Question

The direction of the first minor lobe of 4 element isotropic broadside array separated by λ/2 is ___________

(a) 41.4°

(b) 30°

(c) 60°

(d) 90°

I had been asked this question by my school principal while I was bunking the class.

This intriguing question originated from Radiation Pattern for 4-Isotropic Elements in section Antenna Array of Antennas

Answer 1

The correct option is (a) 41.4°

To explain I would say: The direction of the secondary maxima (minor lobes) occur at θs

\(θ_s=cos^{-1} (\frac{λ}{2πd} \left[-β±\frac{(2s+1)}{N} π\right])\)

⇨ \(θ_s=cos^{-1} (\frac{λ}{2π(λ/2)} \left[±\frac{3}{4} π\right])\) (s=1 for 1^st minor lobe)

⇨ \(θ_s=cos^{-1} (±\frac{3}{4})=41.4°\)