Electronic Applications of the Smith Chart Electronic Applications of the Smith Chart In Waveguide. Circuit, and Component Analysis Phillip H. Smith Second Ed iti on S e Q PUBLISHING. INC. SciTcch Publishing, Inc Rateigh, NC S e Q PUBLISHING. INC. Copyright 1995,2000 by Noble Publishing Corporation Noble Publishing is a division orSciTech Publishing, Inc. All Tights reserved. No part of this book may be reproduced in any fonn or by any means without prior written permission of thc publisher. First edition copyright 1969 by McGraw-Hill. First Noble Publishing edition 1995 First SciTech Publishing. Inc. edition 2006 Printed in the United States of America ISBN: 1-884932-39-8 ISBN 13: 978-I -8849-3239-7 SciTech Publishing 911 Paverstone Drive •. Suitc B Raleigh, NC 276 I 5 Phone: 9 I 9-847-2434 Fax: 9 I 9-847-2568 www.scitechpub.com Library of Congress Cataloging-in-Publication Data Smith, Philip H., 1905- Electronic applications of the Smith Chart ; in waveguide, circuit, and component analysis I Philip H. Smith. -_2nd ed. p. cm. Includes bibliographical references and indelt. ISBN 1-884932-39-8 I. Smith charts. 1. Title. TK7835 .S55 1995 621.381 '0212--dc21 00-045239 To my professional associates, many of whom have unwittingly helped to make this book possible Preface The purpose of this book is to provide the student, the laboratory technician, and the engineer with a comprehensive and practical source volume on SMITH CHARTS and their related overlays. In general, the book describes the mechanics ofthese charts in relation to the guided-wave and circuit theory and, with examples, their practical uses in waveguide, circuit, and component applications. It also describes the construction of boundaries, loci, and forbidden regions, which reveal overall capabilities and limitations of proposed circuits and guided-wave systems. The Introduction to this book relates some of the modifications of the basic SMITH CHART coordinates which have taken place since its inception in the early 1930s. Qualitative concepts of the way in which electromagnetic waves are propagated along conductors are given in Chap. 1. This is followed in Chaps. 2 and 3 by an explanation of how these concepts are related to their quantitative representation on the Hnormalized" impedance coordinates of the SMITH CHART. Chapters 4 and 5 describe the radial and peripheral scales ofthis chart, which show, respectively, the magnitudes and angles of various linear and complex parameters which are related to the impedance coordi nates of the chart. In Chap. 6 an explanation is given of equivalent circuit representations of impedance and admittance on the chart coordinates. Several uses of expanded portions of the chart coordinates are de scribed in Chap. 7, including the graphical determination therefrom of bandwidth and Q of resonant and antiresonant line sections The complex transmission coefficients, their representations on the SMITH CHART, and their uses form the subject of Chap. 8. It is shown therein how voltage and current amplitude and phase (standing wave amplitude and wave position) are represented by these coefficients. viii Impedance matching by means of single and double stubs, by single and double slugs, and by lumped L-circuits is described in Chaps. 9 and 10. Chapter 11 provides examples, illustrating how loci, bounda ries, and forbidden areas are established and plotted. The measurement of impedance by sampling voltage or current along the line at discrete positions, where a slotted line section would be excessively long, is described in Chap. 11. The effect of negative resistance loads on transmission lines, and the construction and use of the negative SMITH CHART and its special radial scales, are described in Chap. 12. Stability criteria as deter mined from this chart are indicated for negative resistance devices such as reflection amplifiers. Chapter 13 discusses, with examples, a number of typical applications of the chart. Chapter 14 describes several instruments which incorporate SMITH CHARTS as a basic component, or which are used with SMITH CHARTS to assist in plotting data thereon or in interpreting data therefrom. For the reader who may desire a more detailed discussion of any particular phase oft he theory or application oft he chart a bibliography is included to which references are made as appropriate throughout the text. Fundamental mathematical relationships for the propagation of elec tromagnetic waves along transmission lines are given in Appendix A and details of the conformal transformation oft he original rectangular to the circular SMITH CHART coordinates are included in Appendix B. A glossary of terms used in connection with SMITH CHARTS follows Chap. 14. Four alternate constructions of the basic SMITH CHART coordinates, printed in red ink on translucent plastic, are supplied in an envelope in the back cover of the book. All of these are individually described in the text. By superimposing these translucent charts on the general purpose complex waveguide and circuit parameter charts described throughout the book, with which they are dimensionally compatible, it is a simple matter to correlate them graphically therewith and to transfer data or other information from one such plot to the other. The overlay plots of waveguide parameters used with these translu cent SMITH CHARTS include the complex transmission and reflec tion coefficients for both positive and negative component coordinates, normalized voltage and current amplitude and phase relationships, normalized polar impedance coordinates, voltage and current phase and magnitude relationships, loci of current and voltage probe ratios, L-type matching circuit components, etc. These are generally referred to as "overlays" for the SMITH CHART because they were originally published as transparent loose sheets in bulletin form and because they were so used. However, as a practical matter it was found to be difficult to transfer the parameters or data depicted thereon to the ix SMITH CHART, which operation is more generally required. Accord ingly, they are printed here on opaque bound pages and used as the background on which the translucent SMITH CHARTS in the back cover can be superimposed. The bound background charts are printed in black ink to facilitate visual separation of the families of curves which they portray from the red impedance and/or admittance curves on the loose translucent SMITH CHARTS. The latter charts have a matte fInish which is erasable to allow pencil tracing of data or other information directly thereon. The writer is indebted to many of his colleagues at Bell Telephone Laboratories for helpful discussions and comments, in particular, in the initial period of the development of the chart to the late Mr. E. J. Sterba for his help with transmission line theory, and to Messrs. E. B. Ferrell and the late J. W. McRae for their assistance in the area of conformal mapping. Credit is also due Mr. W. H. Doherty for suggest ing the parallel impedance chart, and to Mr. B. Klyce for his suggested use of highly enlarge portions of the chart in determining bandwidth of resonant stubs. Mr. R. F. Trombarulo's investigations were helpful in writing sections dealing with the negative resistance chart. The early enthusiastic acceptance of the chart by staff members at MIT Radiation Laboratory stimulated further improvements in de sign of the chart itself. Credit for publication of the book at this time is principally due to encouragement provided by Messrs. H. R. Foster and E. E. Crump of Kay Electric Company [14]. Phillip H. Smith