Electromagnetic Analysis Using Transmission Line Variables

By: Maurice Weiner

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Hardcover | 5 March 2001

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Hardcover
532 Pages

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22.23 x 15.24 x 3.18

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Problems in electromagnetic propagation, especially those with complex geometries, have traditionally been solved using numerical methods, such as the method of finite differences. Unfortunately the mathematical methods suffer from a lack of physical appeal. The researcher or designer often loses sight of the physics underlying the problem, and changes in the mathematical formulation are often not identifiable with any physical change. This book employs a relatively new method for solving electromagnetic problems, one which makes use of a transmission line matrix (TLM). The propagation space is imagined to be filled with this matrix. The propagation fields and physical properties (for example, the presence of conductivity) are then mapped onto the matrix. Mathematically, the procedures are identical with the traditional numerical methods; however, the interpretation and physical appeal of the transmission line matrix are far superior. Any change in the matrix has an immediate physical significance. What is also very important is that the matrix becomes a launching pad for many improvements in the analysis (for example, the nature of coherent waves) using more modern notions of electromagnetic waves. Eventually, the purely mathematical techniques will probably give way to the transmission line matrix method.

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Introduction to Transmission Lines and Their Application to Electromagnetic Phenomena	p. 1
Simple Experimental Example	p. 4
Examples of Impulse Sources	p. 6
Model Outline	p. 10
Application of Model for Small Node Resistance	p. 19
Transmission Line Theory Background	p. 20
Initial Conditions of Special Interest	p. 25
One Dimensional TLM Analysis. Comparison with Finite Difference Method
TLM Iteration Method	p. 27
Reverse TLM Iteration	p. 29
Example of Reverse Iteration for Non-Uniform Line	p. 32
Derivation of Scattering Coefficients for Reverse Iteration	p. 32
Complete TLM Iteration (Combining Forward and Reverse Iterations)	p. 36
Finite Difference Method. Comparison with TLM Method	p. 36
Two Dimensional TLM Analysis. Comparison with Finite Difference Method
Boundary Conditions at 2D Node	p. 40
Static Behavior About 2D Node	p. 43
Non-Static Example: Wave Incident on 2D Node	p. 44
Integral Rotational Properties of Field About the Node	p. 47
2D TLM Iteration Method for Nine Cell Core Matrix	p. 52
2D Finite Difference Method. Comparison With TLM Method	p. 56
Appendices
Effect of Additional Paths on Weighing Process	p. 64
Novel Applications of TLM Method. Description of Neurological Activity Using the TLM Method	p. 67
Notation and Mapping of Physical Properties	p. 72
1D Cell Notation and Mapping of Conductivity and Field	p. 74
Neighboring 1D Cells With Unequal Impedance	p. 78
2D Cell Notation. Mapping of Conductivity and Field	p. 81
3D Cell Notation. Mapping of Conductivity and Field	p. 89
Other Node Controlled Properties
Node Control of 2D Scattering Coefficients Due to Finite Node Resistance	p. 97
Simultaneous Conductivity Contributions	p. 98
Signal Gain	p. 99
Signal Generation. Use of Node Coupling	p. 100
Mode Conversion	p. 105
Example of Mapping: Node Resistance in a Photoconductive Semiconductor
Semiconductor Switch Geometry (2D)	p. 105
Node Resistance Profile in Semiconductor	p. 109
Scattering Equations	p. 112
1D Scattering Equations	p. 113
2D Scattering Equations	p. 116
Effect of Symmetry on Scattering Coefficients	p. 125
3D Scattering Equations: Coplanar Scattering	p. 128
General Scattering, Including Scattering Normal to Propagation Plane
Equivalent TLM Circuit. Quasi-Coupling Effect	p. 137
Neglect of Quasi-Coupling	p. 139
Simple Quasi-Coupling Circuit: First Order Approximation	p. 141
Correction to Quasi-Coupling Circuit: Second Order Approximation	p. 145
Calculation of Load Impedance with Quasi-Coupling	p. 148
Small Coupling Approximation of Second Order Quasi-Coupling	p. 150
General 3D Scattering Process Using Cell Notation	p. 152
Complete Iterative Equations	p. 164
Contributions of Electric and Magnetic Fields to Total Energy	p. 166
Plane Wave Behavior
Response of 2D Cell Matrix to Input Plane Wave	p. 168
Response of 2D Cell Matrix to Input Waves With Arbitrary Amplitudes	p. 178
Response of 3D Cell Matrix to Input Plane Wave	p. 179
Response of 3D Cell Matrix to Input Waves With Arbitrary Amplitudes	p. 183
Appendices
3D Scattering Equations With Both Coplanar and Aplanar Contributions	p. 185
3D Scattering Coefficients With Both Coplanar and Aplanar Contributions	p. 187
3D Scattering Coefficients in Terms of Circuit Parameters	p. 189
Corrections for Plane Wave and Anisotropy Effects	p. 194
Partition of TLM Waves into Component Waves	p. 194
Scattering Corrections for 2D Plane Waves: Plane Wave Correlations Between Cells	p. 196
Changes to 2D Scattering Coefficients	p. 203
Corrections to Plane Wave Correlation
Correlation of Waves in Adjoining Media With Differing Dielectric Constants	p. 206
Modification of Wave Correlation Adjacent a Conducting Boundary	p. 207
Decorrelation Processes
De-Correlation Due to Sign Disparity of Plane and Symmetric Waves	p. 211
Minimal Solution Using Differing Decorrelation Factors to Remove Sign Disparities	p. 222
Non-Essential De-Correlation Caused by Simultaneous Presence of Forward and Backward In-Line Plane Waves With Same Polarity	p. 226
De-Correlation Treatment of Plane Waves Incident on Dielectric Interface	p. 230
Comments on Interaction of a Plane Wave Front and a Source Emitting Both Plane Wave and Symmetric Components	p. 234
Summary of Correlation/Decorrelation Processes	p. 235
Grid Orientation Effects
Dependence of Wave Energy Dispersal on Grid Orientation	p. 235
Transformation Properties Between Grids	p. 239
Averaging Procedure Among Grids
General Procedure and Grid Specification	p. 242
Vector Description of Plane and Symmetric Waves	p. 243
Energy Content of Plane and Symmetric Waves	p. 246
Principal Axis Grid	p. 247
Simple Averaging Example Without Plane Wave Effects	p. 248
General Averaging Procedure Including Plane Wave Correlations	p. 249
Summary of Field Averaging Procedure	p. 255
Averaging Procedure for Node Resistance	p. 257
Comparison of Standard Numerical Methods and TLM Methods Incorporating TLM Correlations/Decorrelations and Grid Orientation	p. 259
Appendices
3D Scattering Corrections for Plane Waves (Wave Correlations)	p. 260
Consistency of Plane Wave Correlations With a Simple Quantum Mechanical Model	p. 263
Boundary Conditions and Dispersion	p. 266
Dielectric-Dielectric Interface	p. 267
Node Coupling: Nearest Node and Multi-coupled Node Approximations
Nearest Nodes for 1D Interface	p. 275
Nearest Nodes at 2D Interface	p. 276
Truncated Cell and Oblique Interface	p. 278
Single Index Cell Notation	p. 280
Simplified Iteration Neglecting the Nearest Node Approximation	p. 283
Non-Uniform Dielectric. Use of Cluster Cells	p. 283
Other Boundary Conditions
Dielectric- Open Circuit Interface	p. 287
Dielectric - Conductor Interface	p. 288
Input/Output Conditions	p. 291
Composite Transmission Line	p. 294
Determination of Initial Static Field By TLM Method	p. 295
Time Varying Source Voltage and Antenna Simulation	p. 299
Dispersion
Dispersion Sources	p. 301
Dispersion Example	p. 302
Propagation Velocity in Terms of Wave Number	p. 306
Dispersive Properties of Node Resistance	p. 306
Node Resistance in Terms of Wave Number	p. 307
Anomalous Dispersion	p. 308
Incorporation of Dispersion into TLM formulation
Dispersion Approximations	p. 309
Outline of Dispersion Calculation Using the TLM Method	p. 310
One Dimensional Dispersion Iteration	p. 311
Initial Conditions With Dispersion Present	p. 322
Stability of Initial Profiles With Dispersion Present	p. 323
Replacement of Non-Uniform Field in Cell With Effective Uniform Field	p. 329
Appendices
Specification of Input/Output Node Resistance to Eliminate Multiple Reflections	p. 330
Cell Discharge Properties and Integration of Transport Phenomena Into the TLM Matrix	p. 333
Charge Transfer Between Cells	p. 334
Relationship Between Field and Cell Charge	p. 337
Dependence of Conductivity on Carrier Properties	p. 341
Integration of Carrier Transport Using TLM Notation Changes in Cell Occupancy and its Effect on TLM Iteration
General Continuity Equations	p. 342
Carrier Generation Due to Light Activation	p. 343
Carrier Generation Due to Avalanching: Identical Hole and Electron Drift Velocities	p. 344
Avalanching With Differing Hole and Electron Drift Velocities	p. 346
Two Step Generation Process	p. 350
Recombination	p. 351
Limitations of Simple Exponential Recovery Model	p. 353
Carrier Drift	p. 353
Cell Charge Iteraction.Equivalence of Drift and Inter-Cell Currents	p. 357
Carrier Diffusion	p. 361
Frequency of Transport Iteration	p. 363
Toal Contribution to Changes in Carrier Cell Occupancy	p. 364
Description of TLM Iteration	p. 366
Specification of Geometry	p. 366
Description of Inputs and TLM Iteration Outline	p. 372
Output Format	p. 377
Output Simulation Data
Conditions During Simulation	p. 379
Behavior During Charge-up.Establishment of Static Field Profile	p. 380
Node Resistance R(n,m) During Activation	p. 386
Output Pulse When Semiconductor is Activated	p. 391
Node Recovery and its Effect on Output Pulse	p. 394
Steady State and Transient Field Profiles	p. 396
Partial Activation of Nodes and Effect on Profiles and Output	p. 399
Cell Charge Following Recovery	p. 402
Role of TLM Waves at Charged Boundary	p. 405
Comparison of Possible Boundary Conditions at the Semiconductor/Dielectric Interface	p. 407
Simulation Results for Boundary with Non-Integral Nearest Nodes	p. 408
Comparison of Output With and Without Matched Input/Output Lines	p. 411
Simulation of Plane Wave Effects. Effect of Alternating Input	p. 413
Appendices
Discussion of Program Statements for Semiconductor Switch	p. 418
Program Statements	p. 426
Program Changes for Arbitrary Dielectric Constant, Cell Density, and Device Size	p. 442
Field Decay in Semiconductor Using the TLM Formulation	p. 444
Spice Solutions	p. 450
Photoconductive Switch	p. 451
Traveling Wave Marx Generator	p. 455
Traveling Marx Wave in a Layered Dielectric	p. 460
Simulation of a Traveling Marx Wave in a Layered Dielectric	p. 462
Pulse Transformation and Generation Using Non-Uniform Transmission Lines
Use of Cell Chain to Simulate Pulse Transformer	p. 467
Pulse Transformer Simulation Results	p. 470
Pulse Sources Using Non-Uniform TLM Lines (Switch at Output)	p. 472
Radial Pulse Source (Switch at Output)	p. 473
Pulse Sources With Gain (PFXL Sources)	p. 476
Darlington Pulser
TLM Formulation of Darlington Pulser	p. 481
SPICE Simulation of Lossy Darlington Pulser	p. 485
Appendices
Introduction to SPICE Format	p. 488
Discussion of Format for Photoconductive Switch	p. 488
TLM Analysis of Leading Edge Pulse in a Transformer	p. 496
TLM Analysis of Leading Edge Wave in PFXL	p. 499
Index	p. 507
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Electromagnetic Analysis Using Transmission Line Variables

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