Finite Antenna Arrays
and FSS
Finite Antenna Arrays
and FSS
Ben A. Munk
A John Wiley & Sons, Inc., Publication
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Library of Congress Cataloging-in-Publication Data:
Munk, Ben (Benedikt A.)
Finite antenna arrays and FSS / Ben A. Munk.
p. cm
“A Wiley-Interscience publication.”
Includes bibliographical references and index.
ISBN 0-471-27305-8 (cloth)
1. Microwave antennas. 2. Antenna arrays. 3. Frequency selective surfaces. I. Title.
TK7871.67.M53M88 2003
621.381
3—dc21
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
2003041132
To the increasing number of my friends who realize that computer power is a
supplement, not a substitute, for brain power.
The constant support of the Electroscience Laboratory and my family—in
particular, my wife Aase—is deeply appreciated.
B. A. M.
Contents
Foreword
Preface
Acknowledgments
Symbols and Definitions
1 Introduction
1.1 Why Consider Finite Arrays? / 1
1.2 Surface Waves Unique to Finite Periodic Structures / 4
1.3 Effects of Surface Waves / 5
1.3.1 Surface Wave Radiation from an FSS / 5
1.3.2 Variation of the Scan Impedance from Column to
Column / 7
1.4 How do We Control the Surface Waves? / 7
1.4.1 Phased Array Case / 7
1.4.2 The FSS Case / 9
1.5 Common Misconceptions / 10
1.5.1 On Common Misconceptions / 10
1.5.2 On Radiation from Surface Waves / 11
1.5.3 Should the Surface Waves Encountered Here Be
Called Edge Waves? / 11
xvii
xxi
xxiii
xxv
1
vii
viii
CONTENTS
1.6 Conclusion / 12
Problems / 13
2 On Radar Cross Section of Antennas in General
15
2.1 Introduction / 15
2.2 Fundamentals of Antenna RCS / 17
2.2.1 The Antenna Mode / 17
2.2.2 The Residual Mode / 20
2.3 How to Obtain a Low σtot by Cancellation (Not
Recommended) / 22
2.4 How do We Obtain Low σtot Over a Broad Band? / 22
2.5 A Little History / 23
2.6 On the RCS of Arrays / 24
2.6.1 Arrays of Dipoles without a Groundplane / 24
2.6.2 Arrays of Dipoles Backed by a Groundplane / 26
2.7 An Alternative Approach: The Equivalent Circuit / 27
2.8 On the Radiation from Infinite Versus Finite Arrays / 29
2.8.1 Infinite Arrays / 29
2.8.2 Finite Array / 29
2.9 On Transmitting, Receiving, and Scattering Radiation
Pattern of Finite Arrays / 31
2.9.1 Example I: Large Dipole Array without
Groundplane / 31
2.9.2 Example II: Large Dipole Array with
Groundplane / 33
2.9.3 Example III: Large Dipole Array with Oversized
Groundplane / 34
2.9.4 Final Remarks Concerning Transmitting,
Receiving, and Scattering Radiation Pattern of
Finite Arrays / 34
2.10 Minimum Versus Nonminimum Scattering Antennas / 34
2.10.1 The Thevenin Equivalent Circuit / 35
2.10.2 Discussion / 35
2.11 Other Nonminimum Scattering Antennas / 36
2.11.1 Large Array of Full-Wave Dipoles / 36
CONTENTS
ix
2.11.2 Effect of a Tapered Aperture / 37
2.11.3 The Parabolic Antenna / 39
2.12 How to Prevent Coupling Between the Elements Through
the Feed Network / 40
2.12.1 Using Hybrids / 40
2.12.2 Using Circulators / 42
2.12.3 Using Amplifiers / 42
2.13 How to Eliminate Backscatter due to Tapered Aperture
Illumination / 43
2.14 Common Misconceptions / 45
2.14.1 On Structural Scattering / 45
2.14.2 On RCS of Horn Antennas / 46
2.14.3 On the Element Pattern: Is It Important? / 46
2.14.4 Are Low RCS Antennas Obtained by Fooling
Around on the Computer? / 48
2.14.5 How Much Can We Conclude from the
Half-Wave Dipole Array? / 48
2.14.6 Do “Small” Antennas Have Lower RCS Than
Bigger Ones? / 48
2.14.7 And the Worst Misconception of All: Omitting
the Loads! / 49
2.15 Summary / 49
Problems / 51
3 Theory
3.1 Introduction / 56
56
3.2 The Vector Potential and the H Field for Column Arrays
of Hertzian Elements / 57
3.3 Case I: Longitudinal Elements / 59
3.3.1 Total Field from Infinite Column Array of
z-Directed Elements of Arbitrary Length 2l / 60
3.3.2 The Voltage Induced in an Element by an
External Field / 61
3.3.3 The Mutual Impedance Zq
,q Between a Column
Array q and an External Element q
3.4 Case II: Transverse Elements / 64
3.4.1 The x Component of Eq / 65
/ 62
x
CONTENTS
3.4.2 The y Component of Eq / 69
3.4.3 The z Component of Eq / 72
3.5 Discussion / 74
3.6 Determination of the Element Currents / 76
3.7 The Double Infinite Arrays with Arbitrary Element
Orientation / 77
3.7.1 How to Get Well-Behaved Expressions / 77
3.8 Conclusions / 81
Problems / 82
4 Surface Waves on Passive Surfaces of Finite Extent
84
4.1 Introduction / 84
4.2 Model / 85
4.3 The Infinite Array Case / 85
4.4 The Finite Array Case Excited by Generators / 89
4.5 The Element Currents on a Finite Array Excited by an
Incident Wave / 89
4.6 How the Surface Waves are Excited on a Finite
Array / 90
4.7 How to Obtain the Actual Current Components / 93
4.8 The Bistatic Scattered Field from a Finite Array / 94
4.9 Parametric Study / 96
4.9.1 Variation of the Angle of Incidence / 96
4.9.2 Variation of the Array Size / 100
4.9.3 Variation of Frequency / 102
4.10 How to Control Surface Waves / 108
4.11 Fine Tuning the Load Resistors at a Single
Frequency / 108
4.12 Variation with Angle of Incidence / 111
4.13 The Bistatic Scattered Field / 114
4.14 Previous Work / 115
4.15 On Scattering from Faceted Radomes / 117