Antenna Theory and Microstrip Antennas

D. G. Fang

9 * Я a Science Press

(сЯР CRC Press Taylor & Francis Group Boca Raton London New York

CRC Press is an imprint of the Taylor & Francis Group, an in fonna business

Contents

Preface ix A b o u t t h e A u t h o r xi C h a p t e r 1 Bas i c C o n c e p t s of A n t e n n a s 1

1.1 Introduction 1 1.2 Radiat ion Mechanism 2 1.3 Two Kinds of Linear Elementary Sources and Huygens' Planar Element 2

1.3.1 Radiation Fields Generated by an Infinitesimal Electric Dipole 3 1.3.2 Radiation Fields Generated by an Infinitesimal Magnetic Dipole 9

1.3.3 Radiation Fields Generated by Huygens' 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 Antenna in Receiving Mode 24

1.4.5 Radar Equation and Friis Transmission Formula 28 Bibliography 29

Problems 30 C h a p t e r 2 Arrays and Array S y n t h e s i s 33

2.1 Introduction 33 2.2 N-Element Linear Array: Uniform Amplitude and Spacing 33 2.3 Phased (Scanning) Array, Grat ing Lobe and Sub-Array 34 2.4 N-Element Linear Array: Uniform Spacing, Nonuniform Amplitude 38

2.4.1 Schelkunoff's Unit Circle Representation (SUCR) 38 2.4.2 Dolpb-Tschebyseheff (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 Antenna Array (Analog Beamforming) 59 2.6.2 Angular Super-Resolut ion for Phased Antenna Array through Phase Weighting- -61 2.6.3 Angular Super-Resolution for Conventional Antenna through Angle Weighting- • -63

2.6.4 Adaptive Beamforming Antenna Array 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 by Using the Combination of GA and Fast

Fourier Transform (FFT) 77 Bibliography 80

vi Contents

Problems 81 C h a p t e r 3 M i c r o s t r i p P a t c h A n t e n n a s 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 Input Impedance from Cavity Model 91 3.2.5 Input Impedance from Transmission Line Model 95 3.2.6 Bandwidth of Input Impedance, 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 DC Fringing 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 the Microstrip Substrate 103 3.4.2 Coarse Determination of the Dimensions for Initial Patch Design 103 3.4.3 Feeding Methods 103 3.4.4 Matching Between the Patch and the Feed 104 3.4.5 Design Example 1.05

3.5 Example of LTCC Microstrip Patch Antenna 107 Bibliography 109 Problems 110

C h a p t e r 4 Spec tra l D o m a i n A p p r o a c h and I t s A p p l i c a t i o n t o Micros tr ip A n t e n n a s I l l

4.1 Introduction I l l 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 Wave Discrete Image Method in Microstrip Structures 153 4.10 Asymptotic Integration Techniques and Their Applications 153

4.10.1 The Saddle Point Method 154 4.10.2 The Steepest Descent Method 155 4.10.3 The Stationary Phase Method 156 4.10.4 Extensions of the Above Asymptotic Formulas 156

Contents v i i

4.10.5 Radiation Patterns of Microstrip Antennas 157 Bibliography 161 Problems 163

C h a p t e r 5 Effect ive M e t h o d s in U s i n g C o m m e r c i a l Software for A n t e n n a D e s i g n 167

5.1 Introduction 167 5.2 The Space Mapping (SM) Technique 167

5.2.1 Original Space Mapping Algorithm 168 5.2.2 Aggressive Space Mapping Algorithm (ASM) 170 5.2.3 Using the Closed Form Created by the Full Wave Solver as a Coarse Model in

ASM 172 5.2.4 Using the Closed Form Created by the Cavity Model as a Coarse Model

in ASM 174

5.3 Extrapolat ion and Interpolation Methods 175 5.3.1 One-Dimensional Asymptotic Waveform Evaluation (AWE) 175 5.3.2 Two-Dimensional Asymptotic Waveform Evaluation (AWE) 179

5.4 Using the Model from Physical Insight to Create a Formula 181 5.4.1 Mutual Impedance Formula Between Two Antenna Elements 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 Hybrid of AWE and ANN 195 5.5.3 Hybrid of SM and ANN 199 5.5.4 Hybrid of SM/ANN and Adaptive Frequency Sampling (AFS) 202

5.6 Summary 203 Bibliography 204 Problems 206

C h a p t e r 6 D e s i g n of Convent iona l and D B F M i c r o s t r i p A n t e n n a 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 Hybrid Series/Parallel Feed 210 6.2.4 Single-Layer or Multilayer Design and Other Considerations 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 Antenna Array 215 6.4.2 Design of a Low Side Lobe Level Microstrip Antenna Array 219 6.4.3 Design of a Compact Single Layer Monopulse Microstrip Antenna Array With

Low Side Lobe Levels 221 6.4.4 Design of an Integrated LTCC mm-Wave Planar Antenna Array 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 the Antenna Array 244 6.6.2 Mutual Coupling Reduction of the Microstrip Antenna Array 244

viii Contents

6.6.3 Adaptive Nulling 246 Bibliography 248

Problems 251 C h a p t e r 7 H i g h F r e q u e n c y M e t h o d s and The ir A p p l i c a t i o n s t o

A n t e n n a s 253 7.1 Introduction 253 7.2 Geometrical Optics 253 7.3 Physical Optics 257 7.4 Diffraction by a Conducting Half Plane Wi th Normal Incidence 260 7.5 Diffraction by a Conducting Half Plane With Arbi trary 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

C h a p t e r 8 P l a n a r N e a r - F i e l d M e a s u r e m e n t and Array D i a g n o s t i c s 279 8.1 Introduction 279 8.2 Fundamental Transformations 279 8.3 Probe Compensation 284 8.4 Integral Equat ion Approach 288 8.5 Array Diagnostics 291

8.5.1 Theory 291 8.5.2 Diagnostics Example of Microstrip Antenna Array 294

Bibliography 295 Problems 296

I n d e x 297