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
\(θ_n=cos^{-1}⁡(\frac{λ}{2πd} [±\frac{2πn}{N}])= cos^{-1}⁡([±\frac{nλ}{Nd}]).\)
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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.
⇨ \(sin(\frac{Nᴪ}{2})=±1\)
⇨ \(\frac{Nᴪ}{2}=±\frac{2s+1}{2} π \)
⇨ \(ᴪ=±\frac{2s+1}{N}π=\frac{2+1}{8} π=\frac{3}{8} π.\)
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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 is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter