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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) \(sin^{-1} (±n)\)The question was asked in an interview for job.This is a very interesting question from Radiation Pattern of 8-Isotropic Elements topic in portion Antenna Array of Antennas

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

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

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

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



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