Question

What is the direction of first null of broadside 8-element isotropic antenna having a separation of λ/2?

(a) 60°

(b) 75.5°

(c) 37.5°

(d) 57.5°

The question was asked in a national level competition.

This intriguing question comes from Radiation Pattern of 8-Isotropic Elements in division Antenna Array of Antennas

Answer 1

Correct answer is (b) 75.5°

For explanation I would say: The nulls of the N- element array is given by

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

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

⇨ \(n=1 (first \,null) cos^{-1} (±\frac{n}{4})=cos^{-1} (±\frac{1}{4})=75.5°. \)