Electromagnetic Sources and Electromagnetic Fields

✍ Scribed by Gaobiao Xiao

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 347
• Series: Modern Antenna
• Edition: 1
• Category: Library

✦ Synopsis

This book presents a modified spherical harmonic expansion method in which the electromagnetic fields and their sources are expanded with the same set of spherical vector basis functions in a similar procedure. Explicit expressions for the electromagnetic fields, potentials, energies, and the related Green’s functions are derived for the spherical modes in both frequency domain and time domain. Based on the formulation, the relationships between the electromagnetic sources, the electromagnetic far fields, and the electromagnetic near fields are clearly revealed. In particular, a nonuniform transmission line model is developed for intuitively characterizing the total radiation process. The introduction of the cutoff radius and the cutoff mode degree provides a simple reference for determining the numbers of degrees of freedom of the fields associated with sources in a bounded region. Based on the theory, an efficient hybrid method for synthesizing antenna arrays with complex footprints is proposed and demonstrated with several numerical examples. Effective algorithms are also developed for reconstructing the radiating part of the current sources.

This book is intended for researchers, engineers, and graduate students who are interested in studying the energy transfer in electromagnetic radiation, synthesis and measurement of antenna arrays, and applications of inverse electromagnetic source problems.

✦ Table of Contents

Preface
Contents
About the Author
Abbreviations
1 Basic Concepts in Electromagnetic Radiation
1.1 Electromagnetic Fields in Free Space
1.1.1 Fields and Potentials
1.1.2 Static Fields
1.1.3 Time Harmonic Fields
1.1.4 Hertzian Dipole
1.2 Electromagnetic Energy and Power
1.2.1 Electric Energy and Magnetic Energy in Time Domain
1.2.2 Electric Energy and Magnetic Energy in Frequency Domain
1.2.3 Electromagnetic Radiation Power
1.3 Electromagnetic Momentum
References
2 Q Factor of a Radiator
2.1 Q Factor for Circuits
2.2 Q Factor for Antennas
References
3 Non-relativistic Radiation of a Moving Charge
3.1 Liénard-Wiechert Potential
3.2 Electromagnetic Fields of a Moving Charge
3.3 Radiation Power
3.4 Energy of a Moving Charge
References
4 Spherical Harmonic Expansion
4.1 Spherical Basis Functions
4.1.1 Expansion of Scalar Functions
4.1.2 Expansion of Vector Functions
4.1.3 Reconstructing a Vector from Its Divergence and Curl
4.2 Spherical Harmonic Expansion in Frequency Domain
4.2.1 Governing Equations for Spherical Harmonics
4.2.2 Spherical Harmonic Fields
4.2.3 The Dyadic Green’s Functions
4.2.4 Spherical Harmonic Expansion for Potentials
4.2.5 Electromagnetic Energies and Radiation Powers
4.2.6 Electric Sources and Magnetic Sources
4.2.7 Discussions
4.3 Translation of Spherical Harmonic Fields
4.3.1 Spherical Harmonic Expansion for Arrays
4.3.2 Spherical Harmonic Expansion for Hertzian Dipole
4.4 Spherical Harmonic Expansion for Static Sources
4.4.1 Spherical Basis Functions with Real Values
4.4.2 Spherical Harmonic Expansion for Static Fields
4.4.3 Spherical Harmonic Expansion for Static Potentials
4.5 Spherical Harmonic Expansion in Time Domain
4.5.1 Time Domain Governing Equations for Spherical Harmonics
4.5.2 Time Domain Green’s Function for Spherical Harmonics
4.6 Spherical Harmonic Expansion in Radially-Nonuniform Media
References
5 Nonuniform Transmission Line Model
5.1 Chu’s Equivalent Circuit Model
5.2 NTL Model in Frequency Domain
5.2.1 Basic Structure of the NTL Model in Free Space
5.2.2 Other Parameters of the NTL Model
5.2.3 FDFD Algorithm for Solving the Telegraphers’ Equations
5.3 NTL Model in Time Domain
5.3.1 Time Domain Equivalent Lumped Element Circuit Model
5.3.2 FDTD Algorithm for Solving the Telegraphers’ Equations
5.4 NTL Model in Radially Varying Media
5.5 NTL Model for Lossy Media
References
6 Pulse Radiator in Free Space
6.1 Separation of the Electromagnetic Energy
6.1.1 Energy Separation Formulation
6.1.2 The Macroscopic Schott Energy of a Moving Charge
6.2 Explicit Expressions for Electromagnetic Energies
6.3 Electromagnetic Power of a Pulse Radiator
6.4 Mutual Electromagnetic Couplings
6.4.1 Electromagnetic Couplings Among Multiple Radiators
6.4.2 Application for Interpreting the Aharonov-Bohm Effect
6.5 Electromagnetic Energies of Time Harmonic Sources
6.5.1 General Expressions in Terms of Fields
6.5.2 Explicit Expressions in Terms of Sources
6.6 Typical Radiators
6.6.1 Hertzian Dipole
6.6.2 Solenoidal Loop Current
6.6.3 Thin Plate Yagi Antenna
6.6.4 Discussions
6.7 Q Factors of Antennas
6.7.1 Conventional Methods
6.7.2 Calculation of Q Factors of Antennas
6.7.3 Numerical Examples
References
7 Synthesis of Far Field Patterns
7.1 Electromagnetic Far Field in Free Space
7.2 Methods for Synthesis of Far Field Patterns
7.2.1 Pattern Synthesis with Optimization Method
7.2.2 Direct Pattern Synthesis Method
7.2.3 Continuous Array Factor and Discrete Array Factor
7.2.4 Hybrid Method for Synthesis of Array Factor
7.3 Pattern Synthesis for Line Source
7.4 Pattern Synthesis for Rectangular Planar Source
7.4.1 Pattern Synthesis with a Single Current Sheet
7.4.2 Synthesis of Non-Mirror Symmetrical Pattern
7.5 Pattern Synthesis for Current on a Spherical Surface
7.6 Summary
References
8 Electromagnetic Inverse Source Problems
8.1 General Principles for Inverse Source Problems
8.1.1 Electric Fields of Sources in Bounded Region
8.1.2 Effective NDFs of the Near Fields
8.1.3 Numerical Algorithm for Reconstructing Current Sources
8.2 Discrete Hertzian Dipole Array
8.3 Reconstruction of Planar Sources from Far Field
8.3.1 Standard Reconstruction Algorithm for Current Sheet
8.3.2 Partial Sampling Algorithm for Current Sheets
8.4 Discussions
References
Subject Index