Question

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 1

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

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

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