Question

The direction of first null of the broadside array of N-Isotropic sources is _____

(a) \(cos^{-1}([±\frac{λ}{Nd}])\)

(b) \(cos^{-1}⁡([±\frac{πλ}{Nd}])\)

(c) \(cos^{-1}⁡([±\frac{2πλ}{Nd}])\)

(d) \(cos^{-1}⁡([±\frac{λ}{2Nd}])\)

I have been asked this question at a job interview.

Enquiry is from Array of N-Isotropic Sources topic in chapter Antenna Array of Antennas

Answer 1

The correct answer is (a) \(cos^{-1}([±\frac{λ}{Nd}])\)

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

Given it’s a broadside array so β=0 and n=1 for first null

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