LowpassButterworth

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

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