Preface ........................................................ ix
1 Mathematical Techniques for Pulse and Transient Circuit
Analysis ..................................................... 1
1.1 Introduction ............................................ 1
1.2 The Classical Method .................................... 1
1.3 The Complex Frequency Method ............................ 7
1.4 The Laplace Transform Method ............................ 9
1.4.1 Application of the Laplace Transform Method ..... 11
1.4.2 Laplace Transforms of Some Basic Signals ........ 12
1.4.3 Some Properties of the Laplace Transformation ... 14
1.4.4 Finding the Inverse Laplace Transform ........... 19
1.4.5 The Laplace Transform Circuit ................... 24
1.4.6 System or Transfer Functions .................... 34
1.4.7 Direct Determination of Rise and Delay Time
Response of Networks ............................ 35
References .................................................. 38
2 Transmission Line Theory and Transient Response ............. 41
2.1 Introduction ........................................... 41
2.2 Circuit Analysis of Transmission Lines ................. 43
2.3 Continuous Sinusoidal Transmission Line Excitation ..... 46
2.3.1 Low Loss and Loss-free Lines .................... 47
2.3.2 The Transmission Line as a Two-port Network ..... 50
2.3.3 Impedance Relations for Terminated Lines ........ 52
2.3.4 Line Reflections ................................ 55
2.4 Transient Transmission Line Response ................... 58
2.4.1 Transient Response of the Infinite Line ......... 58
2.4.2 Transient Response of Lossy Transmission
Lines ........................................... 59
2.4.3 Transient Response of Terminated Lines .......... 61
2.4.4 Input Impedance of Terminated Lines for
Transient Signals ............................... 65
2.4.5 Reflections on Lines with Reactive
Terminations .................................... 66
2.4.6 Reflection Charts or Lattice Diagrams ........... 68
References .................................................. 70
3 Pulse-forming Lines ......................................... 71
3.1 Introduction ........................................... 71
3.2 The Single Pulse-forming Line .......................... 71
3.2.1 Lattice Diagram Representation of Pulse-
forming Action using a Single Transmission
Line ............................................ 74
3.3 Pulse-forming using the Blumlein Pulse-forming Line .... 75
3.3.1 Lattice Diagram Representation of Pulse-
forming Action using a Blumlein Pulse-forming
Line ............................................ 78
3.4 The Laplace Transform Analysis of Pulse-forming
Action by Transmission Lines ........................... 80
3.4.1 Pulse-forming by the Simple Pulse-forming
Line ............................................ 80
3.4.2 Pulse-forming by the Blumlein Pulse-forming
Line ............................................ 83
3.5 Some Other Pulse-forming Line Variants ................ 85
3.5.1 The Stacked Blumlein Pulse-forming Line
Generator ....................................... 85
3.5.2 The Darlington Circuits ......................... 88
3.5.3 Further Darlington-like Pulse-forming Lines ..... 90
3.5.4 The Self-matching Pulse-forming Line ............ 96
3.5.5 The Bi-directional or Zero Integral
Pulse-forming Line .............................. 98
3.5.6 A Pseudo-repetitive Pulse-forming Line .......... 99
3.5.7 Current-fed Pulse-forming Lines ................ 102
References ................................................. 106
4 Pulse-forming Networks ..................................... 107
4.1 Introduction .......................................... 107
4.2 LC Ladder Networks .................................... 108
4.2.1 The Impedance Characteristics of an LC Ladder
Network ........................................ 108
4.2.2 General Transform Equations for a Ladder
Network ........................................ 110
4.2.3 Input Impedance Functions of Open Circuit and
Short Circuit Ladder Networks .................. 112
4.2.4 Propagation Characteristics of an LC Ladder
Network ........................................ 114
4.3 Pulse-forming Action of an LC Ladder Network .......... 117
4.4 The Synthesis of Alternative LC Pulse-forming
Networks .............................................. 121
4.4.1 Guillemin's Method ............................. 124
4.4.2 Current-fed Networks ........................... 129
4.4.3 The Synthesis of Alternative LC Current-fed
Pulse-forming Networks ......................... 133
4.4.4 Guillemin Type Current-fed Pulse-forming
Networks ....................................... 133
4.5 Some Further Comments on Pulse-forming Networks ........ 134
References ................................................. 135
5 Pulse Transformers ......................................... 137
5.1 Introduction .......................................... 137
5.2 The Ideal Transformer and the Concepts of Referral
and Reluctance ........................................ 138
5.2.1 Practical or Non-ideal Transformers ............ 140
5.2.2 Equivalent Circuit of a Transformer ............ 143
5.2.3 Leading Edge Response .......................... 144
5.2.4 Pulse Flat Top Response ........................ 147
5.2.5 Trailing Edge Response ......................... 148
5.2.6 Pulse Transformer Magnetic Core ................ 150
5.3 Air-cored Pulse Transformers .......................... 154
5.3.1 Analysis of Air-cored Pulse Transformer
Circuit Performance ............................ 159
5.3.2 Dual Resonant Operation of Air-cored Pulse
Transformers ................................... 162
5.4 Pulse Transformers with Multiple Windings ............. 163
5.5 Hybrid Wound/Transmission Line Pulse Transformer ...... 167
References ................................................. 168
6 Transmission Line Pulse Transformers ....................... 169
6.1 Introduction .......................................... 169
6.2 Linear Transmission Line Transformers ................. 169
6.2.1 The 1:1 Inverting Transformer .................. 171
6.2.2 The Two-stage Voltage Transformer .............. 173
6.2.3 Detailed Analysis of the Two-stage Voltage
Transformer .................................... 176
6.2.4 Voltage Gain of Multi-stage, Linear
Transmission Line Transformers ................. 179
6.3 Wound Transmission Line Transformers .................. 183
6.3.1 Basic Operation ................................ 184
6.3.2 Model Development .............................. 186
6.3.3 Mutually Coupled Windings ...................... 193
6.3.4 Frequency Response Analysis ................... 194
6.4 Tapered Transmission Line Transformers ................ 197
6.4.1 The Exponentially Tapered Transmission Line
Transformer .................................... 201
References ................................................. 206
7 Pulse Generators using Capacitive and Inductive Energy
Storage .................................................... 209
7.1 Introduction .......................................... 209
7.2 The Basic Principles of Capacitive and Inductive
Energy Discharge ...................................... 209
7.2.1 Pulse Generators based on Inductive Energy
Storage ........................................ 211
7.2.2 The Efficiency of Energy Transfer from
Inductive Energy Stores ........................ 214
7.2.3 Flux Compression Circuits ...................... 218
7.3 Marx Generators ....................................... 220
7.3.1 Circuit Analysis of the Marx Generator ......... 223
7.3.2 Fast Marx Generators ........................... 225
7.3.3 Triggered Marx Generators ...................... 226
7.4 Vector Inversion Generators ........................... 228
7.4.1 The LC Generator ............................... 228
7.4.2 The Spiral Generator ........................... 230
References ................................................. 234
8 Nonlinear Pulsed Circuits .................................. 237
8.1 Introduction .......................................... 237
8.2 Magnetic Switching .................................... 237
8.2.1 Magnetic Pulse Compressors ..................... 240
8.3 Pulse Sharpening using Nonlinear Capacitors ........... 245
8.3.1 The Analysis of Pulse Sharpening on LC
ladders with Nonlinear Capacitors .............. 249
8.3.2 Soliton Generation ............................. 252
8.4 Electromagnetic Shock Wave Generation in Nonlinear
Transmission Lines .................................... 255
8.4.1 Shock Wave Formation on Ferrite Loaded
Transmission Lines ............................. 256
8.4.2 Shock Wave Generation on Nonlinear
Ferroelectric Lines ............................ 257
8.4.3 Ferroelectric Shock Lines: Some Practical
Considerations ................................. 261
References ................................................. 264
Appendix: Table of Laplace Transforms ......................... 267
Index ......................................................... 269
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