.Modelica_LinearSystems2.ZerosAndPoles.Internal.baseFilter

Information

Syntax

zp = baseFilter(analogFilter, order, A_ripple, normalized);

Description

This function constructs a ZerosAndPoles transfer function description of low pass filters with a cut-off angular frequency of one rad/s and a gain of one. Filters returned by this function are the starting point to construct other filters by transformation of the filter transfer function:

   zp(p) = 1 / ( product( p + a[i] ) * product(p^2 + b[i]*p + a[i]) )

using the following rules:

For more details see also [Tietze2002], pp. 815-852.

Example

  // Generate a Butterworth high pass base filter of order 3
  import ZP = Modelica_LinearSystems2.ZerosAndPoles;
  import Modelica_LinearSystems2.Types;

  ZP zp_filter;
algorithm
  zp_filter = ZP.Internal.baseFilter(Types.AnalogFilter.Butterworth, order = 3);

 // zp_filter = 1 /  ( (p + 1)*(p^2 + p + 1) )

Interface

encapsulated function baseFilter
  import Modelica;
  import Modelica.Math;
  import Modelica.Utilities.Streams;
  import Modelica_LinearSystems2;
  import Modelica_LinearSystems2.Utilities.Types;
  import Modelica_LinearSystems2.ZerosAndPoles;
  input Modelica_LinearSystems2.Utilities.Types.AnalogFilter analogFilter = Modelica_LinearSystems2.Utilities.Types.AnalogFilter.CriticalDamping "Analog filter characteristics (CriticalDamping/Bessel/Butterworth/Chebyshev)";
  input Integer order(min = 1) = 2 "Order of filter";
  input Real A_ripple(unit = "dB") = 0.5 "Pass band ripple (only for Chebyshev filter)";
  input Boolean normalized = true "True, if amplitude at f_cut = -3db, otherwise unmodified filter";
  output ZerosAndPoles filter(redeclare Real n1[0], redeclare Real n2[0, 2], redeclare Real d1[if analogFilter == Types.AnalogFilter.CriticalDamping then order else mod(order, 2)], redeclare Real d2[if analogFilter == Types.AnalogFilter.CriticalDamping then 0 else integer(order/2), 2]) "Filter transfer function";
end baseFilter;