butterworth.mws

syntfil[Butterworth]  - compute the Butterworth approximation

Calling sequence:

      Butterworth(order, Os, ap, var)

Parameters:

      order    - order of the Butterworth approximation [-]

      Os       - stopband frequency of the normalized lowpass (NLP) [1/s]

  ap       - passband ripple [dB]

      var      - variable symbol in the tranfer and the characteristic function

Parameter order  must be positive integer. Parameter ap  must be positive number. Parameter   var   must be symbol . Parameter Os  is not utilized and its type is not checked.

Description:

Info level:

Setting of variable infolevel[syntfil]  can be used to get more detailed results.

infolevel[syntfil] =

      2  - print polynomials of inverse transfer function and characteristic function on separate lines with description.

      3  - as level 2 +  print transfer function's poles and parameter epsilon .

Example:

>    with(syntfil):

`Syntfil version 1.53 loaded`

`You can set infolevel[syntfil] variable to 2..5 to get more detailed results!`

>    infolevel[syntfil]:=3;

>    Butterworth(4,2,3,s);

infolevel[syntfil] := 3 

epsilon = 0.997628

Poles of H:

[-.9244281266+.3829106676*j, -.9244281266-.3829106676*j, -.3829106676+.9244281266*j, -.3829106676-.9244281266*j]

Butterworth:

G = 1.000000000+.9976283451*s^4+2.608476475*s^3+3.410162491*s^2+2.611575192*s

Phi = .9976283451*s^4

1.000000000+.9976283451*s^4+2.608476475*s^3+3.410162491*s^2+2.611575192*s, .9976283451*s^4

>    infolevel[syntfil]:=1;

>    G,Phi:=Butterworth(4,2,3,s);

infolevel[syntfil] := 1

G, Phi := 1.000000000+.9976283451*s^4+2.608476475*s^3+3.410162491*s^2+2.611575192*s, .9976283451*s^4

Magnitude frequency response

>    plot(MagnitudeHdB(1/G)(omega),omega=0..3);

[Maple Plot]

See also:

ButterworthNLPOrder

ButterworthPoles, Butterworth_asnew

DroppNLP, TestCharEqn, MagnitudeH, MagnitudeHdB, PhaseH, GroupDelayH,
in addition to Butterworth approximation the following approximations can be used
 Chebyshev, InvChebyschev, InvChebyshevB, Cauer, CauerB, CauerC