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What is the direction of first null of broadside 8-element isotropic antenna having a separation of λ/2?(a) 60°(b) 75.5°(c) 37.5°(d) 57.5°The question was asked in a national level competition.This intriguing question comes from Radiation Pattern of 8-Isotropic Elements in division Antenna Array of Antennas

Answer»

Correct answer is (B) 75.5°

For explanation I would say: The nulls of the N- element array is GIVEN by

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

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

⇨ \(n=1 (FIRST \,null) cos^{-1} (±\frac{n}{4})=cos^{-1} (±\frac{1}{4})=75.5°. \)



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