Antenna Array Questions and Answers – Array of N-Isotropic Sources

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This set of Antenna Array Questions and Answers for Aptitude test focuses on “Array of N-Isotropic Sources”.

1. The direction of nulls for broadside array of N –Isotropic sources is given by _____
a) \(cos^{-1}⁡([±\frac{nλ}{Nd}])\)
b) \(cos^{-1}⁡([±\frac{2nλ}{Nd}])\)
c) \(cos^{-1}⁡([±\frac{2πnλ}{2Nd}])\)
d) \(cos^{-1}⁡([±\frac{nλ}{Nd}])\)
View Answer

Answer: a
Explanation: The nulls of the N- element array is given by \(θ_n=cos^{-1}⁡(\frac{λ}{2πd} [-β±\frac{2πn}{N}])\)
Given it’s a broadside array so β=0
\(θ_n=cos^{-1}⁡(\frac{λ}{2πd} [±\frac{2πn}{N}])= cos^{-1}⁡([±\frac{nλ}{Nd}]).\)

2. The direction of first null of the broadside array of N-Isotropic sources is _____
a) \(cos^{-1}([±\frac{λ}{Nd}])\)
b) \(cos^{-1}⁡([±\frac{πλ}{Nd}])\)
c) \(cos^{-1}⁡([±\frac{2πλ}{Nd}])\)
d) \(cos^{-1}⁡([±\frac{λ}{2Nd}])\)
View Answer

Answer: a
Explanation: The nulls of the N- element array is given by \(θ_n=cos^{-1}⁡(\frac{λ}{2πd} [-β±\frac{2πn}{N}])\)
Given it’s a broadside array so β=0 and n=1 for first null
\(θ_n=cos^{-1}⁡(\frac{λ}{2πd} [±\frac{2πn}{N}])= cos^{-1}⁡([±\frac{nλ}{Nd}])=cos^{-1}⁡([±\frac{λ}{Nd}])\)

3. The direction of nulls for end-fire array of N –Isotropic sources separated by λ/4 is given by ____
a) \(θ_n=cos^{-1}⁡([∓1±\frac{4n}{N}])\)
b) \(θ_n=sin^{-1}⁡([∓1±\frac{4n}{N}])\)
c) \(θ_n=cos^{-1}⁡([∓1±\frac{2n}{N}])\)
d) \(θ_n=cos^{-1}⁡([∓1±\frac{n}{N}])\)
View Answer

Answer: a
Explanation: The nulls of the N- element array is given by \(θ_n=cos^{-1}⁡(\frac{λ}{2πd} [-β±\frac{2πn}{N}])\)
Since its given broad side array \(β=±kd=±\frac{2πd}{λ}=±\frac{π}{2},\)
\(θ_n=cos^{-1}⁡(\frac{2}{π} [∓\frac{π}{2}±\frac{2πn}{N}])\)
\(θ_n=cos^{-1}⁡([∓1±\frac{4n}{N}])\)
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4. The necessary condition for the direction of maximum side lobe level of the N-element isotropic array is _______
a) \(ᴪ=±\frac{2s+1}{N} π \)
b) \(ᴪ=±\frac{2s+2}{N} π\)
c) \(ᴪ=±\frac{2s}{N} π\)
d) \(ᴪ=±\frac{2(s+1)}{N} π\)
View Answer

Answer: a
Explanation: The secondary maxima occur when the numerator of the array factor equals to 1.
⇨ \(sin(\frac{Nᴪ}{2})=±1\)
⇨ \(\frac{Nᴪ}{2}=±\frac{2s+1}{2} π \)
⇨ \(ᴪ=±\frac{2s+1}{N} π .\)

5. The necessary condition for the direction of maximum first side lobe level of the 8-element isotropic array is _______
a) \(\frac{3}{8} π\)
b) \(\frac{3}{4} π\)
c) \(\frac{1}{8} π\)
d) \(\frac{5}{8} π\)
View Answer

Answer: a
Explanation: The secondary maxima occur when the numerator of the array factor equals to 1.
⇨ \(sin(\frac{Nᴪ}{2})=±1\)
⇨ \(\frac{Nᴪ}{2}=±\frac{2s+1}{2} π \)
⇨ \(ᴪ=±\frac{2s+1}{N}π=\frac{2+1}{8} π=\frac{3}{8} π.\)

6. The necessary condition for the direction of maximum second side lobe level of the 4-element isotropic array is _______
a) \(\frac{5}{4} π\)
b) \(\frac{3}{4} π\)
c) \(\frac{1}{8} π\)
d) \(\frac{5}{8} π\)
View Answer

Answer: a
Explanation: The secondary maxima occur when the numerator of the array factor equals to 1.
⇨ \(sin(\frac{Nᴪ}{2})=±1\)
⇨ \(\frac{Nᴪ}{2}=±\frac{2s+1}{2} π \)
⇨ \(ᴪ=±\frac{2s+1}{N}π=\frac{2(2)+1}{4} π=\frac{5}{4} π.\)

7. The Half-power beam width of the N-element isotropic source array can be known when _____
a) \(ᴪ=\frac{2.782}{N}\)
b) \(ᴪ=\frac{1.391}{N}\)
c) \(ᴪ=\frac{1.414}{N}\)
d) \(ᴪ=\frac{3}{N}\)
View Answer

Answer: a
Explanation: Normalized array factor is given by \(AF=\frac{sin(Nᴪ/2)}{N \frac{ᴪ}{2}}=\frac{1}{√2} \)
⇨ \(\frac{Nᴪ}{2}=1.391\)
⇨ \(ᴪ=\frac{2.782}{N} \)
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8. 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) \(\frac{λ}{d}=\frac{1}{1+|cosθ_m |} \)
View Answer

Answer: a
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
⇨ \(\frac{2πd}{λ} (cosθ-cosθ_m)≤2π\)
\(\frac{d}{λ}≤\frac{1}{cosθ-cosθ_m} \)
\(\frac{d}{λ}≤\frac{1}{1+|cosθ_m |} \)

9. Which of the following is the necessary condition to avoid grating lobes in N-Isotropic element broadside array?
a) d < λ
b) d > λ
c) d=λ
d) d < 2λ
View Answer

Answer: a
Explanation: Grating lobes are the minor and unnecessary lobes other than the major lobe.
To avoid grating lobes, kd(cosθ-cosθm)≤2π
\(\frac{d}{λ}≤\frac{1}{1+|cosθ_m |} \)
For broadside to avoid grating lobes (θm=90)
⇨ \(\frac{d}{λ}\) < 1
⇨ d < λ
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10. Which of the following is the necessary condition to avoid grating lobes in N-Isotropic element end-fire array?
a) d < λ/2
b) d < λ
c) d > λ/2
d) d=λ
View Answer

Answer: a
Explanation: Grating lobes are the minor and unnecessary lobes other than the major lobe.
To avoid grating lobes, kd(cosθ-cosθm)≤2π
\(\frac{d}{λ}≤\frac{1}{1+|cosθ_m|} \)
For broadside to avoid grating lobes (θm=0)
⇨ \(\frac{d}{λ}\) < 1/2
⇨ d < λ/2

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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