The radiation pattern of an antenna in spherical coordinates is given by F(θ) = cos4 (θ), 0 ≤ θ ≤ \(\frac{\pi}{2}\). The directivity of the antenna is

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UPSC ESE (Prelims) Electronics and Telecommunication Engineering 19 Feb 2023 Official Paper
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  1. 16.42
  2. 18.02
  3. 20.42
  4. 22.02

Answer (Detailed Solution Below)

Option 2 : 18.02
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Directivity of antenna:

The directivity of an antenna is a measure of its ability to focus or direct radiation in a specific direction. It is related to the radiation pattern and is often given by an integral over the pattern. The higher the directivity, the more concentrated the radiation in a particular direction.

Prad  = \(\int\int cos^8 \theta sin\theta d\theta \phi\)

Prad \(\int^\frac{\pi}{2}_\theta cos^8 \theta sin\theta d\theta \int^2_0 d\phi\)

Prad = \([\frac{(7\times5\times3\times1)(1)}{9\times7\times5\times3\times1}][2\pi]\)

Prad = \(\frac{2\pi}{9}\)

Gd = \(\frac{cos^8 \theta}{\frac{p_rad}{4\pi}}= 18 cos^8 \theta\)

D = Gd max = \(18\times 1 = 18\)

Here, option 2 is correct.

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