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The array factor of 4- isotropic elements of broadside array separated by a λ/4 is given by ____________(a) sinc(cosθ)(b) cos(sinθ)(c) sin(sinθ)(d) sin(cosθ)I had been asked this question by my school principal while I was bunking the class.This question is from Radiation Pattern for 4-Isotropic Elements topic in section Antenna Array of Antennas

Answer» CORRECT option is (a) SINC(cosθ)

The 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

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

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


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