Yikai Chen is a Research Scientist of Temasek Laboratories at National University of Singapore (TL@NUS), Singapore. His current research interests focus on the characteristic mode theory and its applications in antenna engineering. Dr. Chen is a Senior Member of the IEEE and IEEE Antenna and Propagation Society. He is the recipient of the 2013 National Excellent Doctorate Dissertation Award of China.

List of Figures ix

List of Tables xvii

Preface xix

1 Introduction 1

1.1 Backgrounds 1

1.2 An Introduction to Characteristic Mode Theory 3

1.2.1 Traditional Modal Analysis in Antenna Engineering 3

1.2.2 Definition of Characteristic Modes 6

1.2.3 Primary Properties of Characteristic Modes 7

1.2.4 Variants of Characteristic Modes 7

1.3 Characteristic Modes in Antenna Engineering 10

1.3.1 Pioneering CM Studies (1965–1990) 12

1.3.2 Recent CM Developments (1991–2014) 13

1.4 Characteristic Modes in Scattering Computation 19

1.5 Outline of this Book 20

References 22

2 Characteristic Mode Theory for PEC Bodies 37

2.1 Backgrounds 37

2.2 Surface Integral Equations 39

2.2.1 Maxwell’s Equations 39

2.2.2 Electromagnetic Boundary Condition 39

2.2.3 Magnetic Vector Potential and Electric Scalar Potential 40

2.2.4 Electric Field Integral Equation 41

2.2.5 Magnetic Field Integral Equation 43

2.3 Method of Moments 43

2.4 EFIE Based CM Formulation 47

2.4.1 Conventional Derivation 47

2.4.2 Poynting’s Theorem Based Derivation 48

2.4.3 Othogonality of Characteristic Modes 49

2.4.4 Physical Interpretation of Eigenvalues 51

2.4.5 Physical Interpretation of Modal Significances 52

2.4.6 Physical Interpretation of Characteristic Angles 54

2.5 MFIE Based CM Formulation 55

2.5.1 MFIE Based CM Formulation 55

2.5.2 Approximate MFIE-Based CM Formulation 57

2.6 CFIE-Based CM Formulation 59

2.7 Applicability of the CM Formulations 60

2.7.1 Closed and Open Objects 60

2.7.2 Electrically Small and Large Problems 60

2.8 Computation of Characteristic Modes 61

2.8.1 Solution of Generalized Eigenvalue Equation 61

2.8.2 Characteristic Mode Tracking 65

2.9 N umerical Examples 70

2.9.1 PEC Sphere 70

2.9.2 Rectangular PEC Patch 81

2.9.3 N umerical Aspects of Mesh Density 82

2.10 A First Glance on CM Excitations 88

2.11 Summary 95

References 95

3 Characteristic Mode Theory for Antennas in Multilayered Medium 99

3.1 Backgrounds 99

3.2 CM Formulation for PEC Structures in Multilayered Medium 103

3.3 Relationship Between Cavity Model and Characteristic Modes 105

3.4 Physical Investigations on Microstrip Patch Antennas 111

3.4.1 Equilateral Triangular Patch Antenna 112

3.4.2 Concentric Circular Microstrip Antenna 115

3.4.3 Corner-Truncated Circularly Polarized Antenna 117

3.4.4 Dual Band Stacked Microstrip Patch Antenna 120

3.5 Applications to Circularly Polarized Microstrip Antenna Design 125

3.5.1 U-Slot Microstrip Antenna 126

3.5.2 E-Shaped Microstrip Antenna with Low Cross Polarization 131

3.5.3 Summary 138

3.6 Conclusions 139

References 139

4 Characteristic Mode Theory for Dielectric Resonators 143

4.1 Backgrounds 143

4.1.1 A Brief Introduction to DRA 144

4.1.2 Importance of Modal Analysis and its Challenges 146

4.1.3 Early Attempts to DRA Modal Analysis Using Characteristic Mode Theory 147

4.1.4 Contributions of this Chapter 148

4.2 CM Formulations for Dielectric Bodies 149

4.2.1 PMCHWT Surface Integral Equations 149

4.2.2 MoM Matrix Equation 152

4.2.3 Generalized Eigenvalue Equation for Characteristic Electric Current 152

4.2.4 Important CM Quantities 154

4.2.5 Generalized Eigenvalue Equation for Characteristic Magnetic Current 155

4.3 Analysis and Design of DRAs Using CM Theory 156

4.3.1 Cylindrical Dielectric Resonator Antennas 157

4.3.2 Spherical Dielectric Resonator Antennas 164

4.3.3 Rectangular Dielectric Resonator Antennas 170

4.3.4 Triangular Dielectric Resonator Antennas 175

4.3.5 N otched Rectangular Dielectric Resonator Antenna 178

4.4 Computational Efficiency 181

4.5 Conclusions 181

References 182

5 Characteristic Mode Theory for N-Port Networks 187

5.1 Backgrounds 187

5.2 Characteristic Mode Formulations For N-Port Networks 188

5.3 Reactively Controlled Antenna Array Designs Using Characteristic Modes 192

5.3.1 Problem Formulation 192

5.3.2 Design and Optimization Procedure 194

5.3.3 Design Examples 199

5.3.4 Efficiency of CM-Based Approach 202

5.4 Yagi-Uda Antenna Designs Using Characteristic Modes 203

5.4.1 CM-Based Design Method 204

5.4.2 Design Examples 208

5.4.3 Efficiency Investigation 212

5.5 Wideband Array Excitation Design Using Characteristic Modes 214

5.5.1 Tightly Coupled Wideband Arrays 214

5.5.2 Computation of Quasi-Excitations from Characteristic Modes 215

5.6 Conclusions 217

References 217

6 Platform-Integrated Antenna System Design Using Characteristic Modes 221

6.1 Backgrounds 221

6.2 Electrically Small UAV Antenna System Design Using Characteristic Modes 223

6.2.1 Reconfigurable Radiation Pattern Synthesis Using Characteristic Modes 223

6.2.2 Feeding Designs for the Excitation of the Synthesized Currents 235

6.2.3 Experimental Validations 238

6.2.4 Summary 241

6.3 HF Band Shipboard Antenna System Design Using Characteristic Modes 245

6.3.1 CM-Based Broadside Radiation Pattern Synthesis 246

6.3.2 Feeding Structure Design 254

6.3.3 Experimental Validations 258

6.3.4 Practical Implementation 260

6.3.5 Summary 262

6.4 Conclusions 263

References 263

Index 267

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