## Transmission Lines and Lumped Circuits: Fundamentals and Applications (Electromagnetism)

### Miano, Giovanni; Maffucci, Antonio

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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.
* A unified approach for the analysis of networks composed of distributed and lumped circuits
* A simple, concise and completely general way to present the wave propagation on transmission lines, including a thorough study of the line equations in characteristic form
* Frequency and time domain multiport representations of any linear transmission line
* A detailed analysis of the influence on the line characterization of the frequency and space dependence of the line parameters
* A rigorous study of the properties of the analytical and numerical solutions of the network equations
* The associated discrete circuits and the associated resisitive circuits of transmission lines
* Periodic solutions, bifurcations and chaos in transmission lines connected to noninear lumped circuits

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From the Back Cover:

The time-domain analysis of networks composed of linear transmission lines and nonlinear and/or time-varying lumped circuits is at the basis of design and verification of modern high-speed electronic circuits and large power distribution systems.

This book provides an in-depth and comprehensive study of time-domain models of these networks.

The theory of wave propagation on linear transmission lines is presented with an unified approach, that is applicable to any kind of line: two-conductor or multiconductor, lossless or lossy, uniform or nonuniform, with parameters depending or not on frequency.

A general method is described to characterize the terminal behavior of transmission lines, and to obtain equivalent circuit representations, both in the frequency and in the time domain.

Unique feature of this book is the extension of fundamental concepts of the lumped circuit theory, such as those of associated discrete circuit and of associated resistive circuit, to networks of transmission lines and lumped circuits.
The well-posedness of the network equations and their numerical approximations is deeply investigated by using these concepts.

Fascinating phenomena such as periodic solutions, bifurcations and chaos are observed in transmission lines connected to nonlinear active elements.

Key Features
· A simple, concise and completely general way to present the wave propagation on transmission lines, including a thorough study of the line equations in characteristic form.
· Frequency and time domain characterization of the terminal behavior of any linear transmission line.
· A unified approach for the analysis of networks composed of distributed and lumped circuits.
· Bifurcations and chaos in transmission lines.

Benefits
The book is intended as a reference in advanced courses of Circuit Theory and Design, Electromagnetism, Electromagnetic Compatibility, and as a guide for researchers and industrial professionals involved in the computer-aided design of electrical and electronic networks.

The students will find here a simple but rigorous explanation of wave propagation along transmission lines, a completely general method to characterize the terminal behavior of the lines both in frequency and time domain, and a unified approach to study networks composed of distributed and lumped circuits.

The researchers and professionals will appreciate the time domain modeling of distributed circuits, providing simple equivalent circuit representations, ready to be implemented in SPICE-like circuit simulators, for the analysis of large networks.
This book will be of interest to a broad audience of engineers and researchers involved in electromagnetic analysis, design of VLSI circuits, power systems, and CAD software development.

From the Introduction:

Due to the rapid increase in signal speed and advances in electronic circuit technology, interconnections between electronic devices may behave as transmission lines. Unintentional delays, crosstalk voltages, reflections, signal losses, and voltage overshoots on terminal devices affect the correct operation of high-speed electronic circuits (e.g., Paul, 1992). "To meet the challenges of high-speed digital processing, today’s multilayer printed circuit boards must: a) reduce propagation delay between devices; b) manage transmission line reflections and crosstalk (signal integrity); c) reduce signal losses; d) allow for high density interconnections" (Montrose, 1998). Crosstalk, delays and multireflections are also important phenomena in on-chip interconnections for high-performance microprocessors (e.g., Deutsch et al., 1995, 1997; Motorola Inc., 1989). Therefore, for design and verification of these circuits, accurate and efficient simulation techniques are needed. As most electronic devices are time-varying and nonlinear, the analysis of these systems and hence of the transmission lines themselves, must be performed in the time domain.

The analysis of transmission lines in the time domain is also important for power systems to predict the transient behavior of long power lines either excited by external electromagnetic fields, for example, emission of high-power radars, nuclear electromagnetic pulses, lightning strokes, or under disruptions such as short circuits at some places (e.g., Paul, 1992).

This book concerns the time domain analysis of electrical networks composed of transmission lines and lumped circuits. The time domain analysis of lumped circuits is a fundamental and well-understood subject in electrical engineering. Nevertheless, the time domain analysis of networks composed of transmission lines and lumped circuits, and of the transmission lines themselves, are not so well understood.

The primary purposes of this book are threefold.

First, the theory of wave propagation in transmission lines, whether two-conductor or multiconductor, lossless or with losses, with parameters depending or not on the frequency, uniform or nonuniform, is presented in a way that is new, completely general, and yet concise.

The second objective is to give an original and general method to characterize the terminal behavior of transmission lines in both the frequency and time domains. A characterization of the lines dealing exclusively with the voltages and currents at their ends is a prerequisite to tackling the study of networks composed of transmission lines and lumped circuits through all those techniques of analysis typical of lumped circuit theory.

The last objective, but not the least, is the qualitative study of the equations relevant to networks composed of transmission lines and lumped circuits. A unique feature of this book is the extension of some of the 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.

Whether the transmission line model accurately describes actual interconnections or not is a basic question that is beyond the scope of this text. The reader is assumed to be acquainted with it. Here we only recall that, under the assumption of a quasi-transverse electromagnetic (quasi-TEM) mode of propagation, interconnections may be modeled as transmission lines (e.g., Lindell and Gu, 1987; Collin, 1992; Paul, 1994). Whether this assumption is satisfied or not for actual interconnections depends on the frequency spectrum of the signals propagating along them, on their cross-sectional dimensions, and on the electromagnetic properties of the conductors and the medium embedding them. In most cases of interest a simple criterion is the following. The distance between the conductors must be much smaller than the lowest characteristic wavelength of the signals propagating along them.

The first chapter of this book is devoted to the transmission line model. First, we shall recall some of the basic aspects of the quasi-TEM approximation and the equations of the transmission lines. Then, we shall examine closely some general properties of the transmission line equations that are of considerable importance and that we shall be using widely in this book.

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Book Description Elsevier Science Publishing Co Inc, United States, 2001. Hardback. Book Condition: New. New.. 235 x 159 mm. Language: English . Brand New Book. 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 transmission 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. It provides a unified approach for the analysis of networks composed of distributed and lumped circuits. It offers a simple, concise and completely general way to present the wave propagation on transmission lines, including a thorough study of the line equations in characteristic form. It includes frequency and time domain multiport representations of any linear transmission line. It provides a detailed analysis of the influence on the line characterization of the frequency and space dependence of the line parameters. It presents a rigorous study of the properties of the analytical and numerical solutions of the network equations. It covers the associated discrete circuits and the associated resistive circuits of transmission lines. It also includes periodic solutions, bifurcations and chaos in transmission lines connected to nonlinear lumped circuits. Bookseller Inventory # AA59780121897109

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Book Description Elsevier Science Publishing Co Inc, United States, 2001. Hardback. Book Condition: New. New.. 235 x 159 mm. Language: English . Brand New Book. 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 transmission 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. It provides a unified approach for the analysis of networks composed of distributed and lumped circuits. It offers a simple, concise and completely general way to present the wave propagation on transmission lines, including a thorough study of the line equations in characteristic form. It includes frequency and time domain multiport representations of any linear transmission line. It provides a detailed analysis of the influence on the line characterization of the frequency and space dependence of the line parameters. It presents a rigorous study of the properties of the analytical and numerical solutions of the network equations. It covers the associated discrete circuits and the associated resistive circuits of transmission lines. It also includes periodic solutions, bifurcations and chaos in transmission lines connected to nonlinear lumped circuits. Bookseller Inventory # AA59780121897109

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