Question

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 1

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

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

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