Question

The array factor of 8 – isotropic elements of broadside array is given by ____

(a) \(\frac{sin(2kdcosθ)}{2kdcosθ} \)

(b) \(\frac{sin(4kdcosθ)}{4kdcosθ} \)

(c) \(\frac{sin(2kdcosθ)}{kdcosθ} \)

(d) \(\frac{cos(2kdcosθ)}{2kdcosθ} \)

The question was asked in an internship interview.

The question is from Radiation Pattern of 8-Isotropic Elements topic in chapter Antenna Array of Antennas

Answer 1

Correct choice is (b) \(\frac{sin(4kdcosθ)}{4kdcosθ} \)

The best I can explain: Normalized array factor is given by \(AF=\frac{sin(Nᴪ/2)}{N \frac{ᴪ}{2}}\)

And ᴪ=kdcosθ+β

Since its given broad side arrayβ=0,

ᴪ=kdcosθ+β=kdcosθ

\(\frac{Nᴪ}{2}=4kdcosθ\)

\(AF=\frac{sin(Nᴪ/2)}{N \frac{ᴪ}{2}}=\frac{sin(4kdcosθ)}{4kdcosθ} \)