Question

Which of the following is the necessary condition to avoid grating lobes in N-Isotropic element array?

(a) \(\frac{d}{λ}≤\frac{1}{1+|cosθ_m |} \)

(b) \(\frac{d}{λ}≥\frac{1}{1+|cosθ_m |} \)

(c) \(\frac{λ}{d}≤\frac{1}{1+|cosθ_m |} \)

(d) \(\frac{λ}{d}=\frac{1}{1+|cosθ_m |} \)

This question was addressed to me in exam.

The doubt is from Array of N-Isotropic Sources topic in portion Antenna Array of Antennas

Answer 1

Right choice is (a) \(\frac{d}{λ}≤\frac{1}{1+|cosθ_m |} \)

The explanation: Grating lobes are the minor and unnecessary lobes other than the major lobe.

To avoid grating lobes, kd(cosθ-cosθm) ≤ 2π

θm – Direction of maximum radiation

⇨ \(\frac{2πd}{λ}  (cosθ-cosθ_m)≤2π\)

\(\frac{d}{λ}≤\frac{1}{cosθ-cosθ_m} \)

\(\frac{d}{λ}≤\frac{1}{1+|cosθ_m |} \)