Question

What will be the array factor in polynomial form for the 3 element binomial array if Z=e^(-iᴪ)?

(a) 1+2z+z^2

(b) 1+3z+3z^2+z^3

(c) 1+2z+3z^2+z^3

(d) 1+3z+z^2

I got this question in an interview for job.

This key question is from Binomial Array in portion Phased, Adaptive and Binomial Arrays of Antennas

Answer 1

Correct choice is (a) 1+2z+z^2

To explain I would say: The array factor AF = (1+z)^N-1  and N is number of elements.

AF = (1+z)^3-1 = (1+z)^2 = 1+2z+z^2

Binomial array follows the Pascal’s triangle coefficients