Antenna Array Questions and Answers for Aptitude test 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}]))
Answer: a
Clarification: 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}]))
Answer: a
Clarification: 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}]))
Answer: a
Clarification: 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}]))
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)
Answer: a
Clarification: 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)
Answer: a
Clarification: 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)
Answer: a
Clarification: 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})
Answer: a
Clarification: 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} )
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 |} )
Answer: a
Clarification: 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
Answer: a
Clarification: 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
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
Answer: a
Clarification: 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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