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

Which of the following is the necessary condition to avoid grating lob

1.	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» 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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