Question

The direction of nulls for end-fire array of N –Isotropic sources separated by λ/4 is given by ____

(a) \(θ_n=cos^{-1}⁡([∓1±\frac{4n}{N}])\)

(b) \(θ_n=sin^{-1}⁡([∓1±\frac{4n}{N}])\)

(c) \(θ_n=cos^{-1}⁡([∓1±\frac{2n}{N}])\)

(d) \(θ_n=cos^{-1}⁡([∓1±\frac{n}{N}])\)

I got this question in final exam.

This key question is from Array of N-Isotropic Sources in chapter Antenna Array of Antennas

Answer 1

Right answer is (a) \(θ_n=cos^{-1}⁡([∓1±\frac{4n}{N}])\)

Explanation: 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 \(β=±kd=±\frac{2πd}{λ}=±\frac{π}{2},\)

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

\(θ_n=cos^{-1}⁡([∓1±\frac{4n}{N}])\)