Question

An 8-isotropic element broadside array separated by a λ/2 distance has nulls occurring at ____

(a) $cos^{-1} (±\frac{n}{4})$

(b) $cos^{-1} (±\frac{n}{2})$

(c) $sin^{-1} (±\frac{n}{2})$

(d) $sin^{-1} (±\frac{n}{4})$

The question was posed to me in semester exam.

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

Answer 1

Correct answer is (a) $cos^{-1} (±\frac{n}{4})$

To elaborate: The nulls of the N- element array is given by

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

⇨ $θ_n=cos^{-1}⁡(\frac{λ}{2π(λ/2)} [±\frac{2πn}{N}])=cos^{-1} (±\frac{2n}{8})=cos^{-1} (±\frac{n}{4})$