Phased array antennas and subsystems : Floquet analysis, synthesis, BFNs, and active array systems

A comprehensive guide to the latest in phased array antenna analysis and design--the Floquet modal based approach This comprehensive book offers an extensive presentation of a new methodology for phased array antenna analysis based on Floquet modal expansion. Engineers, researchers, and advanced graduate students involved in phased array antenna technology will find this systematic presentation an invaluable reference. Elaborating from fundamental principles, the author presents an in-depth treatment of the Floquet modal based approach. Detailed derivations of theorems and concepts are provided, making Phased Array Antennas a self-contained work. Each chapter is followed by several practice problems. In addition, numerous design examples and guidelines will be found highly useful by those engaged in the practical application of this new approach to phased array structures. Broadly organized into three sections, Phased Array Antennas covers: * The development of the Floquet modal based approach to the analysis of phased array antennas * Application of the Floquet modal based approach to important phased array structures * Shaped beam array synthesis, array beam forming networks, active phased array systems, and statistical analysis of phased arrays Incorporating the most recent developments in phased array technology, Phased Array Antennas is an essential resource for students of phased array theory, as well as research professionals and engineers engaged in the design and construction of phased array antennas. Phased Array Antennas......Page 3 Contents......Page 9 Preface......Page 17 1.2 Array Fundamentals......Page 21 1.2.1 Element Pattern, Directivity, and Gain......Page 22 1.2.2 Copolarization and Cross-Polarization......Page 24 1.2.3 Array Pattern......Page 26 1.2.4 Array Gain......Page 28 1.2.5 Maximum-Array-Gain Theorem......Page 29 1.3 Pencil Beam Array......Page 32 1.3.1 Scan Loss and Beam Broadening......Page 33 1.3.2 Scan Array Design Consideration......Page 34 1.3.3 Grating Lobes......Page 36 1.3.4 Fixed-Value Phase Shifter Versus True Time Delay Phase Shifter......Page 41 1.3.5 Phase Quantization......Page 43 1.4.1 Array Factor: Schelkunoff’s Polynomial Representation......Page 47 1.4.2 Binomial Array......Page 48 1.4.3 Dolph–Chebyshev Array......Page 51 1.4.4 Taylor Line Source Synthesis......Page 58 1.4.5 Bayliss Difference Pattern Synthesis......Page 63 1.5 Planar Aperture Synthesis......Page 66 1.5.1 Taylor’s Circular Aperture Synthesis......Page 68 1.5.2 Bayliss Difference Pattern Synthesis......Page 71 1.6 Discretization of Continuous Sources......Page 73 References......Page 76 Bibliography......Page 77 Problems......Page 78 2.1 Introduction......Page 81 2.2.1 Fourier Transform......Page 82 2.2.2 Periodic Function: Fourier Series......Page 83 2.2.3 Floquet Series......Page 85 2.2.4 Two-Dimensional Floquet Series......Page 87 2.3 Floquet Excitations and Floquet Modes......Page 90 2.4 Two-Dimensional Floquet Excitation......Page 93 2.4.1 Circle Diagram: Rectangular Grids......Page 95 2.4.2 Circle Diagram: Isosceles Triangular Grids......Page 96 2.5 Grating Beams from Geometrical Optics......Page 97 2.6 Floquet Mode and Guided Mode......Page 99 2.7 Summary......Page 102 Problems......Page 103 3.2 TE(z) and TM(z) Floquet Vector Modal Functions......Page 109 3.2.1 TE(z) Floquet Modal Fields......Page 110 3.2.2 TM(z) Floquet Modal Fields......Page 113 3.3 Infinite Array of Electric Surface Current on Dielectric-Coated Ground Plane......Page 114 3.3.1 TE(zmn) and TM(zmn) Modal Source Decomposition......Page 116 3.3.2 TE(zmn) Fields......Page 117 3.3.4 Floquet Impedance......Page 119 3.4 Determination of Blind Angles......Page 123 3.5.1 Array Pattern Using Superposition......Page 126 3.5.2 Array Pattern Using Floquet Modal Expansion......Page 128 3.5.3 Active Element Gain Pattern......Page 130 3.6 Array of Rectangular Horn Apertures......Page 132 3.6.1 Waveguide Modes......Page 133 3.6.2 Waveguide Modes to Floquet Modes......Page 134 3.6.3 Reflection and Transmission Matrices......Page 135 3.6.4 TE(10) Mode Incidence......Page 141 Bibliography......Page 143 Problems......Page 144 4.1 Introduction......Page 149 4.2 Symmetry Property of Floquet Impedance......Page 150 4.2.1 Admittance Seen by Floquet Modal Source......Page 152 4.2.2 Aperture Admittance......Page 155 4.3.1 Mutual Impedance......Page 156 4.4 Array of Multimodal Sources......Page 158 4.5 Mutual Coupling in Two-Dimensional Arrays......Page 159 4.5.1 Rectangular Lattice......Page 160 4.5.2 Arbitrary Lattice......Page 161 4.6.1 Nonexcited Elements Open Circuited......Page 163 4.6.3 Nonexcited Elements Match Terminated......Page 164 4.7 Active Return Loss of Open-Ended Waveguide Array......Page 165 4.8.1 Nonexcited Elements Open Circuited......Page 167 4.9 Radiation Patterns of Open-Ended Waveguide Array......Page 170 4.11.1 Convolution Relation for Aperture Field......Page 172 4.11.2 Mutual Impedance......Page 174 Bibliography......Page 175 Problems......Page 176 5.1 Introduction......Page 179 5.2 Subarray Analysis......Page 180 5.2.1 Subarray Impedance Matrix: Eigenvector Approach......Page 181 5.3 Subarray with Arbitrary Number of Elements......Page 185 5.4 Subarrays with Arbitrary Grids......Page 186 5.5 Subarray and Grating Lobes......Page 187 5.6 Active Subarray Patterns......Page 190 5.7 Four-Element Subarray Fed by Power Divider......Page 193 5.7.1 E-Plane Subarray......Page 194 5.7.2 H-Plane Subarray......Page 195 5.8 Subarray Blindness......Page 198 References......Page 199 Bibliography......Page 200 Problems......Page 201 6.1 Introduction......Page 207 6.2 GSM Approach......Page 208 6.3 GSM Cascading Rule......Page 209 6.4 Transmission Matrix Representation......Page 212 6.5 Building Blocks for GSM Analysis......Page 213 6.5.1 Dielectric Layer......Page 214 6.5.2 Dielectric Interface......Page 215 6.5.3 Array of Patches......Page 216 6.6 Equivalent Impedance Matrix of Patch Layer......Page 223 6.7.1 Stationary Expression......Page 227 6.7.2 GSM from Stationary Expression......Page 231 6.8 Convergence of MoM Solutions......Page 233 6.8.1 Selection of Number of Coupling Modes......Page 234 6.8.2 Failure of MoM Analysis......Page 235 6.8.3 Lower Limit for Number of Expansion Modes......Page 237 6.8.4 Number of Basis Functions......Page 240 6.10 Other Numerical Methods......Page 241 Bibliography......Page 242 Problems......Page 243 7.1 Introduction......Page 247 7.2.1 Generalized Impedance Matrix of Probe Layer......Page 248 7.2.3 Impedance Characteristics......Page 252 7.2.4 Active Element Patterns......Page 255 7.3 EMC Patch Array......Page 258 7.4 Slot-Fed Patch Array......Page 259 7.4.1 Microstripline–Slot Transition......Page 260 7.4.2 Input Impedance......Page 264 7.4.3 Active Element Patterns......Page 266 7.5 Stripline-Fed Slot-Coupled Array......Page 269 7.6 Finite Patch Array......Page 270 References......Page 272 Bibliography......Page 273 Problems......Page 274 8.1 Introduction......Page 277 8.2 Linearly Flared Horn Array......Page 278 8.2.1 Return Loss Characteristics......Page 279 8.2.2 Active Element Pattern......Page 282 8.3 Grazing Lobes and Pattern Nulls......Page 283 8.3.1 Aperture Admittance Formulation......Page 284 8.3.2 Equivalent Circuit......Page 285 8.3.3 Reflection Loss at Grazing Lobe Condition......Page 286 8.4 Surface and Leaky Waves in an Array......Page 290 8.4.1 Surface Wave......Page 292 8.4.2 Leaky Wave......Page 297 8.4.3 Supergain Phenomenon......Page 299 8.5.1 WAIM: Input Admittance Perspective......Page 301 8.6.1 Potter Horn......Page 306 8.6.2 High-Efficiency Horn......Page 307 8.7 Multimodal Circular Horn Elements......Page 309 Bibliography......Page 311 Problems......Page 312 9.1 Introduction......Page 315 9.2.1 Reflection and Transmission Characteristics......Page 316 9.2.2 Cross-Polarization Performance......Page 320 9.2.3 FSS-Loaded Antenna......Page 322 9.3 Screen Polarizer......Page 325 9.3.2 Meander Susceptance......Page 326 9.3.3 Return Loss and Axial Ratio......Page 327 9.3.4 Scan Characteristics......Page 329 9.4.1 Phase Characteristics......Page 332 9.4.2 Design and Performance......Page 336 9.4.3 Circular Polarization......Page 339 9.4.4 Bandwidth Enhancement......Page 342 9.4.5 Contour-Beam Reflect Array......Page 343 References......Page 344 Problems......Page 345 10.1 Introduction......Page 349 10.2 Layers with Different Periodicities: Rectangular Lattice......Page 350 10.2.1 Patch-Fed Patch Subarray......Page 353 10.3 Nonparallel Cell Orientations: Rectangular Lattice......Page 355 10.3.1 Patch Array Loaded with Screen Polarizer......Page 358 10.4 Layers with Arbitrary Lattice Structures......Page 363 Problems......Page 365 11.1 Introduction......Page 367 11.2 Array Size: Linear Array......Page 368 11.3 Element Size......Page 371 11.4 Pattern Synthesis Using Superposition (Woodward’s Method)......Page 374 11.5.1 Mathematical Foundation......Page 377 11.5.2 Application of GSA for Array Synthesis......Page 378 11.5.3 Phase-Only Optimization......Page 379 11.5.4 Contour Beams Using Phase-Only Optimization......Page 383 11.6 Conjugate Match Algorithm......Page 389 11.7 Successive Projection Algorithm......Page 391 11.7.1 Successive Projection and Conjugate Match......Page 394 11.9 Design Guidelines of a Shaped Beam Array......Page 395 References......Page 396 Problems......Page 397 12.1 Introduction......Page 399 12.3.1 Orthogonal Beams......Page 400 12.3.2 Fourier Transform and Excitation Coefficients......Page 403 12.3.3 FFT Algorithm......Page 405 12.3.4 FFT and Butler Matrix......Page 408 12.3.5 Hybrid Matrix......Page 409 12.3.6 Modified Butler BFN for Nonuniform Taper......Page 410 12.3.7 Beam Port Isolation......Page 412 12.4 Blass Matrix BFN......Page 414 12.5 Rotman Lens......Page 416 12.5.1 Rotman Surface Design......Page 417 12.5.2 Numerical Results......Page 420 12.5.3 Physical Implementation......Page 422 12.5.4 Scattering Matrix......Page 423 12.6 Digital Beam Former......Page 430 12.6.1 Digital Phase Shifter......Page 431 12.6.2 System Characteristics......Page 432 12.7 Optical Beam Formers......Page 433 Bibliography......Page 434 Problems......Page 435 13.1 Introduction......Page 437 13.2 Active Array Block Diagrams......Page 438 13.3.1 Number of Elements and Element Size......Page 440 13.3.2 Radiating Element Design Consideration......Page 442 13.4 Solid State Power Amplifier......Page 443 13.4.1 System Characteristics......Page 444 13.5 Phase Shifter......Page 448 13.6 Intermodulation Product......Page 449 13.6.1 Estimation of SSPA Parameters from IM Data......Page 451 13.6.2 IM Beam Locations......Page 452 13.6.3 Multiple-Channel Array: Noise Power Ratio......Page 453 13.7.1 Antenna Noise Temperature......Page 456 13.7.2 Noise Temperature and Noise Figure of Resistive Circuits......Page 458 13.8 Active Array System Analysis......Page 466 13.9 Active Array Calibration......Page 469 13.9.1 Two-Phase-State Method......Page 470 13.9.2 Multiple-Phase Toggle Method......Page 471 13.9.3 Simultaneous Measurement: Hadamard Matrix Method......Page 472 13.10 Concluding Remarks......Page 473 References......Page 474 Bibliography......Page 475 Problems......Page 477 14.1 Introduction......Page 479 14.2 Array Pattern......Page 480 14.3 Statistics of R and I......Page 481 14.4.1 Central Limit Theorem......Page 485 14.4.3 PDF of R(2)+I(2)......Page 488 14.5 Confidence Limits......Page 493 14.5.1 Beam Peak......Page 495 14.5.3 Nulls......Page 496 14.6 Element Failure Analysis......Page 497 References......Page 501 Problems......Page 502 Appendix......Page 503 Index......Page 507 "This comprehensive book offers an extensive presentation of a new methodology for phased array antenna analysis based on Floquet modal expansion. Engineers, researchers, and advanced graduate students involved in phased array antenna technology will find this systematic presentation an invaluable reference." "Elaborating from fundamental principles, the author presents an in-depth treatment of the Floquet modal based approach. Detailed derivations of the theorems and concepts are provided, making Phased Array Antennas a self-contained work. Each chapter is followed by several practice problems. In addition, numerous design examples and guidelines will be found highly useful by those engaged in the practical application of this new approach to phased array structures." "Incorporating the most recent developments in phased array technology, Phased Array Antennas is an essential resource for students of phased array theory, as well as research professionals and engineers engaged in the design and construction of phased array antennas."--BOOK JACKET Phased Array Antennas presents a new methodology for phased array antenna analysis, based on Floquet modal expansion. It includes recent analytical developments in the phased array arena that have been published in journals and conference proceedings