Passive Microwave Device Applications of High-Temperature Superconductors 9780521034173, 9780511526688, 0521480329, 0521034175, 0511526687, 9780521480321

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This book describes the application of new high-temperature superconducting materials to microwave devices and systems. It deals with the fundamentals of the interaction between microwaves and superconductors, and includes a basic description of how microwave devices can be constructed using these materials. Since the discovery of high-temperature superconductors in 1986 there has been an enormous effort worldwide to develop and characterise these materials. Work on applications has proceeded more slowly, however. Nevertheless, commercial applications are now beginning to be possible, including use in passive microwave devices. The advantages of using high-temperature superconductors in these devices is carefully described by the author, enabling scientists and engineers to form a complete understanding of the subject. The rest of the book is devoted to examples of superconducting microwave filters, antennas and systems. The examples chosen relate not only to what can be achieved at present, but indicate trends for future research and what may be expected for superconducting devices in the future. This book will be of value to graduate students and researchers, especially electrical engineers interested in new devices that are possible using high-temperature superconductors, as well as physicists, materials scientists and chemists interested in the application of these materials.

PASSIVE MICROWAVE DEVICE APPLICATIONS OF HIGH-TEMPERATURE SUPERCONDUCTORS

PASSIVE MICROWAVE DEVICE APPLICATIONS OF HIGHTEMPERATURE SUPERCONDUCTORS M. J. LANCASTER School of Electronic and Electrical Engineering University of Birmingham

CAMBRIDGE

UNIVERSITY PRESS

CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521480321 © Cambridge University Press 1997 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1997 This digitally printed first paperback version 2006 A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Lancaster, M. J. Passive microwave device applications of high-temperature superconductors / M. J. Lancaster. p. cm. Includes index. ISBN 0 521 48032 9 (he) 1. High temperature superconductors. 2. Microwave devices Materials. I. Title. TK7872.S8L357 1996 621.38T3-dc20 96-14062 CIP ISBN-13 978-0-521-48032-1 hardback ISBN-10 0-521-48032-9 hardback ISBN-13 978-0-521-03417-3 paperback ISBN-10 0-521-03417-5 paperback

To my mother and father

Contents

Preface page Acknowledgements 1 Superconductivity at microwave frequencies 1.1 Introduction 1.2 London equations and complex conductivity 1.3 Maxwell's equations and superconductors 1.4 Plane waves 1.4.1 Plane waves in superconductors 1.5 Comparison of normal conductors with superconductors 1.6 Surface impedance 1.7 Poynting's theorem and superconductors 1.8 Surface impedance of thin films 1.8.1 Surface resistance and reactance of superconducting films 1.8.2 Surface impedance of thin superconducting films close to Tc 1.8.3 Superconducting thin films on lossy substrates 1.9 Temperature and frequency dependence of complex conductivity 1.9.1 Temperature dependence of classical complex conductivity 1.9.2 Non-local electrodynamics 1.9.3 Microscopic complex conductivity 1.10 The surface impedance of granular superconductors 1.11 The surface impedance of type II superconductors 1.12 References 2 Superconducting transmission lines 2.1 Introduction IX

xiii xv 1 1 2 5 7 8 11 12 15 19 21 22 22 24 25 26 27 32 36 41 45 45

x

Contents

2.2 2.3 2.4 2.5 2.6 2.7

3

4

Wide microstrip with complex impedance boundaries Superconducting wide microstrip Other planar transmission lines Incremental inductance rule for superconductors Phenomenological loss equivalent method Numerical methods for analysis of superconducting transmission lines 2.8 Pulse propagation on superconducting transmission lines 2.9 References Superconducting cavity resonators 3.1 Introduction 3.2 Microwave cavities and quality factors 3.2.1 Conductor quality factor 3.2.2 Dielectric quality factor 3.2.3 Radiation quality factor 3.2.4 Cavity perturbations 3.2.5 Quality factors of cavities based on TEM waveguides 3.3 The cylindrical cavity resonator 3.3.1 Circular waveguide 3.3.2 Cylindrical cavity 3.3.3 Measurements of HTS samples using superconducting cylindrical cavities 3.4 Dielectric resonators 3.5 Coaxial cavity 3.6 Helical cavity resonators 3.7 Cavities constructed from microstrip and stripline 3.7.1 Wide microstrip 3.7.2 Microstrip and stripline resonators 3.8 Coplanar resonators 3.8.1 Packaging and measurements of the coplanar resonator 3.8.2 Radiation losses in a coplanar resonator 3.9 References Microwave measurements 4.1 Introduction 4.2 Measurement system 4.3 Measurement of quality factors 4.4 One-port measurements 4.5 Two-port measurements 4.6 Power dependent measurements

46 50 53 55 56 58 61 64 67 67 68 69 70 71 71 72 74 75 79 83 87 92 97 103 103 105 109 114 117 119 126 126 126 129 132 136 141

Contents

4.7 References Superconducting filters 5.1 Introduction 5.2 Conventional filters 5.3 Dual mode filters 5.4 Cavity and waveguide filters 5.5 Non-linear effects and power handling 5.6 Internal inductance filters 5.7 Lumped element filters 5.8 Filters based on slow-wave transmission lines 5.8.1 Velocity in periodic structures 5.9 Superconducting switches and limiters 5.10 Superconducting phase shifters 5.10.1 Junction phase shifters 5.10.2 Ferroelectric phase shifters 5.11 Further applications 5.11.1 Couplers 5.11.2 Transformers 5.11.3 Splitter/combiner 5.12 References Superconducting delay lines Introduction 6.1 6.2 Substrates for delay lines 6.3 Delay lines 6.4 Choice of transmission line type 6.5 Delay line filters 6.5.1 Reflective delay line filters 6.6 Design of delay line filters 6.7 Comparison with other technologies 6.8 References Superconducting antennas Introduction 7.1 7.2 Fundamental considerations 7.2.1 Maximum antenna gain 7.2.2 Antenna Q 7.2.3 Consideration of losses 7.2.4 Maximum antenna bandwidth 7.3 Superconducting small-dipole and loop antennas 7.3.1 Radiation pattern and directivity 7.3.2 Efficiency and impedance

xi

142 144 144 147 156 159 161 166 170 176 179 180 186 187 188 190 191 192 193 194 203 203 204 205 208 209 213 216 219 224 228 228 229 230 232 233 235 237 237 238

xii

Contents

7.3.3 Matching networks 7.3.4 Bandwidth and Q 7.3.5 Measurements on antennas 7.4 Small antennas 7.5 Transmitting antenna 7.6 Receiving antennas 7.7 Two-element superdirective antenna array 7.8 Superdirective antenna arrays 7.9 Conventional antenna arrays 7.10 Arrays with signal processing capability 7.11 References 8 Signal processing systems 8.1 Introduction 8.1.1 Space applications 8.1.2 Systems based on spectral analysis 8.2 Microwave oscillators 8.3 Superconducting receivers 8.4 Mobile communications 8.5 Spectrum analysers based on chirp filters 8.6 Convolvers and correlators 8.7 Instantaneous frequency meter 8.8 References Appendix 1 The surface impedance of HTS materials A1.1 Introduction A 1.2 Surface resistance A 1.3 Temperature dependence A 1.4 Penetration depth and complex conductivity A1.5 Non-linear surface resistance A1.6 D.c. field dependence A1.7 References Appendix 2 Substrates for superconductors A2.1 Substrate requirements A2.2 Substrate materials A2.3 References Appendix 3 Some useful relations A3.1 Introduction Index

241 243 246 249 253 254 256 262 268 270 272 278 278 280 282 284 291 295 297 302 305 309 314 314 315 318 319 320 321 323 326 326 327 329 332 332 335

Preface

A revolution in the field of superconductivity occurred in 1986 with the discovery of superconductors with a transition temperature greater than the boiling point of liquid nitrogen, and many laboratories around the world began the exciting work of developing these materials. This book stems from one such laboratory, which has been looking at the microwave aspects of these materials, not only from a basic science view point, but also from a desire to demonstrate their potential for new applications. The development of microwave applications has proceeded very rapidly, and in less than ten years superconducting communication and signal processing systems are being flown in space, with many other microwave devices and systems to be found in the market place. This book essentially charts this development from the basic fundamental considerations of superconductors in high-frequency fields to the use of superconductors in microwave passive applications. The book should be suitable as a basic introduction to the microwave applications of superconductors, and can be read independently of any previous knowledge of superconductors. However, the reader is recommended to consult one of the many texts about superconductivity in general in order to obtain a balanced view of the subject. It is expected that a number of different groups will find this book of interest. It could form the text for a specialised undergraduate course or be used in a more general course on microwaves. Examples of both fundamental electromagnetic principles (including plane waves, waveguides and cavities) can be extracted from the first three chapters or, alternatively, examples of microwave devices are given in Chapters 5-8. One of the book's primary uses will be in the introduction of new researchers to the subject, and as a general reference not only for groups working in superconductivity at high frequencies, but also for other groups wanting to know more about the high-frequency applications. By reading this book a new researcher will soon be able to assimilate the basic ideas, concepts and Xlll

xiv

Preface

problems of this field. The book should also be suitable for microwave engineers who have heard about superconductivity but want to find out more about the subject. The book has been written purposely as a mixture of some very detailed mathematical derivations and some sections which are much less detailed. Where detail is included, fundamental concepts relevant to a basic understanding of the entire field are described. Examples include surface impedance, plane waves and Poynting's theorem in Chapter 1, the wide microstrip transmission line in Chapter 2 and the cylindrical cavity in Chapter 3. A fundamental knowledge of this detailed work gives a solid background which can be built upon. The less detailed work in Chapters 5-8 includes a discussion of actual devices and systems, with examples from the literature. Information is given on the basic design principles but with an emphasis on fundamental principles. Some of the examples given here will eventually go out of date but the principles discussed with reference to them will not. In any book some subjects will have to be omitted for various reasons. Probably the most obvious in this text is any information about cryogenics and information on how to cool the devices described. In parallel with superconductivity research, there has been much research into coolers and a wide range is now available. The problem of cooling is not a technical one, but, rather, one of the extra power consumption and size associated with the requirement. As discussed above, this book is essentially about the development of the field of passive microwave device applications of superconductors since the introduction of HTS, so some of the work on lowtemperature superconductors prior to 1986 is not discussed to any great extent. Probably the largest application here is the development of accelerator cavities; however, this is not related directly to the theme of the book.

Acknowledgements

I would like to thank a large number of individuals and organisations for making this book possible. Firstly, my thanks go to all members of the Birmingham University Superconductivity Research Group (UBSRG), which began with the advent of high temperature superconductors and has grown into one of the largest UK groups working on all aspects of superconductivity. The many discussions with the members of this interdisciplinary group have been of enormous benefit over the last few years. Specifically in the microwave group in the School of Electronic and Electrical Engineering, I would like to thank Dr Adrian Porch, not only for reading this text but for the many stimulating discussions we have had and his contribution to much of the work described. I would also like to thank other lecturing members of the group including Professor Tom Maclean, Dr Fred Huang and Dr Zipeng Wu, the former two having worked principally on antennas and delay line filters respectively. Much of the work described has been done by the staff and students of the group, including Bea Avenhaus, Jia Sheng Hong Hong, Leo Ivrissimtzis, Alan Elston, Jeff Powell, Nick Exon, Mazlina Esa, Marcos De Melo, Dung Shing Hung, Martin Holyroyd, Graeme McCaffery, Philip Woodall, Henry Cheung and Janet Li. I would also like to acknowledge specific members of the UBSRG, including Professor Colin Gough its director, Dr Stuart Abell, Professor Peter Edwards, Dr Chris Muirhead and Dr Colin Greaves for much advice and help on many aspects of superconductivity. This should also include Dr Fee Wellhofer, who has provided many of the superconducting thin films used for the devices and measurements described. Our external collaborators have also been a source of inspiration and these include the members of the former ICI group, in particular Professor Neil Alford, Dr Tim Button and Dr Paul Smith. I not only need to thank them for supplying samples but also for discussions on some of the microwave aspects xv

xvi

Acknowledgements

of their materials work. I would also like to thank Professor Richard Humphreys and members of his group at DRA Malvern for supplying thin films and the much valued discussions on many aspects of HTS. Our European collaborative work has also proved invaluable in the writing of this book; specifically I would like to thank Dr Gunter Muller, Professor Dr Bernd Stritzker, Dr Jean Dumas, Professor Dr J. Senateur, Professor Dr Olivier Thomas, Professor Dr Claire Schlenker, Dr Rui Henriques and all members of their groups. There are also a number of visiting research fellows to the school including Dr Y. Huang, Dr A. Gorur and Professor Alan Portis whose contributions have proved valuable and whom I wish to acknowledge. Thanks are also given to other collaborators, too numerous to mention here, in the UK and around the world. Finally I wish to acknowledge the all important financial contributions to this work which include the UK EPSRC, the European Union through an ESPRIT award (No. 6113) and the UK DTI. I would like to thank the University of Birmingham and the School of Electronic and Electrical Engineering for financial contributions and permission for my sabbatical leave.

1 Superconductivity at microwave frequencies

1.1 Introduction This first chapter deals with some fundamental aspects of how superconductors interact with high-frequency fields, and discusses the theoretical tools available for the solution of problems. Although superconductors were discovered in 1911 by H. Kamerlingh Onnes,1 it was not until the early 1930s that significant consideration was given to high-frequency effects. The thermal properties of superconductors were investigated by Gorter and Casimir in 1934,2 and they predicted a temperature dependence of superconducting carriers by minimising the Helmholtz free energy. To do this the carriers within a superconductor were assumed to consist of both superconducting and normal carriers whose relative densities changed as a function of temperature. This two-fluid model was taken further by the London brothers in 1934 to account for the high-frequency properties of superconductors. 3"5 Their contribution is outlined in Section 1.2. The London equations can be used in conjunction with Maxwell's equations in order to allow them to be applicable to superconductors. Complex conductivity also follows from the two-fluid model. This simplifies the problem in that the normal conductivity o can be replaced by a complex conductivity O\ — J02, which accounts for superconducting phenomena. Heinz London also produced some early measurements on the surface resistance of tin, during which he discovered the anomalous skin effect, and Fritz London was the first to suggest that flux in a superconductor is quantised. However, it was not until a number of years later that the significance of these observations was recognised. The backbone of the major theories of superconductivity were accomplished in the 1950s, with Pippard's discussion of non-local effects in 1953,6 the GinzburgLandau phenomenological theory in 19507 and, finally, the theory by Bardeen, Cooper and Schrieffer (BCS theory) in 1957.8 The BCS theory was elucidated for high-frequency fields by Mattis and Bardeen in 1958.9 Further discussion of the important aspects of these works is given in Section 1.9. The discovery 1

2

Superconductivity at microwave frequencies

of high-temperature superconductors (HTSs) by Bednorz and Miiller10 in 1986 has fundamentally changed the outlook for the applications of superconductors and has led to an enormous expansion of work in theoretical, experimental and application areas. Two fundamental concepts are described in this chapter: the complex conductivity and the surface impedance of a superconductor. Complex conductivity can be used in conjunction with Maxwell's equations to predict the effects of high-frequency fields. It can be measured just like the normal conductivity of metals or predicted by the various theories. The theoretical approach is, of course, of paramount importance in yielding a fundamental understanding of the materials. Complex conductivity is introduced in Section 1.2 and its use is discussed with Maxwell's equations in Section 1.3. Following this, plane wave propagation in superconductors is discussed in Section 1.4, leading on to the concept of surface impedance. Surface impedance is important because it simplifies the solution of boundary value problems. The real part, the surface resistance, is discussed extensively and is an important quantity in the prediction of the performance of a microwave device. Complex conductivity is directly related to surface impedance through Maxwell's equations; this is discussed extensively in Sections 1.6 and 1.8. The remainder of the chapter discusses how both complex conductivity and surface impedance can be calculated from fundamental concepts as functions of frequency, temperature, microwave power and steady magnetic fields.

1.2 London equations and complex conductivity Superconductivity is a consequence of paired and unpaired electrons travelling within the lattice of a solid. The paired electrons travel, under the influence of an electric field, without resistive loss. In addition, due to the thermal energy present in the solid, some of the electron pairs are split, so that some normal electrons are always present at temperatures above absolute zero. It is therefore possible to model the superconductor in terms of a complex conductivity O\ — jor2- This section looks into the basis of electron transport in superconductors and shows that superconductors can be represented by a complex conductivity. Although a very simple classical model is assumed, it gives a basis for the understanding of the microscopic processes in superconductors. This is called the 'two-fluid model'. Consider the force exerted on an electron pair, which can be written ^ 2 e E at

(1.2.1)

1.2 London equations and complex conductivity

3

where \ s is the velocity of the electron pair, e is the charge on an electron, m is the mass of an electron and E is the applied electric field. A similar equation can be written for the normal electrons in the solid, travelling at velocity \ n:

where r is the momentum relaxation time. The extra term which appears in this equation is due to the scattering of the normal electrons with the lattice. If the electric field were switched off (E = 0), then the velocity would decay with a characteristic time r. This can be seen by the solution of Equation (1.2.2) in this case. The current densities for the normal electrons (J w) and paired electrons (J 5 ) are J 5 = — nse\s

Jn = -nne\n

(1.2.3)

(1.2.4)

where nn and ns are the normal and paired electron densities respectively. These general equations have two simpler cases, both of which have been tremendously useful in the study of superconductors. Firstly, consider the case when the superconductor is composed only of superconducting electron pairs. Combining Equations (1.2.1) and (1.2.3) gives A-^ = E

(1.2.5)

where A = m/nse2 is the London parameter, which is related to the superconducting penetration depth, as will be seen later. This equation has come to be known as the first London equation, as it was first introduced by the London brothers in 1934. Now take the curl of Equation (1.2.5) to give A-(VxJ,) = VxE

(1.2.6)

and using Faraday's law VxE—

(I 2 7) dt

U

j)

gives A V x J, = - B

(1.2.8)

The constant of integration with respect to time to obtain Equation (1.2.8) has been put to zero; this has been found to be correct for superconductors through experimental observation. Equation (1.2.8) is known as the second London equation. Equations (1.2.5) and (1.2.8) are important because they represent a simple method of introducing superconductivity to Maxwell's equations that enables conventional solution methods to be used. However, these equations are not useful for high-frequency fields in themselves, as there may be a

4

Superconductivity at microwave frequencies

significant number of normal electrons present which contribute to the electrodynamics. This brings us to the second case; here all the time dependencies are taken as sinusoidal, that is, j5

=

j ^ > '

Jn = jnOeJ°>< and E = EoeJa)t

(1.2.9)

The relationship with the current density and the electric field is given by Jo = J«o + J*o = OTF^O

(1.2.10)

In keeping with convention, we will drop the zero subscript on the variables and assume that the time dependence will carry through the equations below, that is, j = j r t + j 5 = arFE

(1.2.11)

Here OJF is the two-fluid model conductivity. Now Equation (1.2.3) can be substituted into Equation (1.2.1) in a similar fashion to that above, and Equation (1.2.4) can be substituted into Equation (1.2.2). Then sinusoidal time dependence is assumed for both (Equations (1.2.9)) and a relationship between J5, in and E results. Using Equation (1.2.11) this results in J = Jn + Js = (OXTF ~ jo2TF)K

(1.2.12)

where O\TF and OITF are

nse2

+

conne2r2

(L2.14) 2 2, com m(l+co2r2) For most practical situations (cor)2 cos) can be made, giving 7 = ^/{jo)ii{px - jo2)) and

(1.4.5)

1.4 Plane waves

9

The real and imaginary parts of both these equations can be separated, resulting in \

(1-4.7)

and Zs = ^y/(a>tt)f2(puo2) where f\(oua2)

(1A8)

= (y/(p + ox) + y/{p - ox)) - j{y/{p - ox) (1.4.9)

and

hipx^oi) = -(y/(p + ox) - V(P ~ O\)) + J-(V(P ~ °\)+ V(P + ^)) P

P

(1.4.10) where p = V(o2x+o22) (1.4.11) These equations are rather unwieldy and in order to simplify the general equations for the propagation constant and the intrinsic impedance of the medium the useful approximation 02 S> O\ can be made. This is the case provided that the temperature is not too close to the transition temperature, where more normal carriers are present. Making the approximation 02 ^> Ox and expanding the square root in Equation (1.4.5) to first order in Ox/02 gives an approximate expression for 7:

The real part of this is the attenuation coefficient, a, and is given by a = Re(y) = ^(a)[to2) (1.4.13) This attenuation coefficient represents an exponential decay of the electric and magnetic fields as the wave propagates in the z direction. The amplitude of the magnetic and electric fields can be represented by (1.4.14) A = A0Qxp(-y/(cofio)z) A characteristic depth (2) can be defined such that the wave is attenuated by e ~l of its initial value, which may be at the surface of the superconductor " R e ( y ) ~ y/(a)fto2) The characteristic depth X is the same as the London penetration depth if 02 — 02TF, and is governed mainly by the properties of the electron pairs, that

10

Superconductivity at microwave frequencies

is, the value of 02 rather than o\. It represents a depth to which electromagnetic fields penetrate superconductors and defines the extent of a region near the surface of a superconductor in which currents can be induced. A distinction must be made between the a.c. penetration depth and the d.c. penetration depth at this point. The depth to which the alternating fields penetrate the surface of the superconductor is always 1/Re(y), and using Equation (1.4.5) gives the actual depth irrespective of the values of O\ and 02. This depth will alter from the value given by Equation (1.4.15) when O\