# Gain at critical frequency for Butterworth and Chebishev filters

In Chebyshev filter the critical freq occurs with gain Gp But in butterworth filter it is always at -3dB; why does this happen? Can anyone explain intuitively on this?

For Chebyshev filter type 1 filter, the roll off is more sharp but result is ripples in pass band. You can control this ripple, which will in turn vary the Gp that you mentioned. See https://en.wikipedia.org/wiki/Chebyshev_filter. If you specify $$\delta$$ as the ripple factor in dB scale (like 1dB), $$\epsilon = \sqrt{10^{\delta /10}-1}$$ in linear scale. The gain Gp = $$\frac{1}{\sqrt{1 + \epsilon^2}}$$ in linear scale. The sharpness of your passband and passband ripple specification will affect $$\epsilon$$ which will inturn affect Gp.