Question

Which of the following expression gives the nulls for the N- element linear array?

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

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

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

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

This question was posed to me in an interview.

Query is from N-element Linear Array topic in section Antenna Array of Antennas

Answer 1

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

To explain: To determine Null points the array factor is set equal to zero.

\(\frac{sin(\frac{Nᴪ}{2})}{\frac{Nᴪ}{2}}=0\)

⇨ \(sin(\frac{Nᴪ}{2})=0  \)

⇨ \(\frac{Nᴪ}{2}=±nπ \)

⇨ \(kdcosθ+β=±\frac{2nπ}{N} \)

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