How does the gain of a parabolic dish antenna change when the operating frequency is doubled?

The gain of a parabolic dish antenna is directly related to its size (diameter) and the frequency at which it operates. Gain is expressed in decibels (dB) and is generally calculated using the formula that incorporates the effective aperture of the antenna and the wavelength of the signal.

When the frequency is doubled, the wavelength is halved because frequency and wavelength are inversely related. The effective aperture of a parabolic antenna is proportional to the square of the frequency, meaning that when you double the frequency, the gain increases. Specifically, gain in dB can be shown to increase approximately by 20 dB for a doubling of frequency due to the increase in the effective aperture area, adjusted for the characteristics of the antenna.

However, in practical terms, it translates to an increase in gain of about 6 dB for a doubling of the frequency. This increase occurs because, for parabolic antennas, the gain changes can also be viewed through the relationship of the antenna's two-dimensional surface area associated with the frequency. Thus, when the operating frequency is doubled, the gain of the parabolic dish antenna increases by 6 dB, thereby confirming that this option is indeed correct.