Electromagnetic Reciprocity in Antenna Theory

Martin Štumpf, PhD, is an Associate Professor at SIX Research Centre, Brno University of Technology, Brno, The Czech Republic. His research interests include analytical and numerical modeling of wave field phenomena with an emphasis on electromagnetic compatibility and antenna engineering. He is a member of the IEEE and the IEEE Electromagnetic Compatibility Society.

Introduction xi

1 Basic Prerequisites 1

1.1 Laplace Transformation 3

1.2 Time Convolution 4

1.3 Time Correlation 5

1.4 EMReciprocity Theorems 6

1.4.1 Reciprocity Theorem of the Time-Convolution Type 8

1.4.2 Reciprocity Theorem of the Time-Correlation Type 9

1.4.3 Application of the Reciprocity Theorems to an Unbounded Domain 11

1.5 Description of the Antenna Configuration 13

1.5.1 Antenna Power Conservation 14

1.5.2 Antenna Interface Relations 16

2 Antenna Uniqueness Theorem 19

2.1 Problem Description 19

2.2 Problem Solution 19

3 Forward-Scattering Theorem in Antenna Theory 23

3.1 Problem Description 23

3.2 Problem Solution 23

4 Antenna Matching Theorems 31

4.1 Reciprocity Analysis of the Time-Correlation Type 31

4.1.1 Transmitting State 31

4.1.2 Receiving State 34

4.1.3 EquivalentMatching Condition 35

5 Equivalent Kirchhoff Network Representations of a Receiving Antenna System 41

5.1 Reciprocity Analysis of the Time-Convolution Type 41

5.1.1 Equivalent Circuits for Plane-Wave Incidence 41

5.1.2 Equivalent Circuits for a Known Volume-Current Distribution 45

6 The Antenna Systemin the Presence of a Scatterer 51

6.1 Receiving Antenna in the Presence of a Scatterer 51

6.2 Transmitting Antenna in the Presence of a Scatterer 56

6.2.1 Analysis Based on the Reciprocity Theorem of the Time-Convolution Type 57

6.2.2 Analysis Based on the Reciprocity Theorem of the Time-Correlation Type 59

7 EMCoupling Between Two Multiport Antenna Systems 65

7.1 Description of the Problem Configuration 65

7.2 Analysis Based on the Reciprocity Theorem of the Time-Convolution Type 68

7.3 Analysis Based on the Reciprocity Theorem of the Time-Correlation Type 71

8 Compensation Theorems for the EMCoupling Between Two Multiport Antennas 77

8.1 Description of the Problem Configuration 77

8.2 Analysis Based on the Reciprocity Theorem of the Time-Convolution Type 79

8.2.1 The Change in Scenario (BA) 79

8.2.2 The Change in Scenario (AB) 82

8.3 Analysis Based on the Reciprocity Theorem of the Time-Correlation Type 85

8.3.1 The Change in Scenario (BA) 85

8.3.2 The Change in Scenario (AB) 88

9 Compensation Theorems for the EMScattering of an Antenna System 95

9.1 Description of the Problem Configuration 95

9.2 Reciprocity Analysis 96

9.2.1 Compensation Theorems in Terms of Electric Current-excited Sensing EM Fields 99

9.2.2 Compensation Theorems in Terms of Voltage-Excited Sensing EM Fields 100

9.2.3 Power Reciprocity Expressions 101

AppendixA Lerch’s Uniqueness Theorem 107

A.1 Problem ofMoments 107

A.2 Proof of Lerch’s Theorem 108

References 111

Index 115