a Matlab package for phased array beam shape inspection

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44 A FIGURES TO CHAPTERS 2–7 1 u y 0 −1 −1 0 1 u x Figure 11: Grating zones of an regular, rectangular plane array. The element spacing is D x = D y = 1.5. The array is phase-steered so that the beam of zone Z(1,0), the solid dot, points to φ = 10.0 ◦ , θ = 60.0 ◦ . The unwrapped phasing angles are δ x = 460.5 ◦ , δ y = 81.2 ◦ .
45 80 60 40 20 θ 0 (°) 0 −20 −40 −60 −80 Z(−1,0) Z(0,0) Z(1,0) Z(2,0) −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 δ / 2π x θ 0 (°) 80 60 40 20 0 −20 −40 −60 −80 Z(2,0) Z(1,0) Z(0,0) Z(−1,0) Z(−2,0) −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 δ / 2π x Figure 12: Beam polar angle as function of the element-to-element phase step. The element spacing is D x = 2.0. In the top panel, the phase step δ x is computed from δ x = 2πD x u x , in the bottom panel, δ x has been shifted to the interval [−π, π[. The beams’ grating zones are also indicated. Note the non-linear dependence of θ 0 on δ x . The top panel is perhaps the better choice when focusing on a single beam when it moves through the full range of pointing directions. The bottom panel instead emphasizes the in fact there are a set of equivalent grating beams, which are all steered simultaneously. The plots were produced by beemsteering.m.
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: 43 E 0 E m û d m P xy ∆ m P u Fi
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 and 56: 55 ARRAY 50×20 1.50×1.50 δx=0.0
Page 57 and 58: 57 ∆X z E p χ P Q ∆Z z r 2 R 2
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

a Matlab package for phased array beam shape inspection

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