Electromagnetic Reciprocity in Antenna Theory E-Book

Martin Stumpf

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 108

Veröffentlichungsjahr: 2017

Beschreibung

Provides a self-contained account on applications of electromagnetic reciprocity theorems to multiport antenna systems The reciprocity theorem is among the most intriguing concepts in wave field theory and has become an integral part of almost all standard textbooks on electromagnetic (EM) theory. This book makes use of the theorem to quantitatively describe EM interactions concerning general multiport antenna systems. It covers a general reciprocity-based description of antenna systems, their EM scattering properties, and further related aspects. Beginning with an introduction to the subject, Electromagnetic Reciprocity in Antenna Theory provides readers first with the basic prerequisites before offering coverage of the equivalent multiport circuit antenna representations, EM coupling between multiport antenna systems and their EM interactions with scatterers, accompanied with the corresponding EM compensation theorems. In addition, the text: * Presents basic prerequisites including the definition of the notation, integral transformations, and EM reciprocity theorems in their general form * Explores multiport antenna forward-scattering theorem, multiport antenna matching theorem and uniqueness theorem * Supplements each chapter with a solved illustrative example Electromagnetic Reciprocity in Antenna Theory is an excellent text for EMC and antenna researchers and students of the subject as well.

Leseprobe

Contents

Cover

Series Page

Title Page

Copyright

Dedication

Introduction

Chapter 1: Basic Prerequisites

1.1 Laplace Transformation

1.2 Time Convolution

1.3 Time Correlation

1.4 EM Reciprocity Theorems

1.5 Description of the Antenna Configuration

Chapter 2: Antenna Uniqueness Theorem

2.1 Problem Description

2.2 Problem Solution

Chapter 3: Forward-Scattering Theorem in Antenna Theory

3.1 Problem Description

3.2 Problem Solution

Exercises

Chapter 4: Antenna Matching Theorems

4.1 Reciprocity Analysis of the Time-Correlation Type

Exercises

Chapter 5: Equivalent Kirchhoff Network Representations of a Receiving Antenna System

5.1 Reciprocity Analysis of the Time-Convolution Type

Exercise

Chapter 6: The Antenna System in the Presence of a Scatterer

6.1 Receiving Antenna in the Presence of a Scatterer

6.2 Transmitting Antenna in the Presence of a Scatterer

Exercise

Chapter 7: EM Coupling Between Two Multiport Antenna Systems

7.1 Description of the Problem Configuration

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

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

Exercise

Chapter 8: Compensation Theorems for the EM Coupling Between Two Multiport Antennas

8.1 Description of the Problem Configuration

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

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

Exercise

Chapter 9: Compensation Theorems for the EM Scattering of an Antenna System

9.1 Description of the Problem Configuration

9.2 Reciprocity Analysis

Exercises

Appendix A: Lerch's Uniqueness Theorem

A.1 Problem of Moments

A.2 Proof of Lerch's Theorem

References

Index

End User License Agreement

List of Tables

Table 1.1

Table 1.2

Table 1.3

Table 3.1

Table 3.2

Table 4.1

Table 4.2

Table 4.3

Table 5.1

Table 5.2

Table 5.3

Table 6.1

Table 6.2

Table 6.3

Table 6.4

Table 6.5

Table 6.6

Table 6.7

Table 7.1

Table 7.2

Table 8.1

Table 8.2

Table 8.3

Table 8.4

Table 8.5

Table 8.6

Table 8.7

Table 8.8

Table 9.1

Table 9.2

List of Illustrations

Figure A.1

Figure 1.1

Figure 1.2

Figure 1.3

Figure 1.4

Figure 1.5

Figure 1.6

Figure 1.7

Figure 2.1

Figure 3.1

Figure 4.1

Figure 5.1

Figure 6.1

Figure 6.2

Figure 6.3

Figure 7.1

Figure 7.2

Figure 8.1

Figure 8.2

Figure 9.1

Figure 9.2

Guide

Cover

Table of Contents

Begin Reading

Chapter 1

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Electromagnetic Reciprocity in Antenna Theory

Martin Štumpf

Copyright © 2018 by The Institute of Electrical and Electronics Engineers, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.

Published simultaneously in Canada.

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ISBN: 978-1-119-46637-6

Dedicated to H. A. Lorentz Chair Emeritus Professor Adrianus T. de Hoop on the occasion of his 90th birthday

Much of the research work included in this book was sponsored by the Czech Science Foundation under Grant 17-05445Y. This research was also partially supported by the Czech Ministry of Education, Youth and Sports under Grant LO1401 (National Sustainability Program). This financial support is gratefully acknowledged.

Special thanks go to Danielle Lacourciere and Mary Hatcher at Wiley-IEEE Press, and to Shikha Pahuja, PM at Thomson Digital, for their professional assistance that helped to publish the book in a timely manner.

Introduction

Reciprocity theorems are among the most intriguing concepts in the study of wave fields. Since its introduction by H.A. Lorentz in 1896 [33], the concept of reciprocity has become an integral part of (almost) all standard textbooks on electromagnetic (EM) theory (e.g., [27], Sec. 3.8). Its early developments in electrical engineering refer to Rayleigh's (acoustic) reciprocity theorem [32] and are closely related to Kirchhoff's networks [5]. Widespread applications of EM reciprocity were initially obstructed by a somewhat narrow understanding of the concept of reciprocity and its conditions of validity [2, 6]. An important step forward in putting EM reciprocity into practical use was the introduction of the concept of reaction [37]. While still limited to the “source-field interaction” only, its illuminating notation has paved the way for the development of novel approximate solutions (e.g., Ref. [8]) and variational computational formulations [26]. The original EM reciprocity with the time-harmonic dependence were extended by Welch, who first presented an EM reciprocity theorem of the time-correlation type applying to homogeneous, isotropic, and lossless media [50] and, subsequently, changed the theorem into its time-convolution type and included conductive losses [51]. A clear distinction between the reciprocity theorem of the time-convolution and time-correlation types has been later given by Bojarski [3] who has stressed the importance of the nature of the time dependence with respect to the radiation condition. His generalized time-domain (TD) reciprocity theorem, however, is restricted to homogeneous and isotropic media, where the EM field representation in terms of the scalar and vector potentials applies. This has been later extended by de Hoop [14], who has introduced the general forms of the EM reciprocity theorems for EM field states in linear, time-invariant, yet arbitrarily inhomogeneous, anisotropic, and dispersive media.

The current understanding of the reciprocity theorem can be briefly stated as follows ([16], Sec. 28.1): “A reciprocity theorem interrelates, in a specific manner, the EM field or wave quantities that characterize two admissible states that could occur in one and the same time-invariant domain of space. Each of the two states can be associated with its own set of time-invariant medium parameters and its own set of source distributions.” In this general sense, the reciprocity theorem is no longer understood as a mere statement about the source-observer interchange, but it is rather envisaged as being representative of the quantitative interaction between the observed field quantity (or the EM field to be actually calculated) and an observational action (or a suitable testing state) in any EM measurement (or computational) configuration. Accordingly, the reciprocity theorem encompasses all the formulations of direct/inverse source/scattering problems [16, 22, 23] and can be thus understood as a truly unifying principle in the wave field modeling [15]. This view is also followed throughout this book, where the EM reciprocity theorem is applied to analyze EM reciprocity properties of multiport antenna systems.

In Chapter 1 we make the reader acquainted with some basic mathematical tools necessary for the reciprocity-based antenna system analysis. In particular, we define the one-sided Laplace transformation and discuss its use in the context of the EM reciprocity theorems of the time-convolution and time-correlation types. Most of the results in the book are then derived under the Laplace transformation, that is, in the complex-frequency domain (FD). Furthermore, the generic (multiport) antenna configuration is described. In particular, we discuss the antenna-system material constitutive parameters and the proper definition of Kirchhoff-type accessible ports.

In Chapter 2 we analyze the conditions that must be placed upon the antenna-system constitutive parameters to get one and the same radiated causal EM wave fields. Since the proof of uniqueness largely relies on Lerch's theorem, this chapter is supplemented with Appendix A, where the theorem along with its proof are given.

In Chapter 3 we provide a special form of the forward-scattering theorem (in the complex-FD) that applies to the analyzed multiport antenna configuration. Its real-FD and time-domain (TD) counterparts are subsequently discussed in the corresponding exercise at the end of the chapter.

In Chapter 4 it is shown that the classic (local) conjugate matching condition has its (global) counterpart expressed in terms of the corresponding scattered and radiated far-field amplitudes. The full equivalence between the two matching conditions is then demonstrated for an important class of small antennas in the accompanying (solved) exercises.

In Chapter 5 we apply the reciprocity theorem of the time-convolution type to one and the same N-port antenna system to find its equivalent Kirchhoff network representations. The corresponding equivalent source generators are specified for the excitation via a known volume-current distribution and via an incident plane wave. The chapter is concluded by a solved exercise, where the relation between the absorption cross section of the load and the antenna gain is rigorously derived for an 1-port antenna system.

The impact of a scatterer on the equivalent Kirchhoff network representations of a multiport antenna system is described in Chapter 6. Both transmitting and receiving situations are studied in detail. In the corresponding exercise, we analyze the contribution of a small raindrop to the equivalent voltage-source strength of a short-wire antenna.

In Chapter 7 the EM reciprocity theorems are applied to analyze the mutual EM coupling between two multiport antenna systems. Here, without loss of generality, the interaction is described in terms of (open-circuited) impedance parameters. Some interesting properties of the transfer-impedance matrix that follow from the application of the time-convolution and time-correlation reciprocity theorems are pointed out.

The EM field transfer between two multiport antenna systems is inevitably affected by the presence of neighboring objects. In Chapter 8 we apply the EM reciprocity theorems to show how the presence of such an object manifests itself in the transfer-impedance matrix. This chapter is further supplemented with an illustrative exercise that results in an efficient formula for lightning-induced EM coupling calculations.

In Chapter 9