Question

Find the value θn at which null occurs for an 8-element broadside array with spacing d.

(a) \(cos^{-1}⁡\frac{λn}{Nd}\)

(b) \(sin^{-1}⁡\frac{λn}{Nd}\)

(c) \(cos^{-1}⁡\frac{2λn}{Nd}\)

(d) \(sin^{-1}⁡\frac{2λn}{Nd}\)

This question was posed to me in class test.

I'm obligated to ask this question of Broadside Array topic in division Antenna Array of Antennas

Answer 1

Correct option is (a) \(cos^{-1}⁡\frac{λn}{Nd}\)

Easiest explanation: Nulls occurs when array factor \(AF=\frac{sin \frac{Nφ}{2}}{\frac{Nφ}{2}} = 0\)

⇨ \(sin\frac{Nφ}{2} = 0   =>\frac{Nφ}{2}=±nπ \,and\, φ=kdcosθ+β=kdcosθ_n=\frac{2π}{λ} dcosθ_n\)

⇨ Null occurs at \(θ_n=cos^{-1}⁡\frac{λn}{Nd}\)