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 propagating 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.
Author(s): Maurice Weiner
Publisher: World Scientific
Year: 2001
Language: English
Commentary: 76320
Pages: 531
City: Singapore; River Edge, NJ
Preface
......Page 8
CONTENTS ......Page 14
I. INTRODUCTION TO TRANSMISSION LINES AND THEIR APPLICATION TO ELECTROMAGNETIC PHENOMENA......Page 21
1.1 Simple Experimental Example ......Page 24
1.2 Examples of Impulse Sources ......Page 26
1.3 Model Outline ......Page 30
1.4 Application of Model for Small Node Resistance ......Page 39
1.5 Transmission Line Theory Background ......Page 40
1.6 Initial Conditions of Special Interest ......Page 45
1.7 TLM Iteration Method ......Page 47
1.8 Reverse TLM Iteration ......Page 49
1.10 Derivation of Scattering Coefficients for Reverse Iteration ......Page 52
1.12 Finite Difference Method . Comparison with TLM Method ......Page 56
Two Dimensional TLM Analysis. Comparison with Finite Difference Method ......Page 58
1.13 Boundary Conditions at 2D Node ......Page 60
1.14 Static Behavior About 2D Node ......Page 63
1.15 Non-Static Example: Wave Incident on 2D Node ......Page 64
1.16 Integral Rotational Properties of Field About the Node ......Page 67
1.17 2D TLM Iteration Method for Nine Cell Core Matrix ......Page 72
1.18 2D Finite Difference Method . Comparison With TLM Method ......Page 76
1A.1 Effect of Additional Paths on Weighing Process ......Page 84
1A.2 Novel Applications of TLM Method: Description of Neurological Activity Using the TLM Method......Page 87
II. NOTATION AND MAPPING OF PHYSICAL PROPERTIES ......Page 92
2.1 1D Cell Notation and Mapping of Conductivity and Field ......Page 94
2.2 Neighboring 1D Cells With Unequal Impedance......Page 98
2.3 2D Cell Notation. Mapping of Conductivity and Field ......Page 101
2.4 3D Cell Notation. Mapping of Conductivity and Field ......Page 109
Other Node Controlled Properties ......Page 116
2.5 Node Control of 2D Scattering Coefficients Due to Finite Node Resistance ......Page 117
2.6 Simultaneous Conductivity Contributions ......Page 118
2.7 Signal Gain ......Page 119
2.8 Signal Generation. Use of Node Coupling ......Page 120
2.10 Semiconductor Switch Geometry (2D) ......Page 125
2.11 Node Resistance Profile in Semiconductor ......Page 129
III. SCATTERING EQUATIONS......Page 132
3.1 1D Scattering Equations......Page 133
3.2 2D Scattering Equations ......Page 136
3.3 Effect of Symmetry on Scattering Coefficients ......Page 145
3.4 3D Scattering Equations: Coplanar Scattering ......Page 148
General Scattering, Including Scattering Normal to Propagation Plane......Page 155
3.5 Equivalent TLM Circuit. Quasi-Coupling Effect ......Page 157
3.6 Neglect of Quasi-Coupling ......Page 159
3.7 Simple Quasi-Coupling Circuit: First Order Approximation ......Page 161
3.8 Correction to Quasi-Coupling Circuit: Second Order Approximation ......Page 165
3.9 Calculation of Load Impedance with Quasi-Coupling ......Page 168
3.10 Small Coupling Approximation of Second Order Quasi-Coupling ......Page 170
3.11 General 3D Scattering Process Using Cell Notation. ......Page 172
3.12 Complete Iterative Equations ......Page 184
3.13 Contribution of Electric and Magnetic Fields to Total Energy......Page 186
3.14 Response of 2D Cell Matrix to Input Plane Wave ......Page 188
3.15 Response of 2D Cell Matrix to Input Waves With Arbitrary Amplitudes......Page 198
3.16 Response of 3D Cell Matrix to Input Plane Wave ......Page 199
3.17 Response of 3D Cell Matrix to Input Waves With Arbitrary Amplitudes ......Page 203
3A.1 3D Scattering Equations: With Both Coplanar and Aplanar Contributions into Unit Cell Lines ZYZ(n,m,q), ZZY(n,m,q) (yz Plane).......Page 205
3A.2 3D Scattering Coefficients With Both Coplanar and Aplanar Contributions Into Unit Cell Lines Zyz(n,m,q) and Zzy(n,m,q) (yz Plane).......Page 207
3A.3 3D Scattering Coefficients, Without Quasi-Coupling, In Terms Of Circuit Parameters. For Co-Planar And Aplanar Scattering Into XY Plane About (n,m,q) Node. Coefficients For YZ And ZX Planes Are Obtained From Table 3.8.......Page 209
4.1 Partition of TLM Waves into Component Waves ......Page 214
4.2 Scattering Corrections for 2D Plane Waves: Plane Wave Correlations Between Cells ......Page 216
4.3 Changes to 2D Scattering Coefficients ......Page 223
Corrections to Plane Wave Correlation ......Page 225
4.4 Correlation of Waves in Adjoining Media With Differing Dielectric Constants ......Page 226
4.5 Modification of Wave Correlation Adjacent a Conducting Boundary ......Page 227
4.6 De-Correlation Due to Sign Disparity of Plane and Symmetric Waves ......Page 231
4.7 Minimal Solution Using Differing Decorrelation Factors to Remove Sign Disparities ......Page 242
4.8 Non-Essential De-Correlation Caused by Simultaneous Presence of Forward and Backward In-Line Plane Waves With Same Polarity ......Page 246
4.9 Decorrelation Treatment of Plane Waves Incident on Dielectric Interface......Page 250
4.10 Comments on Interaction of a Plane Wave Front and a Source Emitting Both Plane Wave and Symmetric Components ......Page 254
4.12 Dependence of Wave Energy Dispersal on Grid Orientation ......Page 255
4.13 Transformation Properties Between Grids ......Page 259
4.14 General Procedure and Grid Specification ......Page 262
4.15 Vector Description of Plane and Symmetric Waves ......Page 263
4.16 Energy Content of Plane and Symmetric Waves ......Page 266
4.17 Principal Axis Grid ......Page 267
4.18 Simple Averaging Example Without Plane Wave Effects ......Page 268
4.19 General Averaging Procedure Including Plane Wave Correlations ......Page 269
4.20 Summary of Field Averaging Procedure ......Page 275
4.21 Averaging Procedure for Node Resistance ......Page 277
4.22 Comparison of Standard Numerical Methods and TLM Methods Incorporating TLM Correlations/Decorrelations and Grid Orientation ......Page 279
4A.1 3D Scattering Corrections For Plane Waves (Wave Correlations)......Page 280
4A.2 Consistency of Plane Wave Correlations With a Simple Quantum Mechanical Model
......Page 283
V. BOUNDARY CONDITIONS AND DISPERSION ......Page 286
5.1 Dielectric-Dielectric Interface ......Page 287
Node Coupling: Nearest Node and Multi-coupled Node Approximations ......Page 293
5.2 Nearest Nodes for 1D Interface......Page 295
5.3 Nearest Nodes at 2D Interface ......Page 296
5.4 Truncated Cell and Oblique Interface ......Page 298
5.5 Single Index Cell Notation ......Page 300
5.7 Non-Uniform Dielectric. Use of Cluster Cells ......Page 303
5.8 Dielectric - Open Circuit Interface ......Page 307
5.9 Dielectric - Conductor Interface ......Page 308
5.10 Input/Output Conditions ......Page 311
5.11 Composite Transmission Line ......Page 314
5.12 Determination of Initial Static Field By TLM Method ......Page 315
Dispersion ......Page 319
5.14 Dispersion Sources ......Page 321
5.15 Dispersion Example ......Page 322
5.17 Dispersive Properties of Node Resistance ......Page 326
5.18 Node Resistance in Terms of Wave Number ......Page 327
5.19 Anomalous Dispersion......Page 328
5.20 Dispersion Approximations ......Page 329
5.21 Outline of Dispersion Calculation Using the TLM Method ......Page 330
5.22 One Dimensional Dispersion Iteration ......Page 331
5.23 Initial Conditions With Dispersion Present ......Page 342
5.24 Stability of Initial Profiles With Dispersion Present ......Page 343
5.25 Replacement of Non-Uniform Field in Cell With Effective Uniform Field ......Page 349
5A.1 Specification of Input/Output Node Resistance to Eliminate Multiple Reflections
......Page 350
VI. CELL DISCHARGE PROPERTIES AND INTEGRATION OF TRANSPORT PHENOMENA INTO THE TRANSMISSION LINE MATRIX
......Page 353
6.1 Charge Transfer Between Cells ......Page 354
6.2 Relationship Between Field and Cell Charge ......Page 357
6.3 Dependence of Conductivity on Carrier Properties ......Page 361
6.4 General Continuity Equations ......Page 362
6.5 Carrier Generation Due to Light Activation ......Page 363
6.6 Carrier Generation Due to Avalanching: Identical Hole and Electron Drift Velocities ......Page 364
6.7 Avalanching With Differing Hole and Electron Drift Velocities ......Page 366
6.8 Two Step Generation Process ......Page 370
6.9 Recombination ......Page 371
6.11 Carrier Drift ......Page 373
6.12 Cell Charge Iteration. Equivalence of Drift and Inter-Cell Currents......Page 377
6.13 Carrier Diffusion ......Page 381
6.14 Frequency of Transport Iteration ......Page 383
6.15 Total Contribution to Changes in Carrier Cell Occupancy ......Page 384
7.1 Specification of Geometry ......Page 386
7.2 Description of Inputs and TLM Iteration Outline ......Page 392
7.3 Output Format ......Page 397
7.4 Conditions During Simulation ......Page 399
7.5 Behavior During Charge-up and Establishment of Static Field Profile......Page 400
7.6 Node Resistance R(n,m) During Activation
......Page 406
7.7 Output Pulse When Semiconductor is Activated ......Page 411
7.8 Node Recovery and its Effect on Output Pulse ......Page 414
7.9 Steady State and Transient Field Profiles ......Page 416
7.10 Partial Activation of Nodes and Effect on Profiles and Output ......Page 419
7.11 Cell Charge Following Recovery ......Page 422
7.12 Role of TLM Waves at Charged Boundary ......Page 425
7.13 Comparison of Possible Boundary Conditions at the Semiconductor/Dielectric Interface ......Page 427
7.14 Simulation Results for Boundary with Non-Integral Nearest Nodes ......Page 428
7.15 Comparison of Output With and Without Matched Input/Output Lines
......Page 431
7.16 Simulation of Plane Wave Effects. Effect of Alternating Input ......Page 433
7A.1 Discussion of Program Statements for Semiconductor Switch ......Page 438
7A.2 Program Statements ......Page 446
7A.3 Program Changes for Arbitrary Dielectric Constant, Cell Density and Device Size......Page 462
7A.4 Field Decay in Semiconductor Using the TLM Formulation ......Page 464
VIII. SPICE SOLUTIONS ......Page 470
8.1 Photoconductive Switch ......Page 471
8.2 Traveling Wave Marx Generator ......Page 475
8.3 Traveling Marx Wave in a Layered Dielectric ......Page 480
8.4 Simulation of a Traveling Marx Wave in Layered Dielectric......Page 482
Pulse Transformation and Generation Using Non-Uniform Transmission Lines ......Page 486
8.5 Use of Cell Chain to Simulate Pulse Transformer ......Page 487
8.6 Pulse Transformer Simulation Results ......Page 490
8.7 Pulse Sources Using Non-Uniform TLM Lines (Switch at Output) ......Page 492
8.8 Radial Pulse Source (Switch at Output) ......Page 493
8.9 Pulse Sources With Gain (PFXL Sources) ......Page 496
8.10 TLM Formulation of Darlington Pulser ......Page 501
8.11 SPICE Simulation of Lossy Darlington Pulser ......Page 505
8A.2 Discussion of Format for Photoconductive Switch ......Page 508
8A.3 TLM Analysis of Leading Edge Pulse in a Transformer ......Page 516
8A.4 TLM Analysis of Leading Edge Wave in PFXL ......Page 519
INDEX ......Page 527
