Electromagnetic Analysis Using Transmission Line Variables: et.jpg

Author(s): Maurice Weiner
Publisher: World Scientific
Date     : 2001
Pages    : 510
Format   : PDF
OCR      : Y
Quality  :
Language : English
ISBN-10  : 981024438X
ISBN-13  :

Product Description
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.
Product Details


[ 本帖最后由 drjiachen 于 2008-12-15 10:14 编辑 ]

CONTENTS
L INTRODUCTION TO TRANSMISSION LINES AND THEIR
APPLICATION TO ELECTROMAGNETIC PHENOMENA 1
1.1 Simple Experimental Example 4
1.2 Examples of Impulse Sources 6
1.3 Model Outline 10
1.4 Application of Model for Small Node Resistance 19
1.5 Transmission Line Theory Background 20
1.6 Initial Conditions of Special Interest 25
One Dimensional TLM Analysis. Comparison with
Finite Difference Method
1.7 TLM Iteration Method 27
1.8 Reverse TLM Iteration 29
1.9 Example of Reverse Iteration for Non-Uniform Line 32
1.10 Derivation of Scattering Coefficients for Reverse Iteration 32
1.11 Complete TLM Iteration (Combining Forward and Reverse
Iterations) 36
1.12 Finite Difference Method . Comparison with TLM Method 36
Two Dimensional TLM Analysis. Comparison with
Finite Difference Method
1.13 Boundary Conditions at 2D Node 40
1.14 Static Behavior About 2D Node 43
1.15 Non-Static Example: Wave Incident on 2D Node 44
1.16 Integral Rotational Properties of Field About the Node 47
1.17 2D TLM Iteration Method for Nine Cell Core Matrix 52
1.18 2D Finite Difference Method . Comparison With TLM Method 56
xm
XIV Electromagnetic Analysis Using Transmission Line Variables
Appendices
1A. 1 Effect of Additional Paths on Weighing Process 64
1A.2 Novel Applications of TLM Method. Description of
Neurological Activity Using the TLM Method 67
H. NOTATION AND MAPPING OF PHYSICAL PROPERTIES.... 72
2.1 1D Cell Notation and Mapping of Conductivity and Field 74
2.2 Neighboring ID Cells With Unequal Impedance 78
2.3 2D Cell Notation. Mapping of Conductivity and Field 81
2.4 3D Cell Notation. Mapping of Conductivity and Field 89
Other Node Controlled Properties
2.5 Node Control of 2D Scattering Coefficients Due to Finite Node
Resistance 97
2.6 Simultaneous Conductivity Contributions 98
2.7 Signal Gain 99
2.8 Signal Generation. Use of Node Coupling 100
2.9 Mode Conversion 105
Example of Mapping:Node Resistance
in a Photoconductive Semiconductor
2.10 Semiconductor Switch Geometry (2D) 105
2.11 Node Resistance Profile in Semiconductor 109
HI, SCATTERING EQUATIONS 112
3.1 ID Scattering Equations 113
3.2 2D Scattering Equations 116
3.3 Effect of Symmetry on Scattering Coefficients 125
3.4 3D Scattering Equations: Coplanar Scattering 128
General Scattering, Including Scattermg
Normal to Propagation Plane
3.5 Equivalent TLM Circuit. Quasi-Coupling Effect 137
3.6 Neglect of Quasi-Coupling 139
3.7 Simple Quasi-Coupling Circuit: First Order Approximation 141
3.8 Correction to Quasi-Coupling Circuit: Second Order Approximation 145
3.9 Calculation of Load Impedance with Quasi-Coupling 148
XV
3.10 Small Coupling Approximation of Second Order
Quasi-Coupling 150
3.11 General 3D Scattering Process Using Cell Notation. 152
3.12 Complete Iterative Equations 164
3.13 Contributions of Electric and Magnetic Fields to Total Energy 166
Plane Wave Behavior
3.14 Response of 2D Cell Matrix to Input Plane Wave 168
3.15 Response of 2D Cell Matrix to Input Waves With
Arbitrary Amplitudes 178
3.16 Response of 3D Cell Matrix to Input Plane Wave 179
3.17 Response of 3D Cell Matrix to Input Waves With
Arbitrary Amplitudes 183
Appendices
3 A. 1 3D Scattering Equations With Both Coplanar and
Aplanar Contributions 185
3A.2 3D Scattering Coefficients With Both Coplanar and Aplanar
Contributions 187
3A.3 3D Scattering Coefficients in Terms of Circuit Parameters 189
. CORRECTIONS FOR PLANE WAVE AND ANISOTROPY
EFFECTS 194
4.1 Partition of TLM Waves into Component Waves 194
4.2 Scattering Corrections for 2D Plane Waves: Plane Wave
Correlations Between Cells 196
4.3 Changes to 2D Scattering Coefficients 203
Corrections to Plane Wave Correlation
4.4 Correlation of Waves in Adjoining Media With Differing
Dielectric Constants 206
4.5 Modification of Wave Correlation Adjacent a Conducting Boundary ... 207
Decorrelation Processes
4.6 De-Correlation Due to Sign Disparity of Plane and Symmetric
Waves 211
4.7 Minimal Solution Using Differing Decorrelation Factors to
Remove Sign Disparities 222
XVI Electromagnetic Analysis Using Transmission Line Variables
4.8 Non-Essential De-Correlation Caused by Simultaneous Presence of
Forward and Backward In-Line Plane Waves With Same Polarity.. 226
4.9 De-Correlation Treatment of Plane Waves Incident on Dielectric
Interface 230
4.10 Comments on Interaction of a Plane Wave Front and a Source
Emitting Both Plane Wave and Symmetric Components 234
4.11 Summary of Correlation/Decorrelation Processes 235
Grid Orientation Effects
4.12 Dependence of Wave Energy Dispersal on Grid Orientation 235
4.13 Transformation Properties Between Grids 239
Averaging Procedure Among Grids
4.14 General Procedure and Grid Specification 242
4.15 Vector Description of Plane and Symmetric Waves 243
4.16 Energy Content of Plane and Symmetric Waves 246
4.17 Principal Axis Grid 247
4.18 Simple Averaging Example Without Plane Wave Effects 248
4.19 General Averaging Procedure Including Plane Wave Correlations.. 249
4.20 Summary of Field Averaging Procedure 255
4.21 Averaging Procedure for Node Resistance 257
4.22 Comparison of Standard Numerical Methods and TLM Methods
Incorporating TLM Correlations/Decorrelations and Grid
Orientation 259
Appendices
4A. 1 3D Scattering Corrections For Plane Waves
( Wave Correlations) 260
4 A. 2 Consistency of Plane Wave Correlations With a Simple Quantum
Mechanical Model 263
V. BOUNDARY CONDITIONS AND DISPERSION 266
5.1 Dielectric-Dielectric Interface 267
Node Coupling: Nearest Node and Multi-coupled Node
Approximations
5.2 Nearest Nodes for ID Interface 275
5.3 Nearest Nodes at 2D Interface 276
XVII
5.4 Truncated Cell and Oblique Interface 278
5.5 Single Index Cell Notation 280
5.6 Simplified Iteration Neglecting the Nearest Node Approximation... 283
5.7 Non-Uniform Dielectric. Use of Cluster Cells 283
Other Boundary Conditions
5.8 Dielectric- Open Circuit Interface 287
5.9 Dielectric - Conductor Interface 288
5.10 Input/Output Conditions 291
5.11 Composite Transmission Line 294
5.12 Determination of Initial Static Field By TLM Method 295
5.13 Time Varying Source Voltage and Antenna Simulation 299
Dispersion
5.14 Dispersion Sources 301
5.15 Dispersion Example 302
5.16 Propagation Velocity in Terms of Wave Number 306
5.17 Dispersive Properties of Node Resistance 306
5.18 Node Resistance in Terms of Wave Number 307
5.19 Anomalous Dispersion 308
Incorporation of Dispersion into TLM Formulation
5.20 Dispersion Approximations 309
5.21 Outline of Dispersion Calculation Using the TLM Method 310
5.22 One Dimensional Dispersion Iteration 311
5.23 Initial Conditions With Dispersion Present 322
5.24 Stability of Initial Profiles With Dispersion Present 323
5.25 Replacement of Non-Uniform Field in Cell
With Effective Uniform Field 329
Appendices
5 A. 1 Specification of Input/Output Node Resistance to Eliminate Multiple
Reflections 330
VL CELL DISCHARGE PROPERTD2S AND INTEGRATION OF
TRANSPORT PHENOMENA INTO THE TLM MATRIX 333
6.1 Charge Transfer Between Cells 334
6.2 Relationship Between Field and Cell Charge 337
xviii Electromagnetic Analysis Using Transmission Line Variables
6.3 Dependence of Conductivity on Carrier Properties 341
Integration of Carrier Transport Using TLM Notation
Changes in Cell Occupancy and its Effect on TLM Iteration
6.4 General Continuity Equations 342
6.5 Carrier Generation Due to Light Activation 343
6.6 Carrier Generation Due to Avalanching: Identical Hole and
Electron Drift Velocities 344
6.7 Avalanching With Differing Hole and Electron Drift Velocities 346
6.8 Two Step Generation Process 350
6.9 Recombination 351
6.10 Limitations of Simple Exponential Recovery Model 353
6.11 Carrier Drift 353
6.12 Cell Charge Iteraction.Equivalence of Drift and Inter-Cell Currents . 357
6.13 Carrier Diffusion 361
6.14 Frequency of Transport Iteration 363
6.15 Total Contribution to Changes in Carrier Cell Occupancy 364
VH. DESCRIPTION OF TLM ITERATION 366
7.1 Specification of Geometry 366
7.2 Description of Inputs and TLM Iteration Outline 372
7.3 Output Format 377
Output Simulation Data
7.4 Conditions During Simulation 379
7.5 Behavior During Charge-up.Establishment of Static Field Profile... 380
7.6 Node Resistance R(n,m) During Activation 386
7.7 Output Pulse When Semiconductor is Activated 391
7.8 Node Recovery and its Effect on Output Pulse 394
7.9 Steady State and Transient Field Profiles 396
7.10 Partial Activation of Nodes and Effect on Profiles and Output 399
7.11 Cell Charge Following Recovery 402
7.12 Role ofTLM Waves at Charged Boundary 405
7.13 Comparison of Possible Boundary Conditions at the
Semiconductor/Dielectric Interface 407
Contents xix
7.14 Simulation Results for Boundary with Non-Integral
Nearest Nodes 408
7.15 Comparison of Output With and Without Matched
Input /Output Lines 411
7.16 Simulation of Plane Wave Effects. Effect of Alternating Input 413
Appendices
7A.1 Discussion of Program Statements for Semiconductor Switch 418
7A.2 Program Statements 426
7 A. 3 Program Changes for Arbitrary Dielectric Constant, Cell
Density, and Device Size 442
7A.4 Field Decay in Semiconductor Using the TLM Formulation 444
Vm. SPICE SOLUTIONS 450
8.1 Photoconductive Switch 451
8.2 Traveling Wave Marx Generator 455
8.3 Traveling Marx Wave in a Layered Dielectric 460
8.4 Simulation of a Traveling Marx Wave in a Layered Dielectric 462
Pulse Transformation and Generation Using Non-Uniform
Transmission Lines
8.5 Use of Cell Chain to Simulate Pulse Transformer 467
8.6 Pulse Transformer Simulation Results 470
8.7 Pulse Sources Using Non-Uniform TLM Lines (Switch at Output) 472
8.8 Radial Pulse Source (Switch at Output) 473
8.9 Pulse Sources With Gain (PFXL Sources) 476
Darlington Pulser
8.10 TLM Formulation of Darlington Pulser 481
8.11 SPICE Simulation of Lossy Darlington Pulser 485
Appendices
8A.1 Introduction to SPICE Format 488
8A.2 Discussion of Format for Photoconductive Switch 488
8A.3 TLM Analysis of Leading Edge Pulse in a Transformer 496
8A.4 TLM Analysis of Leading Edge Wave in PFXL 499
INDEX 507

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