N Element Array
description
Transcript of N Element Array
N Element Array
θ
d
d
1 1 max
2 2 max
3 3 max
4 4 max
N N max
22
1 2 max
v Mp t Mp cos k 0 t
v Mp t Mp cos k x t
v Mp t Mp cos k 2 x t
v Mp t Mp cos k 3 x t
v Mp t Mp cos k (N 1) x t
output v v Mp cos t cos t cos 2 t cos 3 t cos (N 1) t
where
k x kdsin
Phasor Addition
A
G
M
Ba
δ/2
δ
nδ/2
nδ
δ=kdsinθ
TOT 0
TOT 0
TOT
cos(k 0 t) cos(k dsin t)v Mp
cos(k 2dsin t) ...cos(k (n 1)dsin t)
cos( t) cos( t ) cos( t 2 ) ...v v
cos( t (n 1) )
v A cos( t )
0
2
V( ) nR sin Where R is distance AP
2 2
sin n2V( ) nV
n sin2
n dsin sin
b( )d
n sin sin
Directivity Index for an n-Element Array
n 1
1
nDI 10log
2 dn sin
21
2 dn
Linear Array
2 2 2n d L L
sin sin sin sin sin sinb( )
d Ld n sin sinn sin sin
Lsinn , n 1,2,3,...
Nulls:
2
0
1 2LDI 10log 10log
b cos d
Piston Array
D
2
1
Dsin2J
bDsin
5 10 15 20
-0.2
0.2
0.4
0.6
J1(Dsin)
Dsin
J1(Dsin) has zero crossings (nulls) at Dsin = 3.83, 7.02, 10.17, 13.32, 16.47, ....J1(Dsin) has extremes (side lobes) at Dsin = 1.84, 5.33, 8.54, 11.71, 14.86, ....
Bessel Function
sincos 2 d
2
sin
sinsin
L
L2
1
sin
sin2
D
DJ
d
d
2
2sin1
2log10
Lfor
2log10
L
Dfor log102
D
... 5, 3, 1, m2
sin
d
m
... 3, 2, 1, m
sin
L
m
0sinJ of roots
... 4.24, 3.24, 2.23, 1.22, z
sin
1
D
Dz
.... 3 2, 1, ,0
sin
md
m
... 4.48, 3.47, 2.46, 1.43, y where
sin
sinsintan
Ly
LL
.... 3.70, 2.68, 1.64, wwhere
sin
D
w
sin4
1,3,5,7,...
hp
n
dn
Lhp
442.0sin Dhp
51.0sin
2-element array continuous line array circular piston
defining parameters element separation distance – d array length – L array diameter - D
beam pattern functionb() =
directivity indexDI
null anglesb() = 0
null
side lobesb()=1max
half power angles b()=0.5
hp
BW=2hp
(only for beam about array axis)
2 4 6 8
0.2
0.4
0.6
0.8
1
Beam width of a piston array
2
1
Dsin2J
b 0.5Dsin
b
Dsin
Dsin1.6
1.6
sin .51D D