Modern Antennas

Microwave and RF Technology Series The Microwave and RF Technology Series publishes authoritative works for professional engineers, researchers and advanced students across the entire range of microwave devices, sub-systems, systems and applications. The series aims to meet the reader's needs for relevant information useful in practical applications. Engineers involved in microwave devices and circuits, antennas, broadcasting communications, radar, infra-red and avionics will find the series an invaluable source of design and reference information.

Series editors: Hugh Griffiths Professor and Head of Microwaves, Radar and Optics Group, University College London, UK Fellow of the lEE and Senior Member of the IEEE

Bradford L. Smith Senior Intellectual Property Counsel and Engineer, Corporate Research Centre, Alcatel Alsthom, Paris, France Senior Member of the IEEE and French SEE

TItles available

The Microwave Engineering Handbook Volume 1 Microwave components Edited by Bradford L. Smith and Michel-Henri Carpentier

The Microwave Engineering Handbook Volume 2 Microwave circuits, antennas and propagation Edited by Bradford L. Smith and Michel-Henri Carpentier

The Microwave Engineering Handbook Volume 3 Microwave systems and applications Edited by Bradford L. Smith and Michel-Hemi Carpentier

Solid-state Microwave Generation J. Anastassiades, D. Kaminsky, E. Perea and A. Poezevara

Infrared Thermography G. Gaussorgues

Phase Locked Loops J. B. Encinas

Frequency Measurement and Control Chronos Group

Microwave Integrated Circuits Edited by I. Kneppo

Microwave Tube Transmitters L. Sivan

Microwave ElectroDic Devices Theo G. van de Roer

Introduction to A vioDies R. P. G. Collinson

Modern Antennas

S. Drabowitch Ecole Superieure d'Electricite, France A. Papiernik University of Nice-Sophia Antipolis, France H. Griffiths University College London, UK and J. Encinas formerly of the Institut Superieure d'Electronique de Paris, France

Edited by

H. Griffiths (as above) and Bradford L. Smith Alcatel Alsthom, Paris, France

junj SPRINGER-SCIENCE+BUSINESS MEDIA, BV.

First edition 1998

© 1998 S. Drabowitch, A. Papiemik, H. Griffiths, 1. Encinas and B. L. Smith Originally published by Chapman & Hall in 1998 Softcover reprint of the hardcover 1 st edition 1998

ISBN 978-1-4757-2760-9 ISBN 978-1-4757-2758-6 (eBook) DOI 10.1007/978-1-4757-2758-6

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the UK Copyright Designs and Patents Act, 1988, this publication may not be reproduced, stored, or transmitted, in any form or by any means, without the prior permission in writing of the publishers, or in the case of reprographic reproduction only in accordance with the terms of the licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of licences issued by the appropriate Reproduction Rights Organization outside the UK. Enquiries concerning reproduction outside the terms stated here should be sent to the publishers at the London address printed on this page.

The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made.

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

r§l Printed on permanent acid-free text paper, manufactured in accordance with ANSIINISO Z39.48-1992 and ANSIINISO Z39.48-1984 (permanence of Paper).

Contents

List of contributors

Foreword

Acknowledgements

1 Fundamentals of electromagnetism 1.1 Maxwell's equations

1.1.1 Maxwell's equations in an arbitrary medium 1.1.2 Linear media 1.1.3 Conducting media 1.1.4 Reciprocity theorem

1.2 Power and energy 1.2.1 Power volume densities 1.2.2 Energy volume densities 1.2.3 Poynting vector and power

1.3 Plane waves in linear media 1.3.1 Plane waves in an isotropic linear medium 1.3.2 Skin effect

Further reading Exercises

xv

xvi

xvii

1 1 1 4 6 8

10 10 10 11 12 12 18 20 21

2 Radiation 25 2.1 Plane wave spectrum 25

2.1.1 Spectral domain 26 2.1.2 Electromagnetic field in a semi-infinite space with no sources 28 2.1.3 The far field 33

2.2 Kirchhoff's formulation 2.2.1 Green's identity and Green's functions 2.2.2 Kirchhoff's integral formulation 2.2.3 Plane wave spectrum and Kirchhoffs formulation

Further reading Exercises

38 38 39 42 43 44

3 Antennas in transmission 46 3.1 Far field radiation 46

3.1.1 Vector characteristic of the radiation from the antenna 46 3.1.2 Translation theorem 47 3.1.3 Application: radiation produced by an arbitrary current 48 3.1.4 Radiated power 51

vi Contents

3.2 Field radiated from an antenna 3.2.1 Elementary dipoles 3.2.2 Plane-aperture radiation

3.3 Directivity, gain, radiation pattern 3.3.1 Radiated power 3.3.2 Directivity 3.3.3 Gain 3.3.4 Radiation pattern 3.3.5 Input impedance

Further reading Exercises

52 52 55 59 59 60 60 62 63 65 66

4 Receiving antennas 70 4.1 Antenna reciprocity theorem 70

4.1.1 Reciprocity theorem applied to a source-free closed surface 70 4.1.2 Relation between the field on transmit and the field on receive 74

4.2 Antenna effective receiving area 75 4.2.1 Definition 75 4.2.2 Relationship between gain and effective receiving area 76

4.3 Energy transmission between two antennas 77 4.3.1 The Friis transmission formula 77 4.3.2 Radar equation 78

4.4 Antenna behaviour in the presence of noise 79 4.4.1 Power radiated by a body at absolute temperature T 79 4.4.2 Noise temperature of the antenna 82 4.4.3 Noise temperature of the receiving system 83

Further reading 84 Exercises 85

5 Antennas of simple geometry 5.1 Aperture antennas

5.1.1 Parabolic antennas 5.1.2 Rectangular horns

5.2 Wire antennas 5.2.1 Electric dipoles 5.2.2 Travelling wave rectilinear antennas 5.2.3 Loops and helical antennas

Further reading Exercises

6 Printed antennas 6.1 Introduction 6.2 Different types of printed radiating elements 6.3 Field analysis methods

87 87 87 92

101 101 107 109 113 114

117 117 118 121

Contents vii

6.3.1 Methods of analysis of printed antennas 122 6.3.2 The cavity method 122 6.3.3 Application to a rectangular patch 125 6.3.4 Application to a circular patch 128

6.4 Input impedance, bandwidth and radiation pattern 130 6.4.1 Input impedance 130 6.4.2 Bandwidth 131 6.4.3 Radiation pattern 134 6.4.4 Polarization 134

Further reading 137 Exercises 138

7 Large antennas and microwave antennas 140 7.1 Introduction 140 7.2 Structures and applications 142

7.2.1 Structures 142 7.2.2 External characteristics required in applications 145

7.3 Fundamental propagation laws 152 7.3.1 Wavefronts 152 7.3.2 The Huygens-Fresnel principle of wave propagation 153 7.3.3 Stationary phase principle 154 7.3.4 Geometrical optics ray theory 157 7.3.5 Ray theory in quasi-homogeneous media 162

7.4 Antennas as radiating apertures 170 7.4 1 Antenna radiation and equivalent aperture method 170 7.4.2 Examples of microwave antennas and equivalent apertures 171 7.4.3 Far field radiation from an aperture 174 7.4.4 Examples of radiating apertures 179 7.4.5 Polarization of the radiated field: case where the field in the aperture has the characteristic of a plane wave 186 7.4.6 Geometrical properties of the Huygens coordinates 191 7.4.7 Aperture radiation in the near field 193 7.4.8 Gain factor of a radiating aperture 196

Appendix 7 A Deduction of the Huygens-Fresnel principle from the Kirchhoff integral 200 Further reading 201 Exercises 202

8 Primary feeds 207 8.1 General properties 207

8.1.1 Introduction 207 8.1.2 General characteristics of primary feeds 208 8.1.3 Radiation from radially-symmetric structures 215 8.1.4 Primary aperture in an incident field 221

viii Contents

8.2 Horns 8.2.1 General properties 8.2.2 Small flare angle horns and open-ended guides 8.2.3 Flared horns 8.2.4 Multimode horns

8.3 Hybrid modes and corrugated horns 8.3.1 Circular aperture radiating a pure polarization 8.3.2 Search for hybrid mode waves 8.3.3 Radiation pattern

Further reading Exercises

9 Axially symmetric systems 9.1 Introduction 9.2 Symmetry properties - propagation of polarization, radiation

223 223 224 225 226 229 229 229 235 240 241

244 244

patterns 245 9.3 Principal surface 247

9.3.1 Definition 247 9.3.2 Pupil- aperture angle - focal length 248 9.3.3 Equivalent aperture of the system 249

9.4 Transfer function 250 9.5 System gain 252

9.5.1 General expression 252 9.5.2 Expression obtained from the primary gain g' and the transfer function 253 9.5.3 Effect of various factors in the gain function 253 9.5.4 Concept of optimal primary directivity 255

9.6 Radiation patterns 258 9.6.1 Equivalent aperture illumination 258 9.6.2 Axisymmetric primary pattern with pure polarization 258 9.6.3 Effect of blockage 260

9.7 Aberrations in axially-symmetric systems 262 9.7.1 Introduction 262 9.7.2 Main aberrations in the defocusing plane 262

9.8 Axially symmetric systems considered in reception 267 9.8.1 Effect of transferfunction 267 9.8.2 Diffraction in the vicinity of the focus F of an element dS' of a spherical wave S' 269 9.8.3 Analysis of a diffraction pattern - contribution of an elementary crown of the spherical wave - hybrid waves 270 9.8.4 Axial field 271 9.8.5 Transverse distribution of the diffracted field in the focal plane 272 9.8.6 Axially-symmetric systems with a small aperture 90 273

Contents ix

9.8.7 Constant transfer function 275 9.8.8 Non-constant transfer function 277 9.8.9 General case: system with a very large aperture 278

9.9 System considered in reception: transfer of the energy contained in the diffraction pattern to the primary aperture 279

9.9.1 Diffraction pattern produced around the focus by an incident non-axial plane wave 279 9.9.2 Radiation pattern of the system associated with a given primary aperture 281 9.9.3 Examples of applications 282 9.9.4 Axial gain of an axially-symmetric system - effect of the diameter of the primary aperture 283

9.10 Radiation in the Fresnel zone of a Gaussian illumination - application to the transport of energy by radiation (Gobeau's waves) 286 Further reading 288 Exercises 289

10 Focused systems 297 10.1 Introduction 297 10.2 The Cassegrain antenna 298

10.2.1 Introduction 298 10.2.2 Geometry 299 10.2.3 Equivalent primary feed 301 10.2.4 Principal surface 302 10.2.5 Cassegrain with shaped reflectors 303 10.2.6 Diffraction pattern of the subreflector 306 10.2.7 Blockage by the subreflector 312 10.2.8 Schwartzschild aplanetic reflector 316

10.3 Tracking systems 317 10.3.1 Introduction 317 10.3.2 General characteristics of radar echoes 319 10.3.3 Conical scanning 324 10.3.4 'Monopulse' antennas 332 10.3.5 Beacon tracking 349

10.4 Non axially-symmetric systems 349 10.4.1 Offset reflector 349 10.4.2 Shaped reflectors - pattern synthesis 353

Further reading 360 Exercises 361

11 Arrays 363 11.1 Introduction 363

11.1.1 Phased arrays 364 11.1.2 Bandwidth - use of delay lines - subarrays 364

x Contents

11.1.3 Active arrays 366 11.2 General structure of a phased array (examples) 368

11.2.1 General structure 368 11.2.2 Examples of array structures 373

11.3 Linear array theory 378 11.3.1 Basic equation - array factor 378 11.3.2 Unifonn illumination and constant phase gradient 379 11.3.3 Half-power beamwidth 382 11.3.4 Condition to prevent grating lobes from occurring in the scanning region 383 11.3.5 Effect of weighting of the array illumination function 384 11.3.6 Effect of element directivity 384

11.4 Variation of gain as a function of direction 385 11.4.1 Array operating on transmit 385 11.4.2 Array on receive 387 11.4.3 Array active reflection coefficient - mutual coupling 388 11.4.4 Blind angle phenomenon 389 11.4.5 Case where the element spacing is relatively large 392 11.4.6 Study of an array of open-ended guides considered as a periodic structure 392

11.5 Effects of phase quantization 394 11.5.1 Case where all phase shifters are fed in phase 394 11.5.2 Effects of quantization when the phase origin varies from one phase shifter to another 396

11.6 Frequency-scanned arrays 400 11.7 Analogue beamforming matrices 402

11. 7.1 Introduction 402 11.7.2 General properties of multi-port networks 403 11. 7.3 Beamforming applications 405 11. 7.4 Examples of matrices 408 11.7.5 Non-orthogonal directional beams 414

11.8 Further topics 418 11.8.1 Active modules 418 11.8.2 Digital beamforming 422 11.8.3 Circular, cylindrical and confonnal arrays 425 11.8.4 Sparse and random arrays 434

Appendix llA Comparison of linear and circular arrays 440 Further reading 447 Exercises 448

12 Fundamentals of polarimetry 451 12.1 Introduction 451

12.1.1 Application of polarimetry in radar and telecommunications 451

Contents xi

12.1.2 Some historical references 453 12.1.3 Basics 453

12.2 Fully polarized waves 455 12.2.1 Definition 455 12.2.2 Algebraic representation of elliptical polarization 456 12.2.3 Normalized Cartesian coordinate system 457 12.2.4 Base of circular polarizations 458 12.2.5 Polarization ratio 460 12.2.6 Polarization diagram 461 12.2.7 Polarization coupling to the receiving antenna 464

12.3 Partially polarized waves 467 12.3.1 Definition and physical origin 467 12.3.2 Coherence matrix 469 12.3.3 Completely unpolarized wave 471 12.3.4 Completely polarized wave 472 12.3.5 Stokes parameters 473 12.3.6 Decomposition of a partially polarized wave 474 12.3.7 Geometrical interpretation of the preceding results: Stokes parameters and Poincare sphere 474 12.3.8 Polarization coupling and Stokes vectors 476

12.4 Polarimetric representation of radar targets 479 12.4.1 Introduction 479 12.4.2 Sinclair diffraction matrix 479

12.5 Partially polarized waves: The Mueller Matrix 490 12.5.1 The Mueller matrix 490 12.5.2 Application example 490 12.5.3 Examples of responses to different incident polarizations 492

12.6 Polarizers and polarization separators for telecommunications antennas and polarimetric radars 494

12.6.1 Introduction 494 12.6.2 Non-symmetrical polarization separator 494 12.6.3 Semi-symmetrical polarization separator 495 12.6.4 Symmetrical polarization separator (turnstile) 496 12.6.5 Dielectric vane polarizer 497

Further reading 499 Exercises 499

13 Antennas and signal theory 13.1 Introduction

500 500

13.2 Equivalence of an aperture and a spatial frequency filter 501 13.2.1 Concept of spatialfrequency 501 13.2.2 Consequences of the limitation of the aperture dimensions on the properties of the radiation characteristic function 502 13.2.3 Consequences of the limitation of the aperture dimensions

xii Contents

on the 'gain' function of the antenna 506 13.3 Synthesis of an aperture to radiate a given radiation pattern 507

13.3.1 Statement of problem 507 13.3.2 Generalization of the approximation method 509 13.3.3 Use of sampling methods 511 13.3.4 Role of phase - stationary phase method 513 13.3.5 Pattern synthesis for a focusing system 517

13.4 Superdirective antennas 518 13.4.1 Introduction 518 13.4.2 Role of the 'invisible' domain of radiation 518

13.5 The antenna as a filter of angular signals 520 13.5.1 Introduction 520 13.5.2 Optical or microwave imaging and linear filters 521 13.5.3 False echoes and resolving power 522 13.5.4 Case where the antenna is treated as an aperture 523 13.5.5 Spectrum of fixed echoes of a rotating radar 524

Further reading 525 Exercises 526

14 Signal processing antennas 528 14.1 Introduction 528 14.2 Synthetic antennas in radar and sonar 529

14.2.1 Principles of synthetic antennas 529 14.2.2 Synthetic receive array with non-directional beam 530 14.2.3 Synthetic receive array with multiple beams 531 14.2.4 Examples of spatio-temporal coding 532

14.3 Imaging of coherent sources 537 14.3.1 Introduction 537 14.3.2 Two-source distribution 538 14.3.3 Estimation of the elevation angle of a low-altitude target above a reflecting plane 539 14.3.4 Effect of noise: a posteriori probabilities and decision theory 541

14.4 Imaging of incoherent sources 544 14.4.1 Introduction 544 14.4.2 Conditions for incoherence 544 14.4.3 Multiplicative arrays 545 14.4.4 Relationship between an angular distribution of incoherent sources and the observed field: the Van Cittert-Zernicke Theorem 548 14.4.5 Sampling of the coherence function 551 14.4.6 Measurement of the coefficients of correlation or covariance - C(n-n') 551 14.4.7 The covariance matrix 553

14.5 High resolution imagery and the maximum entropy method 554

Contents xiii

14.5.1 Introduction 554 14.5.2 Classical method of 'correlogram' 555 14.5.3 Method of Maximum Entropy 556 14.5.4 Estimation of T under conditions of Maximum Entropy 556 14.5.5 Factorization of T( -r) - properties 557 14.5.6 Determination of the coefficients an in equation (14.71) 558 14.5.7 Generalization: ARMA model 560 14.5.8 Numerical example 560 14.5.9 Minimum redundance arrays 561

14.6 Other methods of spectral estimation 563 14.6.1 Introduction 563 14.6.2 The MUSIC algorithm 564 14.6.3 Other superresolution algorithms 567 14.6.4 Superresolution with circular arrays 569

14.7 Spatial filtering 570 14.7.1 Introduction 570 14.7.2 What is an adaptive array? 570 14.7.3 Simple example: two-element array 571 14.7.4 Howells-Applebaum correlation loop 574 14.7.5 Minimum noise criterion 577 14.7.6 Effect of internal receiver noise 578 14.7.7 Time-domain behaviour of the correlation loop 579 14.7.8 Multiple correlation loops: the coherent sidelobe canceller (CSLC) 583 14.7.9 The optimum array 585 14.7.10 Interpretation 588 14.7.11 Digital implementation 588

Appendix 14A Entropy and probability 590 Further reading 597 Exercises 598

15 Antenna measurements 15.1 Introduction 15.2 Gain measurements

15.2.1 Comparison with a standard-gain hom 15.2.2 Two-antenna measurement 15.2.3 Three-antenna measurement 15.2.4 Extrapolation

15.3 Radiation pattern measurements 15.3.1 Anechoic chambers and far-field ranges 15.3.2 Compact ranges 15.3.3 Wavefront quality 15.3.4 Near-field techniques 15.3.5 Other techniques

600 600 601 601 601 602 602 604 604 608 610 611 613

xiv Contents

15.3.6 Polarization 15.4 Time-domain gating

15.4.1 Principles 15.4.2 Limitations

15.5 Antenna noise temperature and GIT 15.5.1 Measurement of antenna noise temperature 15.5.2 Direct measurement of GIT using solar noise

15.6 Impedance and bandwidth Further reading Exercises

Index

616 617 617 619 620 620 620 622 624 625

626

List of contributors Serge Drabowitch Docteur Ingenieur. Professor at the Ecole Superieure d'Electricite. Member of the College Scientifique of THOMSON; Senior Member of the IEEE and the French SEE.

Albert Papiernik Professor at the University of Nice-Sophia Antipolis, France.

Hugh Griffiths Professor, and Head of Microwaves, Radar and Optics Group, University College London; Fellow of the lEE and Fellow of the Royal Academy of Engineering; Senior Member of the IEEE.

Jean Encinas (now deceased) Institut Superieure d'Electronique de Paris, France

Bradford L. Smith Senior Intellectual Property Counsel and Engineer, Corporate Research Centre, Alcatel Alsthom in Paris, France; Senior Member of the IEEE and the French SEE

Foreword Why yet another book on antennas ? The aim of the authors was to offer a didactic text appropriate for advanced graduate students, as well as a practical work for practicing engineers; to combine a solid theoretical treatment with a practical development which should allow the serious reader to undertake antenna design from fIrst principles.

To accomplish these goals, the authors bring together their contributions from both industry and the academic environment. The developments of the various topics start at a level which is accessible to a novice in the speciality, but give a treatment which culminates at an advanced level.

Another important feature of the book is its use of practical examples illustrating real engineering problems and designs. In most cases, the explanation is sufficient to grasp the principles of operation of the related equipment, and, where appropriate, the reader is referred to a relevant bibliography for more complete and hence more sophisticated methodologies of design.

Of particular note are the chapters on specialist subjects such as antennas and signal theory, and signal processing antennas, showing how the antenna may be combined with signal processing techniques in imaging applications, in angular superresolution, and in adaptive arrays to suppress interference and jamming. Another example is the chapter on the use of polarimetry to enhance the wealth of information which may be extracted, for example, from radar signals.

Michel-Henri Carpentier Series Editor, Microwaves and RF Technology Series

Acknowledgements In a work of this kind it is impossible to acknowledge individually all the people who have contributed, either directly or indirectly. However, we would like to mention by name certain colleagues and friends whose knowledge and understanding of the subject has been a particular inspiration: Professor Eric Roubine, Professor Jean-Charles Bolomey, Patrice Brachat and Professor Alex Cullen.

We thank our numerous colleagues and students, past and present, from the Antennas Laboratory of THOMSON-CSF, from the Laboratoire d'Electronique Antennes et Telecommunications of the University of Nice-Sophia Antipolis, from CNET­France Telecom, from Roke Manor Research, and from the Department of Electronic and Electrical Engineering at University College London. Many have helped by reading early versions of the manuscript and seeking out errors, or suggesting better ways of expressing ourselves.

Special thanks are due to several people for helping obtain photographs and illustrations, and for obtaining permission for their publication. In particular, Dr Paul Brennan of University College London, for his help with the subtleties of desktop publishing. Also Dr Wolfram Titze of University College London; Prof. David Olver, Prof. Peter Clarricoats and Dr Clive Parini of Queen Mary and Westfield College, University of London; Georges Bienvenu of Thomson-Marconi Sonar; David Hall and Jane Ward of Matra-Marconi Space; Antoine Roederer, John Reddy and Kees van't Klooster of the European Space Agency; Darren Seymour­Russell of the Defence Research Agency; David Gentle of the National Physical Laboratory; and John Holloway of Siemens Plessey Systems.

Finally we· acknowledge the contribution of our friend Jean Encinas, who died suddenly while this book was being written. This book is dedicated to his memory.