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

Answer»

Right CHOICE is (a) sinc(2cosθ)

Best 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

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

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



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