Design an analog Butterworth filter that has $-2$ passband attenuation at frequency of $20 \mathrm{rad} / \mathrm{sec} \&$ at least $-\operatorname{10dB}$ stop band attenuation at $30 \mathrm{rad} / \mathrm{sec}$.

Solution:

Given:

$ \begin{aligned}\\ &A_p=-2 d B \\\\ &A_s=-10 d B \\\\ &f\Omega_p=20 \mathrm{rad} / \mathrm{sec} . \\\\ &\Omega_s=30 \mathrm{rad} / \mathrm{sec} .\\ \end{aligned}\\ $

$ \begin{aligned}\\ A p &=20 \log \delta_q \\\\ -2 &=20 \log \delta_7 \\\\ \therefore \delta_7 &=0.7943\\ \end{aligned}\\ $

$ \begin{aligned}\\ A_s &=20 \log \delta_2 \\\\ …