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The array factor of 8 – isotropic elements of broadside array separated by a λ/2 is given by ____(a) sinc(4cosθ)(b) sin(2πcosθ)(c) sinc(4πsinθ)(d) sin(2sinθ)This question was addressed to me in an international level competition.Enquiry is from Radiation Pattern of 8-Isotropic Elements in division Antenna Array of Antennas

Answer» CORRECT answer is (a) SINC(4cosθ)

Easiest explanation: Normalized ARRAY factor is given by \(AF=\frac{sin(Nᴪ/2)}{N \frac{ᴪ}{2}}\)

And ᴪ=kdcosθ+β

Since its given BROAD side array β=0,

ᴪ=kdcosθ+β=kdcosθ

\(\frac{Nᴪ}{2}=4kdcosθ=4(\frac{2π}{λ})(\frac{λ}{2})cosθ=4πcosθ \)

\(AF=\frac{sin(Nᴪ/2)}{N \frac{ᴪ}{2}}=\frac{sin(4πcosθ)}{4πcosθ}=sinc(4cosθ).\)


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