Phased Arrays - MATLAB Simulations for Radar Systems Design - page 324

Figure 8.5d. Three-dimensional plot for the radiation pattern in Fig. 8.5a.

Solving for ψ yields

λ m
d

 

-------

ψ m = asin ± ; m = 012… ,,,

(8.38)

 

where the subscript is used as a maxima indicator. The first maximum
occurs at , and is denoted as the main beam (lobe). Other maxima
occurring at are called grating lobes. Grating lobes are undesirable and
must be suppressed. The grating lobes occur at non-real angles when the abso-
lute value of the arc-sine argument in Eq. (8.38) is greater than unity; it follows
that . Under this condition, the main lobe is assumed to be at
(broadside array). Alternatively, when electronic beam steering is considered,
the grating lobes occur at

m

ψ 0 =

m

0

≥ 1

d < λ ψ = 0

λ n
d

------

sin ψ – sin ψ 0 = ± ; n = 12… ,,

(8.39)

Thus, in order to prevent the grating lobes from occurring between ± 90° , the

element spacing should be d < λ 2 ⁄ .

The radiation pattern attains secondary maxima (sidelobes) when the numer-
ator of Eq. (8.35) is maximum, or equivalently