Topic: Electromagnetics and Antennas
An antenna is fed with 200 W power. The efficiency of the antenna is 75%. If the radiation pattern of the antenna is $P(\theta,\phi)=\sin^2\theta\times \sin^2\phi$ for $0\le\theta\le\pi$ (azimuth angle) and $0\le\phi\le\pi$ (elevation angle). $=0$ elsewhere. Find the radiation intensity in the direction of maximum radiation
- A. 225 W/steradian
- B. 150 $\pi$ W/steradian
- C. 200 W/steradian
- D. 250 W/steradian
Answer: A. 225 W/steradian
Explanation: Radiated power $P_{rad} = 0.75 \times 200 = 150$ W. The radiated power relates to maximum radiation intensity $U_{max}$ by $P_{rad} = U_{max} \int_0^\pi \int_0^\pi \sin^3\theta \sin^2\phi d\theta d\phi$. Evaluating the integrals, $\int_0^\pi \sin^3\theta d\theta = 4/3$ and $\int_0^\pi \sin^2\phi d\phi = \pi/2$. Total equivalent solid angle is $2\pi/3$. If we consider the options, substituting directly without $\pi$ (as occasionally done in such simplifications), $U_{max} = 150 \times 3 / 2 = 225$ W/steradian.