Question

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

(a) cos^-1 (±n)

(b) \(cos^{-1} (±\frac{n}{2})\)

(c) \(sin^{-1} (±\frac{n}{2})\)

(d) sin^-1 (±n)

I have been asked this question in my homework.

This is a very interesting question from Radiation Pattern for 4-Isotropic Elements in portion Antenna Array of Antennas

Answer 1

The correct choice is (a) cos^-1 (±n)

Best explanation: The nulls of the N- element array is given by

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

⇨ \(θ_n=cos^{-1}(⁡\frac{λ}{2π(λ/4)}\left[±\frac{2πn}{N}\right])=cos^{-1} (±\frac{4n}{4})=cos^{-1} (±n)  \left[n=1,2,3 \,and \,n≠N,2N…\right]\)