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

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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

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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

⇨ $\frac{2πd}{λ} (cosθ-cosθ_m)≤2π$

$\frac{d}{λ}≤\frac{1}{cosθ-cosθ_m}$

$\frac{d}{λ}≤\frac{1}{1+|cosθ_m |}$

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