Cover image for Electromagnetic analysis using transmission line variables
Title:
Electromagnetic analysis using transmission line variables
Personal Author:
Edition:
2nd ed.
Publication Information:
New Jersey, NJ. ; World Scientific, c2010.
Physical Description:
xxi, 492 p. : ill. ; 24 cm.
ISBN:
9789814287487

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30000010262869 QC665.E4 W43 2011 Open Access Book Book
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Summary

Summary

New Edition: Electromagnetic Analysis Using Transmission Line Variables (3rd Edition)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 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, using more modern notions of electromagnetic waves. Eventually, the purely mathematical techniques will probably give way to the transmission line matrix method.Major revisions occur in chapters IV and VII in this second edition. The revised chapters now present an up-to-date and concise treatment on plane wave correlations and decorrelations, and provide a revised formulation of simulation to solve transient electromagnetic problems. It also takes into account semiconductors with arbitrary dielectric constant, using much smaller cell size, and extending the range of applicability and improving accuracy.


Table of Contents

Prefacep. vii
1 Introduction to Transmission Lines and Their Application to Electromagnetic Phenomenap. 1
1.1 Simple Experimental Examplep. 4
1.2 Examples of Impulse Sourcesp. 6
1.3 Model Outlinep. 9
1.4 Application of Model to Small Node Resistancep. 17
1.5 Transmission Line Theory Backgroundp. 17
1.6 Initial Conditions of Special Interestp. 22
One Dimensional TLM Analysis. Comparison with Finite Difference Methodp. 24
1.7 TLM Iteration Methodp. 24
1.8 Reverse TLM Iterationp. 25
1.9 Derivation of Scattering Coefficients For Reverse Iterationp. 29
1.10 Complete TLM Iteration (Combining Forward and Reverse Iterations)p. 31
1.11 Finite Difference Method. Comparison with TLM Methodp. 32
Two Dimensional TLM Analysis. Comparison with Finite Difference Methodp. 33
1.12 Boundary Conditions at 2D Nodep. 35
1.13 Static Behavior about 2D Nodep. 37
1.14 Non-static Example: Wave Incident on 2D nodep. 38
1.15 Integral Rotational Properties of Field about the Nodep. 42
1.16 2D TLM Iteration Method for Nine Cell Core Matrixp. 46
1.17 2D Finite Difference Method. Comparison with TLM Methodp. 50
1.18 Final Comments: Inclusion of Time Varying Signals and Phase Coherencep. 56
Appendicesp. 57
App. 1A.1 Effect of Additional Paths on Weighing Processp. 57
App. 1A.2 Novel Applications of TLM Method: Description of Neurological Activity Using the TLM Methodp. 60
2 Notation and Mapping of Physical Propertiesp. 65
2.1 1D Cell Notation and Mapping of Conductivity and Fieldp. 67
2.2 Neighboring 1D Cells with Unequal Impedancep. 70
2.3 2D Cell Notation, Mapping of Conductivity and Fieldp. 72
2.4 Simultaneous Conductivity Contributionsp. 80
2.5 3D Cell Notation, Mapping of Conductivity and Fieldp. 82
Other Node Controlled Propertiesp. 88
2.6 Node Control of 2D Scattering Coefficients Due to Finite Node Resistancep. 89
2.7 Signal Gainp. 90
2.8 Signal Generation. Use of Node Couplingp. 91
2.9 Mode Conversionp. 94
Example of Mapping: Node Resistance in Photoconductive Semiconductorp. 95
2.10 Semiconductor Switch Geometry (2D)p. 95
2.11 Node Resistance Profile in Semiconductorp. 98
3 Scattering Equationsp. 101
3.1 1D Scattering Equationp. 101
3.2 2D Scattering Equationsp. 104
3.3 Effect of Symmetry on Scattering Coefficientsp. 113
3.4 3D Scattering Equations: Coplanar Scatteringp. 116
General Scattering, Including Scattering Normal to Propagation Planep. 124
3.5 Simple 3D Equivalent TLM Circuitp. 125
3.6 Quasi-Couplingp. 126
3.7 Neglect of Quasi-Couplingp. 127
3.8 Simple Quasi-Coupling Circuit. First Order Approximationp. 129
3.9 Correction to Quasi-Coupling Circuit: Second Order Approximationp. 133
3.10 Calculation of Load Impedance with Quasi-Couplingp. 136
3.11 Small Coupling Approximation of Second Order Quasi-Couplingp. 138
3.12 General 3D Scattering Process Using Cell Notationp. 140
3.13 Complete Iterative Equationsp. 150
3.14 Contribution of Electric and Magnetic Fields to the Total Energyp. 153
Plane Wave Behaviorp. 154
3.15 Response of 2D Cell Matrix to Input Plane Wavep. 154
3.16 Response of 2D Cell Matrix to Input Waves with Arbitrary Amplitudesp. 163
3.17 Response of 3D Cell Matrix to Input Plane Wavep. 164
3.18 Final Comments of Uniform Waves versus Plane Wavesp. 167
Appendicesp. 168
App. 3A.1 Consistency of 3D Circuit with the TLM Static Solutionsp. 168
App. 3A.2 3D Scattering Coefficients, Without Quasi-Coupling in Terms of Circuit Parametersp. 169
App. 3A.3 3D Scattering Coefficients with Both Coplanar and Aplanar Contributions into Unit Cell Lines (yz and zx Planes)p. 172
App. 3A.4 3D Scattering Equations: with Both Coplanar and Aplanar Contributions into Unit Cell Lines (yz and zx Planes)p. 174
4 Corrections for Plane Waves and Grid Anisotropy Effectsp. 177
4.1 Partition of TLM Waves into Component Wavesp. 177
4.2 Scattering Corrections for 2D Plane Waves: Plane Wave Correlations Between Cellsp. 179
4.3 Changes to 2D Scattering Coefficientsp. 186
Corrections to Plane Wave Correlationsp. 188
4.4 Correlation of Waves in Adjoining Media with Differing Dielectric Constantsp. 188
4.5 Modification of Wave Correlation Adjacent a Conducting Boundaryp. 190
Decorrelation Processesp. 192
4.6 Decorrelation Due to Sign Disparity of Plane and Symmetric Wavesp. 192
4.7 Related Scattering Criteria and Sign Conditions for Removal of the Sign Disparityp. 196
4.8 Minimal Solution Using Differing Decorrelation Factors to Remove Sign Disparitiesp. 198
4.9 Decorrelation of Forward and Backward Plane Waves with Same Polarity in Neighboring Series TLM Lines Without Lossesp. 202
4.10 Decorrelation of Forward and Backward Plane Waves with the Same Polarity Occupying the Same TLM Linep. 205
4.11 Decorrelation Treatment at Boundary Interfacesp. 208
4.12 Comments on Interaction of Plane Wave Front with a Half-Infinite Conducting Planep. 210
4.13 Summary of Correlation/Decorrelation Processesp. 212
Treatment of Grid Orientation Effectsp. 213
4.14 Dependence of Wave Energy Dispersal on Grid Orientation for Symmetric and Plane Wavesp. 213
4.15 Selection of Grid for Plane Wavesp. 216
4.16 Transformation Properties between Gridsp. 217
4.17 Possible Mini-Plane Wave Fronts Associated with Each Cell. Plane Wave Partitioningp. 218
Grid(s) Selection. Propagation Vector Independencep. 220
4.18 Transformation of Fields to Principal Gridp. 220
4.19 Incorporation of Symmetric Wavesp. 221
4.20 Iteration Method Using Principal Grid Transformationsp. 222
4.21 Treatment of Separate TLM Correlated Wave Sourcesp. 224
4.22 Final Commentsp. 226
Appendicesp. 226
App. 4A.1 3D Scattering Corrections of Plane Waves (Plane Wave Correlations)p. 226
App. 4A.2 Consistency of Plane Wave Correlations with a Simple Quantum Mechanical Modelp. 229
5 Boundary Conditions and Dispersionp. 233
5.1 Dielectric-Dielectric Interfacep. 234
Node Coupling: Nearest Node and Multi-Coupled Node Approximationsp. 238
5.2 Nearest Nodes for 1D Interfacep. 241
5.3 Nearest Nodes at 2D Interfacep. 242
5.4 Truncated Cells and Oblique Interfacep. 244
5.5 Cell Index Notation at a Dielectric Interface Used in Simulationsp. 245
5.6 Simplified Iteration Neglecting the Nearest Node Approximationp. 247
5.7 Non-Uniform Dielectric. Use of Cluster Cellsp. 248
Other Boundary Conditionsp. 251
5.8 Dielectric - Open Circuit Interfacep. 251
5.9 Dielectric - Conductor Interfacep. 252
5.10 Input/Output Conditionsp. 254
5.11 Composite Transmission Linep. 256
5.12 Determination of Initial Static Field by TLM Methodp. 257
Dispersionp. 260
5.13 TLM Methods for Treating Dispersionp. 260
5.14 Dispersion Sourcesp. 262
5.15 Dispersion Examplep. 262
5.16 Propagation Velocity Dispersionp. 265
5.17 Node Resistance Dispersionp. 266
5.18 Anomalous Dispersionp. 267
Incorporation of Dispersion into TLM Formulationp. 268
5.19 Dispersion Approximationsp. 268
5.20 Outline of Dispersion Calculation Using the TLM Methodp. 269
5.21 One Dimensional Dispersion Iterationp. 269
5.22 Initial Conditions with Dispersion Presentp. 280
5.23 Stability of Initial Profiles with Dispersion Presentp. 281
5.24 Replacement of Non-uniform Field in Cell with Effective Uniform Fieldp. 284
Appendixp. 284
App. 5A.1 Specification of Input/Output Node Resistance to Eliminate Multiple Reflectionsp. 284
6 Cell Discharge Properties and Integration of Transport Phenomena into the Transmission Line Matrixp. 287
6.1 Charge Transfer between Cellsp. 288
6.2 Relationship between Field and Cell Chargep. 291
6.3 Dependence of Conductivity on Carrier Propertiesp. 295
Integration of Carrier Transport Using TLM Notation. Changes in Cell Occupancy and Its Effect on the TLM Iterationp. 296
6.4 General Continuity Equationsp. 296
6.5 Carrier Generation Due to Light Activationp. 296
6.6 Carrier Generation Due to Avalanching: Identical Hole and Electron Drift Velocitiesp. 297
6.7 Avalanching with Differing Hole and Electron Drift Velocitiesp. 300
6.8 Two Step Generation Processp. 303
6.9 Recombinationp. 304
6.10 Limitations of Simple Exponential Recovery Modelp. 306
6.11 Carrier Driftp. 307
6.12 Cell Charge Iteration. Equivalence of Drift and Inter-Cell Currents Using TLM Notationp. 310
6.13 Carrier Diffusionp. 315
6.14 Frequency of Transport Iterationp. 317
6.15 Total Contribution to Changes in Carrier Cell Occupancyp. 318
7 Description of TLM Iterationp. 321
7.1 Specification of Geometryp. 324
7.2 Use of TLM Matrixp. 326
7.3 Various Regions which Incorporate Plane Wave Correlation/Decorrelation (PWC Effects) into the Iterationp. 329
7.4 Simplified Decorrelation Procedure Used for Simulations in Chapter VIIp. 330
7.5 Description of Inputs, Arrays, and Initial Conditionsp. 336
7.6 Plane Wave Correllation (PWC) Inputsp. 338
7.7 Iteration Outlinep. 339
7.8 Node Resistance R(n,m) Changes. Use of Light Activationp. 340
Symmetric Scattering Simulationsp. 345
7.9 Symmetric Field Evolution with and without Node Activationp. 345
PWC Simulations. Comparison of PWC and Symmetric Resultsp. 256
7.10 Comparison of Output Waveforms and Static Profiles for Symmetric and PWC Simulationsp. 356
7.11 Comparison of Forward and Backward Waves when Using Wave Correlationp. 362
7.12 Risetime and Alternating Field Effects in the Guided Regionp. 364
7.13 Field Profile Evolution during Transient Charge-up Phasep. 366
7.14 Effect of Load Mismatch on Output and Field Profilep. 370
7.15 Node Recovery and its Effect on Output Pulse and Field Profilep. 370
7.16 Effects of Risetime on Conductivityp. 374
7.17 Partial Activation of Nodes and Effect on Profiles and Outputp. 375
7.18 Cell Charge Following Recoveryp. 377
7.19 Role of TLM Waves at Charged Boundaryp. 380
7.20 Incorporation of 3D Scattering Parameters into 2D Iteration. Application to Magnetostatic Solutionsp. 381
7.21 Summary: Comparison of PWC and Symmetric Simulation Resultsp. 383
Appendicesp. 385
7A.1 Outline Discussion of Program Statements for Activated Semiconductor Switchp. 385
7A.2 Program Statements for Optically Activated Semiconductor Switchp. 397
7A.3 Matching Node Resistors for Input & Output Sectionsp. 437
7A.4 Field Decay in Semiconductor Using the TLM Formulationp. 438
8 Spice Solutionsp. 441
8.1 Photoconductive/Avalanche Switchp. 441
8.2 Traveling Wave Marx Generatorp. 445
8.3 Traveling Marx Wave in a Layered Dielectricp. 450
Pulse Transformation and Generation Using Non-Uniform Transmission Linesp. 451
8.4 Use of Cell Chain to Simulate Pulse Transformerp. 452
8.5 Pulse Transformer Simulation Resultsp. 455
8.6 Pulse Source Using Non-Uniform TLM Lines (Switch at Output)p. 456
8.7 Radial Pulse Source (Switch at Output)p. 458
8.8 Pulse Sources with Gain (PFXL Sources)p. 459
Darlington Pulserp. 466
8.9 TLM Formulation of Darlington Pulserp. 469
8.10 SPICE Simulation of Lossy Darlington Pulserp. 470
Appendicesp. 470
8A.1 Introduction To SPICE Formatp. 470
8A.2 Discussion of Format for Photoconductive Switchp. 470
8A.3 TLM Analysis of Leading Edge Pulse in a Transformerp. 477
8A.4 TLM Analysis of Leading Edge Wave in PFXLp. 480
Biography of Maurice Weinerp. 487
Indexp. 489