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Title:
Time-domain computer analysis of nonlinear hybrid systems
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Publication Information:
London : CRC Press,, 2002
ISBN:
9780849313967

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30000010051954 TK7867 S95 2002 Open Access Book Book
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Summary

Summary

The analysis of nonlinear hybrid electromagnetic systems poses significant challenges that essentially demand reliable numerical methods. In recent years, research has shown that finite-difference time-domain (FDTD) cosimulation techniques hold great potential for future designs and analyses of electrical systems.

Time-Domain Computer Analysis of Nonlinear Hybrid Systems summarizes and reviews more than 10 years of research in FDTD cosimulation. It first provides a basic overview of the electromagnetic theory, the link between field theory and circuit theory, transmission line theory, finite-difference approximation, and analog circuit simulation. The author then extends the basic theory of FDTD cosimulation to focus on techniques for time-domain field solving, analog circuit analysis, and integration of other lumped systems, such as n-port nonlinear circuits, into the field-solving scheme.

The numerical cosimulation methods described in this book and proven in various applications can effectively simulate hybrid circuits that other techniques cannot. By incorporating recent, new, and previously unpublished results, this book effectively represents the state of the art in FDTD techniques. More detailed studies are needed before the methods described are fully developed, but the discussions in this book build a good foundation for their future perfection.


Table of Contents

Prefacep. ix
The Authorp. xi
Chapter 1 Introductionp. 1
1.1 Introductionp. 1
1.2 Electromagnetic Systemsp. 2
1.3 Hybrid Electromagnetic Systemsp. 8
1.4 Organization of the Bookp. 13
Chapter 2 Electromagnetic Field Theoryp. 19
2.1 Introductionp. 19
2.2 Electromagnetic Theoryp. 20
2.2.1 Coulomb's lawp. 20
2.2.2 Gauss's lawp. 23
2.2.3 Faraday's lawp. 24
2.2.4 Ampere's lawp. 25
2.2.5 Continuity equationp. 28
2.2.6 Magnetic vector potentialp. 29
2.2.7 Maxwell's equationsp. 30
2.2.8 Wave equations and field retardationp. 33
2.2.9 Time-harmonic field solutionp. 40
2.2.10 Boundary conditionsp. 42
2.3 Example of Solving Electromagnetic Field Distributionp. 45
Chapter 3 Circuit Equivalence and Transmission Line Theoryp. 67
3.1 Circuit Theory as Field Approximationp. 67
3.1.1 Circuit basis under quasi-static approximationp. 67
3.1.2 Circuit equations for some lumped elementsp. 71
3.1.3 Circuit model at different frequency rangesp. 78
3.1.4 Transient response of a lumped circuitp. 82
3.2 Transmission Line Theoryp. 88
3.2.1 General transmission line solutionp. 89
3.2.2 Lossless transmission linep. 96
3.2.3 Lumped-element equivalent model for a transmission linep. 101
3.3 Scattering Parameters of an n-port Networkp. 105
3.3.1 Definition of S parametersp. 105
3.3.2 Definitions of other network parametersp. 109
Chapter 4 Finite-Difference Formulationp. 111
4.1 Introductionp. 111
4.2 Finite-Difference Methodp. 113
4.2.1 Forward, backward and central differencesp. 113
4.2.2 Finite-difference approximation in a nonuniform gridp. 118
4.3 System Solution and Stability Conditionp. 121
4.3.1 Jacobian matrix and system solutionp. 121
4.3.2 Application examplep. 123
4.3.3 Stability conditionp. 127
Chapter 5 Solving Electromagnetic Fields in the Time Domain-FDTD Method
5.1 Introductionp. 141
5.2 Finite-Difference Time-Domain Methodp. 142
5.2.1 Maxwell's equationsp. 142
5.2.2 Three-dimensional FDTD formulationp. 144
5.2.3 Two-dimensional FDTD formulationp. 151
5.3 Issues of FDTD Numerical Implementationp. 154
5.3.1 Stability conditionp. 154
5.3.2 Absorbing boundary conditionsp. 156
5.3.3 Unconditionally stable FDTD algorithmp. 164
5.3.4 Numerical dispersion in FDTDp. 168
5.4 Examples of FDTD Applicationp. 173
Chapter 6 Circuit Formulation and Computer Simulationp. 179
6.1 Introductionp. 179
6.2 Constitutive Relation of Devicesp. 180
6.3 Modified Nodal Formulation of Circuit Simulationp. 191
6.4 Transient Analysis of Linear Circuitp. 197
6.5 Nonlinear Device Models in Circuit Simulationp. 203
6.5.1 Diode modelp. 204
6.5.2 Bipolar junction transistor modelp. 206
6.5.3 MOS transistor modelp. 209
6.6 Newton Method for Solving Systems with Nonlinear Devicesp. 212
6.7 Timestep Control in Transient Simulationp. 216
Chapter 7 Formulation for Hybrid System Simulation in the Time Domainp. 223
7.1 Introductionp. 223
7.2 Maxwell's Equations and Supplemental Current Equationsp. 225
7.3 Hybrid Circuit Simulation with Lumped Elementsp. 231
7.3.1 FDTD equations for RLC componentsp. 231
7.3.2 Examples of hybrid circuit simulationp. 239
7.4 Electron Beam in FDTD Simulationp. 242
7.4.1 Interaction between electromagnetic field and an electron beamp. 242
7.4.2 FDTD algorithm for modeling an electron beamp. 243
7.4.3 Electron-beam modeling for a planar DC diodep. 245
7.4.4 Small-signal space-charge waves in FDTDp. 249
Chapter 8 Interfacing FDTD Field Solver with Lumped Systemsp. 255
8.1 Introductionp. 255
8.2 Linking FDTD Method with a SPICE-like Circuit Simulatorp. 258
8.2.1 Equivalent circuit model of a distributed systemp. 258
8.2.2 Implementation of the circuit-field model for hybrid simulationp. 261
8.2.3 Example of the circuit-field model in FDTDp. 265
8.3 Modeling a Multiport S-Parameter Network in FDTDp. 267
8.3.1 Scattering parameters, port voltage, and port currentp. 268
8.3.2 Modeling a S-parameter block in FDTD gridp. 272
8.4 Multiport Behavioral Model in FDTDp. 278
8.4.1 Behavioral modelp. 278
8.4.2 Behavioral model block in an FDTD gridp. 279
8.5 Examples of General Hybrid System Cosimulationp. 281
Chapter 9 Simulation of Hybrid Electromagnetic Systemsp. 289
9.1 Introductionp. 289
9.2 FDTD Characterization and De-embeddingp. 290
9.3 Examples of Hybrid System Cosimulationp. 295
9.3.1 Commercial simulatorsp. 295
9.3.2 Application of the circuit-field modelp. 297
9.3.3 Application of the multiport modelp. 307
9.3.4 General hybrid system cosimulationp. 312
9.4 Analysis of Packaging Structure with On-chip Circuitsp. 320
9.4.1 Analysis of packaging structuresp. 321
9.4.2 Simulation of packaging structures with on-chip circuitsp. 324
Chapter 10 Optical Device Simulation in FDTDp. 329
10.1 Introductionp. 329
10.2 Active Gain Media in VCSELp. 331
10.3 FDTD Formulation for Systems with Nonlinear Gain Mediap. 336
10.4 FDTD Analysis of VCSEL Structuresp. 339
10.4.1. One-dimensional structuresp. 339
10.4.2. Gain media in 2D structuresp. 343
10.5 Cosimulation for VCSEL Source and other Circuitsp. 351
Appendix I Vector Differential Operators and Vector Identitiesp. 357
I.1 Vector Differential Operatorsp. 357
I.2 Vector Identitiesp. 358
Appendix II Laplace Transformationp. 361
Referencesp. 369
Indexp. 391