PHASED ARRAY ANTENNAS
Second edition
R. C. HANSEN
CONTENTS
Preface to Second Edition xvii
1 Introduction 1
1.1
Array Background 1
1.2
Systems Factors 2
1.3
Annotated
Reference Sources 3
1.3.1 Adaptive Antenna Reference Books 5
2
Basic Array Characteristics 7
2.1 Uniformly Excited Linear Arrays 7
2.1.1 Patterns 7
2.1.2 Beamwidth 9
2.13 Sidelobes 11
2.14 Grating Lobes 11
2.15 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 201
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 Time Delay Deployment 27
2.3.4 Phaser
Quantization Lobes 28
2.3.5 Subarray Quantization Lobes 32
2.3.6 QL Decollimation; Overlapped
Subarrays 35
2.4 Directivity 36
2.4.1 Linear Array Directivity 36
2.4.2 Directivity of Arrays of Short
Dipoles 39
2.4.3 Directivity of Arrays of
Resonant Elements 40
2.4.4 Planar Array Directivity 42
References 46
3 Linear Array Pattern Synthesis 49
2.1
Introduction 49
3.1.1 Pattern Formulations 49
3.1.2 Physics vs Mathematics 51
3.1.3 Taylor Narrow-Beam Design Principles
52
3.2 Dolph-Chebyshev Arrays 53
3.2.1 Half-Wave Spacing 53
3.2.2 Spacing Less Than Half-Wave 59
3.3 Taylor One-Parameter Distribution 60
3.3.1 One-Parameter Design 60
3.3.2 Bickmore-Spellmire
Two-Parameter Design 65
3.4 Taylor N-Bar Aperture Distribution 66
3.5 Low-Sidelobe Distributions 72
3.5.1 Comparison of Distributions 72
3.5.2 Average Sidelobe Level 75
3.6 Villeneuve N-Bar Array Distribution 76
3.7 Difference Patterns 79
3.7.1 Canonical Patterns 79
3.7.2 Bayliss Patterns 81
3.7.3 Sum and Difference
Optimization 85
3.7 4 Discrete Zolotarev
Distributions 87
3.8 Sidelobe Envelope Shaping 89
3.9 Shaped Beam Synthesis 92
3.9.1 Woodward-Lawson Systhesis 92
3.9.2 Elliott Synthesis 94
3.10 Thinned Arrays 98
3.10.1 Probabilistic Design 98
3.10.2 Space Tapering 102
3.10.3 Minimum Redundancy Arrays 103
References 104
4 Planar and Circular Array Pattern Synthesis 109
4.1 Circular Planar Arrays 109
4.1.1 Flat Plane Slot Arrays 109
4.1.2 Hansen One-Parameter Pattern
110
4.1.3 Taylor Circular N-Bar Pattern
114
4.1.4 Circular Bayliss Difference
Pattern 118
4.1.5 Difference Pattern
Optimization 123
4.2 Non-Circular Apertures 125
4.2.1 Two-Dimensional optimization
125
4.2.2 Ring Sidelobe Synthesis 126
References 127
5 Array Elements 129
5.1 Dipoles 129
5.1.1 Thin Dipoles 129
5.1.2 Bow-Tie and Open Sleeve
Dipoles 136
5.2 Waveguide Slots 139
5.2.1 Broad Wall Longitudinal Slots
140
5.2.2. Edge Slots 145
5.2.3 Stripline Slots 147
5.2.4 Open End Waveguides 147
5.2.5 Substrate Integrated Waveguide
148
5.3 TEM Horns 149
5.3.1 Development of TEM Horns 149
5.3.2 Analysis and Design of Horns
151
5.3.3 TEM Horn Arrays 152
5.3.4 Millimeter Wave Antennas 153
5.4 Microstrip Patches and Dipoles 154
5.4.1 Transmission Line Model 157
5.4.2 Cavity and other Models 159
5.4.3 Parasitic Patch Antennas 159
5.4.4 Balanced-Fed Patches 163
References 163
6 Array Feeds 171
6.1 Series Feeds 171
6.1.1 Resonant Arrays 171
6.1.1.1 Impedance and Bandwidth 171
6.1.1.2 Resonant Slot Array Design 176
6.1.2 Travelling Wave Arrays 178
6.1.2.1 Frequency Squint and Single Beam Condition 178
6.1.2.2 Calculation of Element Conductance 181
6.1.2.3 TW Slot Array Design 185
6.1.3 Frequency Scanning 188
6.1.4 Phaser Scanning 193
6.2 Shunt (Parallel) Feeds 194
6.2.1 Corporate Feeds 194
6.2.2 Distributed Arrays 196
6.3 Two-Dimensional Feeds 197
6.3.1 Fixed Beam Arrays 197
6.3.2 Sequential Excitation
Arrays 199
6.3.3 Electronic Scan in One
Plane 199
6.3.4 Electronic Scan in Two
Planes 201
6.4 Photonic Feed Systems 207
6.4.1 Fiber Optic Delay Feeds
207
6.4.1.1 Binary Delay Lines 207
6.4.1.2 Acousto-Optical Switched Delay 209
6.4.1.3 Modulators and Photodetectors 210
6.4.2 Wavelength Division Fiber
Delay 211
6.4.2.1 Dispersive Fiber Delay 211
6.4.2.2 Bragg Fiber Grating Delay 212
6.4.2.3 Travelling Wave Fiber Delay 212
6.4.3
Optical Delay 213
6.4.4 Optical Fourier Transform 213
6.5 Systematic Errors 214
6.5.1 Parallel Phasers 214
6.5.2 Series Phasers 215
6.5.3 Systematic Error Compensation
216
References 216
7 Mutual Coupling 221
7.1 Introduction 221
7.2 Fundamentals of Scanning Arrays 221
7.2.1 Current Sheet Model 221
7.2.2 Free and Forced Excitations
223
7.2.3 Scan Impedance and Scan
Element Pattern 225
7.2.3.1 Transmit vs Receive SEP 228
7.2.3.2 Measurement of Scan Impedance 233
7.2.4 Minimum Scattering Antennas
233
7.3 Spatial Domain Approaches to Mutual Coupling 235
7.3.1 Canonical Couplings 235
7.3.1.1 Dipole and Slot Mutual Impedance 235
7.3.1.2 Microstrip Patch Mutual Impedance 239
7.3.1.3 Horn Mutual Impedance 241
7.3.2 Impedance Matrix Solution 242
7.3.3 The Grating Lobe Series244
7.4 Spectral Domain Approaches 246
7.4.1 Dipoles and Slots 246
7.4.2 Microstrip Patches 258
7.4.3 Printed Dipoles 261
7.4.4 Printed TEM Horns 262
7.4.5 Unit Cell Simulators 266
7.5 Scan Compensation and Blind Angles 266
7.5.1 Blind Angles 266
7.5.2 Scan Compensation 269
7.5.2.1 Coupling Reduction 269
7.5.2.2
Compensation Feed Networks 269
7.5.2.3 Multimode Elements 272
7.5.2.4 External
Wave Filter 276
References 277
8 Finite Arrays 285
8.1 Methods of Analysis 285
8.1.1 Overview 285
8.1.2 Finite-by-Infinite Arrays 289
8.2 Scan Performance of Small Arrays 293
8.3 Finite-by-Infinite Array Gibbsian Model 300
8.3.1 Salient Scan Impedance
Characteristics 300
8.3.2 A Gibbsian Model for Finite
Arrays 310
References 313
9 Superdirective Arrays 317
9.1 Historical Notes 317
9.2 Maximum Array Directivity 318
9.2.1 Broadside Directivity for
Fixed Spacing 318
9.2.2 Directivity as Spacing
Approaches Zero 320
9.2.3 Endfire Directivity 321
9.2.4 Bandwidth, Efficiency, and
Tolerances 322
9.3 Constrained Optimization 330
9.3.1 Dolph-Chebyshev
Superdirectivity 330
9.3.2 Constraint on Q or Tolerances
336
9.4 Matching of Superdirective Arrays 338
9.4.1 Network Loss Magnification 340
9.4.2 HTS Arrays 340
References 340
10 Multiple-Beam Antennas 343
10.1 Introduction 343
10.2 Beamformers 343
10.2.1 Networks 344
10.2.1.1 Power Divider BFN 344
10.2.1.2 Butler Matrix 344
10.2.1.3 Blass and Nolen Matrices 348
10.2.1.5 2-D BFN 350
10.2.1.5.McFarland 2-D Matrix 350
10.2.2 Lenses 351
10.2.2.1 Rotman Lens BFN 351
10.2.2.2 Bootlace Lenses 368
10.2.2.3 Dome Lenses 372
10.2.2.4 Other Lenses 374
10.2.3 Digital Beamforming 377
10.3 Low Sidelobes and Beam Interpolation 378
10.3.1 Low Sidelobe
Techniques 378
10.3.1.1 Interlaced Beams 378
10.3.1.2 Resistive Tapering 379
10.3.1.3 Lower Sidelobes via Lossy Networks 379
10.3.1.4 Beam Superposition 381
10.3.2
Beam Interpolation Circuits 383
10.4 Beam Orthogonality 385
10.4.1 Orthogonal
Beams 385
10.4.1.1
Meaning of Orthogonality 385
10.4.1.2 Orthogonality of Distributions 386
10.4.1.3 Orthogonality of Arrays 388
10.4.2 Effects of
Non-Orthogonality389
10.4.2.1 Efficiency Loss 389
10.4.2.2 Sidelobe Changes 390
References 393
11 Conformal Arrays 399
11.1 Scope 399
11.2 Ring Arrays 400
11.2.1 Continuous Ring
Antenna 400
11.2.2 Discrete Ring
Array 403
11.2.3 Beam Cophasal Excitation
407
11.3 Arrays on Cylinders 411
11.3.1 Slot Patterns 411
11.3.2 Array Pattern 412
11.3.2.1 Grating Lobes 416
11.3.2.2 Principal Sidelobes 419
11.3.2.3 Cylindrical Depolarization 421
11.3.3 Slot Mutual
Admittance 422
11.3.3.1 Modal Series 426
11.3.3.2 Admittance Data 430
11.3.4 Scan
Element Pattern 430
11.4 Sector Arrays on Cylinders 434
11.4.1 Patterns and Directivity
434
11.4.2 Comparison of
Planar and Sector Arrays 437
11.4.3 Ring and
Cylindrical Array Hardware 441
11.5 Arrays on Cones and Spheres 442
11.5.1 Conical
Arrays 443
11.5.1.1 Lattices on a Cone 444
11.5.1.2
Conical Depolarization and Coordinate Systems 447
11.5.1.3 Projective Synthesis 455
11.5.1.4 Patterns and Mutual Coupling 455
11.5.1.5 Conical Array Experiments 456
11.5.2 Spherical Arrays 457
References 458
12 Connected Arrays 465
12.1 History of Connected Arrays 465
12.2 Connected Array Principles 465
12.3 Connected Dipole Currents 467
12.3.1 Simulation
Results: Current Phases 467
12.3.2 Simulation
Results: Current Amplitudes 468
12.3.3 Simulation
Results: SEP 474
12.4 Connection by Reactance 474
12.5 Connected Array Extensions 476
References 476
13 Reflectarrays and Retrodirective Arrays 479
13.1 Reflectarrays 479
13.1.1 History of
Reflectarrays 479
13.1.2 Geometric Design
480
13.1.3 Elements 481
13.1.4 Phasing of
Elements 482
13.1.5 Bandwidth 484
13.1.6 Reflectarray
Extensions 485
13.2 Retrodirective Arrays 486
13.2.1 History of Retrodirective
Arrays 486
13.2.2 Recent Progress
487
13.2.3 Advanced
Applications 491
References 491
14 Reflectors With Arrays 497
14.1 Focal Plane Arrays 497
14.1.1 Focal Plane
Fields and Coma 497
14.1.2 Recovering Coma Scan
Loss 502
14.1.3 Coma Correction
Limitations 502
14.2 Near-Field Electromagnetic Optics 503
14.2.1 Near-Field
Cassegrain 503
14.2.1.1 System Trades and Restrictions 507
14.2.2 Near-Field
Gregorian 507
References 510
15 Measurements and Tolerances 513
15.1 Measurement of Low-Sidelobe Patterns 513
15.2 Array Diagnostics 516
15.3 Waveguide Simulators 518
15.4 Array Tolerances 524
15.4.1 Directivity
Reduction and Average Sidelobe Level 524
15.4.2 Beam Pointing
Error 526
15.4.3 Peak Sidelobes
527
References 529
Author Index
Subject Index