
Timed Arrays
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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....System requirements
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