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The radiation pattern of an antenna in spherical coordinates is given by \(F(\theta)=\cos^8\theta\), \(0\le \theta\le \pi/2\). The directivity of the antenna is

1. 10 dB
2. 12.6 dB
3. 11.5 dB
4. 18 dB

Correct answer: 12.6 dB

Solution

For a pattern proportional to \(\cos^8\theta\), the directivity is found by integrating the normalized power over the sphere and comparing it with the maximum at \(\theta=0\). The resulting directivity is about 18.2 in linear scale, which is approximately \(12.6\) dB.

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