Question

An 8-isotropic element end-fire array separated by a λ/4 distance has first null occurring at ____

(a) 60

(b) 30

(c) 90

(d) 150

I have been asked this question at a job interview.

Question is from Radiation Pattern of 8-Isotropic Elements in division Antenna Array of Antennas

Answer 1

Right answer is (a) 60

To explain: The nulls of the N- element array is given by \(θ_n=cos^{-1}⁡(\frac{λ}{2πd} [-β±\frac{2πn}{N}])\)

Since its given broad side array \(β=±kd=±\frac{2πd}{λ}=±\frac{π}{2},\)

\(θ_n=cos^{-1}⁡(\frac{2}{π} [∓\frac{π}{2}±\frac{2πn}{8}])\)

\(=cos^{-1}⁡([∓1±\frac{n}{2}])\)

First null at n=1; \(θ_n= =cos^{-1}⁡([1±\frac{1}{2}]) (considering \,β=-\frac{π}{2}) \)

\(θ_n =cos^{-1} (\frac{1}{2})\,or \,cos^{-1} (3/2) \)

\(θ_n =cos^{-1} (\frac{1}{2})=60.\)