Foundations of Antenna Radiation Theory Eigenmode Analysis

Understand the theory and function of wireless antennas with this comprehensive guide

As wireless technology continues to develop, understanding of antenna properties and performance will only become more critical. Since antennas can be understood as junctions of waveguides, eigenmode analysis—the foundation of waveguide theory, concerned with the unexcited states of systems and their natural resonant characteristics—promises to be a crucial frontier in the study of antenna theory.

Foundations of Antenna Radiation Theory incorporates the modal analysis, generic antenna properties and design methods discovered or developed in the last few decades, not being reflected in most antenna books, into a comprehensive introduction to the theory of antennas. This book puts readers into conversation with the latest research and situates students and researchers at the cutting edge of an important field of wireless technology.

The book also includes:

• Detailed discussions of the solution methods for Maxwell equations and wave equations to provide a theoretical foundation for electromagnetic analysis of antennas
• Recent developments for antenna radiation in closed and open space, modal analysis and field expansions, dyadic Green’s functions, time-domain theory, state-of-the-art antenna array synthesis methods, wireless power transmission systems, and more
• Innovative material derived from the author’s own research

Foundations of Antenna Radiation Theory is ideal for graduate or advanced undergraduate students studying antenna theory, as well as for reference by researchers, engineers, and industry professionals in the areas of wireless technology.

Professor Wen Geyi is a Fellow of the IEEE. He has published very widely on theories of microwaves and antennas. He has authored four books and over 100 journal publications and holds more than 40 patents.

Chapter 1 Eigenvalue Theory

1.1 Maxwell Equations

1.1.1 Wave Equations

1.1.2 Properties of Electromagnetic Fields

1.1.2.1 Superposition Theorem

1.1.2.2 Conservation of Electromagnetic Field Energy

1.1.2.3 Equivalence Theorems

1.1.2.4 Reciprocity

1.2 Methods for Partial Differential Equations

1.2.1 Method of Separation of Variables

1.2.1.1 Rectangular Coordinate System

1.2.1.2 Cylindrical Coordinate System

1.2.1.3 Spherical Coordinate System

1.2.2 Method of Green’s function

1.2.2.1 Green’s functions for Helmholtz Equation

1.2.2.2 Dyadic Green’s functions and Integral Representations   

1.2.3 Variational Method

1.3 Eigenvalue Problem for Hermitian Matrix

1.3.1 Properties

1.3.2 Rayleigh Quotient

1.4 Eigenvalue Problems for the Laplace Operator on Scalar Field

1.4.1 Rayleigh Quotient

1.4.2 Properties of Eigenvalues

1.4.3 Completeness of Eigenfunctions

1.4.4 Differential Equations with Variable Coefficients    

1.4.5 Green’s function and Spectral Representation

1.5 Eigenvalue Problems for the Laplace Operator on Vector Field

1.5.1 Rayleigh Quotient

1.5.2 Completeness of Vector Modal Functions

1.5.3 Classification of Vector Modal Functions

1.6 Ritz Method for the Solution of Eigenvalue Problem

1.7 Helmholtz Theorems

1.7.1 Helmholtz Theorem for the Field in Infinite Space

1.7.2 Helmholtz Theorem for the Field in Finite region

1.7.3 Helmholtz Theorem for Time-dependent Field

1.8 Curl Operator

1.8.1 Eigenfunctions of Curl Operator

1.8.2 Plane-Wave Expansions for Dyadic Green’s functions

Chapter 2 Radiation in Waveguide

2.1 Vector Modal Functions for Waveguide

2.1.1 Classification of Vector Modal Functions

2.1.2 Vector Modal Functions for Typical Waveguides

2.1.2.1 Rectangular Waveguide

2.1.2.2 Circular Waveguide

2.1.2.3 Coaxial Waveguide

2.2 Radiated Fields in Waveguide

2.2.1 Modal Expansions for the Fields and Dyadic Green’s Functions

2.2.2 Dyadic Green’s functions for Semi-infinite Waveguide

2.3 Waveguide Discontinuities

2.3.1 Excitation of Waveguide

2.3.2 Conducting Obstacles in Waveguide

2.3.3 Coupling by Small Aperture

2.4 Transient Fields in Waveguide

Chapter 3 Radiation in Cavity Resonator

3.1 Radiated Fields in Cavity Resonator

3.1.1 Classification of Vector Modal Functions for Cavity Resonator

3.1.2 Modal Expansions for the Fields and Dyadic Green’s functions

3.2 Cavity with Openings

3.3.1 Cavity with One Port

3.3.2 Cavity with Two Ports

3.4 Waveguide Cavity Resonator

3.4.1 Field Expansions by Vector Modal Functions of Waveguide

3.4.2 Modal Representations of Dyadic Green’s functions

3.5 Vector Modal Functions for Typical Waveguide Cavity Resonators

3.5.1 Rectangular Waveguide Cavity

3.5.2 Circular Waveguide Cavity

3.5.3 Coaxial Waveguide Cavity

3.6 Radiation in Waveguide Revisited

3.7 Transient Fields in Cavity Resonator

Chapter 4 Radiation in Free Space (I): Generic Properties

4.1 Antenna Parameters              

4.1.1 Power, Efficiencies and Impedance

4.1.2 Field Regions, Radiation Pattern, Radiation Intensity, Directivity and Gain

4.1.3 Vector Effective Length, Equivalent Area and Antenna Factor

4.1.4 Antenna Quality Factor

4.2 Theory of Spherical Waveguide

4.2.1 Vector Modal Functions for Spherical Waveguide

4.2.2 Modal Expansions of Fields and Dyadic Green’s functions

4.2.3 Properties of Spherical Vector Wave Functions

4.2.4 Far-Zone fields

4.3 Stored Field Energies and Radiation Quality Factor

4.3.1 Stored Field Energies in General Materials

4.3.2 Stored Field Energies of Antenna

4.3.3 Radiated Field Energy

4.3.4 Evaluation of Radiation Quality Factor

4.4 Modal Quality Factors

4.4.1 Stored Field Energies Outside the Circumscribing Sphere of Antenna

4.4.2 Two Inequalities for Spherical Hankel Functions

4.4.3 Properties of Modal Quality Factors

4.4.4 Lower Bound for Antenna Quality Factor

4.5 Upper Bounds for the Products of Gain and Bandwidth

4.5.1 Directive Antenna

4.5.2 Omni-directional Antenna

4.5.3 Best Possible Antenna Performance-Guidelines for Small Antenna Design

4.6 Expansions of Radiated Fields in Time Domain

Chapter 5 Radiation in Free Space (II): Modal Analysis

5.1 Basic Antenna Types

5.2 Equivalent Current Distributions of Antenna

5.3 Antenna as a Waveguide Junction

5.4 Integral Equation Formulations

5.4.1 Compensation Theorem for Time-harmonic Fields

5.4.2 Integral Equations for Composite Structure

5.4.3 Integral Equation for Wire Antenna

5.5 Vertical Dipole          

5.6 Horizontal Dipole

5.7 Loop

5.8 Spherical Dipole

5.9 Dipole near Conducting Sphere

5.10 Finite Length Wire Antenna

5.11 Aperture Antenna

5.12 Microstrip Patch Antenna

5.13 Resonant Mode Theory for Antenna Design

5.13.1 Formulations

5.13.2 Applications

Chapter 6 Radiation in Free Space (III): Array Analysis and Synthesis

6.1 Introduction to Array Analysis

6.1.1 Array Factor

6.1.2 Linear array

6.1.2.1 Linear Array with Uniform Amplitude

6.1.2.2 Linear Array with Non-uniform amplitude             

6.1.3 Circular Array

6.1.4 Planar Array

6.2 Introduction to Array Synthesis with Conventional Methods

6.2.1 Array Factor and Space Factor for Line Source

6.2.2 Schelkunoff Unit Circle Method

6.2.3 Dolph-Chebyshev Method

6.2.4 Fourier Transform Method

6.2.4.1 Continuous Line Source

6.2.4.2 Linear Array

6.3 Power Transmission Between Two Antennas

6.3.1 The General Power Transmission Formula

6.3.2 Power Transmission between Two Planar Apertures

6.3.3 Power Transmission between Two Antennas with Large Separation

6.4 Synthesis of Antenna Arrays with MMPTE

6.4.1 Power Transmission between Two Antenna Arrays

6.4.1.1 Unconstrained Optimization

6.4.1.2 Weighted Optimization

6.4.1.3 Constrained Optimization

6.4.2 Applications

6.5 Synthesis of Arrays with EMMPTE

6.5.1 Array with Specified Energy Distribution

6.5.2 Arrays with Specified Power Distribution

6.5.3 Applications

Appendix A Vector Analysis

Appendix B Dyadic Analysis

Appendix C SI Unit System

Appendix D Unified Theory for Fields (UTF)

D.1 Lorentz Transformation

D.2 Maxwell-Like Equations Derived from an Ontological Vector Field

D.3 Field Equations Derived from an Ontological Scalar Field

D.3.1 Wave Equation Derived from an Ontological Scalar Field

D.3.2 Maxwell-Like Equations Derived from an Ontological Scalar Field

D.3.3 Conservation Laws

D.3.3.1 Conservation of Energy

D.3.3.2 Conservation of Momentum

D.4 Interaction between Two Systems   

D.5 Applications

D5.1 Maxwell Equations Derived from a Static Electric Field

D5.2 Maxwell-Like Equations Derived from a Static Gravitational Field

D.6 Maxwell-Like Equations Derived from Einstein Field Equations

D.7 Universal Laws of Nature Derived from UTR

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