a Matlab package for phased array beam shape inspection

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34 A FIGURES TO CHAPTERS 2–7 A. Figures to Chapters 2–7 Listing of the figures the is on p. 3. There are a few more figures in this compilation than are referred to in the main text. Also, there are considerable amount of details, both in the figures and in their captions, that are not handled elsewhere in the notes. For many of figures we indicate the Matlab m-files in the e3ant package that were used to generate them.
35 s(t, r; û) E p û û 0 0 R m ∑ { s m (t, û)∝ s(t, R m ; û) T m (û 0 ) 1 2 m M Ψm (û 0 , ¯ω) { a m a m s m (t − T, û) TS PS a m s m (t, û) e −iΨm z(t, û, û 0 ) TS { z(t, û, û 0 , ¯ω) PS Figure 1: Beam steering, reception view in the continuous-time domain. A far-away point source in direction û produces time- and space varying incoming electric field s(t, r, û)E p near the antenna array of M elements. The vector E p is taken to be complex-valued to represent polarization; it may depend on the direction û, but not on the position r or the time t. The elements sniff the incoming field at points R m so that a (complex-valued, to represent the polarization) voltage s m (t) is generated across the terminals of element m. This voltage is amplified by a real factor a m and fed to the beam-former system, which may be either a time-steering system (TS) or a phase-steering system (PS). In the TS system, the signal a m s m at element m is delayed by an amount T m which depends on the element position and the desired steering direction û 0 , before being fed to an adder which produces the final beam-formed signal z(t). In the PS version of the beam-former, there is no explicit delaying, but instead the phase of a m s m (t) is adjusted by an angle Ψ m , computed from the element position, the desired beam direction, and the average frequency ¯ω of the incoming pulse. The figure represents the array elements by semi-spheres to suggest an isotropic element gain in the upper half-sphere. When desired, a non-isotropic √ element power gain g E can be explicitly incorporated by replacing a m by a m gE (û).
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: 33 Table 1: Predicting SNR for the
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 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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