Butterworth Filters

Butterworth filters are characterized by having a maximally flat pass-band magnitude response, or equivalently:

$\left.{\frac {\partial ^{N}\left|H\left(j\omega \right)\right|}{\partial \omega ^{N}}}\right|_{\omega =0}=0$

(1)

This means that the $N^{\text{th}}$ derivative of the magnitude at DC is zero.