How much does the gain of an ideal parabolic reflector antenna increase when the operating frequency is doubled?

The gain of a parabolic reflector (dish) antenna is directly proportional to its electrical area, which is its physical area measured in wavelengths. When you double the operating frequency, the wavelength is cut in half. Because area is a two-dimensional measurement, halving the wavelength means the dish is now twice as wide and twice as tall in terms of wavelength. This increases the total electrical area by a factor of four (2 squared). In decibels, a power factor of four corresponds to a 6 dB increase (10 * log10(4) ≈ 6). Therefore, doubling the frequency of an ideal parabolic dish yields an additional 6 dB of gain. Distractors commonly offer 3 dB, which is the value for doubling power, but not for squaring the electrical area.