Question

The Half-power beam width of the N-element isotropic source array can be known when _____

(a) \(ᴪ=\frac{2.782}{N}\)

(b) \(ᴪ=\frac{1.391}{N}\)

(c) \(ᴪ=\frac{1.414}{N}\)

(d) \(ᴪ=\frac{3}{N}\)

I had been asked this question in quiz.

My doubt stems from Array of N-Isotropic Sources in section Antenna Array of Antennas

Answer 1

The correct option is (a) \(ᴪ=\frac{2.782}{N}\)

To explain: Normalized array factor is given by \(AF=\frac{sin(Nᴪ/2)}{N \frac{ᴪ}{2}}=\frac{1}{√2} \)

⇨ \(\frac{Nᴪ}{2}=1.391\)

⇨ \(ᴪ=\frac{2.782}{N} \)