Question

A 4-isotropic element broadside array separated by a λ/2 distance has nulls occurring at ____________

(a) \(cos^{-1} (±\frac{n}{2}) \)

(b) \(cos^{-1} (±\frac{4n}{2}) \)

(c) \(sin^{-1} (±\frac{n}{2}) \)

(d) \(sin^{-1} (±\frac{n}{4}) \)

I got this question in semester exam.

This intriguing question comes from Radiation Pattern for 4-Isotropic Elements in portion Antenna Array of Antennas

Answer 1

Right option is (a) \(cos^{-1} (±\frac{n}{2}) \)

The best I can explain: The nulls of the N- element array is given by

\(θ_n=cos^{-1}⁡(\frac{λ}{2πd} \left[-β±\frac{2πn}{N}\right])=cos^{-1}⁡(\frac{λ}{2πd} \left[±\frac{2πn}{N}\right])\)

⇨ \(θ_n=cos^{-1}⁡(\frac{λ}{2π(λ/2)}\left[±\frac{2πn}{N}\right])=cos^{-1} (±\frac{2n}{4})=cos^{-1} (±\frac{n}{2}) \)