Spherical-wave source-scattering matrix analysis of antennas and antenna-antenna interactions

160 Pages·2013·9.23 MB·English

by  Lewis, Richard L.

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National Institute of Standards and Technology
NIST Technical Note 1373
Spherical-Wave Source-Scattering
Matrix Analysis of Antennas
and Antenna-Antenna Interactions
Richard Lindsay Lewis
QC
100
.U5753
NO. 1373
1995

NIST Technical Note 1373
Spherical-Wave Source-Scattering
Matrix Analysis of Antennas
and Antenna-Antenna Interactions
Richard Lindsay Lewis
Electromagnetic Fields Division
Electronics and Electrical Engineering Laboratory
National Institute of Standards and Technology
325 Broadway
Boulder, Colorado 80303-3328
July 1995
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U.S. DEPARTMENT OF COMMERCE, Ronald H. Brown, Secretary
TECHNOLOGY ADMINISTRATION, Mary L. Good, Under Secretary for Technology
NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Arati Prabhakar, Director
National Institute of Standards and Technology Technical Note
Natl. Inst. Stand. Technol., Tech. Note 1373, 156 pages (July 1994)
CODEN:NTNOEF
U.S. GOVERNMENT PRINTING OFFICE
WASHINGTON: 1995
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
CONTENTS
Chapter
INTRODUCTION
I. 1
ELECTROMAGNETIC FIELD EXPANSIONS
II. 5
2.1 Introduction 5
2.2 Representation of the Fields at the Terminal Surface S
and at the Spherical Surface S 5
2.3 Dyadic Green's Function Representations 9
2.4 Orthogonality Relations for the Vector Spherical-Wave Functions 15
2.5 Conclusions 18
SPHERICAL-WAVE SOURCE-SCATTERING MATRIX REPRESENTATION
III.
OF AN ANTENNA
19
3.1 Introduction 19
3.2 Formulation of the Source-Scattering Matrix Representation 19
3.3 Reciprocity Relations 20
3.4 Power Gain and Effective Area of an Antenna 21
3.5 Conclusions 25
FUNCTIONAL TRANSFORMATIONS INDUCED BY COORDINATE-SYSTEM
IV.
ROTATIONS AND TRANSLATIONS 26
4.1 Introduction 26
4.2 The Rotation of Coordinates Transformation 26
4.3 Application of the Fano-Racah Recursion Formula 31
4.3.1 The Derivation of a Numerical Calculation Formula 31
4.3.2 Analytical Formula Relating Rotation Coefficients
to Associated Legendre Functions 33
4.4 The Translation of Coordinates Transformation 35
4.5 Conclusions 39
V. SCATTERING MATRIX ANALYSIS OF COUPLED ANTENNAS: GENERAL
SOLUTION FOR SYSTEM TWO-PORT
40
5.1 Introduction 40
5.2 Modal Coefficient-Transformation Solution to the
Coupled Antenna Problem 45
5.2.1 Heuristic Development of the Two-Port Equations 45
5.2.2 Explicit Determination of the Translation Coefficients 48
5.2.3 The Two-Port Equation for Oppositely Directed
Transmission 51
5.2.4 Antenna Coupling Expressed in Terms of Each Antenna's
Spherical-Wave Source-Scattering-Matrix Elements 53
5.3 Conclusions 57
VI. INTERRELATIONS BETWEEN THE TRANSMISSION EQUATIONS 58
6.1 Introduction 58
6.2 Establishment of Equalities between the Contragradient
Vector-Wavefunction Translation Coefficients 58
6.3 Equivalence of the Coupling Equations Representing
Oppositely Directed Transmission for the Case of
Reciprocal Antennas 61
6.4 Application of the Transmission Equations to Near-Field
to Far-Field Antenna Pattern Transformations
(Spherical Scanning) 63
6.4.1 Equivalence of the Transmitting Test-Antenna and
Receiving Test-Antenna Spherical-Scanning
Computer Algorithms 63
6.4.2 Relating Probe Receiving Coefficients in the Doubly-
Primed Coordinate System to Probe Transmitting
Coefficients in the Singly-Primed Coordinate System;
Rotation of a Singly-Primed Antenna into the
Orientation of a Doubly-Primed Antenna 64
6.5 On the Validity of Interchanging the Order of Summation of
n «* v Infinite Double Series 67
6.6 Conclusions 74
REDUCTION OF THE TWO-ANTENNA COUPLING EQUATION TO
VII.
THE MODAL-EXPANSION EQUATION WHEN ONE ANTENNA AN
IS
ELEMENTARY DIPOLE
75
7.1 Introduction 75
7.2 Modal Expansion Coefficients for an Elementary Dipole
Current Source 75
.
7.3 Equality between the Transverse Radiated Field and the
Antenna-Dipole Coupling Equation: Receiving Electric
Dipole Case 78
7.4 Transmitting Electric Dipole Case .'...; 81
7.5 Conclusions 83
SPHERICAL SCANNING
VIII. 84
8.1 Introduction 84
8.2 Probe-Correction Case Formulation for Spherical Scanning
Assuming a Transmitting Test Antenna and Receiving Probe 85
8.2.1 Basic Theoretical Development 85
8.2.2 Computation Algorithms for Discrete Data-Sampling Points 89
8.2.3 An Efficient Computational Algorithm for Computing
the Far-Field Pattern from Near-Field Measurements 94
8.2.3.1 Computation of Wm* 94
8.2.3.2 Completion of the Near-Field to Far-Field
Computation Algorithm 101
8.3 Recapitulation of the Spherical-ScanningAlgorithm's
Data-Processing Steps 108
8.4 A Modified Spherical-ScanningAlgorithm for Radiation
Confined to a Single Hemisphere 109
iv
8.5 Conclusions 114
NUMERICAL COMPARISONS AND SIMULATIONS FOR VALIDATING
IX.
SPHERICAL-SCANNING COMPUTER CODE
115
9.1 Introduction 115
9.2 Numerical Self-Consistency Tests and Simulations 116
9.3 Computational Aspects of Spherical-ScanningData Processing 122
9.3.1 Computational Limitations of the Probe-Translation Algorithm 122
9.3.2 Probe-Rotation Angles Corresponding to Measured-Data
Components 125
9.4 Experimental Verification 128
9.5 Conclusions 134
CONCLUSIONS
X. 135
BIBLIOGRAPHY
138
APPENDIX A: EXPANSION OF AN INCIDENT PLANE-WAVE FIELD
AS A SERIES OF VECTOR SPHERICAL-WAVE FUNCTIONS 142
FIGURES
Fi*s&ure
2-1. Notation for describing an antenna's spherical-wave source-scattering matrix
(radial-distance r is measured from 0) 6
4-1. Coordinate system transformations 27
4-2. The Eulerian angles a, (3, and y 28
5-1. Two antenna transmission-system schematic 41
5-2. Simplified configuration for studying a two-antenna transmission system
(<£' = </>") 46
6-1. Rotation of a doubly primed antenna into the orientation of a singly primed
antenna 65
9-1. Test parameters 130
9-2. Open-array near-field test setup 130
9-3. Near-field plot principal polarization 131
9-4. Transformed far-field plot principal polarization 131
9-5. Sum elevation 132
9-6. Sum azimuth 132
9-7. Delta azimuth 133
9-8. SLS azimuth 133
VI
ACKNOWLEDGMENTS
I would especially like to acknowledge the encouragement and support of my Ph.D. thesis
advisor, Dr. Samuel W. Maley, without which this work could not have been completed, and
the steadfast encouragement of the second reader on my thesis committee, Dr. Norris S.
Nahman. I should also like to thank my former instructors and Ph.D. committee members, Dr.
Frank S. Barnes, Dr. Carl T. A. Johnk, and Dr. Karl E. Gustafson for their encouragement and
support over the years. Finally, I should like to thank my colleagues, in the Electromagnetic
Fields Division of the National Institute of Standards and Technology, for their many
contributions to my appreciation of the science we have been engaged in carrying out.
vn
DEDICATION
TO MY FAMILY
MY
WIFE:
Betty L. Lewis
OUR CHILDREN:
Pamela Dorothy Lewis
Michelle Mary (Lewis) Grey
Kim Belinda (Cole) Gildow
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