Timed Arrays
Wideband and Time Varying Antenna Arrays
Published on 20. April 2015
224 pages
978-1-119-07191-4 (ISBN)
Description
Introduces timed arrays and design approaches to meet the newhigh performance standards
The author concentrates on any aspect of an antenna array thatmust be viewed from a time perspective. The first chapters brieflyintroduce antenna arrays and explain the difference between phasedand timed arrays. Since timed arrays are designed for realistictime-varying signals and scenarios, the book also reviews widebandsignals, baseband and passband RF signals, polarization and signalbandwidth. Other topics covered include time domain, mutualcoupling, wideband elements, and dispersion. The author alsopresents a number of analog and digital beamforming networks forcreating and manipulating beams. The book concludes with anoverview of the methods to integrate time delay into the arraydesign and of several other adaptive arrays that prove useful inmany different systems.
* Examines RF signal concepts such as polarization and signalbandwidth and their applications to timed antenna arrays
* Covers arrays of point source, elements in timed antennaarrays, active electronically scanned array technology, and timedelay in corporate fed arrays
* Includes complete design examples for placing time delay inarrays
Timed Arrays: Wideband and Time Varying Antenna Arrays iswritten for practicing engineers and scientists in wirelesscommunication, radar, and remote sensing as well as graduatestudents and professors interested in advanced antenna topics.
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05/2015
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Person
Randy Haupt, PhD., is Professor and Department Head of EECS at the Colorado School of Mines. He received his PhD from the University of Michigan and retired from the USAF as a LtCol. Dr. Haupt 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 is a Fellow of the IEEE and Applied Computational Electromagnetics Society (ACES).
Content
List of Figures x
Preface xix
1 Timed and Phased Array Antennas 1
1.1 Large Antennas 1
1.2 Collection of Elements 3
1.3 Overview of an Array Architecture 6
1.4 Transient Versus Steady State 7
1.5 Time Versus Phase 7
1.6 Book Overview 8
References 9
2 RF Signals 10
2.1 The Carrier and Modulation 10
2.2 Noise and Interference 12
2.3 Polarization 15
2.4 Signal Bandwidth 17
Reference 18
3 Arrays of Point Sources 19
3.1 Point Sources 19
3.2 Far Field 20
3.3 Array Sampling in the Time Domain 21
3.4 Array Sampling in the Frequency Domain 22
3.5 Grating Lobes: Spatial Aliasing 23
3.6 Subarrays and Panels 26
3.7 Electronic Beam Steering 29
3.8 Amplitude Weighting 31
3.8.1 Dolph-Chebyshev Taper 32
3.8.2 Taylor Tapers 33
3.8.3 Bayliss 34
3.9 Thinned Arrays 36
References 39
4 Elements in Timed Arrays 41
4.1 Element Characteristics 41
4.1.1 Polarization 42
4.1.2 Impedance 43
4.1.3 Phase center 44
4.1.4 Conformal 44
4.1.5 Size 44
4.1.6 Directivity 45
4.1.7 Bandwidth 45
4.1.8 Balun 45
4.2 Elements 46
4.2.1 Dipole Array 46
4.2.2 Patch Array 47
4.2.3 Spiral Array 50
4.2.4 Helical Array 52
4.2.5 Tapered Slot Antenna (TSA) Array 53
4.2.6 Tightly Coupled Arrays 55
4.2.7 Fragmented Arrays 62
4.3 Mutual Coupling 63
4.4 Element Dispersion 66
4.5 Scaled Arrays 68
4.6 Interleaved Arrays 70
References 75
5 Array Beamforming 78
5.1 PCB Transmission Lines 78
5.2 S-parameters 81
5.3 Matching Circuits 82
5.4 Corporate Feeds 82
5.5 Distributed Versus Centralized Amplification 83
5.6 Blass Matrix 84
5.7 Butler Matrix 85
5.8 Lenses 86
5.9 Reflectarrays 89
5.10 Digital Beamforming 91
References 93
6 Active Electronically Scanned Array Technology 95
6.1 Semiconductor Technology for T/R Modules 96
6.2 T/R Module Layout 98
6.3 Amplifiers 100
6.4 Switches 109
6.5 Phase Shifter 114
6.6 Attenuators 120
6.7 Limiter 121
6.8 Circulator 121
6.9 Correcting Errors through Calibration and Compensation 121
References 123
7 Time Delay in a Corporate-Fed Array 126
7.1 Pulse Dispersion 128
7.2 Phased Array Bandwidth 130
7.3 Time Delay Steering Calculations 133
7.4 Time Delay Units 135
7.5 Unit Cell Constraints 138
7.6 Time Delay Bit Distribution at the Subarray Level 141
References 147
8 Adaptive Arrays 149
8.1 Signal Correlation Matrix 150
8.2 Optimum Array Weights 152
8.3 Adaptive Weights Without Inverting the Correlation Matrix 154
8.4 Algorithms for Nondigital Beamformers 155
8.4.1 Partial Adaptive Nulling 156
8.4.2 Adaptive Nulling with Weight Constraints 158
8.4.3 Adaptive Nulling with Cancellation Beams 159
8.5 Reconfigurable Arrays 160
8.6 Reconfigurable Elements 165
8.7 Time-Modulated Arrays 167
8.8 Adaptive Thinning 172
8.9 Other Adaptive Array Alternatives 177
8.9.1 Beam Switching 178
8.9.2 Direction Finding 178
8.9.3 Retrodirective Array 181
8.9.4 MIMO 181
References 184
List of Symbols and Abbreviations 188
Index 194
LIST OF FIGURES
Chapter 1
1.1 (a) Green Bank Telescope reflector [4] (Courtesy of NRAO). (b) PAVE PAWS radar [5] (Courtesy of BMDO). 1.2 Four different geometrical layouts of an array: (a) linear array, (b) planar array, (c) conformal array, and (d) random array. 1.3 Concept of an antenna phase center. 1.4 Three different element lattices and corresponding unit cells. 1.5 Generic array architecture. 1.6 Two signals adding in and out of phase. 1.7 Pulse dispersion: (a) Two identical pulses (coherent) added together. (b) Two identical pulses (not coherent) that start at different times added together. (c) Two identical pulses (coherent) that start at different times are added together.Chapter 2
2.1 A stream of bits corresponds to a signal amplitude. The baseband signal modulates the carrier. Examples of OOK, BPSK, and QPSK are shown here. 2.2 OOK, BPSK, and QPSK with an SNR of 10?dB. 2.3 Pulse dispersion or spreading occurs when high frequencies are attenuated. 2.4 When the direct and attenuated reflected signal add together, the pulse is dispersed. 2.5 Wave polarization. 2.6 CP Gaussian pulse.Chapter 3
3.1 Antenna far field definition. 3.2 Plane wave incident on linear array. 3.3 Array sampling of plane wave from broadside and endfire directions (a) ?s?=?0°, (b) ?s?=?90°, and (c) ?s arbitrary. 3.4 Directivity of a linear uniform array as a function of element spacing for five different array sizes. 3.5 Directivity of a 10 × 10 planar uniform array as a function of element spacing for square and triangular element lattices. 3.6 Power of 2 subarrays in a linear array. 3.7 Beam squint as a function of frequency and steering angle. 3.8 Beam squint associated with a 32-element phased array when the main beam is steered to 60° at the center frequency. 3.9 Array factors at the center, high, and low frequencies of a 32-element timed array when the main beam is steered to 60°. 3.10 Beam steering a 32-element array to 60°: (a) time delay (b) time delay translated into phase at three frequencies. 3.11 Amplitude weights for a 30?dB Chebyshev taper. 3.12 Array factor for a 30?dB Chebyshev taper. 3.13 Amplitude weights for a 30?dB =5 Taylor taper. 3.14 Array factor for a 30?dB =5 Taylor taper. 3.15 Amplitude weights for a 30?dB =5 Bayliss taper. 3.16 Array factor for a 30?dB =5 Bayliss taper. 3.17 25?dB Taylor taper for the 64?×?64 planar array. 3.18 64?×?64 element array thinned to get a 25?dB =5 Taylor taper. 3.19 Solid line is an array factor cut of the 64?×?64 element array thinned to get a 25?dB =5 Taylor pattern. The dashed line is a cut from the desired low sidelobe pattern. The dotted line is the rms average sidelobe level predicted by (3.49). 3.20 Photograph of the random arrangement of elements in the LWA1 array. Reprinted by permission of Ref. [21]; © 2013 IEEE.Chapter 4
4.1 Combining two linear polarized elements to get circular polarization (in this case, LHCP). 4.2 Four linearly polarized patches are rotated and phased to get circular polarization: (a) phasing and placement for limited scan and (b) phasing and placement for wide scan. 4.3 (a) Four linearly polarized broadband horns are rotated and phased to get circular polarization. (b) Measured (dotted) and calculated (solid) pulses transmitted by array at boresight. Reprinted by permission of Ref. [3]; © 2010 IEEE. 4.4 Currents on a coax-fed dipole antenna. 4.5 Dipole type antennas: (a) thin dipole, (b) monopole, (c) fat dipole, (d) bicone, (e) bicone with spherical caps, and (f) ellipsoidal. 4.6 Bent wire dipole element in the LWA1 array. Reprinted by permission of Ref. [9]; © 2013 IEEE. 4.7 Dipole arrays. (a) Dipoles in MERA array. (Courtesy of the National Electronics Museum) [5] © 2013 Wiley. (b) Crossed dipoles in HAARP array (Courtesy Michael Kleiman, US Air Force) [12]. 4.8 8?×?8 planar array of patches. 4.9 Broadband patch antennas: (a) coplanar and (b) stacked. 4.10 Examples of spiral antennas: (a) 2 arm Archimedes [5] © 2010, (b) two-arm logarithmic spiral. Reprinted by permission of Ref. [21]; © 2009 IEEE, and (c) conical log spiral [22] © 2010. 4.11 Photograph of the (a) front and (b) side views of a sinuous antenna. Reprinted by permission of Ref. [25]; © 2004 IEEE. 4.12 Geometry of a 4?×?4 helical array. Reprinted by permission of Ref. [27]; © 2010 IEEE. 4.13 (a) Exploded view of the stripline notch element and (b) linear array of five elements. Reprinted by permission of Ref. [31]; © 2000 IEEE. 4.14 Antipodal TSA. 4.15 Measured cross-pol and co-pol patterns of an 8?×?8 planar array for broadside scan and the center element co-pol pattern. Reprinted by permission of Ref. [31]; © 2000 IEEE. 4.16 Measured versus calculated (FDTD) VSWR of planar arrays at (a) broadside scan, (b) E-plane 50 scan, and (c) H-plane 50 scan. Reprinted by permission of Ref. [31]; © 2000 IEEE. 4.17 A 324-element dual-polarized TSA array. Reprinted by permission of Ref. [34]; © 2012 IEEE. 4.18 The BOR element array is 16?×?9?cm. Reprinted by permission of Ref. [35]; © 2007 IEEE. 4.19 Diagram of a PUMA array: (a) Top view of dipole layer; (b) crosssectional view of a unit-cell, showing the location where a module split occurs; and (c) isometric view of a PUMA module with exploded dielectric cover layers. Reprinted by permission of Ref. [38]; © 2012 IEEE. 4.20 Three 8?×?8 PUMA modules. Reprinted by permission of Ref. [39]; © 2013 IEEE. 4.21 Broadside VSWR of three dual-polarized PUMA arrays: (a) 5?GHz maximum frequency. (b) 21?GHz maximum frequency. (c) 45?GHz maximum frequency. (d) Models of the PUMAv2 (left) and the PUMAv3 (right) compared to a penny. Reprinted by permission of Ref. [39]; © 2013 IEEE. 4.22 8?×?8 element array of overlapping dipoles above a ground plane. Reprinted by permission of Ref. [40]; © 2012 IEEE. 4.23 (a) Unit cell of a tightly coupled bowtie array with resistive FSS and superstrate and (b) top view of unit cell (dimensions in mm). Reprinted by permission of Ref. [41]; © 2012 IEEE. 4.24 Unit cell of a fragmented array. Reprinted by permission of Rf. [42]; © 2011 IEEE. 4.25 VSWR of fragmented element in planar array....