Question

What is the direction of first null of broadside 8-element isotropic antenna having a separation of \frac{λ}{4}?

(a) 0

(b) 60

(c) 30

(d) 120

I got this question by my college professor while I was bunking the class.

I need to ask this question from Radiation Pattern of 8-Isotropic Elements topic in portion Antenna Array of Antennas

Answer 1

Right choice is (b) 60

Easy explanation: The nulls of the N- element array is given by

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

\(θ_n=cos^{-1}⁡(\frac{λ}{2π(\frac{λ}{4})}\left[±\frac{2πn}{N}\right])=cos^{-1} (±\frac{4n}{8})=cos^{-1} (±\frac{n}{2})=cos^{-1} (±1/2)=60\)