Question

What is the direction of first null of broadside 4-element isotropic antenna having a separation of λ/2?

(a) 60°

(b) 30°

(c) 180°

(d) 0°

The question was posed to me in exam.

Enquiry is from Radiation Pattern for 4-Isotropic Elements topic in portion Antenna Array of Antennas

Answer 1

The correct answer is (a) 60°

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

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

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

⇨ \(n=1 (first \,null) cos^{-1} (±\frac{n}{2})=cos^{-1} (±\frac{1}{2})=60° or 120°. \)