Time-Domain Electromagnetic Reciprocity in Antenna Modeling

TABLE OF CONTENTS
Preface xiii

Acronyms xv

1 Introduction 1

1.1 Synopsis 2

1.2 Prerequisites 5

1.2.1 One-Sided Laplace Transformation 6

1.2.2 Lorentz’s Reciprocity Theorem 8

2 Cagniard-Dehoop Method of Moments for Thin-Wire Antennas 15

2.1 Problem Description 15

2.2 Problem Formulation 16

2.3 Problem Solution 18

2.4 Antenna Excitation 20

2.4.1 Plane-Wave Excitation 20

2.4.2 Delta-Gap Excitation 21

Illustrative Example 22

3 Pulsed EM Mutual Coupling Between Parallel Wire Antennas 25

3.1 Problem Description 25

3.2 Problem Formulation 26

3.3 Problem Solution 27

4 Incorporating Wire-Antenna Losses 29

4.1 Modification of the Impedance Matrix 30

5 Connecting a Lumped Element to The Wire Antenna 31

5.1 Modification of the Impedance Matrix 32

6 Pulsed EM Radiation from a Straight Wire Antenna 35

6.1 Problem Description 35

6.2 Source-Type Representations for the TD Radiated EM Fields 36

6.3 Far-Field TD Radiation Characteristics 38

7 EM Reciprocity Based Calculation of Td Radiation Characteristics 41

7.1 Problem Description 41

7.2 Problem Solution 42

Illustrative Numerical Example 43

8 Influence of a Wire Scatterer on a Transmitting Wire Antenna 47

8.1 Problem Description 47

8.2 Problem Solution 48

Illustrative Numerical Example 49

9 Influence of a Lumped Load on EM Scattering of a Receiving Wire Antenna 53

9.1 Problem Description 53

9.2 Problem Solution 54

Illustrative Numerical Example 55

10 Influence of a Wire Scatterer on a Receiving Wire Antenna 59

10.1 Problem Description 59

10.2 Problem Solution 59

Illustrative Numerical Example 61

11 EM-Field Coupling to Transmission Lines 65

11.1 Introduction 65

11.2 Problem Description 68

11.3 EM-Field-To-Line Interaction 68

11.4 Relation to Agrawal Coupling Model 71

11.5 Alternative Coupling Models Based on EM Reciprocity 73

11.5.1 EM Plane-Wave Incidence 73

11.5.2 Known EM Source Distribution 74

12 EM Plane-Wave Induced Thévenin’s Voltage on Transmission Lines 77

12.1 Transmission Line Above the Perfect Ground 77

12.1.1 Thévenin’s Voltage at x = x1 78

12.1.2 Thévenin’s Voltage at x = x2 81

12.2 Narrow Trace on a Grounded Slab 83

12.2.1 Thévenin’s Voltage at x = x1 85

12.2.2 Thévenin’s Voltage at x = x2 88

Illustrative Numerical Example 89

13 VED-Induced Thévenin’s Voltage on Transmission Lines 93

13.1 Transmission Line Above the Perfect Ground 93

13.1.1 Excitation EM Fields 94

13.1.2 Thévenin’s Voltage at x = x1 97

13.1.3 Thévenin’s Voltage at x = x2 98

13.2 Influence of Finite Ground Conductivity 98

13.2.1 Excitation EM Fields 98

13.2.2 Correction to Thévenin’s Voltage at x = x1 100

13.2.3 Correction to Thévenin’s Voltage at x = x2 101

Illustrative Numerical Example 101

14 Cagniard-Dehoop Method of Moments for Planar-Strip Antennas 103

14.1 Problem Description 105

14.2 Problem Formulation 106

14.3 Problem Solution 107

14.4 Antenna Excitation 109

14.4.1 Plane-Wave Excitation 110

14.4.2 Delta-Gap Excitation 111

14.5 Extension to a Wide-Strip Antenna 111

Illustrative Numerical Example 117

15 Incorporating Strip-Antenna Losses 121

15.1 Modification of the Impeditivity Matrix 122

15.1.1 Strip with Conductive Properties 123

15.1.2 Strip with Dielectric Properties 123

15.1.3 Strip with Conductive and Dielectric Properties 124

15.1.4 Strip with Drude-Type Dispersion 124

16 Connecting a Lumped Element to The Strip Antenna 125

16.1 Modification of the Impeditivity Matrix 126

17 Including a Pec Ground Plane 129

17.1 Problem Description 129

17.2 Problem Formulation 130

17.3 Problem Solution 131

17.4 Antenna Excitation 132

Illustrative Numerical Example 133

A Green’s Function Representation in an Unbounded, Homogeneous, and Isotropic Medium 137

B Time-Domain Response of an Infinite Cylindrical Antenna 141

B.1 Transform-Domain Solution 141

B.2 Time-Domain Solution 143

C Impedance Matrix 147

C.1 Generic Integral IA 147

C.2 Generic Integral IB 149

C.3 TD Impedance Matrix Elements 150

D Mutual-Impedance Matrix 151

D.1 Generic Integral JA 151

D.2 Generic Integral JB 153

D.3 TD Mutual-Impedance Matrix Elements 154

E Internal Impedance of a Solid Wire 157

F VED-Induced EM Coupling to Transmission Lines — Generic Integrals 159

F.1 Generic Integral I 159

F.2 Generic Integral J 163

F.3 Generic Integral K 165

G Impeditivity Matrix 169

G.1 Generic Integral J 169

G.1.1 Generic Integral JA 171

G.1.2 Generic Integral JB 175

H A Recursive Convolution Method and Its Implementation 177

H.1 Convolution-Integral Representation 177

H.2 Illustrative Example 179

H.3 Implementation of the Recursive Convolution Method 180

I Conductance and Capacitance of a Thin High-Contrast Layer 183

J Ground-Plane Impeditivity Matrix 187

J.1 Generic Integral I 187

J.1.1 Generic Integral IA 189

J.1.2 Generic Integral IB 193

K Implementation of CDH-Mom for Thin-Wire Antennas 195

K.1 Setting Space-time Input Parameters 195

K.2 Antenna Excitation 197

K.2.1 Plane-Wave Excitation 197

K.2.2 Delta-Gap Excitation 199

K.3 Impedance Matrix 200

K.4 Marching-on-in-Time Solution Procedure 202

K.5 Calculation of Far-Field TD Radiation Characteristics 203

L Implementation of VED-Induced Thévenin’s Voltages on a Transmission Line 205

L.1 Setting Space-Time Input Parameters 205

L.2 Setting Excitation Parameters 206

L.3 Calculating Thévenin’s Voltages 207

L.4 Incorporating Ground Losses 211

M Implementation of CDH-Mom for Narrow-Strip Antennas 215

M.1 Setting Space-Time Input Parameters 215

M.2 Delta-Gap Antenna Excitation 217

M.3 Impeditivity Matrix 217

M.4 Marching-on-in-Time Solution Procedure 200

References 223

Index 227