Question

The direction of nulls for broadside array of N –Isotropic sources is given by _____

(a) \(cos^{-1}⁡([±\frac{nλ}{Nd}])\)

(b) \(cos^{-1}⁡([±\frac{2nλ}{Nd}])\)

(c) \(cos^{-1}⁡([±\frac{2πnλ}{2Nd}])\)

(d) \(cos^{-1}⁡([±\frac{nλ}{Nd}])\)

The question was posed to me in a national level competition.

My enquiry is from Array of N-Isotropic Sources in portion Antenna Array of Antennas

Answer 1

Right choice is (a) \(cos^{-1}⁡([±\frac{nλ}{Nd}])\)

The explanation is: 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

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