DiPaolo, Franco, Ph.D. “Frontmatter” Networks and Devices Using Planar Transmission Lines Boca Raton: CRC Press LLC,2000 ©2000 CRC Press LLC Franco Di Paolo Networks and Devices Using Planar Transmission Lines ©2000 CRC Press LLC This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe. © 2000 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-8493-1835-1 Library of Congress Card Number 00-008424 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper Library of Congress Cataloging-in-Publication Data Di Paolo, Franco. Networks and devices using planar transmission lines / Franco di Paolo. p. cm. Includes bibliographical references and index. ISBN 0-8493-1835-1 (alk. paper) 1. Strip transmission lines. 2. Electric lines—Carrier transmission—Mathematics. 3. Telecommunication—Mathematics. 4. Electronic apparatus and appliances. I. Title. TK7872.T74 P36 2000 621.381 ′ 32—dc21 00-008424 CIP ©2000 CRC Press LLC ABSTRACT This book has one objective: to join in one text all the practical information and physical principles that permit a planar transmission line device to work properly. The eight appendices have been written with the aim of helping the reader review the theoretical concepts in the 11 chapters. This book is intended for microwave engineers studying the design of microwave and radio frequency planar transmission line passive devices in industry, as well as for students in microwave and RF disciplines. More than 500 up-to-date references make this book a collection of the most recent studies on planar transmission line devices, a characteristic that also makes this book attractive to researchers. Chapters are dedicated to the analysis of planar transmission lines and their related devices, i.e., directional couplers, directional filters, phase shifters, circulators, and isolators. A special feature is a complete discussion of ferrimagnetic devices, such as phase shifters, isolators, and circulators, with three appendices completely dedicated to the theoretical aspect of ferrimagnetism. Also provided are more than 490 figures to simply and illustrate the input–output transfer functions of a particular device, information that is otherwise difficult to find. This book is highly recommended for graduate students in RF and microwave engineering, as well as professional designers. ©2000 CRC Press LLC The Author Franco Di Paolo was born in Rome, Italy, in 1958. He received a doctorate in Electronic Engineering in 1984 from the Università degli studi di Roma, “La Sapienza.” His first job was with Ericsson-Rome, designing wide band RF and microwave circuits for RX and TX optical networks. He has been a senior research engineer at Elettronica-Rome Microwave Labs. Currently he is chief research engineer at Telit, Microwave Satellite Communication Division, in Rome. Dr. Di Paolo is author of other technical publications and is an IEEE member. He is an associate of the Microwave Theory and Techniques Society, the Ultrasonics, Ferroelectrics and Frequency Control Society, and the Circuit and Systems Society. ©2000 CRC Press LLC CONTENTS CHAPTER 1Fundamental Theory of Transmission Lines 1.1Generalities 1.2“Telegraphist” and “Transmission Line” Equations 1.3Solutions of Transmission Line Equations 1.4Propagation Constant and Characteristic Impedance 1.5Transmission Lines with Typical Terminations 1.6“Transmission” and “Impedance” Matrices 1.7Consideration About Matching Transmission Lines 1.8Reflection Coefficients and Standing Wave Ratio 1.9Nonuniform Transmission Lines 1.10Quarter Wave Transformers 1.11Coupled Transmission Lines 1.12The Smith Chart 1.13Some Examples Using the Smith Chart 1.14Notes on Planar Transmission Line Fabrication References CHAPTER 2Microstrips 2.1Geometrical Characteristics 2.2Electric and Magnetic Field Lines 2.3Solution Techniques for the Electromagnetic Problem 2.4Quasi Static Analysis Methods 2.5Coupled Modes Analysis Method 2.6Full Wave Analysis Method 2.7Design Equations 2.8Attenuation 2.9Practical Considerations References CHAPTER 3Striplines 3.1Geometrical Characteristics 3.2Electric and Magnetic Field Lines 3.3Solution Techniques for the Electromagnetic Problem 3.4Extraction of Stripline Impedance with a Conformal Transformation 3.5Design Equations 3.6Attenuation 3.7Offset Striplines 3.8Practical Considerations References CHAPTER 4Higher Order Modes and Discontinuities in ␮ Strip and Stripline 4.1Radiation 4.2Surface Waves 4.3Higher Order Modes 4.4Typical Discontinuities 4.5Bends 4.6Open End ©2000 CRC Press LLC 4.7Gap 4.8Change of Width 4.9“T” Junctions 4.10Cross Junction References CHAPTER 5Coupled Microstrips 5.1Geometrical Characteristics 5.2Electric and Magnetic Field Lines 5.3Solution Techniques for the Electromagnetic Problem 5.4Quasi Static Analysis Methods 5.5Coupled Modes Analysis Method 5.6Full Wave Analysis Method 5.7Design Equations 5.8Attenuation 5.9A Particular Coupled Microstrip Structure: The Meander Line References CHAPTER 6Coupled Striplines 6.1Geometrical Characteristics 6.2Electric and Magnetic Field Lines 6.3Solution Techniques for the Electromagnetic Problem 6.4Design Equations 6.5Attenuation 6.6A Particular Coupled Stripline Structure: The Meander Line 6.7Practical Considerations References CHAPTER 7Microstrip Devices 7.1Simple Two Port Networks 7.2Directional Couplers 7.3Signal Combiners 7.4Directional Filters 7.5Phase Shifters 7.6The Three Port Circulator 7.7Ferrimagnetic Phase Shifters 7.8Ferrimagnetic Isolators 7.9Comparison among Ferrimagnetic Phase Shifters References CHAPTER 8Stripline Devices 8.1Introduction 8.2Typical Two Ports Networks 8.3Directional Couplers 8.4Signal Combiners 8.5Directional Filters 8.6Phase Shifters 8.7The Three Port Circulator 8.8Ferrimagnetic Phase Shifters ©2000 CRC Press LLC 8.9Ferrimagnetic Isolators 8.10Comparison among Ferrimagnetic Phase Shifters References CHAPTER 9Slot Lines 9.1Geometrical Characteristics 9.2Electric and Magnetic Field Lines 9.3Solution Techniques for the Electromagnetic Problem 9.4Closed Form Equations for Slot Line Characteristic Impedance 9.5Connections Between Slot Lines and Other Lines 9.6Typical Nonferrimagnetic Devices Using Slotlines 9.7Magnetization of Slot Lines on Ferrimagnetic Substrates 9.8Slot Line Isolators 9.9Slot Line Ferrimagnetic Phase Shifters 9.10Coupled Slot Lines References CHAPTER 10Coplanar Waveguides 10.1Geometrical Characteristics 10.2Electric and Magnetic Field Lines 10.3Solution Techniques for the Electromagnetic Problem 10.4Closed Form Equations for “CPW” Characteristic Impedance 10.5Closed Form Equations for “CPW” Attenuation 10.6Connections Between “CPW” and Other Lines 10.7Typical Nonferrimagnetic Devices Using “CPW” 10.8Magnetization of “CPW” on Ferrimagnetic Substrates 10.9“CPW” Isolators 10.10“CPW” Ferrimagnetic Phase Shifters 10.11Practical Considerations 10.12Coupled Coplanar Waveguides References CHAPTER 11Coplanar Strips 11.1Geometrical Characteristics 11.2Electric and Magnetic Field Lines 11.3Solution Techniques for the Electromagnetic Problem 11.4Design Equations 11.5Attenuation 11.6Connections Between “CPS” and Other Lines 11.7Use of “CPS” References APPENDIX 1Solution Methods for Electrostatic Problems A1.1The Fundamental Equations of Electrostatics A1.2Generalities on Solution Methods for Electrostatic Problems A1.3Finite Difference Method A1.4Image Charge Method A1.5Fundamentals on Functions with Complex Variables A1.6Conformal Transformation Method ©2000 CRC Press LLC A1.7The Schwarz-Christoffel Transformation References APPENDIX 2Wave Equation, Waves, and Dispersion A2.1Introduction A2.2Maxwell’s Equations and Boundary Conditions A2.3Wave Equations in Harmonic Time Dependence A2.4The Propagation Vectors and Their Relationships with Electric and Magnetic Fields A2.5The Time Dependence A2.6Plane Wave Definitions A2.7Evaluation of Electromagnetic Energy A2.8Waves in Guiding Structures with Curvilinear Orthogonal Coordinates Reference System A2.9“TE” and “TM” Modes in Rectangular Waveguide A2.10“TE” and “TM” Modes in Circular Waveguide A2.11Uniform Plane Waves and “TEM” Equations A2.12Dispersion A2.13Electrical Networks Associated with Propagation Modes A2.14Field Penetration Inside Nonideal Conductors References APPENDIX 3Diffusion Parameters and Multiport Devices A3.1Simple Analytical Network Representations A3.2Scattering Parameters and Conversion Formulas A3.3Conditions on Scattering Matrix for Reciprocal and Lossless Networks A3.4Three Port Networks A3.5Four Port Networks A3.6Quality Parameters for Directional Couplers A3.7Scattering Parameters in Unmatched Case References APPENDIX 4Resonant Elements, “Q”, Losses A4.1The Intrinsic Losses of Real Elements A4.2The Quality Factor “Q” A4.3Elements of Filter Theory A4.4Butterworth, Chebyshev, and Cauer Low Pass Filters A4.5Filter Generation from a Normalized Low Pass A4.6Filters with Lossy Elements References APPENDIX 5Charges, Currents, Magnetic Fields, and Forces A5.1Introduction A5.2Some Important Relationships of Classic Mechanics A5.3Forces Working on Lone Electric Charges A5.4Forces Working on Electrical Currents A5.5Magnetic Induction Generated by Currents A5.6Two Important Relationships of Quantum Mechanics A5.7The Foundations of Atom Theory ©2000 CRC Press LLC A5.8The Atom Structure in Quantum Mechanics A5.9The Precession Motion of the Atomic Magnetic Momentum A5.10Principles of Wave Mechanics. References APPENDIX 6The Magnetic Properties of Materials A6.1Introduction A6.2Fundamental Relationships for Static Magnetic Fields and Materials A6.3The Definitions of Materials in Magnetism A6.4Statistics Functions for Particles Distribution in Energy Levels A6.5Statistic Evaluation of Atomic Magnetic Moments A6.6Anisotropy, Magnetostriction, Demagnetization in Ferromagnetic Materials A6.7The Weiss Domains in Ferromagnetic Materials A6.8Application of Weiss’ Theory to Some Ferromagnetic Phenomena A6.9The Heisenberg Theory for the Molecular Field A6.10Ferromagnetic Materials and Their Applications A6.11Antiferromagnetism A6.12Ferrimagnetism References APPENDIX 7The Electromagnetic Field and the Ferrite A7.1Introduction A7.2The Chemical Composition of Ferrites A7.3The Ferrite Inside a Static Magnetic Field A7.4The Permeability Tensor of Ferrites A7.5“TEM” Wave Inside an Isodirectional Magnetized Ferrite A7.6Linear Polarized, Uniform Plane Wave Inside an Isodirectional Magnetized Ferrite: The Faraday Rotation A7.7Electromagnetic Wave Inside a Transverse Magnetized Ferrite A7.8Considerations on Demagnetization and Anisotropy A7.9The Behavior of Not Statically Saturated Ferrite A7.10The Quality Factor of Ferrites at Resonance A7.11Losses in Ferrites A7.12Isolators, Phase Shifters, Circulators in Waveguide with Isodirectional Magnetization A7.13Isolators, Phase Shifters, Circulators in Waveguide with Transverse Magnetization A7.14Field Displacement Isolators and Phase Shifters A7.15The Ferrite in Planar Transmission Lines A7.16Other Uses of Ferrite in the Microwave Region A7.17Use of Ferrite Until UHF A7.18Harmonic Signal Generation in Ferrite A7.19Main Resonance Reduction and Secondary Resonance in Ferrite References APPENDIX 8Symbols, Operator Definitions, and Analytical Expressions A8.1Introduction A8.2Definitions of Symbols and Abbreviations A8.3Operator Definitions and Associated Identities [...]... analysis and physics, is required Chapter 1 introduces all the concepts of the general theory of transmission lines Chapter 2 is dedicated to microstrip networks that are widely diffused in planar devices Chapter 3 is dedicated to the stripline, perhaps the first planar transmission line developed Chapter 4 introduces the main problems that can be encountered in planar transmission line networks and devices. .. transmission line devices, are not the goal of this text and are not included here The author hopes this text will help the reader understand the world of planar transmission line networks and devices and will aid in deciding how to choose the proper device The author also hopes this text will stimulate the reader to study and research other new devices Franco Di Paolo January 2000 ©2000 CRC Press LLC... Ph.D “Fundamental Theory of Transmission Lines Networks and Devices Using Planar Transmission Lines Boca Raton: CRC Press LLC,2000 CHAPTER 1 Fundamental Theory of Transmission Lines 1.1 GENERALITIES In telecommunication theory, “transmission line” means a region of the space where “RF” signals can propagate with the best compromise between minimum attenuation and available region of the space The particular... Chapter 7, and stripline devices are studied Chapter 9 introduces the slotline, a full planar transmission line, i.e., a transmission line with both conductors on the same plane This chapter also studies the most important devices that can be built with slotlines Chapter 10 is dedicated to the coplanar waveguide, another full planar transmission line Also in this chapter, the most typical devices employing... “v” and “i” can be set as functions of coordinates and time, and so they can be written more appropriately as: ∂v ∂i = −L ∂x ∂t (1.2.3) ∂i ∂v = −C ∂x ∂t (1.2.4) These last two equations are called “telegraphist’s equations,” and relate time variation of voltage and current along a t.l with its physical characteristics as inductance “L” and capacitance “C” per * Microstrip and stripline transmission lines. .. polarization*** of the “RF” fields and only a fundamental mode**** of propagation, and these characteristics can also be used to distinguish among lines Of course, polarization and mode of propagation are strongly a frequencydependent phenomena, and at some frequencies other modes than the fundamental one can propagate.***** * In this text transmission lines will be called lines or abbreviated with “t.l.”... current and voltage and write: i (x) = i + e (r− k x ) e (j− jk x ) v(x) = v + e (r− k x ) e (j− jk x ) and (1.4.6) The mean power “Wt” transmitted along the line will be: Wt [ ] Re v(x)i * (x) 2 ⊥ − (1.4.7) and 1.4.6 becomes: Wt = v + i + e(r−2 k x ) 2 or, using 1.3.13: Wt = v +2 e(r−2 k x ) 2 ζ (1.4.8) The mean power “Wr” dissipated in “R” and “Wg” dissipated in “Gp” are given by: ( ) Wr = R i + 2 2 and. .. many transmission line networks such as filters and matching networks 1.6 “TRANSMISSION” AND “IMPEDANCE” MATRICES With “transmission matrices” we have a representation of the transmission line that simply relates input and output line excitations Let us examine Figure 1.6.1 a, where a t.l of length “ᐉ” and characteristic impedance “ζ” is excitated at one extreme with voltage “vi” and current “i i ” The... 0.5  + ω 2 RC + LG p      2 (1.4.2) 2 (1.4.3) The ideal lossless lines are those where R = 0 = Gp, and in this case from 1.4.2 and 1.4.3: kr = 0 and k j = jω ( LC) 0.5 (1.4.4) In practice, lines are never without losses So, the practical approximation to the lossless case is when the length “ᐉ ” of the t.l is so that: l Ӷ ζ/ R and l Ӷ σ / Gp * Remember that unless otherwise stated we will use the... Delta Operator Functions in a Spherical Coordinate System A8.7 The Divergence and Stokes Theorems and Green Identities A8.8 Elliptic Integrals and Their Approximations References ©2000 CRC Press LLC PREFACE By planar transmission line” we mean a transmission line whose conductors are on planes Examples are microstrips and slotlines By “device” we mean a component that is capable of having some electrical . “Frontmatter” Networks and Devices Using Planar Transmission Lines Boca Raton: CRC Press LLC,2000 ©2000 CRC Press LLC Franco Di Paolo Networks and Devices Using Planar Transmission Lines . Franco. Networks and devices using planar transmission lines / Franco di Paolo. p. cm. Includes bibliographical references and index. ISBN 0-8493-1835-1 (alk. paper) 1. Strip transmission lines. . Transmission Lines Networks and Devices Using Planar Transmission Lines Boca Raton: CRC Press LLC,2000 1 ©2000 CRC Press LLC CHAPTER 1 Fundamental Theory of Transmission Lines 1.1