a Matlab package for phased array beam shape inspection
a Matlab package for phased array beam shape inspection a Matlab package for phased array beam shape inspection
36 A FIGURES TO CHAPTERS 2–7 D=0.1; θ = 60, θ = 60 0 g 90 1.5 120 60 1 150 30 0.5 180 0 Directivity 1.16 1.14 1.12 1.1 1.08 210 330 1.06 1.04 240 270 300 1.02 0 20 40 60 80 100 elevation polar angle (a) (b) 150 D=0.4; θ =60, θ = 60 0 g 90 2.5 120 60 2 1.5 1 30 2.5 2.4 2.3 2.2 0.5 180 0 Directivity 2.1 2 1.9 210 330 1.8 1.7 240 270 300 1.6 0 20 40 60 80 100 elevation polar angle (c) (d) Figure 2: Gain pattern and directivity of an vertical array of two isotropic elements. Panels (a) and (b) are for element separation d = 0.1λ, panels (c) and (d) are for d = 0.4λ. The beam steering in panels (a) and (c) has been to 60 ◦ from boresight (horizontal beam). The 3D gain pattern is obtained from the curves shown by rotating them around the vertical axis, which is also the direction of the array axis. The polar plots are labeled by the beam elevation angle, and the gain is in absolute units. Both of these arrays are dense (D < 0.5λ), so there are no grating lobes apart the main lobe, but there nevertheless is a rather well-developed ordinary side lobe in (c).
37 D=1.0; θ 0 = 60, θ g = −8, 60 120 90 2 1.5 60 3 2.8 2.6 150 1 30 2.4 0.5 180 0 Directivity 2.2 2 1.8 210 330 1.6 1.4 1.2 240 270 300 1 0 20 40 60 80 100 elevation polar angle (a) (b) d / λ = 1.8; θ 0 =60 ° , θ g = −53 ° −14 ° 18 ° 60 ° 90 2 120 60 1.5 150 1 30 0.5 180 0 Directivity 2.25 2.2 2.15 2.1 2.05 2 210 330 1.95 1.9 1.85 240 270 300 1.8 0 20 40 60 80 100 Elevation (c) (d) Figure 3: Gain pattern and directivity of an vertical array of two isotropic elements. Panels (a) and (b) are for element separation d = 1.0λ, panels (c) and (d) are for d = 1.8λ. The beam steering in panels (a) and (c) has been to 60 ◦ from boresight (horizontal). The 3D gain pattern is obtained from the curves shown by rotating them around the vertical axis, which is also the direction of the array axis. The polar plots are labeled by the beam elevation angle, and the gain is in absolute units. In (a), there are two grating lobes and one ordinary, but large, side-lobe, while in (c), all the lobes have equal directivity, and are grating lobes.
- 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: 35 s(t, r; û) E p û û 0 0 R m
- 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 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
37<br />
D=1.0; θ 0<br />
= 60, θ g<br />
= −8, 60<br />
120<br />
90<br />
2<br />
1.5<br />
60<br />
3<br />
2.8<br />
2.6<br />
150<br />
1<br />
30<br />
2.4<br />
0.5<br />
180 0<br />
Directivity<br />
2.2<br />
2<br />
1.8<br />
210<br />
330<br />
1.6<br />
1.4<br />
1.2<br />
240<br />
270<br />
300<br />
1<br />
0 20 40 60 80 100<br />
elevation polar angle<br />
(a)<br />
(b)<br />
d / λ = 1.8; θ 0<br />
=60 ° , θ g<br />
= −53 ° −14 ° 18 ° 60 °<br />
90<br />
2<br />
120<br />
60<br />
1.5<br />
150<br />
1<br />
30<br />
0.5<br />
180 0<br />
Directivity<br />
2.25<br />
2.2<br />
2.15<br />
2.1<br />
2.05<br />
2<br />
210<br />
330<br />
1.95<br />
1.9<br />
1.85<br />
240<br />
270<br />
300<br />
1.8<br />
0 20 40 60 80 100<br />
Elevation<br />
(c)<br />
(d)<br />
Figure 3: Gain pattern and directivity of an vertical <strong>array</strong> of two isotropic elements.<br />
Panels (a) and (b) are <strong>for</strong> element separation d = 1.0λ, panels (c) and (d) are<br />
<strong>for</strong> d = 1.8λ. The <strong>beam</strong> steering in panels (a) and (c) has been to 60 ◦ from<br />
boresight (horizontal). The 3D gain pattern is obtained from the curves shown<br />
by rotating them around the vertical axis, which is also the direction of the<br />
<strong>array</strong> axis. The polar plots are labeled by the <strong>beam</strong> elevation angle, and the<br />
gain is in absolute units. In (a), there are two grating lobes and one ordinary,<br />
but large, side-lobe, while in (c), all the lobes have equal directivity, and are<br />
grating lobes.
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