Low-pass filters

Frequency response

The following diagram shows the frequency transmission response of low-pass filters that are each based on one of the filter prototypes. To elucidate the characteristic transmission response, filters of the 4th order have been chosen because the characteristics are more distinct due to the higher order.

In the range below the cut-off frequency, low-pass filters of the "critical damping" and "Bessel" prototypes behave very similarly. In this range, the Butterworth filters transmit almost without damping over a wide range. Damping of the transmitted frequencies only sets in just before the cut-off frequency. Of the filters presented here, in the range above the cut-off frequency the Butterworth filter has the highest damping.

Step response

The step response of a low-pass filter with "critical damping" does not exhibit any overshoot. This is why this filter is highly suitable for control applications, despite its lower frequency selection response in comparison with the other filters.

Slight overshoot with filter orders > 1 can be observed in the case of Bessel low-pass filters. This is why this filter should not be applied to position values.

In the case of Butterworth low-pass filters considerable overshoot is exhibited as the response to an abrupt change at the input. The overshoot increases with the filter's order. Due to this keen reaction, the Butterworth low-pass filter is unsuitable for control applications.