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# Circuit Oriented Electromagnetic Modeling Using the PEEC Techniques

ISBN: 978-1-119-07840-1 May 2017 Wiley-IEEE Press 464 Pages

## Description

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.

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