List of Figures | p. ix |
List of Tables | p. xiii |
Preface | p. xv |
Electrical Solitons: Theory | p. 1 |
Introduction | p. 3 |
The ôSolitonsö | p. 7 |
A Brief Overview and History of the Soliton | p. 7 |
The KdV Soliton | p. 13 |
The Solitary Wave Solution | p. 13 |
The Periodic Soliton: The Cnoidal Wave Solution | p. 15 |
Asymptotics of the Cnoidal Wave | p. 19 |
The Cnoidal Wave vs. the Periodic Sech2 Wave | p. 20 |
Transient Dynamics of the KdV | p. 20 |
Solitary Wave ≠Soliton | p. 20 |
Soliton Collisions | p. 22 |
Summary | p. 26 |
Elliptic Integrals, Functions and Their Link to Differential Equations | p. 28 |
Arclength of a Circle | p. 28 |
Arclength of an Ellipse | p. 30 |
Elliptic Functions | p. 31 |
Example PDEs | p. 32 |
The Heart of the Soliton: Inverse Scattering | p. 35 |
Inverse Scattering Method | p. 36 |
A Math Problem | p. 36 |
KdV Solution via the Inverse Scattering Method | p. 38 |
Solution of the KdV Initial Value Problem | p. 42 |
The Eigenvalue Problem Using the Schrödinger Operator | p. 42 |
Asymptotic Solution to the Inverse Scattering Method | p. 47 |
Reflectionless Potentials | p. 48 |
Non-Reflectionless Potentials | p. 52 |
Soliton Definition | p. 55 |
Transient Solutions of the KdV | p. 56 |
Hirota's Direct Method | p. 56 |
Transient Solution Summary | p. 58 |
The Three Faces of the KdV Soliton | p. 58 |
Conservative and Dissipative Soliton Systems | p. 61 |
Conservation Laws | p. 61 |
The Lossy KdV | p. 63 |
Electrical Solitons: Design | p. 69 |
Electrical Nonlinear Transmission Line and Electrical Solitons | p. 71 |
The Nonlinear Transmission Line | p. 71 |
Toda Lattice | p. 73 |
NLTL Lattice | p. 74 |
KdV Approximation of the NLTL | p. 77 |
The Lossy NLTL | p. 80 |
The Electrical Soliton in the Lab | p. 85 |
Toda Lattice, NLTL Lattice and KdV Solitons | p. 86 |
Scaling and Transformations: Lab → NLTL → KdV | p. 87 |
NLTL Characterization | p. 93 |
Inverse Scattering on the NLTL | p. 96 |
Soliton Damping on the NLTL | p. 97 |
Numerical Accuracy | p. 100 |
Electrical Solitons: Application | p. 103 |
NLTL as a Two-Port System | p. 105 |
Pulse Compression and Tapered NLTL | p. 105 |
Shockwave NLTL | p. 110 |
Harmonic Generation | p. 117 |
Summary | p. 118 |
The Soliton Oscillator | p. 119 |
Basic Topology | p. 119 |
Instability Mechanisms | p. 121 |
Case I - Voltage Limiting Amplifier | p. 121 |
Case II - Linear Amplifier | p. 122 |
Identification of Three Instability Mechanisms | p. 122 |
NLTL Soliton Oscillator - Working Model | p. 125 |
Operating Principles | p. 125 |
Bias adjustment | p. 126 |
Amplifier operation | p. 126 |
Stability Mechanisms - Solution | p. 127 |
Distortion reduction | p. 127 |
Perturbation rejection | p. 127 |
Single mode selection | p. 129 |
System Design and Amplifier Dynamics | p. 129 |
Summary | p. 140 |
The Circular Soliton Oscillator | p. 141 |
CMOS, Low MHz Prototype | p. 141 |
Oscillator Implementation | p. 142 |
Amplifier design | p. 143 |
NLTL design | p. 144 |
Termination | p. 144 |
Experimental Verification | p. 146 |
Adaptive bias control | p. 146 |
Startup soliton dynamics | p. 147 |
Perturbation rejection | p. 147 |
Steady-state soliton oscillation | p. 151 |
Soliton propagation in steady-state | p. 151 |
Bipolar, Microwave Prototype | p. 154 |
Oscillator Implementation | p. 157 |
Experimental Results | p. 162 |
CMOS, Chip-scale, GHz Prototype | p. 165 |
Oscillator Implementation | p. 165 |
Test and Measurement | p. 167 |
Experimental Results | p. 167 |
Summary | p. 170 |
The Reflection Soliton Oscillator | p. 173 |
Operating Principle | p. 175 |
Reflection at the Amplifier End | p. 176 |
Reflection at the Open End | p. 179 |
Amplifier Design | p. 181 |
Need for an Adaptive Bias Scheme | p. 181 |
Reflection Amplifier with an Adaptive Bias | p. 181 |
Improved R-C Network | p. 186 |
Experiments | p. 186 |
Comparison with Haus's Oscillator | p. 193 |
Summary | p. 194 |
Chaotic Soliton Oscillator and Chaotic Communications | p. 197 |
Chaos and Chaotic Communications | p. 198 |
Chaotic Soliton Oscillator | p. 200 |
Simulation of the Chaotic Soliton Oscillator | p. 202 |
Simulation of Chaotic Binary Communication | p. 203 |
Summary | p. 208 |
Phase Noise of Soliton Oscillators | p. 211 |
Phase Noise Fundamentals | p. 212 |
Phase Noise Due to Direct Phase Perturbation | p. 215 |
Distributed Noise Sources | p. 215 |
Lumped Noise Sources | p. 223 |
Amplitude-to-Phase Noise Conversion | p. 225 |
Distributed Noise Sources | p. 227 |
Lumped Noise Sources | p. 228 |
Indirect vs. Direct Phase Perturbations | p. 229 |
Experimental Verification | p. 229 |
Oscillator Prototypes | p. 229 |
Phase Noise Measurement | p. 230 |
Intensity of Noise Sources | p. 232 |
Measurement-Theory Comparison | p. 235 |
Summary | p. 238 |
Bibliography | p. 239 |
Index | p. 247 |
Table of Contents provided by Ingram. All Rights Reserved. |