cauerpoleszeros.html

syntfil[CauerPolesZeros] - compute the poles and zeros of the transfer function for the Cauer approximation

syntfil[CauerBPolesZeros] - compute the poles and zeros of the transfer function for the type B Cauer approximation

syntfil[CauerCPolesZeros] - compute the poles and zeros of the transfer function for the type C Cauer approximation

Calling sequence:

CauerPolesZeros(order, Os, ap)

CauerBPolesZeros(order, Os, ap)

CauerCPolesZeros(order, Os, ap)

Parameters:

order - order of the Cauer approximation [-]

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

ap - passband ripple [dB]

Parameter order must be positive integer and for type B and C in addition even. Parameters Os and ap must be positive numbers where Os > 1 .

Description:

This function returns the leading coefficient of denominator polynomial of the transfer function and two 1D arrays of transfer function's poles and zeros.

Number of poles is given by order parameter, and the number of zeros for even order is equal to order and for odd order is equal to order -1. In case of type B and C the number of zeros is equal to order -2.

Type B Cauer approximation is computed from standard Cauer approximation (type A).

Type C Cauer approximation is computed from type B Cauer approximation.

Info level:

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

infolevel[syntfil] =

2 - print leading coefficient of denominator polynomial of transfer function and two 1D arrays of transfer function's poles and zeros on separate lines with description

3 - as level 2 + print parameter .

4 - as level 3 + print characteristic function's poles and zeros.

5 - for type B - as level 4 + print transfer and characteristic function's poles and zeros for type A,

- for type C - as level 4 + print transfer and characteristic function's poles and zeros for type A and B.

Example:

> with(syntfil):

> CauerPolesZeros(4,2,3);

> CauerBPolesZeros(4,2,3);

> infolevel[syntfil]:=3:

> CauerCPolesZeros(4,2,3);

epsilon = .9976283451

CauerCPolesZeros:

Gc = 33.01648338

Poles = [-.3554897032+.2913038752*I, -.3554897032-.2913038752*I, -.9366802015e-1+.9438822515*I, -.9366802015e-1-.9438822515*I]

Zeros = [2.504897318*I, -2.504897318*I]

See also:

CauerNLPOrder

Cauer, CauerBOmega, Cauer_asnew

NLP2LP, NLP2HP, NLP2BP, NLP2BP2, NLP2BS, BodePlot

in addition to Cauer approximation the following approximations can be used
ButterworthPoles, ChebyshevPoles, InvChebyschevPolesZeros, InvChebyshevBPolesZeros