In many low-pass filter applications it is necessary that the closed-loop gain is as close to unity as possible within the passband. The Butterworth filter is best suited for such applications.
This filter is also called a maximally flat or flat-flat filter. Ideal and the practical frequency responses for three types of Butterworth low-pass filters are depicted in fig. (a) by solid line and dashed lines respectively. As the roll-off becomes steeper, they approach the ideal filter characteristics more closely.
The frequency responses for three types of high-pass Butterworth filters are shown in fig. (b). By contrast, for the first order high-pass filter, the gain increases at the rate of 20 db per decade in the stop-band while increase is 40 db per decade for the second-order high-pass filter and so on.
Butterworth low-pass and high-pass filters are simple in design, and are the most popular active filters. Here will discuss only Butterworth filters.