Question

The power radiated by a lossless antenna is 10W, the directional characteristics of the antenna are represented by the radiaiton intensity of $U(\theta ,\varphi )=B_0{\cos }^3\theta ,0\le \theta \le \frac{\pi }{2}.0\le \varphi \le 2\pi$
The power gain (in dB) of the antenna is ______

Answer 1

$P_{rad}=\underset{s}{\int }U(\theta ,\varphi )\sin \theta d\theta d\varphi$

$P_{rad}=\underset{\theta =0}{\overset{\frac{\pi }{2}}{\int }}\underset{\varphi =0}{\overset{2\pi }{\int }}{B}_0{\cos }^3\theta \sin \theta d\theta d\varphi$

$\Rightarrow 10=\frac{\pi }{2}\left(B_0\right)$

$\Rightarrow B_0=6.36$

$U(\theta .\varphi )=6.36{\cos }^3\theta$

$D=4\pi \frac{U(\theta ,\varphi )}{P_{rad}}$

$D=8$

$\frac{G_P}{G_D}=e_{cd}=1$

$G_P=G_D=D$

$G_P=8$

${\left(G_P\right)}_{indB}=10\log \left(8\right)=9dB$