DEDICATION xv
PREFACE xvii
ACKNOWLEDGEMENTS xxi
ACRONYMS xxv
1 Introduction 1
References, 6
2 Circuit Analysis for PEEC Methods 9
2.1 Circuit Analysis Techniques, 9
2.2 Overall Electromagnetic and Circuit Solver Structure, 9
2.3 Circuit Laws, 11
2.4 Frequency and Time Domain Analyses, 13
2.5 Frequency Domain Analysis Formulation, 14
2.6 Time Domain Analysis Formulations, 17
2.7 General Modified Nodal Analysis (MNA), 22
2.8 Including Frequency Dependent Models in Time Domain Solution, 28
2.9 Including Frequency Domain Models in Circuit Solution, 31
2.10 Recursive Convolution Solution, 39
2.11 Circuit Models with Delays or Retardation, 41
Problems, 43
References, 44
3 Maxwell’s Equations 47
3.1 Maxwell’s Equations for PEEC Solutions, 47
3.2 Auxiliary Potentials, 52
3.3 Wave Equations and Their Solutions, 54
3.4 Green’s Function, 58
3.5 Equivalence Principles, 60
3.6 Numerical Solution of Integral Equations, 63
Problems, 65
References, 66
4 Capacitance Computations 67
4.1 Multiconductor Capacitance Concepts, 68
4.2 Capacitance Models, 69
4.3 Solution Techniques for Capacitance Problems, 74
4.4 Meshing Related Accuracy Problems for PEEC Model, 79
4.5 Representation of Capacitive Currents for PEEC Models, 82
Problems, 85
References, 86
5 Inductance Computations 89
5.1 Loop Inductance Computations, 90
5.2 Inductance Computation Using a Solution or a Circuit Solver, 95
5.3 Flux Loops for Partial Inductance, 95
5.4 Inductances of Incomplete Structures, 96
5.5 Computation of Partial Inductances, 99
5.6 General Inductance Computations Using Partial Inductances and Open Loop Inductance, 107
5.7 Difference Cell Pair Inductance Models, 109
5.8 Partial Inductances with Frequency Domain Retardation, 119
Retardation, 123
Problems, 125
References, 131
6 Building PEEC Models 133
6.1 Resistive Circuit Elements for Manhattan-Type Geometries, 134
6.2 Inductance–Resistance (Lp,R)PEEC Models, 136
6.3 General (Lp,p,R)PEEC Model Development, 138
6.4 Complete PEEC Model with Input and Output Connections, 148
6.5 Time Domain Representation, 154
Problems, 154
References, 155
7 Nonorthogonal PEEC Models 157
7.1 Representation of Nonorthogonal Shapes, 158
7.2 Specification of Nonorthogonal Partial Elements, 163
7.3 Evaluation of Partial Elements for Nonorthogonal PEEC Circuits, 169
Problems, 181
References, 182
8 Geometrical Description and Meshing 185
8.1 General Aspects of PEEC Model Meshing Requirements, 186
8.2 Outline of Some Meshing Techniques Available Today, 187
8.3 SPICE Type Geometry Description, 194
8.4 Detailed Properties of Meshing Algorithms, 196
8.5 Automatic Generation of Geometrical Objects, 202
8.6 Meshing of Some Three Dimensional Pre-determined Shapes, 205
8.7 Approximations with Simplified Meshes, 207
8.8 Mesh Generation Codes, 208
Problems, 209
References, 210
9 Skin Effect Modeling 213
9.1 Transmission Line Based Models, 214
9.2 One Dimensional Current Flow Techniques, 215
9.3 3D Volume Filament (VFI) Skin-Effect Model, 227
9.4 Comparisons of Different Skin-Effect Models, 238
Problems, 244
References, 246
10 PEEC Models for Dielectrics 249
10.1 Electrical Models for Dielectric Materials, 249
10.2 Circuit Oriented Models for Dispersive Dielectrics, 254
10.3 Multi-Pole Debye Model, 257
10.4 Including Dielectric Models in PEEC Solutions, 260
10.5 Example for Impact of Dielectric Properties in the Time Domain, 276
Problems, 281
References, 281
11 PEEC Models for Magnetic Material 285
11.1 Inclusion of Problems with Magnetic Materials, 285
11.2 Model for Magnetic Bodies by Using a Magnetic Scalar Potential and Magnetic Charge Formulation, 292
11.3 PEEC Formulation Including Magnetic Bodies, 295
11.4 Surface Models for Magnetic and Dielectric Material Solutions in PEEC, 300
Problems, 307
References, 308
12 Incident and Radiated Field Models 309
12.1 External Incident Field Applied to PEEC Model, 310
12.2 Far-Field Radiation Models by Using Sensors, 312
12.3 Direct Far-Field Radiation Computation, 318
Problems, 322
References, 322
13 Stability and Passivity of PEEC Models 325
13.1 Fundamental Stability and Passivity Concepts, 327
13.2 Analysis of Properties of PEEC Circuits, 332
13.3 Observability and Controllability of PEEC Circuits, 334
13.4 Passivity Assessment of Solution, 337
13.5 Solver Based Stability and Passivity Enhancement Techniques, 342
13.6 Time Domain Solver Issues for Stability and Passivity, 359
Acknowledgment, 364
Problems, 364
References, 365
A Table of Units 369
A.1 Collection of Variables and Constants for Different Applications, 369
B Modified Nodal Analysis Stamps 373
B.1 Modified Nodal Analysis Matrix Stamps, 373
B.2 Controlled Source Stamps, 380
References, 382
C Computation of Partial Inductances 383
C.1 Partial Inductance Formulas for Orthogonal Geometries, 385
C.2 Partial inductance formulas for nonorthogonal geometries, 398
References, 407
D Computation of Partial Coefficients of Potential 409
D.1 Partial Potential Coefficients for Orthogonal Geometries, 410
D.2 Partial Potential Coefficient Formulas for Nonorthogonal Geometries, 418
References, 421
E Auxiliary Techniques for Partial Element Computations 423
E.1 Multi-function Partial Element Integration, 423
Subdivisions for Nonself-Partial Elements, 428
References, 429
INDEX 431
