Time-domain computer analysis of nonlinear hybrid systems

Wenquan Sui0849313961, 9780849313967

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 By incorporating recent, new, and previously unpublished results, this book effectively represents the state of the art in FDTD techniques.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.

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Table of contents :
Contents……Page 0
Time Domain Computer Analysis of Nonlinear Hybrid Systems……Page 1
Table of Contents……Page 3
Preface……Page 7
The Author……Page 9
1.1 Introduction……Page 10
1.2 Electromagnetic Systems……Page 11
1.3 Hybrid Electromagnetic Systems……Page 17
1.4 Organization of the Book……Page 22
2.1 Introduction……Page 28
2.2.1 Coulomb’s law……Page 29
2.2.2 Gauss’s law……Page 32
2.2.3 Faraday’s law……Page 33
2.2.4 Ampere’s law……Page 34
2.2.5 Continuity equation……Page 37
2.2.6 Magnetic vector potential……Page 38
2.2.7 Maxwell’s equations……Page 39
2.2.8 Wave equations and field retardation……Page 42
2.2.9 Time-harmonic field solution……Page 49
2.2.10 Boundary conditions……Page 51
2.3 Examples of Solving Electromagnetic Field Distribution……Page 54
3.1.1 Circuit basis under quasi-static approximation……Page 76
3.1.2 Circuit equations for some lumped elements……Page 80
3.1.3 Circuit model at different frequency ranges……Page 87
3.1.4 Transient response of a lumped circuit……Page 91
3.2 Transmission Line Theory……Page 97
3.2.1 General transmission line solution……Page 98
3.2.2 Lossless transmission line……Page 105
3.2.3 Lumped-element equivalent model for a transmission line……Page 110
3.3.1 Definition of S parameters……Page 114
3.3.2 Definitions of other network parameters……Page 118
4.1 Introduction……Page 120
4.2.1 Forward, backward and central differences……Page 122
4.2.2 Finite-difference approximation in a nonuniform grid……Page 127
4.3.1 Jacobian matrix and system solution……Page 130
4.3.2 Application example……Page 132
4.3.3 Stability condition……Page 136
5.1 Introduction……Page 149
5.2.1 Maxwell’s equation……Page 150
5.2.2 Three-dimentional FDTD formulation……Page 152
5.2.3 Two-dimensional FDTD formulation……Page 159
5.3.1 Stability condition……Page 162
5.3.2 Absorbing boundary conditions……Page 164
5.3.3 Unconditionally stable FDTD algorithm……Page 172
5.3.4 Numerical dispersion in FDTD……Page 176
5.4 Examples of FDTD Applications……Page 181
6.1 Introduction……Page 186
6.2 Constituitive Relation of Devices……Page 187
6.3 Modified Nodal Formation of Circuit Simulation……Page 198
6.4 Transient Analysis of Linear Circuit……Page 204
6.5 Nonlinear Device Models in Circuit Simulation……Page 210
6.5.1 Diode model……Page 211
6.5.2 Bipolar junction transistor model……Page 213
6.5.3 Metal-oxide-silicon transistor model……Page 216
6.6 Newton Method for Solving Systems with Nonlinear Devices……Page 219
6.7 Timestep Control in a Transient Simulation……Page 223
7.1 Introduction……Page 229
7.2 Maxwell’s Equations and Supplemental Current Equations……Page 231
7.3.1 FDTD equations for RLC components……Page 237
7.3.2 Examples of hybrid circuit simulation……Page 245
7.4.1 Interaction between electromagnetic field and an electron beam……Page 248
7.4.2 FDTD algorithm for modeling an electron beam……Page 249
7.4.3 Electron-beam modeling for a planar DC diode……Page 251
7.4.4 Small-signal space-charge waves in FDTD……Page 255
8.1 Introduction……Page 260
8.2.1 Equivalent circuit model of a distributed system……Page 263
8.2.2 Implementation of the circuit-field model for hybrid simulation……Page 266
8.2.3 Example of the circuit-field model in FDTD……Page 270
8.3 Modeling a Multiport S-Parameter Network in FDTD……Page 272
8.3.1 Scattering parameters, port voltage, and port current……Page 273
8.3.2 Modeling a S-Parameter block in FDTD grid……Page 277
8.4.1 Behavioral model……Page 283
8.4.2 Behavioral model block in an FDTD grid……Page 284
8.5 Examples of General Hybrid System Cosimulation……Page 286
9.1 Introduction……Page 293
9.2 FDTD Characterization and De-embedding……Page 294
9.3.1 Commercial simulators……Page 299
9.3.2 Applications of the circuit-field model……Page 301
9.3.3 Application of the multiport model……Page 311
9.3.4 General hybrid system cosimulation……Page 316
9.4 Analysis of Packaging Structures with On-chip Circuits……Page 324
9.4.1 Analysis of packaging structures……Page 325
9.4.2 Simulation of packaging structures with on-chip circuits……Page 328
10.1 Introduction……Page 333
10.2 Active Gain Media in VCSEL……Page 335
10.3 FDTD Formulation for Systems with Nonlinear Gain Media……Page 340
10.4.1 One-dimensional structures……Page 343
10.4.2 Gain media in 2D structures……Page 347
10.5 Cosimulation for VCSEL Source and Other Circuits……Page 355
I.1 Vector Differential Operators……Page 361
I.2 Vector Identities……Page 362
Appendix II: Laplace Transformation……Page 364
References……Page 371