Question 8.18: Compare the directivities of two arrays consisting of three ...

From (8.71), we compute

D = \frac{\left\lgroup\sum\limits_{n = -M}^{M}{I_{n}} \right\rgroup^{2} }{\sum\limits_{n = -M}^{M}{I_{n}^{2}} } (8.71)

(a) Uniform array D =\frac{(1+1+1)^{2}}{1+1+1}=3\Rightarrow D=4.77  dB .

(b) Binomial array D=\frac{(1+2+1)^{2}}{1+4+1}=\frac{16}{6}= 2.667 \Rightarrow D=4.26  dB .

The directivity of a uniform array is greater than that of a binomial array.