Example Problem $14\mathrm{.}12$

Design a lowpass active filter with a dc gain of $4$ and a corner frequency of $500$ Hz $.$

Solution:

The corner frequency is

${}_c=2f_c=2(500)=\frac{1}{R_f{C}_f}$

The dc gain is

$H(0)=-\frac{R_f}{R_i}=-4$

If we select $C_f=0\mathrm{.}2F$

$R_f=\frac{1}{2(500)0\mathrm{.}2{10}^{-6}}=1\mathrm{.}59k$ do with proper details