Question

Find the Nulls of the 8-element array in which elements are separated by λ/4 and phase difference is 0?

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

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

(c) \(θ_n=sin^{-1}⁡(\left[±\frac{n}{2}\right])\)

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

I have been asked this question during an online interview.

My question is taken from N-element Linear Array topic in chapter Antenna Array of Antennas

Answer 1

The correct choice is (a) \(θ_n=cos^{-1}⁡(\left[±\frac{n}{2}\right])\)

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

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

⇨ \(θ_n=cos^{-1}⁡(\left[±\frac{4n}{8}\right])\)

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