a Matlab package for phased array beam shape inspection

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56 A FIGURES TO CHAPTERS 2–7 ARRAY 50×20 1.50×1.50 δx=0.0° θ=0.00° W=0.68° ELEMENT JITTER ∆t=1000 ps ∆ψ=81.0° ∆a/a=20.1% ∆AF=−64.5%±1.9 ∆θ=−0.001°±0.025 ∆W=−0.001°±0.018 20 (a) Beam amplitude jitter 20 (b) Beam direction jitter % / bin 10 % / bin 10 0 −70 −65 −60 ∆ AF [%] max 0 −0.05 0 0.05 ∆θ [°] 20 (c) Beam width jitter % / bin 10 0 −0.05 0 0.05 ∆W [°] Figure 24: Jitter simulation 4. Simulated array factor jitter in a 50 × 20 element array in x-direction, when element timing jitter is ∆t = 1000 ps, the corresponding element phase jitter 81 ◦ , and the element amplitude jitter is 20% around 1. The undistorted beam has been directed in vertical direction, and has half-power width of 0.68 ◦ in the x-direction.
57 ∆X z E p χ P Q ∆Z z r 2 R 2 R 1 TA ɛ L r 1 VHF x Figure 25: TA: Geometry for computing the effective volume. We make two simplifications to the actual geometry. First, we assume flat Earth. Second, we assume that the VHF antenna rotation axes is along the y-axis in the figure, that is, perpendicular to the line from TA to the VHF antenna, which is our x-axis. The effective volume is computed using Eq. (96). Q is the center point of the common volume. P is a point in the computation grid. The angle χ is the angle between the polarization vector and the direction of the scattered wave. We did, by oversight, take χ to be constant over the whole computation grid. We did let the distances r 1 and r 2 to vary in the proper way, though.
Page 1 and 2:
E3ANT A Matlab Package for Phased A
Page 3 and 4:
List of Figures 1. Beam steering. .
Page 5 and 6: 5 2. Time steering and phase steeri
Page 7 and 8: 2.2 Monochromatic signals—time-st
Page 9 and 10: 3.1 Transmission 9 lobes have equal
Page 11 and 12: 3.2 Reception 11 current I goes via
Page 13 and 14: 3.2 Reception 13 equations. But fir
Page 15 and 16: 15 “losing sensitivity” (due) t
Page 17 and 18: 4.2 Array factor as 2-D discrete Fo
Page 19 and 20: 4.6 Parseval’s theorem 19 closed
Page 21 and 22: 4.9 The power integral for an array
Page 23 and 24: 4.12 Computing the antenna directiv
Page 25 and 26: 4.14 2-D beam cross section 25 or m
Page 27 and 28: 5.1 Timing accuracy versus pointing
Page 29 and 30: 6.1 Method 29 excitation amplitudes
Page 31 and 32: 31 electric field and the scatterin
Page 33 and 34: 33 Table 1: Predicting SNR for the
Page 35 and 36: 35 s(t, r; û) E p û û 0 0 R m
Page 37 and 38: 37 D=1.0; θ 0 = 60, θ g = −8, 6
Page 39 and 40: 39 (a) (b) (c) (d) Figure 5: Random
Page 41 and 42: 41 A + Z 2 I A Z 1 B + Z 3 V V (B)
Page 43 and 44: 43 E 0 E m û d m P xy ∆ m P u Fi
Page 45 and 46: 45 80 60 40 20 θ 0 (°) 0 −20
Page 47 and 48: 47 10 Beam width (°) 9 8 7 6 5 4 M
Page 49 and 50: 49 Y X Figure 17: A 3D view of an a
Page 51 and 52: 51 45 40 Directivity (dBi) 35 30 25
Page 53 and 54: 53 ARRAY 50×20 1.50×1.50 δx=0.0
Page 55: 55 ARRAY 50×20 1.50×1.50 δx=0.0
Page 59 and 60: 0.02 59 12×4 1.4×1.4 φ 0 =0.0°
Page 61 and 62: 61 V eff for a long pulse (km 3 ) V
Page 63 and 64: 63 V eff for a long pulse (km 3 ) V
Page 65 and 66: 65 B. Pointing geometry The functio
Page 67 and 68: 67 KIRUNA Lat=67.86 Lon=20.44 Hgt=0
Page 69: 69 C. Matlab functions There are tw
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a Matlab package for phased array beam shape inspection

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