WOLFRAM SYSTEMMODELER

LowpassButterworth

Output the input signal filtered with a low pass Butterworth filter of any order

Wolfram Language

In[1]:=
SystemModel["Modelica.Blocks.Continuous.LowpassButterworth"]
Out[1]:=

Information

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

This block defines the transfer function between the input u and the output y as an n-th order low pass filter with Butterworth characteristics and cut-off frequency f. It is implemented as a series of second order filters and a first order filter. Butterworth filters have the feature that the amplitude at the cut-off frequency f is 1/sqrt(2) (= 3 dB), i.e., they are always "normalized". Step responses of the Butterworth filter of different orders are shown in the next figure:

Butterworth.png

If transients at the simulation start shall be avoided, the filter should be initialized in steady state (e.g., using option initType=Modelica.Blocks.Types.Init.SteadyState).

Parameters (7)

n

Value: 2

Type: Integer

Description: Order of filter

f

Value:

Type: Frequency (Hz)

Description: Cut-off frequency

initType

Value: Modelica.Blocks.Types.Init.NoInit

Type: Init

Description: Type of initialization (1: no init, 2: steady state, 3: initial state, 4: initial output)

x1_start

Value: zeros(m)

Type: Real[m]

Description: Initial or guess values of states 1 (der(x1)=x2)

x2_start

Value: zeros(m)

Type: Real[m]

Description: Initial or guess values of states 2

xr_start

Value: 0.0

Type: Real

Description: Initial or guess value of real pole for uneven order otherwise dummy

y_start

Value: 0.0

Type: Real

Description: Initial value of output (states are initialized in steady state if possible)

Outputs (3)

x1

Type: Real[m]

Description: states 1 of second order filters (der(x1) = x2)

x2

Type: Real[m]

Description: states 2 of second order filters

xr

Type: Real

Description: state of real pole for uneven order otherwise dummy

Connectors (2)

u

Type: RealInput

Description: Connector of Real input signal

y

Type: RealOutput

Description: Connector of Real output signal