Question 3-93O1

The gain of a parabolic dish antenna is directly proportional to the square of the operating frequency (or inversely proportional to the square of the wavelength). This is because the antenna's effective aperture becomes larger in terms of wavelengths when the frequency increases, allowing it to focus electromagnetic energy more tightly. Mathematically, the gain (G) is approximately $G \propto (\frac{D}{\lambda})^2$, where D is the dish diameter and $\lambda$ is the wavelength. Since $\lambda = c/f$ (where c is the speed of light and f is frequency), we can write $G \propto (Df)^2$. If the operating frequency (f) is doubled, the gain is multiplied by $2^2 = 4$. To express this in decibels (dB), we use the formula $10 \log_{10}(\text{power ratio})$. $10 \log_{10}(4) \approx 6.02 \text{ dB}$. Therefore, doubling the operating frequency increases the gain by approximately 6 dB. * **A) Gain does not change:** Incorrect, as gain is strongly dependent on frequency. * **B) Gain is multiplied by 0.707:** Incorrect, this would represent a decrease in gain, not an increase. * **D) Gain increases 3 dB:** Incorrect, a 3 dB increase means the gain doubled, but doubling the frequency quadruples the gain.