Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 51

Letting = exp (j ), we can write the array factor of an equally spaced array as a polynomial, A( ), in , and many characteristics of the array pattern can be estimated by examining the distribution of the zeros of the array polynomial on a unit circle. In general, an N -element linear array has N - 1 zeros, 0m (m = 1,2,..., N - 1), distributed around the unit circle. Find A( ) and locate all 0m on a unit circle for the following linear arrays:
a) a two-element array,
b) a three-element binomial array,
c) a five-element uniform array,
d) a five-element array having amplitude ratios 1:2:3:2:1 (as in Example 11-9).
e) Based on the locations of 0m for the two arrays in parts (c) and (d), explain why the pattern for the array in part (d) has lower sidelobes but a wider beamwidth.