2 Edge Diffracted Fields from the Finite Ground Plane of a Microstrip
Antenna..................................................................272
7.7 Fresnel Diffraction in Three Dimensions.......................................273
Bibliography........................................................................275
Problems...........................................................................276
Chapter 8 Planar Near-Field Measurement and Array Diagnostics.........279
8.1 Introduction...................................................................279
8.2 Fundamental Transformations.................................................279
8.3 Probe Compensation..........................................................284
8.4 Integral Equation Approach...................................................288
8.5 Array Diagnostics.............................................................291
8.5.1 Theory...................................................................291
8.5.2 Diagnostics Example of Microstrip AntennaArray...........................294
Bibliography........................................................................295
Problems...........................................................................296
Index................................................................................297
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Preface
There are many excellent textbooks and handbooks on antenna theory and design. Re-
cently, due to the increasing importance of microstrip antennas,severalexcellent textbooks
and handbooks on them have been published and this topic has become a separate course.
Thepurposeofthisbookistoserveeitherasatextbooktocoverbothantennafundamentals
and microstrip antennas or a self-study book for those attempting to plunge into this area.
This book tries to make a good balance between the antenna fundamentals and microstrip
antennas.
For the full wave analysis and optimization of antenna designs, there are many excellent
books on computational electromagnetics and especially several powerful commercial soft-
ware packages are available. This book is devoted to the introduction of techniques useful
for the effective application of the software. The spectral domain approach is an impor-
tanttoolinanalyzingthemicrostripstructuresincludingthemicrostripantennas,near-field
measurementandhigh-frequencymethod. Thisbookgivesasystematicintroductiontothis
approach. The main purposeof introducingthis approachis notfor numericalcomputation
but for the understanding of some significant concepts.
Theliteratureonantennasisvastandthereareavarietyofmathematicalformalismsand
numericalschemes, which often intimidate those who attempt to enter this field. In univer-
sities, it is a great challenge for professors to cover sufficient fundamentals with reasonably
in-depth practical knowledge in a one-term course. In industry, one may find it hard to get
a generalunderstanding of the field before engagingin any specialized techniques. I believe
that a concise and readable book, with both scope and depth, theoretical background, ap-
plication materials and recent progress will be a welcome addition to the arsenal of books
on this subject.
In this book, the presentation principle is to explain profound and abstract concepts in
simple and concise terms. I tried to organize the contents logically and uniformly to lead
the readers to draw inferences about other cases from one instance. Problems and answers
provide a necessary supplement to the text and are used as an instrument to help the
readers to gain insights and to facilitate understanding of the subtle points, usefulness of
theprinciples andthe techniquesdiscussedinthe text. This bookincludesmyteachingand
researchexperiencesinthisareaovermanyyears. Moreover,thisbookcontainssomerecent
developments including our own research results published in international journals. The
contents of this book have been used as teaching materials in Laval University (Canada)
in 1987 and in Chinese University of Hong Kong (Hong Kong) in 2002 and in Nanjing
University of Science and Technology for more than a decade. For senior undergraduate-
level course (two credits), the materials in Chapter 1 through Chapter 3 should be covered.
The materials in Chapter 4 through Chapter 6 are suitable for a graduate-levelcourse with
two credits and those in Chapter 4 through Chapter 8 are suitable for a graduate course
with three credits.
I have benefited from many experts through their excellent books and papers. I would
like to express my sincere thanks to them, especially to Professors C. A. Balanis, W. L.
Stutzman and G. A. Thiele, R. S. Elliot, R. E. Collin and F. J. Zucker, and S. M. Lin
for their antenna books; J. A. Kong, N. H. Fang for their electromagnetic theory books;
K. F. Lee and W. Chen, S. S. Zhong for their microstrip antenna books; R. H. Clarke, J.
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