Transmission Lines and Lumped Circuits: Fundamentals and Applications

by Giovanni Miano, Antonio Maffucci

Overview

The theory of transmission lines is a classical topic of electrical engineering. Recently this topic has received renewed attention and has been a focus of considerable research. This is because the transmisson line theory has found new and important applications in the area of high-speed VLSI interconnects, while it has retained its significance in the area of power transmission. In many applications, transmission lines are connected to nonlinear circuits. For instance, interconnects of high-speed VLSI chips can be modelled as transmission lines loaded with nonlinear elements. These nonlinearities may lead to many new effects such as instability, chaos, generation of higher order harmonics, etc. The mathematical models of transmission lines with nonlinear loads consist of the linear partial differential equations describing the current and voltage dynamics along the lines together with the nonlinear boundary conditions imposed by the nonlinear loads connected to the lines. These nonlinear boundary conditions make the mathematical treatment very difficult. For this reason, the analysis of transmission lines with nonlinear loads has not been addressed adequately in the existing literature. The unique and distinct feature of the proposed book is that it will present systematic, comprehensive, and in-depth analysis of transmission lines with nonlinear loads.

Product Details

ISBN-13:	9780121897109
Publisher:	Elsevier Science
Publication date:	01/30/2001
Series:	Electromagnetism
Pages:	479
Product dimensions:	6.00(w) x 9.00(h) x (d)

About the Author

Antonio Maffucci is Associate Professor of Electrical Engineering at the University of Cassino and Southern Lazio. Since 2014, he has also been associated to the INFN, Frascati National Laboratories. His research focuses on issues of electromagnetic and circuit modeling, computational electromagnetics, electromagnetic compatibility, nanotechnology. He is the author of 160 international publications, 3 reviews, 1 book, 7 book chapters and 4 receiverships.

Table of Contents

Transmission Line Equations and Properties
Ideal Two-Conductor Transmission Lines Connected to Lumped Circuits
Ideal Multiconductor Transmission Lines
Lossy Two-Conductor Transmission Lines
Lossy Two-Conductor Transmission Lines with Frequency-Dependent Parameters
Lossy Multiconductor Transmission Lines
Nonuniform Transmission Lines
Transmission Line Equations in Characteristic Form
Lumped Nonlinear Networks Interconnected by Transmission Lines
Qualitative Analysis of an Ideal Two-Conductor Line Connected to Nonlinear Resistors: Periodic Solutions, Bifurcations and Chaos
Appendix A: Some Useful Notes on the Matrix Operators
Appendix B: Some Useful Notes on the Laplace Transformation
Appendix C: Some a-priori Estimates
Appendix D: Tables of Equivalent Representations of Transmission Lines

Preface

This book deals with the analysis of networks composed of transmission lines and lumped circuits. It is intended for senior and graduate students in electrical and electronic engineering. It will also be a useful reference for industrial professionals and researchers concerned with computer-aided circuit analysis and design. As far as the transmission line model is concerned, it is assumed that the reader is acquainted with the subject at the level of undergraduate courses in electrical engineering (e.g., Collins, 1992; Paul, 1994; Franceschetti, 1997).

Introductory courses on transmission line theory deal with the basic concepts of traveling and standing waves, and analyze, in the frequency domain, transmission lines connected to independent sources and impedances. They introduce several basic notions, such as those of traveling wave, standing wave, characteristic impedance, power flux, reflection coefficients, voltage standing-wave ratio, and impedance transformation, tackle the problem of impedance matching, and teach how to use the Smith chart. However, frequency domain analysis techniques are not useful for high-speed electronic circuits and distribution systems of electrical energy, which consist of many transmission lines connected to many nonlinear and time-varying lumped circuits.

This book concerns the time domain analysis of electrical networks composed of linear time invariant transmission lines and lumped circuits that, in general, can be nonlinear and/or time varying. The theory of wave propagation in linear time invariant transmission lines, two-conductor or multiconductor, without losses or with losses, with prameters dependent or not upon frequency, uniform or nonuniform, is presented in a way that is new, completely general, and yet concise. The terminal behavior of these lines is characterized in the time domain through convolution relations with delays. A characterization dealing exclusively with the voltages and currents at the line ends is a prerequisite to tackling the study of networks composed of transmission lines and lumped circuits by way of all those techniques of analysis and computation that are typical of lumped circuit theory. The most widely used circuit simulator, SPICE, simulates transmission lines by using this approach.

A unique feature of this book is the extension of some concepts of lumped circuit theory, such as those of associated discrete circuit (Chua and Lin, 1975) and associated resistive circuit (Hasler and Neirynck, 1986) to networks composed of lumped and distributed elements. The qualitative study of equations relevant to networks composed of transmission lines and lumped circuits is carried out. In particular, it is shown that transmission lines connecting nonlinear locally active resistors may exhibit fascinating nonlinear phenomena such as bifurcations and chaos.

This book has profited by the many suggestions and comments made by our colleagues over the years. In particular, we appreciate the support for the development of this text from the Department of Electrical Engineering of the University of Naples, Federico II.

The authors are indebted to Isaak D. Mayergoyz for his encouragement throughout this project. In particular, Giovanni Miano expresses his sincere gratitude to him for his hospitality during the initial stage of writing. The writing of this book has benefited enormously from the scientific atmosphere at the Department of Electrical Engineering of the University of Maryland.

We express our special thanks to Gregory T. Franklin, Marsha Filion, and Angela Dooley of Academic Press for their refined courtesy and continued assistance and to Franco Lancio who designed the cover of this book.

During the last months this book has taken up time usually devoted to our wives, Gabriella and Michela. The book was written thanks to their patience and understanding.