Electromagnetism and Interconnections E-Book

Stephane Charruau

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 259

Veröffentlichungsjahr: 2013

Beschreibung

Electromagnetism and Interconnections: Advanced Mathematical Tools for Computer-aided Simulation

This book covers the theoretical problems of modeling electrical behavior of the interconnections encountered in everyday electronic products. The coverage shows the theoretical tools of waveform prediction at work in the design of a complex and high-speed digital electronic system. Scientists, research engineers, and postgraduate students interested in electromagnetism, microwave theory, electrical engineering, or the development of simulation tools software for high speed electronic system design automation will find this book an illuminating resource.

Leseprobe

Table of Contents

Acknowledgments

Introduction

Chapter 1. Theoretical Foundations of Electromagnetism

1.1. Elements of the theory of distributions applied to electromagnetism

1.2. Vector analysis review according to the theory of distributions

1.3. Maxwell’s equations according to the theory of distributions

1.4. Conclusion

Chapter 2. Full Wave Analysis

2.1. Discontinuities in electromagnetism

2.2. Potentials in electromagnetism

2.3. Topology of electromagnetic interferences

2.4. Conclusion

Chapter 3. Electromagnetism in Stratified Media

3.1. Electrical and magnetic currents in stratified media

3.2. Straight stratified media

3.3. Conclusion

Chapter 4. Transmission Line Equations

4.1. Straight homogenous dielectric media with lossless conductors

4.2. TEM mode of wave propagation

4.3. Quasi-TEM approximation for lossy conductors and dielectrics

4.4. Weakly bent transmission lines in the quasi-TEM approximation

4.5. Conclusion

Chapter 5. Direct Time-domain Methods

5.1. “Direct” methods in the time domain

5.2. Lossless coupled transmission lines in homogenous media

5.3. Conclusion

Chapter 6. Discretization in the Time Domain

6.1. Finite difference method in the time domain

6.2. Matrix velocity operator interpolation method

6.3. Conclusion

Chapter 7. Frequency Methods

7.1. Laplace transform method for lossy transmission lines

7.2. Coming back in the time domain

7.3. Method of the discrete Fourier transform

7.4. Conclusion

Chapter 8. Time-domain Wavelets

8.1. Theoretical introduction

8.2. Application to digital signal propagation

8.3. Conclusion

Chapter 9. Applications of the Wavelet Method

9.1. Coupled lossy transmission lines in the TEM approximation

9.2. Extension to 3D wavelets and electromagnetic perturbations

9.3. Conclusion

Appendix A. Physical Data

Appendix B. Technological Data

Appendix C. Lineic Capacitors

Appendix D. Modified Relaxation Method

Appendix E. Cylindrical Wavelets

Appendix F. Wavelets and Elliptic Operators

References

Index

First published in Great Britain and the United States in 2009 by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUKwww.iste.co.ukJohn Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USAwww.wiley.com

© ISTE Ltd, 2009

The rights of Stéphane Charruau to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Cataloging-in-Publication Data

Charruau, Stéphane.

Electromagnetism and interconnections: advanced mathematical tools for computer-aided simulation / Stéphane Charruau.

p. cm.

Includes bibliographical references and index.

ISBN 978-1-84821-107-0

1. Telecommunication lines--Computer simulation. 2. Electromagnetic waves--Mathematical models. I. Title.

TK5103.15.C45 2009

621.381--dc22

2008043382

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN: 978-1-84821-107-0

Acknowledgments

Before anything else, the author would like to dedicate this book to his wife Chantal and his daughters Coralie, Laure, Olivia and Héloïse to whom the author pays homage for their emotional support during the many years of work on this book.

The author expresses his appreciation to Professor André Touboul of the University of Bordeaux and researcher at the Laboratoire d’Etudes de l’Intégration des Composants et Systèmes Electroniques for scientific discussions regarding mathematical methods and their application to interconnections modeling.

The author thanks Mrs. Hélène Misson PhD of the University of Bordeaux for help in computations, curve generation, text typing and mathematical equation editing.

The author extends thanks to Mr. Olivier Meili, graduate student of the University of Bordeaux, for having produced illustrations and carrying out a typing review.

The author acknowledges Mr. Dominique Gili-Lacoste from the society Trièdre Concept for help in three-dimensional image generation.

Introduction

This book is intended for scientists, research engineers and graduate students interested in electromagnetism, microwave theory, electrical engineering and the development of simulation tool software devoted to very high-speed electronic system design automation or in the application of mathematics to these topics.

The subject matter of this book concerns the theoretical problems of modeling the electrical behavior of the interconnections met in electronic products that have become ubiquitous in daily life since the end of the 20th century. Most electronic products have digital processors that have more and more inner and outer conductors with smaller and smaller geometries. This means increasingly more parasitic electromagnetic effects occur inside and outside these processors that then cannot work correctly. The aim of this book is to show the theoretical tools of waveform prediction at the design stage of a complex and high-speed digital electronic system.

The topics that the book covers are not new; indeed transmission line analysis has a very long history. In the middle of the 19th century, the technical problems posed by the bad quality of transmissions traveling through submarine cables led telecommunications engineers, mainly those working in Britain, to become interested in Maxwell’s theory published in 1873. One of their number, Heaviside, formulated Maxwell’s equations in their modern form in 1884. Since that time and up to Word War II, Heaviside’s formalism greatly supported the development of wireless transmissions, then that of radars and their waveguide technology, while Lord Kelvin’s line modeling based on chaining a huge number of lumped electrical networks was used in phone transmissions analysis.

The first theoretical approach of two weakly coupled lines based on Kelvin’s line modeling was presented by Dr Campbell in 1912. The extension of this work to the most general case of strongly coupled line equations using matrix functions came in 1937 with the work of L. A. Pipes. Then in 1947, M. Cotte studied the propagation of pulses along two coupled lossless lines by means of Heaviside’s operational calculus in order to understand the results of electrical perturbation measurements of power mains.

In 1955, the “stripline” and “microstrip” techniques established a bridge between the world of the classical transmission lines and that of waveguides. At that time, S. A. Schelkunoff proposed a theory of the TEM (transverse electrical magnetic) mode of lossless propagation based on a conversion of Maxwell’s equations into lossless transmission line equations, thus completing the previously mentioned bridge. L. Brillouin studied rigorous theoretical approaches to the losses inside transmission lines from 1932 to 1960 but the solution remained difficult to apply by researchers involved in the development of digital electronics since 1963.

Nowadays, the electrical behavior of lossy lines is modeled in accordance with the assumption of the so-called “quasi-TEM” approximation by means of the modal analysis of the transmission line matrix equation in the frequency domain. The FFT (fast Fourier transform) method is widely used now in the software packages within CAD (computer-aided design) systems devoted to the industrial development of electronic modules. This latter method cannot handle the nonlinearities set by the electrical behavior of semiconductors used by these modules. Handling nonlinearities in lossy lines requires classically the time domain convolution method that uses too much computer time and memory space. Furthermore, modern substrates needed by these electronic modules can be flexible and bent. In any case, the network of interconnections lies on stacked layers linked by vertical conductors called “vias”. The curvature of modern substrates and the vias leads to the need for three-dimensional (or 3D) modeling.

The book is divided into nine chapters, each one beginning with an introductory passage giving the leading thread of the chapter. A brief conclusion aimed at the most important results is presented at the end of each chapter. A glossary of terms and a list of references appear at the end of the book.

Chapter 1 is devoted to the theoretical foundations of electromagnetism in terms of highlighting the natural symmetries between the distributions met in electromagnetism.

Chapter 2 concerns full wave analysis based on Maxwell’s equations and their boundary conditions with an original topological approach to electromagnetic interferences.

Chapter 3 is devoted to the equations of electromagnetism in “stratified media”, even those being bent, where up-to-date electronic interconnections are designed.

Chapter 4 is devoted to the transformation of these equations into transmission line equations, including an original skin effect modeling suited to the design of interconnections.

Chapter 5 concerns the direct time domain methods compatible with handling nonlinearity in complex lossless networks, using advanced powerful matrix methods.

Chapter 6 concerns the discretization process in the time domain needed for the cases of lumped circuits between transmission lines or in heterogenous media.

Chapter 7 deals with the frequency methods which account naturally for the losses in dielectrics and conductors as well as in complex networks, even with bifurcations.

Chapter 8 presents the new time-domain wavelets which are well suited for high-speed digital signals running in complex lossy nonlinear networks.

Chapter 9 presents the applications of the new time-domain wavelets to lossy coupled lines and the problems of 3D electromagnetic perturbations.

Chapter 1

Theoretical Foundations of Electromagnetism

This first chapter is devoted to a brief overview of electromagnetism needed for modeling the electrical behavior of interconnections traveled by very high speed digital or pulsed signals. After a quick look at the historical development of electromagnetism, the tremendous interest in the theory of distributions applied to electromagnetism is highlighted in terms of digital signal transmission analysis. Then, the strictly useful elements of this theory and the necessary vector analysis are discussed, thus allowing an original derivation of Maxwell’s equations from the intuitive geometric properties of the linear relations between electromagnetic features which are modeled by polar and axial vector distributions. The integral forms of Maxwell’s equations are presented.

1.1. Elements of the theory of distributions applied to electromagnetism

1.1.1. Choosing a presentation of the foundations of electromagnetism

Electromagnetism phenomena [ROC] [JAC1], the foundations of transmission lines analysis, concern the interactions between electricity and magnetism in nature observed experimentally by Oersted in 1819 (magnetic field created by an electrical current) and by Faraday in 1830 (electrical current created by a variable magnetic field), completed by the propagation of electromagnetic waves discovered by Hertz in 1887. The results of Oersted’s experiments were translated into mathematical laws by Biot and Savart in 1820 and then by Ampere, and those of Faraday by Lenz and then by Foucault in 1850, thus leading to Maxwell’s theory of 1873, the equations of which got their final form thanks to Heaviside in 1884.

Electromagnetism was developed from the experimental results obtained during the first part of the 19th century, continuing to Maxwell’s equations and Hertz waves at the end of the century, so most of the classical presentations follow the historical approach.