Antenna Array Questions and Answers – Radiation Pattern of 8-Isotropic Elements

«
»

This set of Antenna Array Questions & Answers for Exams focuses on “Radiation Pattern of 8-Isotropic Elements”.

1. The array factor of 8 – isotropic elements of broadside array is given by ____
a) \(\frac{sin(2kdcosθ)}{2kdcosθ} \)
b) \(\frac{sin(4kdcosθ)}{4kdcosθ} \)
c) \(\frac{sin(2kdcosθ)}{kdcosθ} \)
d) \(\frac{cos(2kdcosθ)}{2kdcosθ} \)
View Answer

Answer: b
Explanation: Normalized array factor is given by \(AF=\frac{sin(Nᴪ/2)}{N \frac{ᴪ}{2}}\)
And ᴪ=kdcosθ+β
Since its given broad side arrayβ=0,
ᴪ=kdcosθ+β=kdcosθ
\(\frac{Nᴪ}{2}=4kdcosθ\)
\(AF=\frac{sin(Nᴪ/2)}{N \frac{ᴪ}{2}}=\frac{sin(4kdcosθ)}{4kdcosθ} \)
advertisement

2. An 8-isotropic element broadside array separated by a λ/2 distance has nulls occurring at ____
a) \(cos^{-1} (±\frac{n}{4})\)
b) \(cos^{-1} (±\frac{n}{2})\)
c) \(sin^{-1} (±\frac{n}{2})\)
d) \(sin^{-1} (±\frac{n}{4})\)
View Answer

Answer: a
Explanation: The nulls of the N- element array is given by
\(θ_n=cos^{-1}⁡(\frac{λ}{2πd}[-β±\frac{2πn}{N}])=cos^{-1}⁡(\frac{λ}{2πd} [±\frac{2πn}{N}])\)
⇨ \(θ_n=cos^{-1}⁡(\frac{λ}{2π(λ/2)} [±\frac{2πn}{N}])=cos^{-1} (±\frac{2n}{8})=cos^{-1} (±\frac{n}{4}) \)

3. An 8-isotropic element broadside array separated by a λ/4 distance has nulls occurring at ____
a) cos-1(±n)
b) \(cos^{-1} (±\frac{n}{2})\)
c) \(sin^{-1} (±\frac{n}{2})\)
d) \(sin^{-1} (±n)\)
View Answer

Answer: b
Explanation: The nulls of the N- element array is given by
\(θ_n=cos^{-1}⁡(\frac{λ}{2πd}\left[-β±\frac{2πn}{N}\right])=cos^{-1}⁡(\frac{λ}{2πd} [±\frac{2πn}{N}])\)
⇨ \(θ_n=cos^{-1}⁡(\frac{λ}{2π(λ/4)}) [±\frac{2πn}{N}])=cos^{-1} (±\frac{4n}{8})=cos^{-1} (±\frac{n}{2}) [n=1,2,3 \,and\, n≠N,2N…]\)
advertisement
advertisement

4. The array factor of 8- isotropic elements of broadside array separated by a λ/4 is given by ____
a) sinc(cosθ)
b) cos(sinθ)
c) sin(sinθ)
d) sinc(2cosθ)
View Answer

Answer: d
Explanation: Normalized array factor is given by
\(AF=\frac{sin(Nᴪ/2)}{N \frac{ᴪ}{2}}\)
And ᴪ=kdcosθ+β
Since its given broad side array β=0,
ᴪ=kdcosθ+β=kdcosθ
\(\frac{Nᴪ}{2}=4kdcosθ=4(\frac{2π}{λ})(\frac{λ}{4})cosθ=2πcosθ\)
\(AF=\frac{sin(Nᴪ/2)}{N \frac{ᴪ}{2}}=\frac{sin(2πcosθ)}{2πcosθ}=sinc(2cosθ).\)

5. The array factor of 8 – isotropic elements of broadside array separated by a λ/2 is given by ____
a) sinc(4cosθ)
b) sin(2πcosθ)
c) sinc(4πsinθ)
d) sin(2sinθ)
View Answer

Answer: a
Explanation: Normalized array factor is given by \(AF=\frac{sin(Nᴪ/2)}{N \frac{ᴪ}{2}}\)
And ᴪ=kdcosθ+β
Since its given broad side array β=0,
ᴪ=kdcosθ+β=kdcosθ
\(\frac{Nᴪ}{2}=4kdcosθ=4(\frac{2π}{λ})(\frac{λ}{2})cosθ=4πcosθ \)
\(AF=\frac{sin(Nᴪ/2)}{N \frac{ᴪ}{2}}=\frac{sin(4πcosθ)}{4πcosθ}=sinc(4cosθ).\)
advertisement

6. What is the direction of first null of broadside 8-element isotropic antenna having a separation of λ/2?
a) 60°
b) 75.5°
c) 37.5°
d) 57.5°
View Answer

Answer: b
Explanation: The nulls of the N- element array is given by
\(θ_n=cos^{-1}⁡(\frac{λ}{2πd} [-β±\frac{2πn}{N}])=cos^{-1}⁡(\frac{λ}{2πd} [±\frac{2πn}{N}])\)
⇨ \(θ_n=cos^{-1}⁡(\frac{λ}{2π(λ/2)} [±\frac{2πn}{N}])=cos^{-1} (±\frac{2n}{8})=cos^{-1} (±\frac{n}{4}) \)
⇨ \(n=1 (first \,null) cos^{-1} (±\frac{n}{4})=cos^{-1} (±\frac{1}{4})=75.5°. \)

7. What is the direction of first null of broadside 8-element isotropic antenna having a separation of \frac{λ}{4}?
a) 0
b) 60
c) 30
d) 120
View Answer

Answer: b
Explanation: The nulls of the N- element array is given by
\(θ_n=cos^{-1}⁡(\frac{λ}{2πd} [-β±\frac{2πn}{N}])=cos^{-1}⁡(\frac{λ}{2πd} [±\frac{2πn}{N}])\)
\(θ_n=cos^{-1}⁡(\frac{λ}{2π(\frac{λ}{4})}\left[±\frac{2πn}{N}\right])=cos^{-1} (±\frac{4n}{8})=cos^{-1} (±\frac{n}{2})=cos^{-1} (±1/2)=60\)
advertisement

8. The necessary condition for maximum of the first side lobe of n element array is ______
a) \(\frac{Nᴪ}{2}=±\frac{5π}{2}\)
b) \(\frac{Nᴪ}{2}=±\frac{3π}{2}\)
c) \(\frac{Nᴪ}{2}=±\frac{π}{2}\)
d) \(\frac{Nᴪ}{2}=±\frac{4π}{2}\)
View Answer

Answer: b
Explanation: The secondary maxima occur when the numerator of the array factor equals to 1.
⇨ \(sin(\frac{Nᴪ}{2})=±1\)
⇨ \(\frac{Nᴪ}{2}=±\frac{2s+1}{2} π \)
⇨ \(\frac{Nᴪ}{2}=±\frac{3π}{2}\) [s=1 for first minor lobe].

9. The direction of the first minor lobe of 8 element isotropic broadside array separated by λ/2 is ___
a) 41.4°
b) 76.6°
c) 67.7°
d) 90°
View Answer

Answer: b
Explanation: The direction of the secondary maxima (minor lobes) occur at θs
\(θ_s=cos^{-1} (\frac{λ}{2πd} \left[-β±\frac{(2s+1)}{N} π\right])\)
⇨ \(θ_s=cos^{-1} (\frac{λ}{2π(λ/2)} [±\frac{3}{8}π]) \) (s=1 for 1st minor lobe)
⇨ \(θ_s=cos^{-1} (±\frac{3}{8})=67.7°\)
advertisement

10. An 8-isotropic element end-fire array separated by a λ/4 distance has first null occurring at ____
a) 60
b) 30
c) 90
d) 150
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 \(β=±kd=±\frac{2πd}{λ}=±\frac{π}{2},\)
\(θ_n=cos^{-1}⁡(\frac{2}{π} [∓\frac{π}{2}±\frac{2πn}{8}])\)
\(=cos^{-1}⁡([∓1±\frac{n}{2}])\)
First null at n=1; \(θ_n= =cos^{-1}⁡([1±\frac{1}{2}]) (considering \,β=-\frac{π}{2}) \)
\(θ_n =cos^{-1} (\frac{1}{2})\,or \,cos^{-1} (3/2) \)
\(θ_n =cos^{-1} (\frac{1}{2})=60.\)

Sanfoundry Global Education & Learning Series – Antennas.

To practice all exam questions on Antenna Array, here is complete set of 1000+ Multiple Choice Questions and Answers .

Participate in the Sanfoundry Certification contest to get free Certificate of Merit. Join our social networks below and stay updated with latest contests, videos, internships and jobs!

advertisement
advertisement

Leave a Comment

Manish Bhojasia - Founder & CTO at Sanfoundry
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