Question

The direction of the first minor lobe of 8 element isotropic broadside array separated by λ/2 is ___

(a) 41.4°

(b) 76.6°

(c) 67.7°

(d) 90°

I have been asked this question in my homework.

This key question is from Radiation Pattern of 8-Isotropic Elements topic in chapter Antenna Array of Antennas

Answer 1

Right choice is (b) 76.6°

The explanation: The direction of the secondary maxima (minor lobes) occur at θs

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

⇨ \(θ_s=cos^{-1} (\frac{λ}{2π(λ/2)} [±\frac{3}{8}π]) \)    (s=1 for 1^st minor lobe)

⇨ \(θ_s=cos^{-1} (±\frac{3}{8})=67.7°\)