Phased Array Antennas: Floquet Analysis, Synthesis, BFNs, Metamaterial, and Active Array Systems 2nd edition [Kõva köide]

About the Author xix
Foreword xxi
Preface xxiii
Acknowledgments xxix
About the Companion Website xxxi

1 Phased Array Fundamentals: Pattern Analysis and Synthesis 1
1.1 Introduction 1
1.2 Array Fundamentals 1
1.3 Pencil Beam Array 13
1.4 Linear Array Synthesis 33
1.5 Planar Aperture Synthesis 54
1.6 Discretization of Continuous Source 61
1.7 Array-Fed Reflector 64
1.8 Confocal Array-Fed Reflector 70
1.9 Summary 76

2 Introduction to Floquet Modes in Infinite Arrays 83
2.1 Introduction 83
2.2 Fourier Spectrum and Floquet Series 84
2.3 Floquet Excitation and Floquet Modes 94
2.4 Two-Dimensional Floquet Excitation 97
2.5 Grating Beams from Geometrical Optics 103
2.6 Floquet Mode and Guided Mode 104
2.7 Summary 108

3 Floquet Modal Functions 115
3.1 Introduction 115
3.2 TEz and TMz Floquet Vector Modal Functions 115
3.3 Infinite Array of Electric Surface Current on Dielectric Coated Ground
Plane 121
3.4 Determination of Blind Angles 129
3.5 Active Element Pattern 133
3.6 Array of Rectangular Horn Apertures 141

4 Finite Array Analysis 161
4.1 Introduction 161
4.2 Symmetry Property of Floquet Admittance 162
4.3 Mutual Coupling 169
4.4 Array of Multimodal Sources 172
4.5 Mutual Coupling in Two-Dimensional Arrays 173
4.6 Active Input Impedance of Finite Array 176
4.7 Active Reflection Coefficient of Open-Ended Waveguide Array 178
4.8 Radiation Patterns of Finite Array 182
4.9 Radiation Patterns of Open-Ended Waveguide Array 185
4.10 Active Element Patterns of Real Finite Array 187
4.11 Array with Nonuniform Spacing 197
4.12 Finite Array Analysis Using Convolution 198

5 Array of Subarrays 207
5.1 Introduction 207
5.2 Subarray Analysis 208
5.3 Subarray with Rectangular Grid 213
5.4 Subarrays with Arbitrary Grid 214
5.5 Subarray and Grating Lobes 216
5.6 Active Subarray Pattern 218
5.7 Four-element Subarray Fed by a Power Divider 223
5.8 Subarray Blindness 227
5.9 Subarray with Sequentially Rotating Elements 228
5.10 Concluding Remarks 234

6 The GSM Approach for Multilayer Array Structures 243
6.1 Introduction 243
6.2 Generalized Scattering Matrix Approach 244
6.3 GSM Cascading Rule 245
6.4 Transmission Matrix Representation 249
6.5 Building Blocks for GSM Analysis 250
6.6 Equivalent Impedance Matrix of Patch Layer 261
6.7 Stationary Character of MoM Solutions 265
6.8 Convergence of MoM Solutions 272
6.9 Advantages of GSM Approach 280
6.10 Other Numerical Methods 281

7 Analysis of Microstrip Patch Arrays 287
7.1 Introduction 287
7.2 Probe-Fed Patch Array 288
7.3 Electromagnetically Coupled Patch Array 302
7.4 Slot-Fed Patch Array 303
7.5 Stripline-Fed Slot-Coupled Array 314
7.6 Finite Patch Array 315
7.7 Ring-slot Element 317

8 Array of Waveguide Horns 327
8.1 Introduction 327
8.2 Linearly Flared Horn Array 328
8.3 Grazing Lobes and Pattern Nulls 334
8.4 Surface and Leaky Waves in Array 340
8.5 Wide-Angle Impedance Matching (WAIM) 351
8.6 Multimodal Rectangular/Square Horn Elements 357
8.7 Multimodal Step-Circular Horn 360
8.8 Muti-flared High-efficiency Horns 361
8.9 Excitation of Waveguide Horn 362

9 FSS, Polarizer, and Reflect-array Analysis 371
9.1 Introduction 371
9.2 Frequency-Selective Surface 371
9.3 Screen Polarizer 382
9.4 Printed Reflect Array 389

10 Metamaterial Analysis and Fundamental Properties 407
10.1 Introduction 407
10.2 Origin of Constitutive Parameters: Maxwellian Point of View 409
10.3 Solutions of Maxwell's Equation in a Periodic Array Medium 411
10.4 Constitutive Parameters for 2D Obstacles 418
10.5 Constitutive Parameters for 3D Obstacles 427
10.6 On the Uniqueness and Structure of [ ] Tensor 430
10.7 The Lorentz Model Versus Floquet Model 434
10.8 Floquet Versus Lorentz: Test on Metamaterial Slab 436
10.9 Floquet Versus Lorentz: Nonresonant Obstacles 441
10.10 Mode Degeneracy and Non-Maxwellian Medium 443
10.11 Concluding Remarks 451

11 Multilayer Array Analysis with Different Periodicities and Cell
Orientations 459
11.1 Introduction 459
11.2 Layers with Different Periodicities: Rectangular Lattice 460
11.3 Nonparallel Cell Orientations: Rectangular Lattice 465
11.4 Layers with Arbitrary Lattice Structures 473
11.5 Summary 475

12 Shaped Beam Array Design: Optimization Algorithms 479
12.1 Introduction 479
12.2 Array Size: Linear Array 480
12.3 Element Size 483
12.4 Pattern Synthesis (WoodwardLawson's Method) 486
12.5 Gradient Search Algorithm 489
12.6 Conjugate Field Matching Algorithm 500
12.7 Successive Projection Algorithm 505
12.8 Projection Matrix Algorithm 509
12.9 Other Optimization Algorithms 514
12.10 Design Guidelines of Shaped Beam 515
12.11 Pattern Null Algorithms 516

13 Beam Forming Networks in Multiple-Beam Arrays 533
13.1 Introduction 533
13.2 BFN Using Power Dividers/Combiners 534
13.3 Butler Matrix Beam Former 534
13.4 Blass Matrix BFN 548
13.5 Rotman Lens 550
13.6 Digital Beam Former 566
13.7 Optical Beam Formers 569

14 Active Phased Array Antenna 575
14.1 Introduction 575
14.2 Active Array Block Diagrams 576
14.3 Aperture Design of Array Antenna 578
14.4 Solid State Power Amplifier (SSPA) 582
14.5 Phase Shifter 587
14.6 Time Delay Unit 588
14.7 Intermodulation Product 590
14.8 Noise Temperature and Noise Figure of Antenna Subsystems 597
14.9 Active Array System Analysis 607
14.10 Active Array Calibration 611
14.11 Concluding Remarks 615

15 Statistical Analysis of Phased Array Antenna 621
15.1 Introduction 621
15.2 Array Pattern 622
15.3 Statistics of R and I 624
15.4 Probability Density Function of |F(u)| 629
15.5 Confidence Limits 638
15.6 Element Failure Analysis 644
15.7 Concluding Remarks 648

References 650
Bibliography 650
Problems 650
Appendix A1 Shannon's Sampling Theorem 653
Appendix A2 A Proof of the Identity 655
Index 657

Arun K. Bhattacharyya retired from RF Center of Excellence group of Lockheed Martin Space Systems in 2024. He also worked for Hughes Space and Communication (now Boeing) and Northrop space systems. He was an associate professor at the University of Saskatchewan, Canada and a visiting professor at Seoul National University, South Korea. He has authored over 100 technical papers and five book-chapters and has 25 issued patents. He is an IEEE fellow since 2002 and has received numerous awards including Hughes Technical Excellence award, Distinguished Engineer award at Northrop Grumman and the 2020 Extraordinary Engineering and Technology Award at Lockheed Martin Space.