1. N Element Array θ d

2. Phasor Addition A G M B a
δ/2 δ
nδ/2 nδ
δ=kdsinθ

3. Directivity Index for an n-Element Array

4. Linear Array
Nulls:

5. Piston Array Bessel FunctionD q
Bessel Function
J1(pDsinq/l)
pDsinq/l
J1(pDsinq/l) has zero crossings (nulls) at pDsinq/l = 3.83, 7.02, 10.17, 13.32, 16.47, ....
J1(pDsinq/l) has extremes (side lobes) at pDsinq/l = 1.84, 5.33, 8.54, 11.71, 14.86, ....

6. 2-element array continuous line array circular piston
defining parameters
element separation distance – d
array length – L
array diameter - D
beam pattern function
b() =
directivity index DI
null angles
b() = 0
null
side lobes
b()=1
max
half power angles
b()=0.5
hp
BW=2hp
(only for beam about array axis)

7. Beam width of a piston array