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The array factor of 8- isotropic elements of broadside array separated by a λ/4 is given by ____(a) sinc(cosθ)(b) cos(sinθ)(c) sin(sinθ)(d) sinc(2cosθ)This question was posed to me during an online exam.My question is based upon Radiation Pattern of 8-Isotropic Elements topic in portion Antenna Array of Antennas

Answer»

The correct choice is (d) sinc(2cosθ)

The explanation is: 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

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

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



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