Question

An 8-isotropic element broadside array separated by a λ/4 distance has nulls occurring at ____

(a) cos^-1(±n)

(b) \(cos^{-1} (±\frac{n}{2})\)

(c) \(sin^{-1} (±\frac{n}{2})\)

(d) \(sin^{-1} (±n)\)

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Answer 1

Correct answer is (b) \(cos^{-1} (±\frac{n}{2})\)

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

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

⇨ \(θ_n=cos^{-1}⁡(\frac{λ}{2π(λ/4)}) [±\frac{2πn}{N}])=cos^{-1} (±\frac{4n}{8})=cos^{-1} (±\frac{n}{2})  [n=1,2,3 \,and\, n≠N,2N…]\)