Albert Ruehli, Giulio Antonini, Lijun Jiang
Circuit Oriented Electromagnetic Modeling Using the Peec Techniques
Albert Ruehli, Giulio Antonini, Lijun Jiang
Circuit Oriented Electromagnetic Modeling Using the Peec Techniques
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As the first book to address electromagnetic modeling using the Partial Element Equivalent Circuit (PEEC) method, this tome is the result of more than twenty years of combined research by the authors. Offering fundamentals, derivations, applications, and examples of the PEEC method, this resource helps readers to bridge the gap between electromagnetics and circuits. After an introduction to circuit analysis techniques, laws, and frequency analyses, coverage dives into instructions for building PEEC models in various forms. The book concludes with a number of solution methods, test problems,…mehr
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As the first book to address electromagnetic modeling using the Partial Element Equivalent Circuit (PEEC) method, this tome is the result of more than twenty years of combined research by the authors. Offering fundamentals, derivations, applications, and examples of the PEEC method, this resource helps readers to bridge the gap between electromagnetics and circuits. After an introduction to circuit analysis techniques, laws, and frequency analyses, coverage dives into instructions for building PEEC models in various forms. The book concludes with a number of solution methods, test problems, and examples.
Bridges the gap between electromagnetics and circuits by addressing electrometric modeling (EM) using the Partial Element Equivalent Circuit (PEEC) method
This book provides intuitive solutions to electromagnetic problems by using the Partial Element Equivalent Circuit (PEEC) method. This book begins with an introduction to circuit analysis techniques, laws, and frequency and time domain analyses. The authors also treat Maxwell's equations, capacitance computations, and inductance computations through the lens of the PEEC method. Next, readers learn to build PEEC models in various forms: equivalent circuit models, non-orthogonal PEEC models, skin-effect models, PEEC models for dielectrics, incident and radiate field models, and scattering PEEC models. The book concludes by considering issues like stability and passivity, and includes five appendices some with formulas for partial elements.
Leads readers to the solution of a multitude of practical problems in the areas of signal and power integrity and electromagnetic interference
Contains fundamentals, applications, and examples of the PEEC method
Includes detailed mathematical derivations
Circuit Oriented Electromagnetic Modeling Using the PEEC Techniques is a reference for students, researchers, and developers who work on the physical layer modeling of IC interconnects and Packaging, PCBs, and high speed links.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Bridges the gap between electromagnetics and circuits by addressing electrometric modeling (EM) using the Partial Element Equivalent Circuit (PEEC) method
This book provides intuitive solutions to electromagnetic problems by using the Partial Element Equivalent Circuit (PEEC) method. This book begins with an introduction to circuit analysis techniques, laws, and frequency and time domain analyses. The authors also treat Maxwell's equations, capacitance computations, and inductance computations through the lens of the PEEC method. Next, readers learn to build PEEC models in various forms: equivalent circuit models, non-orthogonal PEEC models, skin-effect models, PEEC models for dielectrics, incident and radiate field models, and scattering PEEC models. The book concludes by considering issues like stability and passivity, and includes five appendices some with formulas for partial elements.
Leads readers to the solution of a multitude of practical problems in the areas of signal and power integrity and electromagnetic interference
Contains fundamentals, applications, and examples of the PEEC method
Includes detailed mathematical derivations
Circuit Oriented Electromagnetic Modeling Using the PEEC Techniques is a reference for students, researchers, and developers who work on the physical layer modeling of IC interconnects and Packaging, PCBs, and high speed links.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Produktdetails
- Produktdetails
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 464
- Erscheinungstermin: 19. Juni 2017
- Englisch
- Abmessung: 261mm x 185mm x 27mm
- Gewicht: 966g
- ISBN-13: 9781118436646
- ISBN-10: 1118436644
- Artikelnr.: 37329167
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 464
- Erscheinungstermin: 19. Juni 2017
- Englisch
- Abmessung: 261mm x 185mm x 27mm
- Gewicht: 966g
- ISBN-13: 9781118436646
- ISBN-10: 1118436644
- Artikelnr.: 37329167
ALBERT E. RUEHLI is an Adjunct Professor at MST Rolla, Missouri. He received his PhD, EE, at the University of Vermont and an honorary doctorate from Lulea University, Sweden. Ruehli received the Golden Jubilee Medal, the Guillemin-Cauer Prize from the IEEE CAS and the Richard Stoddart Award from the IEEE EMC Society. GIULI ANTONINI is a Full Professor in the Department of Industrial and Information Engineering and Economics at the Universit degli Studi dell'Aquila in L'Aquila, Italy. He received his PhD from the University of Rome "Sapienza." He worked on the development of the PEEC method for more than 15 years. LIJUN JIANG is an Associate Professor in the Department of EEE at the University of Hong Kong. He received HP STAR Award, Y.T. Lo Outstanding Research Award, IBM Research Technical Achievement Award, and other awards. He serves as the Associate Editor for IEEE Transactions on Antennas and Propagation and for PIER.
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
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
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
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
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
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
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
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