Question

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 1

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

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

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