How much does the gain of an ideal parabolic reflector antenna increase when the operating frequency is doubled?
Why A parabolic dish's gain depends on its aperture measured in wavelengths: G is proportional to (pi*D/lambda)^2, or equivalently proportional to frequency squared for a fixed dish diameter. Doubling the frequency halves the wavelength, so the (D/lambda) ratio doubles and the gain goes up by a factor of 4. A power ratio of 4 is 10*log(4) = 6 dB.
Watch out The choice that says 3 dB is the trap: 3 dB is only a doubling of power, but gain scales with the square of frequency, not linearly, so the increase is 6 dB.
Dish gain goes as frequency squared: double f, times 4 power, 6 dB. Same 6 dB if you double the dish diameter.