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A 4-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)I have been asked this question in my homework.This is a very interesting question from Radiation Pattern for 4-Isotropic Elements in portion Antenna Array of Antennas

Answer»

The correct choice is (a) cos^-1 (±n)

Best explanation: The NULLS of the N- ELEMENT ARRAY is given by

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

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



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