Electrical Solitons : Theory, Design, and Applications book cover
1st Edition

Electrical Solitons
Theory, Design, and Applications

ISBN 9781439829806
Published December 14, 2010 by CRC Press
264 Pages 115 B/W Illustrations

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Book Description

The dominant medium for soliton propagation in electronics, nonlinear transmission line (NLTL) has found wide application as a testbed for nonlinear dynamics and KdV phenomena as well as for practical applications in ultra-sharp pulse/edge generation and novel nonlinear communication schemes in electronics. While many texts exist covering solitons in general, there is as yet no source that provides a comprehensive treatment of the soliton in the electrical domain.

Drawing on the award winning research of Carnegie Mellon’s David S. Ricketts, Electrical Solitons Theory, Design, and Applications is the first text to focus specifically on KdV solitons in the nonlinear transmission line. Divided into three parts, the book begins with the foundational theory for KdV solitons, presents the core underlying mathematics of solitons, and describes the solution to the KdV equation and the basic properties of that solution, including collision behaviors and amplitude-dependent velocity. It also examines the conservation laws of the KdV for loss-less and lossy systems.

The second part describes the KdV soliton in the context of the NLTL. It derives the lattice equation for solitons on the NLTL and shows the connection with the KdV equation as well as the governing equations for a lossy NLTL. Detailing the transformation between KdV theory and what we measure on the oscilloscope, the book demonstrates many of the key properties of solitons, including the inverse scattering method and soliton damping.

The final part highlights practical applications such as sharp pulse formation and edge sharpening for high speed metrology as well as high frequency generation via NLTL harmonics. It describes challenges to realizing a robust soliton oscillator and the stability mechanisms necessary, and introduces three prototypes of the circular soliton oscillator using discrete and integrated platforms.

Table of Contents

I Electrical Solitons: Theory


The "Solitons"

A Brief Overview and History of the Soliton

The KdV Soliton

The Solitary Wave Solution

The Periodic Soliton: The Cnoidal Wave Solution

Transient Dynamics of the KdV

The Heart of the Soliton: Inverse Scattering

Inverse Scattering Method

A Math Problem

KdV Solution via the Inverse Scattering Method

Solution of the KdV Initial Value Problem

Asymptotic Solution to the Inverse Scattering Method

Soliton Defnition

Transient Solutions of the KdV

The Three Faces of the KdV Soliton

Conservative and Dissipative Soliton Systems

Conservation Laws

The Lossy KdV


II Electrical Solitons: Design

Electrical Nonlinear Transmission Line and Electrical Solitons

The Nonlinear Transmission Line

Toda Lattice

NLTL Lattice

KdV Approximation of the NLTL

The Lossy NLTL

The Electrical Soliton in the Lab, M.W. Chen and E. Shi

Toda Lattice, NLTL Lattice and KdV Solitons

Scaling and Transformations: Lab ! NLTL ! KdV

NLTL Characterization

Inverse Scattering on the NLTL

Soliton Damping on the NLTL

Numerical Accuracy


III Electrical Solitons: Application

NLTL as a Two-Port System, X. Li and M.W. Chen

Pulse Compression and Tapered NLTL

Shockwave NLTL

Harmonic Generation

The Soliton Oscillator

Basic Topology

Instability Mechanisms

Identifcation of Three Instability Mechanisms

NLTL Soliton Oscillator | Working Model

System Design and Amplifier Dynamics

The Circular Soliton Oscillator

CMOS, Low MHz Prototype

Bipolar, Microwave Prototype

CMOS, Chip-scale, GHz Prototype

The Reection Soliton Oscillator, O.O. Yildirim

Operating Principle

Amplifier Design


Comparison with Haus’s Oscillator

Chaotic Soliton Oscillator and Chaotic Communications, O.O. Yildirim, N. Sun, and X. Li

Chaos and Chaotic Communications

Chaotic Soliton Oscillator

Simulation of the Chaotic Soliton Oscillator

Simulation of Chaotic Binary Communication

Phase Noise of Soliton Oscillators, X. Li

Phase Noise Fundamentals

Phase Noise Due to Direct Phase Perturbation

Amplitude-to-Phase Noise Conversion

Experimental Verification

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David S. Ricketts is an Assistant Professor of ECE at Carnegie Mellon University in Pittsburgh, Pennsylvania.