Question

Find the Nulls of the N-element array in which elements are separated by λ/4 and phase difference is 0?

(a) \(θ_n=cos^{-1}⁡(\left[±\frac{4n}{N}\right])\)

(b) \(θ_n=cos^{-1}⁡(\left[±\frac{2n}{N}\right])\)

(c) \(θ_n=sin⁡(\left[±\frac{4n}{N}\right])\)

(d) \(θ_n=sin^{-1}⁡(\left[±\frac{4n}{N}\right])\)

The question was asked in my homework.

My question comes from N-element Linear Array topic in portion Antenna Array of Antennas

Answer 1

The correct answer is (a) \(θ_n=cos^{-1}⁡(\left[±\frac{4n}{N}\right])\)

Easy explanation: The nulls of the N- element array is given by \(θ_n=cos^{-1}⁡(\frac{λ}{2πd} \left[-β±\frac{2πn}{N}\right])\)

⇨ \(θ_n=cos^{-1}⁡(\frac{λ}{2πλ/4} [0±\frac{2πn}{N}])\)

⇨ \(θ_n=cos^{-1}⁡([±\frac{4n}{N}])\)