Preface xv

Acknowledgments xvii

List of Contributors xix

Notation xxi

1 Introduction 1
Trevor S. Bird

1.1 Aims and Scope 1

1.2 Historical Perspective 3

1.3 Overview of Text 4

References 7

2 Basics of Antenna Mutual Coupling 9
Trevor S. Bird

2.1 Introduction 9

2.2 Electromagnetic Field Quantities 9

2.2.1 Definitions 9

2.2.2 Field Representations in Source-Free Regions 11

2.3 Mutual Coupling Between Elementary Sources 12

2.3.1 Radiation 12

2.3.2 Generalized Infinitesimal Current Elements 14

2.3.3 Mutual Coupling Between Infinitesimal Current Elements 15

2.4 Network Representation of Mutual Coupling 18

2.4.1 Extension to Combination of Elements 18

2.4.2 Mutual Impedance and Admittance Matrix Formulation 19

2.4.3 Scattering Matrix Representation 20

2.5 Radiation from Antennas in the Presence of Mutual Coupling 23

2.5.1 Far-Field Radiation 23

2.5.2 Magnetic Current Only 25

2.5.3 Electric Current Only 25

2.6 Conclusion 26

References 26

3 Methods in the Analysis of Mutual Coupling in Antennas 27
Trevor S. Bird

3.1 Introduction 27

3.2 Mutual Coupling in Antennas with Continuous Sources 30

3.2.1 Impedance and Admittance with Continuous Sources 30

3.2.2 Reaction 31

3.2.3 Definition of Circuit Quantities 32

3.3 On Finite and Infinite Arrays 34

3.3.1 Finite Array Analysis by Element-by-Element Method 35

3.3.2 Infinite Periodic Array Analysis 36

3.4 Integral Equation Methods Used in Coupling Analysis 36

3.4.1 Introduction 36

3.4.2 Green's Function Methods 37

3.4.2.1 Free-Space Green's Function for Harmonic Sources 38

3.4.2.2 Free-Space Green's Function for Transient Sources 40

3.4.2.3 Fields with Sources 40

3.4.3 Solution by Weighted Residuals 43

3.5 Some Other Methods Used in Coupling Analysis 46

3.5.1 Unit Cell Analysis in Periodic Structure Method 46

3.5.2 Mode Matching Methods 51

3.5.3 Moment Methods 52

3.5.4 Method of Characteristic Modes 52

3.5.5 Minimum Scattering Element Method 53

3.6 Practical Aspects of Numerical Methods in Mutual Coupling Analysis 54

3.6.1 Introduction 54

3.6.2 Numerical Quadrature 55

3.6.3 Matrix Inversion 56

3.7 Conclusion 58

References 59

4 Mutual Coupling in Arrays of Wire Antennas 63
Trevor S. Bird

4.1 Introduction 63

4.2 Formulation of the Problem 63

4.2.1 Moment Method 66

4.2.2 Moment Method Solution for the Dipole 67

4.3 Mutual Impedance 68

4.3.1 Closed Form Expressions for Mutual Impedance 70

4.3.2 Asymptotic Approximations to Mutual Impedance 73

4.4 Arrays of Wire Antennas 76

4.4.1 Full-Wave Dipole Above a Perfect Ground 77

4.4.2 The Yagi-Uda Array 80

4.4.3 7 x 7 array of closely packed elements 83

4.5 Concluding Remarks 84

References 84

5 Arrays of Planar Aperture Antennas 87
Trevor S. Bird

5.1 Introduction 87

5.2 Mutual Coupling in Waveguide and Horn Arrays 88

5.2.1 Integral Equation Formulation 88

5.2.2 Modal Representation 91

5.2.3 Modeling of Profiled Horns and Mode Matching 94

5.2.4 Asymptotic Approximation of Mutual Admittance 97

5.3 Coupling in Rectangular Waveguides and Horns 99

5.3.1 Self-Admittance of TE10 Mode 102

5.3.2 Example of Mutual Coupling Between Different-Sized Waveguides 104

5.3.3 Application to Horns 106

5.3.4 Waveguide-Fed Slot Arrays 111

5.3.5 Asymptotic Approximation of Coupling in Rectangular Apertures 112

5.3.6 Coupling in Horns Approximated with Quadratic Phase 114

5.4 Coupling in Arrays of Coaxial Waveguides and Horns 114

5.4.1 Self-Admittance of TE11 Mode in Coaxial Waveguide 118

5.4.2 TEM Mode Coupling in Coaxial Waveguide 120

5.4.3 Asymptotic Approximation of Coupling in Coaxial Waveguide Apertures 123

5.4.4 Coaxial and Circular Aperture Array Examples 127

5.5 Mutual Coupling Between Apertures of General Cross-Section 129

5.5.1 Elliptical Apertures 129

5.5.2 General Apertures 134

5.6 Coupling in Apertures Loaded with Dielectrics and Metamaterials 135

5.6.1 Dielectric-Loaded Apertures 136

5.6.2 Metamaterial-Loaded Apertures 142

5.7 Concluding Remarks 148

References 148

6 Arrays of Microstrip Patch Antennas 153
Trevor S. Bird

6.1 Introduction 153

6.2 Representation of Mutual Coupling Between Patch Antennas 155

6.2.1 E-Current Model of Coupling 159

6.2.2 Cavity Model (H-Model) of Coupling 162

6.2.3 Full-Wave Solution 165

6.3 Applications of Microstrip Arrays 167

6.3.1 Mutual Coupling Between Microstrip Patches 167

6.3.2 Steering by Switching Parasitic Elements 167

6.3.3 A Metasurface from Microstrip Patches 170

6.4 Concluding Remarks 174

References 174

7 Mutual Coupling Between Antennas on Conformal Surfaces 177
Trevor S. Bird

7.1 Introduction 177

7.2 Mutual Admittance of Apertures on Slowly Curving Surfaces 178

7.2.1 Green's Function Formulation for Curved Surfaces 178

7.2.2 The Cylinder 179

7.2.3 The Sphere 182

7.3 Asymptotic Solution for Fields Near Convex Surfaces 184

7.3.1 Review of Literature for Convex Surfaces 184

7.3.2 Asymptotic Solution for the Surface Fields 186

7.4 Mutual Coupling of Apertures in Quadric Surfaces 187

7.4.1 Closed-Form Expressions for Mutual Coupling Between Rectangular Waveguides in a Cylinder 188

7.4.2 Expressions for Mutual Coupling Between Circular Waveguides in a Sphere 194

7.4.3 Mutual Coupling Between Microstrip Patches on a Cylinder 197

7.5 Extension of Canonical Solution to Large Convex Surfaces with Slowly Varying Curvature 201

7.6 Applications of Coupling on Curved Surfaces 210

7.6.1 Mutual Coupling in a Waveguide Array on a Cylinder 210

7.6.2 Mutual Coupling Between Monopoles on a Cylinder 211

7.6.3 Mutual Coupling Between Waveguides on an Ellipsoid 215

7.7 Conclusion 216

References 217

8 Mutual Coupling Between Co-Sited Antennas and Antennas on Large Structures 221
Derek McNamara and Eqab Almajali

8.1 Preliminaries and Assumptions 221

8.1.1 The Problem at Hand 221

8.1.2 Course Adopted 223

8.2 Full-Wave CEM Modeling View of a Single Antenna 223

8.3 Full-Wave CEM Modeling View of Coupled Antennas in the Presence of a Host Platform 225

8.3.1 Field Point of View 225

8.3.2 Two-Port Network Parameter Point of View 227

8.4 Useful Expressions for Coupling in the Presence of a Host Platform 230

8.4.1 Motivation 230

8.4.2 Reciprocity and Reaction Theorems Revisited 230

8.4.3 Generalized Reaction Theorem 233

8.4.4 Expressions for Mutual Impedance and Open Circuit Voltage 234

8.4.5 Power Coupling 235

8.5 Supplementary Comments on CEM Modeling Methods 236

8.6 Full-Wave CEM Modeling of Coupled Antennas on a Platform -- The Ideal 243

8.7 Reduced Complexity Antenna Electromagnetic Models 244

8.7.1 Necessity for Simplified Antenna Models 244

8.7.2 Huygens' Box Model 244

8.7.3 Spherical Wave Expansion Models 246

8.7.4 Infinitesimal Dipole Models 246

8.7.5 Planar Aperture Models 24