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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 By incorporating recent, new, and previously unpublished results, this book effectively represents the state of the art in FDTD techniques.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
Preface | p. ix |
The Author | p. xi |
Chapter 1 Introduction | p. 1 |
1.1 Introduction | p. 1 |
1.2 Electromagnetic Systems | p. 2 |
1.3 Hybrid Electromagnetic Systems | p. 8 |
1.4 Organization of the Book | p. 13 |
Chapter 2 Electromagnetic Field Theory | p. 19 |
2.1 Introduction | p. 19 |
2.2 Electromagnetic Theory | p. 20 |
2.2.1 Coulomb's law | p. 20 |
2.2.2 Gauss's law | p. 23 |
2.2.3 Faraday's law | p. 24 |
2.2.4 Ampere's law | p. 25 |
2.2.5 Continuity equation | p. 28 |
2.2.6 Magnetic vector potential | p. 29 |
2.2.7 Maxwell's equations | p. 30 |
2.2.8 Wave equations and field retardation | p. 33 |
2.2.9 Time-harmonic field solution | p. 40 |
2.2.10 Boundary conditions | p. 42 |
2.3 Example of Solving Electromagnetic Field Distribution | p. 45 |
Chapter 3 Circuit Equivalence and Transmission Line Theory | p. 67 |
3.1 Circuit Theory as Field Approximation | p. 67 |
3.1.1 Circuit basis under quasi-static approximation | p. 67 |
3.1.2 Circuit equations for some lumped elements | p. 71 |
3.1.3 Circuit model at different frequency ranges | p. 78 |
3.1.4 Transient response of a lumped circuit | p. 82 |
3.2 Transmission Line Theory | p. 88 |
3.2.1 General transmission line solution | p. 89 |
3.2.2 Lossless transmission line | p. 96 |
3.2.3 Lumped-element equivalent model for a transmission line | p. 101 |
3.3 Scattering Parameters of an n-port Network | p. 105 |
3.3.1 Definition of S parameters | p. 105 |
3.3.2 Definitions of other network parameters | p. 109 |
Chapter 4 Finite-Difference Formulation | p. 111 |
4.1 Introduction | p. 111 |
4.2 Finite-Difference Method | p. 113 |
4.2.1 Forward, backward and central differences | p. 113 |
4.2.2 Finite-difference approximation in a nonuniform grid | p. 118 |
4.3 System Solution and Stability Condition | p. 121 |
4.3.1 Jacobian matrix and system solution | p. 121 |
4.3.2 Application example | p. 123 |
4.3.3 Stability condition | p. 127 |
Chapter 5 Solving Electromagnetic Fields in the Time Domain-FDTD Method | |
5.1 Introduction | p. 141 |
5.2 Finite-Difference Time-Domain Method | p. 142 |
5.2.1 Maxwell's equations | p. 142 |
5.2.2 Three-dimensional FDTD formulation | p. 144 |
5.2.3 Two-dimensional FDTD formulation | p. 151 |
5.3 Issues of FDTD Numerical Implementation | p. 154 |
5.3.1 Stability condition | p. 154 |
5.3.2 Absorbing boundary conditions | p. 156 |
5.3.3 Unconditionally stable FDTD algorithm | p. 164 |
5.3.4 Numerical dispersion in FDTD | p. 168 |
5.4 Examples of FDTD Application | p. 173 |
Chapter 6 Circuit Formulation and Computer Simulation | p. 179 |
6.1 Introduction | p. 179 |
6.2 Constitutive Relation of Devices | p. 180 |
6.3 Modified Nodal Formulation of Circuit Simulation | p. 191 |
6.4 Transient Analysis of Linear Circuit | p. 197 |
6.5 Nonlinear Device Models in Circuit Simulation | p. 203 |
6.5.1 Diode model | p. 204 |
6.5.2 Bipolar junction transistor model | p. 206 |
6.5.3 MOS transistor model | p. 209 |
6.6 Newton Method for Solving Systems with Nonlinear Devices | p. 212 |
6.7 Timestep Control in Transient Simulation | p. 216 |
Chapter 7 Formulation for Hybrid System Simulation in the Time Domain | p. 223 |
7.1 Introduction | p. 223 |
7.2 Maxwell's Equations and Supplemental Current Equations | p. 225 |
7.3 Hybrid Circuit Simulation with Lumped Elements | p. 231 |
7.3.1 FDTD equations for RLC components | p. 231 |
7.3.2 Examples of hybrid circuit simulation | p. 239 |
7.4 Electron Beam in FDTD Simulation | p. 242 |
7.4.1 Interaction between electromagnetic field and an electron beam | p. 242 |
7.4.2 FDTD algorithm for modeling an electron beam | p. 243 |
7.4.3 Electron-beam modeling for a planar DC diode | p. 245 |
7.4.4 Small-signal space-charge waves in FDTD | p. 249 |
Chapter 8 Interfacing FDTD Field Solver with Lumped Systems | p. 255 |
8.1 Introduction | p. 255 |
8.2 Linking FDTD Method with a SPICE-like Circuit Simulator | p. 258 |
8.2.1 Equivalent circuit model of a distributed system | p. 258 |
8.2.2 Implementation of the circuit-field model for hybrid simulation | p. 261 |
8.2.3 Example of the circuit-field model in FDTD | p. 265 |
8.3 Modeling a Multiport S-Parameter Network in FDTD | p. 267 |
8.3.1 Scattering parameters, port voltage, and port current | p. 268 |
8.3.2 Modeling a S-parameter block in FDTD grid | p. 272 |
8.4 Multiport Behavioral Model in FDTD | p. 278 |
8.4.1 Behavioral model | p. 278 |
8.4.2 Behavioral model block in an FDTD grid | p. 279 |
8.5 Examples of General Hybrid System Cosimulation | p. 281 |
Chapter 9 Simulation of Hybrid Electromagnetic Systems | p. 289 |
9.1 Introduction | p. 289 |
9.2 FDTD Characterization and De-embedding | p. 290 |
9.3 Examples of Hybrid System Cosimulation | p. 295 |
9.3.1 Commercial simulators | p. 295 |
9.3.2 Application of the circuit-field model | p. 297 |
9.3.3 Application of the multiport model | p. 307 |
9.3.4 General hybrid system cosimulation | p. 312 |
9.4 Analysis of Packaging Structure with On-chip Circuits | p. 320 |
9.4.1 Analysis of packaging structures | p. 321 |
9.4.2 Simulation of packaging structures with on-chip circuits | p. 324 |
Chapter 10 Optical Device Simulation in FDTD | p. 329 |
10.1 Introduction | p. 329 |
10.2 Active Gain Media in VCSEL | p. 331 |
10.3 FDTD Formulation for Systems with Nonlinear Gain Media | p. 336 |
10.4 FDTD Analysis of VCSEL Structures | p. 339 |
10.4.1. One-dimensional structures | p. 339 |
10.4.2. Gain media in 2D structures | p. 343 |
10.5 Cosimulation for VCSEL Source and other Circuits | p. 351 |
Appendix I Vector Differential Operators and Vector Identities | p. 357 |
I.1 Vector Differential Operators | p. 357 |
I.2 Vector Identities | p. 358 |
Appendix II Laplace Transformation | p. 361 |
References | p. 369 |
Index | p. 391 |