Elliott_Antenna_Theory_and_Design:Content
Foreword to the Revised Edition ix
Preface to the Revised Edition xi
Preface xix
I SOURCE-FIELD RELATIONS SINGLE ANTENNA ELEMENTS 1
1 The Far-Field Integrals, Reciprocity, Directivity 3
1.1 Introduction 3
1.2 Electrostatics and Magnetostatics in Free Space 4
1.3 The Introduction of Dielectric, Magnetic, and Conductive Materials 7
1.4 Time-Varying Fields 10
1.5 The Retarded Potential Functions I1
1.6 Poynting's Theorem 13
1.7 The Stratton-Chu Solution 17
1.8 Conditions at Infinity 21
1.9 Field Values in the Excluded Regions 25
1.10 The Retarded Potential Functions: Reprise 26
1. l l The Far Field: Type I Antennas 27
1.12 The Schelkunoff Equivalence Principle 31
1.13 The Far Field: Type IL Antennas 36
1.14 The Reciprocity Theorem 39
1.15 Equivalence of the Transmitting and Receiving Patterns of an
Antenna 41
1.16 Directivity and Gain 46
1.17 Receiving Cross Section 48
I . I8 Polarization of the Electric Field 53
2 Radiation Patterns of Dipoles, Loops, and Helices 58
2.1 Introduction 58
2.2 The Center-Fed Dipole 58
2.3 Images in a Ground Plane 65
2.4 A Monopole Above a Ground Plane 67
2.5 A Dipole in Front of a Ground Plane 68
xiv
2.6 The Small Current Loop 69
2.7 Traveling Wave Current on a Loop 71
2.8 The End-Fire Helix 73
3 Radiation Patterns of Horns, Slots and Patch Antennas 79
3.1 Introduction 79
3.2 The Open-Ended Waveguide 79
3.3 Radiation from Horns 83
3.4 Center-Fed Slot in Large Ground Plane 86
3.5 Waveguide-Fed Slots 88
3.6 Theory of Waveguide-Fed Slot Radiators 91
3.7 Patch Antennas 99
II ARRAY ANALYSIS AND SYNTHESIS 111
4 Linear Arrays: Analysis 113
4.1 Introduction 113
4.2 Pattern Formulas for Arrays with Arbitrary Element Positions 114
4.3 Linear Arrays: Preliminaries I1 7
4.4 Schelkunoff's Unit Circle Representation 128
5 Linear Arrays: Synthesis 141
5.1 Introduction 141
5.2 Sum and Difference Patterns 142
5.3 Dolph-Chebyshev Synthesis of Sum Patterns 143
5.4 Sum Pattern Beamwidth of Linear Arrays 148
5.5 Peak Directivity of the Sum Pattern of a Linear Array 153
5.6 A Relation Between Beamwidth and Peak Directivity for Linear
Arrays 157
5.7 Taylor Synthesis of Sum Patterns 157
5.8 Modified Taylor Patterns 162
5.9 Sum Patterns with Arbitrary Side Lobe Topography 165
5.10 Discretization of a Continuous Line Source Distribution 172
5.1 1 Bayliss Synthesis of Difference Patterns 181
5.12 Difference Patterns with Arbitrary Side Lobe Topography 185
5.13 Discretization Applied to Difference Patterns 187
5.14 Design of Linear Arrays to Produce Null-Free Patterns 190
6 Planar Arrays: Analysis and Synthesis 196
6.1 Introduction 196
6.2 Rectangular Grid Arrays: Rectangular Boundary and Separable
Distribution I9 7
6.3 Circular Taylor Patterns 213
6.4 Modified Circular Taylor Patterns: Ring Side Lobes of Individually
Arbitrary Heights 218
6.5 Modified Circular Taylor Patterns: Undulating Ring Side Lobes 221
6.6 Sampling Generalized Taylor Distributions: Rectangular Grid
Arrays 225
6.7 Sampling Generalized Taylor Distributions: Circular Grid Arrays 230
6.8 An Improved Discretizing Technique for Circular Grid Arrays 233
6.9 Rectangular Grid Arrays with Rectangular Boundaries: Nonseparable
Tseng-Cheng Distributions 237
6.10 A Discretizing Technique for Rectangular Grid Arrays 243
6.1 1 Circular Bayliss Patterns 250
6.12 Modified Circular Bayliss Patterns 256
6.13 The Discretizing Technique Applied to Planar Arrays Excited
to Give a Difference Pattern 256
6.14 Comparative Performance of Separable and Nonseparable
Excitations for Planar Apertures 261
6.15 Fourier Integral Representation of the Far Field 265
Ill SELF-IMPEDANCE AND MUTUAL IMPEDANCE, FEEDING STRUCTURES 275
7 Self-Impedance and Mutual Impedance of Antenna Elements 277
7.1 Introduction 277
7.2 The Current Distribution on an Antenna: General Formulation 278
7.3 The Cylindrical Dipole: Arbitrary Cross Section 281
7.4 The Cylindrical Dipole: Circular Cross Section, Hallen's
Formulation 284
7.5 The Method of Moments 286
7.6 Solution of Hallen's Integral Equation: Pulse Functions 287
7.7 Solution of Hallen's Integral Equation: Sinusoidal Basis Functions 294
7.8 Self-Impedance of Center-Fed Cylindrical Dipoles: Induced EMF
Method 297
7.9 Self-Impedance of Center-Fed Cylindrical Dipoles: Storer's
Variational Solution 305
7.10 Self-Impedance of Center-Fed Cylindrical Dipoles: Zeroth and First
Order Solutions to Hallen's Integral Equation 308
7.1 1 Self-Impedance of Center-Fed Cylindrical Dipoles: King-Middleton
Second-Order Solution 314
7.12 Self-Impedance of Center-Fed Strip Dipoles 321
7.13 The Derivation of a Formula for the Mutual Impedance Between
Slender Dipoles 325
7.14 The Exact Field of a Dipole: Sinusoidal Current Distribution 329
7.15 Computation of the Mutual Impedance Between Slender Dipoles 332
7.16 The Self-Admittance of Center-Fed Slots in a Large Ground Plane:
Booker's Relation 336
7.17 Arrays of Center-Fed Slots in a Large Ground Plane:
Self-Admittance and Mutual Admittance 342
7.18 The Self-Impedance of a Patch Antenna 344
8 The Design of Feeding Structures for Antenna Elements and Arrays 351
8.1 Introduction 351
8.2 Design of a Coaxially Fed Monopole with Large Ground Plane 352
8.3 Design of a Balun-Fed Dipole Above a Large Ground Plane 355
8.4 Two-Wire-Fed Slots: Open and Cavity-Backed 359
xvi
8.5 Coaxially Fed Helix Plus Ground Plane 361
8.6 The Design of an Endfire Dipole Array 363
8.7 Yagi-Uda Type Dipole Arrays: Two Elements 368
8.8 Yagi-Uda Type Dipole Arrays: Three or More Elements 373
8.9 Frequency-Independent Antennas: Log-Periodic Arrays 375
8.10 Ground Plane Backed Linear Dipole Arrays 386
8.1 1 Ground Plane Backed Planar Dipole Arrays 390
8.12 The Design of a Scanning Array 393
8.13 The Design of Waveguide-Fed Slot Arrays: The Concept
of Active Slot Admittance (Impedance) 397
8.14 Arrays of Longitudinal Shunt Slots in a Broad Wall of Rectangular
Waveguides: The Basic Design Equations 402
8.15 The Design of Linear Waveguide-Fed Slot Arrays 407
8.16 The Design of Planar Waveguide-Fed Slot Arrays 414
8.17 Sum and Difference Patterns for Waveguide-Fed Slot Arrays;
Mutual Coupling Included 418
IV CONTINUOUS APERTURE ANTENNAS 427
9 Traveling Wave Antennas 429
9.1 Introduction 429
9.2 The Long Wire Antenna 430
9.3 Rhombic and Vee-Antennas 432
9.4 Dielectric-Clad Planar Conductors 437
9.5 Corrugated Planar Conductors 440
9.6 Surface Wave '~xcitation 442
9.7 Surface Wave Antennas 446
9.8 Fast Wave Antennas 453
9.9 Trough Waveguide Antennas 464
9.10 Traveling Wave Arrays of Quasi-Resonant Discretely Spaced Slots
[Main Beam at 8, = arccos(Plk)] 467
9.1 1 Traveling Wave Arrays of Quasi-Resonant Discretely Spaced Slots
(Main Beam Near Broadside) 474
9.12 Frequency Scanned Arrays 476
10 Reflectors and Lenses 482
10.1 Introduction 482
10.2 Geometrical Optics: The Eikonal Equation 483
10.3 Simple Reflectors 490
10.4 Aperture Blockage 495
10.5 The Design of a Shaped Cylindrical Reflector 498
10.6 The Design of a Doubly Curved Reflector 504
10.7 Radiation Patterns of Reflector Antennas: The Aperture Field
Method 508
10.8 Radiation Patterns of Reflector Antennas: The Current
Distribution Method 518
10.9 Dual Shaped Reflector Systems 521
10.10 Single Surface Dielectric Lenses 525
10.1 1 Stepped Lenses 529
10.12 Surface Mismatch, Frequency Sensitivity, and Dielectric Loss
for Lens Antennas 532
10.13 The Far Field of a Dielectric Lens Antenna 534
10.14 The Design of a Shaped Cylindrical Lens 536
10.15 Artificial Dielectrics: Discs and Strips 538
10.16 Artificial Dielectrics: Metal Plate (Constrained) Lenses 542
10.17 The Luneburg Lens 545
APPENDICES 557
A. Reduction of the Vector Green's Formula for E 559
B. The Wave Equations for A and D 562
C. Derivation of the Chebyshev Polynomials 564
D. A General Expansion of cosm v 567
E. Approximation to the Magneticvector Potential Function
for Slender Dipoles 569
F. Diffraction by Plane Conducting Screens: Babinet's Principle 573
G. The Far-Field in Cylindrical Coordinates 581
H. The Utility of a Csc, 8 Pattern 585
Index 587
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