Demonstrates to use the rise time instead of the cut-off frequency to define a filter



This information is part of the Modelica Standard Library maintained by the Modelica Association.

Filters are usually parameterized with the cut-off frequency. Sometimes, it is more meaningful to parameterize a filter with its rise time, i.e., the time it needs until the output reaches the end value of a step input. This is performed with the formula:

f_cut = fac/(2*pi*riseTime);

where "fac" is typically 3, 4, or 5. The following image shows the results of a simulation of this example model (riseTime = 2 s, fac=3, 4, and 5):


Since the step starts at 1 s, and the rise time is 2 s, the filter output y shall reach the value of 1 after 1+2=3 s. Depending on the factor "fac" this is reached with different precisions. This is summarized in the following table:

Filter order Factor fac Percentage of step value reached after rise time
1 3 95.1 %
1 4 98.2 %
1 5 99.3 %
2 3 94.7 %
2 4 98.6 %
2 5 99.6 %

Parameters (2)


Value: 2

Type: Integer

Description: Filter order


Value: 2

Type: Time (s)

Description: Time to reach the step input

Components (4)


Type: Filter


Type: Step


Type: Filter


Type: Filter