Radiating Nonuniform Transmission-Line Systems and the Partial Element Equivalent Circuit Method

Preface

Acknowledgments

List of Symbols

Introduction

1 Fundamentals of Electrodynamics

1.1 Maxwell Equations Derived from Conservation Laws - an Axiomatic Approach

1.2 The Electromagnetic Field as a Gauge Field - a Gauge Field Approach

1.3 The Relation Between the Axiomatic Approach and the Gauge Field Approach

1.4 Solutions of Maxwell Equations

1.5 Boundary Value Problems and Integral Equations

References

2 Nonuniform Transmission-Line Systems

2.1 Multiconductor Transmission Lines: General Equations

2.2 General Calculation Methods for the Product Integral/Matrizant

2.3 Semi-Analytic and Numerical Solutions for Selected Transmission Lines in the TLST

2.4 Analytic Approaches

References

3 Complex Systems and Electromagnetic Topology

3.1 The Concept of Electromagnetic Topology

3.2 Topological Networks and BLT Equations

3.3 Transmission Lines and Topological Networks

3.4 Shielding

References

4 The Method of Partial Element Equivalent Circuits (PEEC Method)

4.1 Fundamental Equations

4.2 Derivation of the Generalized PEEC Method in the Frequency Domain

4.3 Classification of PEEC Models

4.4 PEEC Models for the Plane Half Space

4.5 Geometrical Discretization in PEEC Modeling

4.6 PEEC Models for the Time Domain and the Stability Issue

4.7 Skin Effect in PEEC Models

4.8 PEEC Models Based on Dyadic Green's Functions for Conducting Structures in Layered Media

4.9 PEEC Models and Uniform Transmission Lines

4.10 Power Considerations in PEEC Models

References

Appendix A: Tensor Analysis, Integration and Lie Derivative

A.1 Integration Over a Curve and Covariant Vectors as Line Integrands

A.2 Integration Over a Surface and Contravariant Vector Densities as Surface Integrands

A.3 Integration Over a Volume and Scalar Densities as Volume Integrands

A.4 PoincarŽe Lemma

A.5 Stokes' Theorem

A.6 Lie Derivative

References

Appendix B: Elements of Functional Analysis

B.1 Function Spaces

B.2 Linear Operators

B.3 Spectrum of a Linear Operator

B.4 Spectral Expansions and Representations

References

Appendix C: Some Formulas of Vector and Dyadic Calculus

C.1 Vector Identities

C.2 Dyadic Identities

C.3 Integral Identities

Reference

Appendix D: Adaption of the Integral Equations to the Conductor Geometry

Appendix E: The Product Integral/Matrizant

E.1 The Differential Equation and Its Solution

E.2 The Determination of the Product Integral

E.3 Inverse Operation

E.4 Calculation Rules for the Product Integral

References

Appendix F: Solutions for Some Important Integrals

F.1 Integrals Involving Powers of square root x2 + b2

F.2 Integrals Involving Exponential and Power Functions

F.3 Integrals Involving Trigonometric and Exponential Functions

Reference

Index