Question

What is the direction of first null of broadside 4-element isotropic antenna having a separation of λ/4?

(a) 0

(b) 60

(c) 30

(d) 120

The question was posed to me at a job interview.

I'd like to ask this question from Radiation Pattern for 4-Isotropic Elements topic in section Antenna Array of Antennas

Answer 1

Correct option is (a) 0

Easiest explanation: The nulls of the N- element array is given by

\(θ_n=cos^{-1}⁡(\frac{λ}{2πd} \left[-β±\frac{2πn}{N}\right])=cos^{-1}⁡(\frac{λ}{2πd} \left[±\frac{2πn}{N}\right])\)

\(θ_n=cos^{-1}⁡(\frac{λ}{2π(λ/4)}\left[±\frac{2πn}{N}\right])=cos^{-1} (±\frac{4n}{4})=cos^{-1}(±n)=0\)