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1 Fundamentals of Electrodynamics 1
1.1 Maxwell Equations Derived from Conservation Laws – an Axiomatic Approach 1
1.1.1 Charge Conservation 3
1.1.2 Lorentz Force and Magnetic Flux Conservation 5
1.1.3 Constitutive Relations and the Properties of Spacetime 11
1.1.4 Remarks 12
1.2 The Electromagnetic Field as a Gauge Field – a Gauge Field Approach 13
1.2.1 Differences of Physical Fields that are Described by Reference Systems 14
1.2.2 The Phase of Microscopic Matter Fields 15
1.2.3 The Reference Frame of a Phase 16
1.2.4 The Gauge Fields of a Phase 18
1.2.5 Dynamics of the Gauge Field 21
1.3 The Relation Between the Axiomatic Approach and the Gauge Field Approach 24
1.3.1 Noether Theorem and Electric Charge Conservation 24
1.3.2 Minimal Coupling and the Lorentz Force 24
1.3.3 Bianchi Identity and Magnetic Flux Conservation 26
1.3.4 Gauge Approach and Constitutive Relations 27
1.4 Solutions of Maxwell Equations 28
1.4.1 Wave Equations 29
1.4.1.1 Decoupling of Maxwell Equations 29
1.4.1.2 Equations of Motion for the Electromagnetic Potentials 30
1.4.1.3 Maxwell Equations in the Frequency Domain and Helmholtz Equations 31
1.4.1.4 Maxwell Equations in Reciprocal Space 32
1.4.2 Boundary Conditions at Interfaces 33
1.4.3 Dynamical and Nondynamical Components of the Electromagnetic Field 33
1.4.3.1 Helmholtz’s Vector Theorem, Longitudinal and Transverse Fields 33
1.4.3.2 Nondynamical Maxwell Equations as Boundary Conditions in Time 35
1.4.3.3 Longitudinal Part of the Maxwell Equations 36
1.4.3.4 Transverse Part of the Maxwell Equations 37
1.4.4 Electromagnetic Energy and the Singularities of the Electromagnetic Field 39
1.4.5 Coulomb Fields and Radiation Fields 41
1.4.6 The Green’s Function Method 44
1.4.6.1 Basic Ideas 45
1.4.6.2 Self-Adjointness of Differential Operators and Boundary Conditions 46
1.4.6.3 General Solutions of Maxwell Equations 49
1.4.6.4 Basic Relations Between Electromagnetic Green’s Functions 49
1.5 Boundary Value Problems and Integral Equations 50
1.5.1 Surface Integral Equations in Short 50
1.5.2 The Standard Electric Field Integral Equations of Antenna Theory and
Radiating Nonuniform Transmission-Line Systems 51
1.5.2.1 Pocklington’s Equation 51
1.5.2.2 Hall′en’s Equation 52
1.5.2.3 Mixed-Potential Integral Equation 53
1.5.2.4 Schelkunoff ’s Equation 55
References 55
2 Nonuniform Transmission-Line Systems 57
2.1 Multiconductor Transmission Lines: General Equations 59
2.1.1 Geometric Representation of Nonuniform Transmission Lines 59
2.1.1.1 Local Coordinate System 59
2.1.1.2 Tangential Surface Vector 61
2.1.1.3 Volume and Surface Integrals 61
2.1.2 Derivation of Generalized Transmission-Line Equations 62
2.1.2.1 Continuity Equation 62
2.1.2.2 Reconstruction of the Densities 63
2.1.3 Mixed Potential Integral Equation 64
2.1.3.1 Thin-Wire Approximation 65
2.1.3.2 Representation as Matrix Equations 65
2.1.3.3 Current and Charge Trial Function 65
2.1.3.4 Generalized Telegrapher Equations and TLST 66
2.1.4 Computation of Generalized Transmission-Line Parameters 67
2.1.4.1 Parameters 67
2.1.4.2 Source Terms 69
2.1.4.3 Solution of the Extended Telegrapher Equations 69
2.1.4.4 Returning to Voltages? 70
2.1.4.5 Discussion of the New Parameters 72
2.1.4.6 Asymmetric Parameter Matrices 73
2.1.5 Numerical Evaluation of the Parameters 74
2.1.5.1 Starting Values for the Iteration 74
2.1.5.2 First Iteration 75
2.1.5.3 Taylor Series Expansion of the Product Integral 76
2.1.5.4 Eigenvalue Decomposition 78
2.1.5.5 Discussion of the Numerical Methods 79
2.2 General Calculation Methods for the Product Integral/Matrizant 79
2.2.1 Picard Iteration 80
2.2.2 Volterra’s Method and the Product Integral 81
2.2.3 Recursion Formulas for Linear Interpolation 83
2.2.4 Approximation by Power Series 85
2.2.5 Interpolation from Diagonalization 88
2.2.6 Numerical Integration 91
2.2.6.1 Euler–Cauchy Method 93
2.2.6.2 Integration by trapezoidal rule 93
2.2.6.3 Explicit Runge–Kutta Method 94
2.2.6.4 Hermite Integration 96
2.2.6.5 Improving Accuracy by the Romberg Method 98
2.2.6.6 Controlling Step Size and Error 99
2.2.7 Remarks on Efficiency and the Choice of an Appropriate Method 101
2.3 Semi-Analytic and Numerical Solutions for Selected Transmission Lines in the TLST 102
2.3.1 The Straight, Finite Length Wire Above Ground 102
2.3.2 The Semi-Infinite Line 107
2.3.3 Field Coupling to an Infinite Line 109
2.3.4 The Skewed Wire Transmission Line 111
2.3.5 The Periodic Transmission Line 115
2.3.6 Cross Talk in a Nonuniform Multiconductor Transmission Line 118
2.4 Analytic Approaches 119
2.4.1 Classical Telegrapher Equations for Nonuniform Transmission Lines 119
2.4.1.1 Basic Definitions and Equations 119
2.4.2 Calculation Methods for the General Solution 122
2.4.2.1 The Piecewise-Constant Approximation of the Characteristic
Impedance Matrix 122
2.4.2.2 The Continuous Approximation of the Characteristic Impedance Matrix 124
2.4.2.3 Circulant Nonuniform MTLs 128
2.4.2.4 General Approach to Calculate the Matrizant 130
2.4.3 Matrizant Reduction 132
References 135
3 Complex Systems and Electromagnetic Topology 139
3.1 The Concept of Electromagnetic Topology 139
3.2 Topological Networks and BLT Equations 143
3.2.1 Wave Quantities 144
3.2.2 BLT 1 Equation 145
3.2.3 BLT 2 Equation 147
3.2.4 Admittance Representation 149
3.3 Transmission Lines and Topological Networks 152
3.3.1 Transformation into a Propagation Matrix 155
3.3.2 Equivalent Scattering Matrices 156
3.3.3 Admittance Matrix 157
3.4 Shielding 157
3.4.1 Model for the Transfer Impedance Based on NMTLT 158
3.4.1.1 Transfer Parameters of Cables 158
3.4.1.2 Determination of the Per-unit-length Parameters 160
3.4.1.3 Computation of the Transfer Impedance 163
3.4.2 Shielding of an Anisotropic Spherical Shell 168
3.4.2.1 Shielding of a Plane Wall 171
3.4.2.2 Spherical Shell 171
3.4.2.3 Application to Thin Conductive Shells 172
3.4.2.4 Conclusions 177
References 177
4 The Method of Partial Element Equivalent Circuits (PEEC Method) 179
4.1 Fundamental Equations 179
4.1.1 Maxwell Equations and Real Media for Interconnections 179
4.1.2 Mixed Potential Integral Equations (MPIE) 183
4.2 Derivation of the Generalized PEEC Method in the Frequency Domain 186
4.2.1 The PEEC Equation System in the Frequency Domain 186
4.2.2 Generalized Partial Elements and Circuit Interpretation 191
4.3 Classification of PEEC Models 193
4.3.1 Classification in Dependence on Media 193
4.3.1.1 PEEC Models for Conductors 193
4.3.1.2 PEEC Models for Dielectrics 194
4.3.2 Classification in Dependence on the Relation of the Maximum Frequency of
Interest to the Discretization Length 194
4.3.2.1 PEEC Models with Generalized Partial Elements 194
4.3.2.2 PEEC Models with Center-to-Center Retardation 195
4.3.2.3 Quasi-Static PEEC Models 196
4.4 PEEC Models for the Plane Half Space 197
4.5 Geometrical Discretization in PEEC Modeling 201
4.5.1 Orthogonal Cells 201
4.5.2 Nonorthogonal Cells 202
4.5.3 Triangular Cells 205
4.6 PEEC Models for the Time Domain and the Stability Issue 209
4.6.1 Standard PEEC Models for the Time Domain 210
4.6.2 General Remarks on Stability of PEEC Model Solutions 211
4.6.3 Stability Improvement of PEEC Models with Center-to-Center Retardation 212
4.6.4 Stable Time Domain PEEC Models by Parametric Macromodeling the
Generalized Partial Elements 214
4.6.4.1 Stable Time Domain PEEC Models by Full-Spectrum Convolution
Macromodeling (FSCM) 214
4.6.4.2 Stable Time Domain PEEC Models by Macromodeling Using
Foster’s Rational Functions and Circuit Synthesis 219
4.7 Skin Effect in PEEC Models 220
4.7.1 Cross-Sectional Discretization of Wires 220
4.7.2 Skin Effect Modeling by Means of a Global Surface Impedance 221
4.7.3 Skin Effect Modeling by Means of a Local Mean Surface Impedance 222
4.8 PEEC Models Based on Dyadic Green’s Functions for Conducting Structures in
Layered Media 227
4.8.1 Motivation 227
4.8.2 The DGFLM–PEEC Method 228
4.8.3 DGFLM–PEEC Model for the Stripline Region 233
4.8.3.1 Green’s Functions for the Stripline Region 234
4.8.3.2 Discussion of the Behavior of the Green’s Functions 235
4.8.3.3 Frequency Domain DGFLM-PEEC Model 236
4.8.3.4 DGFLM–PEEC Models in the Time Domain 243
4.9 PEEC Models and Uniform Transmission Lines 248
4.10 Power Considerations in PEEC Models 252
4.10.1 General Remarks 252
4.10.2 Power Analysis of Magnetic and Electric Couplings 253
4.10.3 Power Analysis of PEEC Models 255
References 257
Appendix A: Tensor Analysis, Integration and Lie Derivative 261
A.1 Integration Over a Curve and Covariant Vectors as Line Integrands 261
A.2 Integration Over a Surface and Contravariant Vector Densities as Surface Integrands 263
A.3 Integration Over a Volume and Scalar Densities as Volume Integrands 264
A.4 Poincar′e Lemma 265
A.5 Stokes’ Theorem 266
A.6 Lie Derivative 266
References 267
Appendix B: Elements of Functional Analysis 269
B.1 Function Spaces 270
B.1.1 Metric Spaces 270
B.1.2 Linear Spaces, Vector Spaces 272
B.1.3 Normed Spaces 273
B.1.4 Inner Product Spaces and Pseudo Inner Product Spaces 274
B.1.5 Hilbert Spaces 276
B.1.6 Finite Expansions and Best Approximation 277
B.1.7 The Projection Theorem 278
B.1.8 Basis of a Hilbert Space 278
B.2 Linear Operators 278
B.2.1 Definition of a Linear Operator, Domain and Range of an Operator 278
B.2.2 Bounded Operators and the Norm of an Operator 279
B.2.3 Continuous Operators 279
B.2.4 Linear Functionals 279
B.2.5 The Riesz Representation Theorem 279
B.2.6 Adjoint and Pseudo Adjoint Operators 280
B.2.7 Compact Operators 280
B.2.8 Invertible Operators, Resolvent Operator 280
B.2.9 Self-Adjoint, Normal and Unitary Operators 281
B.3 Spectrum of a Linear Operator 281
B.3.1 Standard Eigenvalue Problem, Spectrum and Resolvent Set 281
B.3.2 Classification of Spectra by Operator Properties 283
B.4 Spectral Expansions and Representations 284
B.4.1 Linear Independence of Eigenfunctions 284
B.4.2 Spectral Theorem for Compact and Self-Adjoint Operators 285
B.4.3 Remarks on the Relation Between Differential and Integral Operators 286
B.4.4 A Comment on Sobolev Spaces 287
References 287
Appendix C: Some Formulas of Vector and Dyadic Calculus 289
C.1 Vector Identities 289
C.2 Dyadic Identities 290
C.3 Integral Identities 290
C.3.1 Vector-Dyadic Green’s First Theorem 290
C.3.2 Vector-Dyadic Green’s Second Theorem 290
Reference 290
Appendix D: Adaption of the Integral Equations to the Conductor Geometry 291
Appendix E: The Product Integral/Matrizant 295
E.1 The Differential Equation and Its Solution 295
E.2 The Determination of the Product Integral 295
E.3 Inverse Operation 296
E.4 Calculation Rules for the Product Integral 297
References 297
Appendix F: Solutions for Some Important Integrals 299
F.1 Integrals Involving Powers of √ x2 + b2 299
F.2 Integrals Involving Exponential and Power Functions 299
F.3 Integrals Involving Trigonometric and Exponential Functions 301
Reference 302
Index 303
介绍一本书 Radiating Nonuniform Transmission-Line Systems and PEEC method 2009: abbr_9d0f76c8e7fd2e72a60517e651300a95.rar
