Planar Arrays
Figure 1 shows a 
element array with uniform excitation (ten
elements in the x direction an eight
in the y direction). The element
spacing is set to ,
where is free space wavelength. The elements radiate
uniformly in the forward half-plane and have no backwards radiation. In case the
array shows a maximum at and ,
please find:
Figure 1 Geometry of the problem
1. the progressive
phase shift between elements in the x and y directions.
Let ,
where ,
and with
we
obtain:
For the specific case
and
.
Hence,
2. the directivity of the array.
Considering that
the elements radiate uniformly only in the
forward half-plane
(the directivity
will be twice the one of an array with bidirectional elements)
and the
array is large and radiates
nearly
broadside
(for large planar arrays, which are nearly
broadside, the directivity reduces to
,
where
and
are the directivities of broadside linear
arrays, respectively)
3. the position of the grating
lobe (if one exists).
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