PAA contents

A WILEY-INTERSCIENCE PUBLICATION
JOHN WILEY & SONS, INC.
NEW YORK/CHICHESTER/WEINHEIM/BRISBANE/SINGAPORE/TORONTO

PHASED ARRAY ANTENNAS, First Edition

R. C. HANSEN

Preface xv

1 Introduction 1

1.1 Array Background 1
1.2 Systems Factors 2
1.3 Annotated Reference Sources 4

2 Basic Array Characteristics 7

2.1 Uniformly Excited Linear Arrays
     2.1.1 Patterns 7
     2.1.2 Beamwidth 9
     2.1.3 Sidelobes 11
     2.1.4 Grating Lobes 11
     2.1.5 Bandwidth 15
2.2 Planar Arrays 17
     2.2.1 Array Coordinates 17
     2.2.2 Beamwidth 18
     2.2.3 Grating Lobes: Rectangular Lattice 20
     2.2.4 Grating Lobes: Hexagonal Lattice 23
2.3 Beam Steering and Quantization Lobes 25
     2.3.1 Steering Increment 25
     2.3.2 Steering Bandwidth 26
     2.3.3 Phaser Quantization Lobes 26
     2.3.4 Subarray Quantization Lobes 31
     2.3.5 QL Decollimation; Overlapped Subarrays 33
2.4 Directivity 34
     2.4.1 Linear Array Directivity 34
     2.4.2 Directivity of Arrays of Short Dipoles 38
     2.4.3 Directivity of Arrays of Resonant Elements 39
     2.4.4 Planar Array Directivity 41
References 45

3 Linear Array Pattern Synthesis 47

3.1 Introduction 47
     3.1.1 Pattern Formulations 47
     3.1.2 Physics Versus Mathematics 49
     3.1.3 Taylor Narrow-Beam Design Principles 50
3.2 Dolph-Chebyshev Arrays 51
     3.2.1 Half-Wave Spacing 51
     3.2.2 Spacing Less Than Half-Wave 57
3.3 Taylor One-Parameter Distribution 59
     3.3.1 One-Parameter Design 59
     3.3.2 Bickmore-Spellmire Two-Parameter Distribution 63
3.4 Taylor N-Bar Aperture Distribution 64
3.5 Low-Sidelobe Distributions 71
     3.5.1 Comparison of Distributions 71
     3.5.2 Average Sidelobe Level 73
3.6 Villeneuve N-Bar Array Distribution 74
3.7 Difference Patterns 77
     3.7.1 Canonical Patterns 77
     3.7.2 Bayliss Patterns 78
     3.7.3 Sum and Difference Optimization 83
     3.7.4 Discrete Zolotarev Distributions 84
3.8 Sidelobe Envelope Shaping 85
3.9 Shaped Beam Synthesis 90
     3.9.1 Woodward-Lawson Synthesis 90
     3.9.2 Elliott Synthesis 93
3.10 Thinned Arrays 96
     3.10.1 Probabilistic Design 96
     3.10.2 Space Tapering 101
     3.10.3 Minimum Redundancy Arrays 102
References 102

4 Planar and Circular Array Pattern Synthesis 106

4.1 Circular Planar Arrays 106
     4.1.1 Flat Plane Slot Arrays 106
     4.1.2 Hansen One-Parameter Pattern 107
     4.1.3 Taylor Circular N-Bar Pattern 112
     4.1.4 Circular Bayliss Difference Pattern 116
     4.1.5 Difference Pattern Optimization 121
     4.2 Noncircular Apertures 121
     4.2.1 Two-Dimensional Optimization 121
     4.2.2 Ring Sidelobe Synthesis 123
References 125

5 Array Elements 127

5.1 Dipoles 127
     5.1.1 Thin Dipoles 127
     5.1.2 Bow-Tie and Open Sleeve Dipoles 133
5.2 Waveguide Slots 137
     5.2.1 Broad Wall Longitudinal Slots 138
     5.2.2 Edge Slots 143
     5.2.3 Stripline Slots 145
     5.2.4 Open End Waveguides 145
5.3 TEM Horns 146
     5.3.1 Development of TEM Horns 146
     5.3.2 Analysis and Design of Horns 148
     5.3.3 TEM Horn Arrays 149
     5.3.4 Millimeter Wave Antennas 150
5.4 Microstrip Patches and Dipoles 150
     5.4.1 Transmission Line Model 153
     5.4.2 Cavity and Other Models 155
     5.4.3 Parasitic Patch Antennas 156
References 158

6 Array Feeds 164

6.1 Series Feeds 164
     6.1.1 Resonant Arrays 164
          6.1.1.1 Impedance and Bandwidth 164
          6.1.1.2 Resonant Slot Array Design 168
     6.1.2 Travelling Wave Arrays 170
          6.1.2.1 Frequency Squint and Single Beam Condition 171
          6.1.2.2 Calculation of Element Conductance 175
         6.1.2.3 TW Slot Array Design 177
     6.1.3 Frequency Scanning 181
     6.1.4 Phaser Scanning 184
6.2 Shunt (Parallel) Feeds 188
     6.2.1 Corporate Feeds 188
     6.2.2 Distributed Arrays 189
6.3 Two-Dimensional Feeds 191
     6.3.1 Fixed Beam Arrays 191
     6.3.2 Sequential Excitation Arrays 193
     6.3.3 Electronic Scan in One Plane 193
     6.3.4 Electronic Scan in Two Planes 195
6.4 Photonic Feed Systems 200
     6.4.1 Fiber Optic Delay Feeds 202
          6.4.1.1 Binary Delay Lines 202
          6.4.1.2 Acousto-Optical Switched Delay 204
          6.4.1.3 Modulators and Photodetectors 204
     6.4.2 Wavelength Division Fiber Delay 205
          6.4.2.1 Dispersive Fiber Delay 205
          6.4.2.2 Bragg Fiber Grating Delay 206
          6.4.2.3 Travelling Wave Fiber Delay 207
     6.4.3 Optical Delay 207
     6.4.4 Optical Fourier Transform 207
6.5 Systemic Errors 208
     6.5.1 Parallel Phasers 208
     6.5.2 Series Phasers 210
     6.5.3 Systematic Error Compensation 210
References 211

7 Mutual Coupling 215

7.1 Introduction 215
7.2 Fundamentals of Scanning Arrays 215
     7.2.1 Current Sheet Model 215
     7.2.2 Free and Forced Excitations 217
     7.2.3 Scan Impedance and Scan Element Pattern 219
     7.2.4 Minimum Scattering Antennas 222
7.3 Spatial Domain Approaches to Mutual Coupling 224
     7.3.1 Canonical Couplings 224
          7.3.1.1 Dipole and Slot Mutual Impedance 224
          7.3.1.2 Microstrip Patch Mutual Impedance 228
          7.3.1.3 Horn Mutual Impedance 229
     7.3.2 Impedance Matrix Solution 231
     7.3.3 The Grating Lobe Series 232
7.4 Spectral Domain Approaches 235
     7.4.1 Dipoles and Slots 235
     7.4.2 Microstrip Patches 246
     7.4.3 Printed Dipoles 250
     7.4.4 Printed TEM Horns 252
     7.4.5 Unit Cell Simulators 254
7.5 Scan Compensation and Blind Angles 254
     7.5.1 Blind Angles 254
     7.5.2 Scan Compensation 257
          7.5.2.1 Coupling Reduction 257
          7.5.2.2 Compensation Feed Networks 258
          7.5.2.3 Multimode Elements 261
          7.5.2.4 External Wave Filter 264
References 265

8 Finite Arrays 273

8.1 Methods of Analysis 273
     8.1.1 Overview 273
     8.1.2 Finite-by-Infinite Arrays 276
8.2 Scan Performance of Small Arrays 281
8.3 Finite-by-Infinite Array Gibbsian Model 287
     8.3.1 Salient Scan Impedance Characteristics 287
     8.3.2 A Gibbsian Model for Finite Arrays 297
References 301

9 Superdirective Arrays 304

9.1 Historical Notes 304
9.2 Maximum Array Directivity 305
     9.2.1 Broadside Directivity for Fixed Spacing 305
     9.2.2 Directivity as Spacing Approaches Zero 307
     9.2.3 Endfire Directivity 308
     9.2.4 Bandwidth, Efficiency, and Tolerances 309
9.3 Constrained Optimization 317
     9.3.1 Dolph-Chebyshev Superdirectivity 317
     9.3.2 Constraint on Q or Tolerances 323
9.4 Matching of Superdirective Arrays 325
     9.4.1 Matching of Superdirective Arrays 326
     9.4.2 HTS Arrays 326
References 327

10 Multiple-Beam Antennas 330

10.1 Introduction 330
10.2 Beamformers 330
     10.2.1 Networks 331
          10.2.1.1 Power Divider BFN 331
          10.2.1.2 Butler Matrix 331
          10.2.1.3 Blass and Nolen Matrices 335
          10.2.1.4 2-D BFN 337
          10.2.1.5 McFarland 2-D Matrix 337
     10.2.2 Lenses 341
          10.2.2.1 Rotman Lens BFN 341
          10.2.2.2 Bootlace Lenses 356
          10.2.2.3 Dome Lenses 361
          10.2.2.4 Other Lenses 362
     10.2.3 Digital Beamforming 364
10.3 Low Sidelobes and Beam Interpolation 365
     10.3.1 Low-Sidelobe Techniques 365
          10.3.1.1 Interlaced Beams 365
          10.3.1.2 Resistive Tapering 366
          10.3.1.3 Lower Sidelobes via Lossy Networks 366
          10.3.1.4 Beam Superposition 369
     10.3.2 Beam Interpolation Circuits 370
10.4 Beam Orthogonality 372
     10.4.1 Orthogonal Beams 372
          10.4.1.1 Meaning of Orthogonality 372
          10.4.1.2 Orthogonality of Distributions 373
          10.4.1.3 Orthogonality of Arrays 375
     10.4.2 Effects of Nonorthogonality 376
          10.4.2.1 Efficiency Loss 376
          10.4.2.2 Sidelobe Changes 377
References 380

11 Conformal Arrays 384

11.1 Scope 384
11.2 Ring Arrays 385
     11.2.1 Continuous Ring Antenna 385
     11.2.2 Discrete Ring Array 389
     11.2.3 Beam Cophasal Excitation 393
11.3 Arrays on Cylinders 395
     11.3.1 Slot Patterns 397
     11.3.2 Array Pattern 397
          11.3.2.1 Grating Lobes 401
          11.3.2.2 Principal Sidelobes 406
          11.3.2.3 Cylindrical Depolarization 407
     11.3.3 Slot Mutual Admittance 411
          11.3.3.1 Modal Series 413
          11.3.3.2 Admittance Data 417
     11.3.4 Scan Element Pattern 420
11.4 Sector Arrays on Cylinders 422
     11.4.1 Patterns and Directivity 422
     11.4.2 Comparison of Planar and Sector Arrays 424
     11.4.3 Ring and Cylindrical Array Hardware 426
11.5 Arrays on Cones and Spheres 429
     11.5.1 Conical Arrays 430
          11.5.1.1 Lattices on a Cone 432
          11.5.1.2 Conical Depolarization and Coordinate Systems 435
          11.5.1.3 Projective Synthesis 443
          11.5.1.4 Patterns and Mutual Coupling 443
          11.5.1.5 Conical Array Experiments 443
     11.5.2 Spherical Arrays 445
References 446

12 Measurements and Tolerances 453

12.1 Measurement of Low-Sidelobe Patterns 453
12.2 Array Diagnostics 455
12.3 Waveguide Simulators 458
12.4 Array Tolerances 464
     12.4.1 Directivity Reduction and Average Sidelobe Level 465
     12.4.2 Beam Pointing Error 466
     12.4.3 Peak Sidelobes 468

References 470
Author Index 473

Subject Index 482

Preface

Although array antennas have many decades of history, the last two decades have experienced a maturation, both in the understanding and design of arrays, and in the use of large sophisticated arrays. Radars utilizing electronic scanning arrays are in common use, from airport surveillance to missile detection and tracking; names of U.S. military systems such as Aegis, Patriot, and Pave Paws are well known. This book is a comprehensive treatment of all aspects of phased arrays; much has changed since the only other such work, Microwave Scanning Antennas, appeared in 1966. Most noteworthy has been the parallel development of inexpensive computer power and the theoretical understanding of nearly all aspects of phased array design. Design algorithms suitable for computers are emphasized here, with numerical tips and short algorithms sprinkled throughout the chapters. The work is prepared from the dual viewpoint of a design engineer and an antenna array analyst.
Following an introductory chapter is Chapter 2 on basic array characteristics, covering grating lobes, quantization lobes, bandwidth, and directivity. Highly efficient linear aperture and array synthesis techniques are covered next, including sum and difference patterns. Chapter 4 treats synthesis of planar arrays. Array elements are covered next, including not only the classic dipoles and slots, but TEM horns and patches. In Chapter 6, feeds for linear and planar arrays, both fixed beam and scanning, are examined; photonic time delay and feeders are included. Array performance is strongly affected by mutual impedance; Chapter 7 investigates ways of calculating this for various array elements, including an extensive treatment of ways of calculating array performance with mutual effects included. Among these are unit cell, spectral moment method, finite impedance matrix, and scattering techniques. Finite arrays are examined in Chapter 8, including the recently developed Gibbsian models. Next is an extensive review of superdirective arrays; the implications of high-temperature superconductors for antennas is an important feature. Multiple-beam arrays, as opposed to multiple-beam reflector feeds, are treated in Chapter 10. Included are one-dimensional and two-dimensional Butler and Rotman lenses, and the practical meaning of beam orthogonality. Conformal arrays, ranging from ring arrays to arrays on cones, are covered next; much previously unpublished material is included in this chapter. Finally, Chapter 12 discusses array diagnostics, waveguide simulators in depth, and array tolerances. Extensive references to the archival literature are used in each chapter to offer additional sources of data.

Robert C. Hansen
Tarzana, CA

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