Timed Arrays

RANDY HAUPT, PhD, is professor and department head of EECS at the Colorado School of Mines. Prior to that, he was an RF staff consultant at Ball Aerospace & Technologies, Corp., senior scientist and department head at the Applied Research Laboratory of Penn State, professor and department head of ECE at Utah State, professor and chair of EE at the University of Nevada Reno, and professor of EE at the USAF Academy. Dr. Haupt was the Federal Engineer of the Year in 1993 and is a Fellow of the IEEE and the Applied Computational Electromagnetics Society (ACES). He received his PhD from the University of Michigan and retired from the USAF as a Lt. Col. after starting his career as a lieutenant graduating from the USAF Academy.

• List of Figures xPreface xix1 Timed and Phased Array Antennas 11.1 Large Antennas 11.2 Collection of Elements 31.3 Overview of an Array Architecture 61.4 Transient Versus Steady State 71.5 Time Versus Phase 71.6 Book Overview 8References 92 RF Signals 102.1 The Carrier and Modulation 102.2 Noise and Interference 122.3 Polarization 152.4 Signal Bandwidth 17Reference 183 Arrays of Point Sources 193.1 Point Sources 193.2 Far Field 203.3 Array Sampling in the Time Domain 213.4 Array Sampling in the Frequency Domain 223.5 Grating Lobes: Spatial Aliasing 233.6 Subarrays and Panels 263.7 Electronic Beam Steering 293.8 Amplitude Weighting 313.8.1 Dolph–Chebyshev Taper 323.8.2 Taylor Tapers 333.8.3 Bayliss 343.9 Thinned Arrays 36References 394 Elements in Timed Arrays 414.1 Element Characteristics 414.1.1 Polarization 424.1.2 Impedance 434.1.3 Phase center 444.1.4 Conformal 444.1.5 Size 444.1.6 Directivity 454.1.7 Bandwidth 454.1.8 Balun 454.2 Elements 464.2.1 Dipole Array 464.2.2 Patch Array 474.2.3 Spiral Array 504.2.4 Helical Array 524.2.5 Tapered Slot Antenna (TSA) Array 534.2.6 Tightly Coupled Arrays 554.2.7 Fragmented Arrays 624.3 Mutual Coupling 634.4 Element Dispersion 664.5 Scaled Arrays 684.6 Interleaved Arrays 70References 755 Array Beamforming 785.1 PCB Transmission Lines 785.2 S‐parameters 815.3 Matching Circuits 825.4 Corporate Feeds 825.5 Distributed Versus Centralized Amplification 835.6 Blass Matrix 845.7 Butler Matrix 855.8 Lenses 865.9 Reflectarrays 895.10 Digital Beamforming 91References 936 Active Electronically Scanned Array Technology 956.1 Semiconductor Technology for T/R Modules 966.2 T/R Module Layout 986.3 Amplifiers 1006.4 Switches 1096.5 Phase Shifter 1146.6 Attenuators 1206.7 Limiter 1216.8 Circulator 1216.9 Correcting Errors through Calibration and Compensation 121References 1237 Time Delay in a Corporate‐Fed Array 1267.1 Pulse Dispersion 1287.2 Phased Array Bandwidth 1307.3 Time Delay Steering Calculations 1337.4 Time Delay Units 1357.5 Unit Cell Constraints 1387.6 Time Delay Bit Distribution at the Subarray Level 141References 1478 Adaptive Arrays 1498.1 Signal Correlation Matrix 1508.2 Optimum Array Weights 1528.3 Adaptive Weights Without Inverting the Correlation Matrix 1548.4 Algorithms for Nondigital Beamformers 1558.4.1 Partial Adaptive Nulling 1568.4.2 Adaptive Nulling with Weight Constraints 1588.4.3 Adaptive Nulling with Cancellation Beams 1598.5 Reconfigurable Arrays 1608.6 Reconfigurable Elements 1658.7 Time‐Modulated Arrays 1678.8 Adaptive Thinning 1728.9 Other Adaptive Array Alternatives 1778.9.1 Beam Switching 1788.9.2 Direction Finding 1788.9.3 Retrodirective Array 1818.9.4 MIMO 181References 184List of Symbols and Abbreviations 188Index 194