1st Edition

Electrical Solitons Theory, Design, and Applications

By David S. Ricketts, Donhee Ham Copyright 2011
    264 Pages 115 B/W Illustrations
    by CRC Press

    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.

    I Electrical Solitons: Theory

    Introduction

    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

    Experiments

    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

    Biography

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