Scilab Function
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calcul_3eme_ordre - return the zeros and the pole of a third order digital PLL type 2

Library

Calling Sequence

[tau1,tau,tau2] = calcul_3eme_ordre(fn,phi,kv,icp,N)

Parameters

Description

Computation of poles and zeros of a third order pll type 2 are made with the open loop transfert function of the loop :

$\displaystyle A\left(s\right)\,=\,G\left(s\right)H\left(s\right)
$

where $ G\left(s\right)$ is the transfert function of the direct gain and $ H\left(s\right)$ is the feedback gain. At the frequency cut-off $ f_{n}$ of the open loop transfert function :

$\displaystyle \Vert A\left(j\omega_{n}\right) \Vert^{2}\,=\,1
$

$\displaystyle \frac{d\varphi\left(\omega_{n}\right)}{d\omega_{n}}\,=\,0
$

and then

$\displaystyle \tau_2\,=\,\frac{-\tan \left(\varphi \left(\omega _{n}\right)\right)+1/\cos \left(\varphi \left(\omega _{n}\right)\right)}{\omega _{n}}
$

$\displaystyle \tau_1\,=\,\frac{1}{\tau_{2}\omega^2_{n}}
$

$\displaystyle \tau\,=\,\frac{K_{cp}K_{v}}{N\omega _{n}^{2}}\, \frac{\sqrt{1+\omega _{n}^{2}\tau _{1}^{2}}}{\sqrt{1+\omega _{n}^{2}\tau _{2}^{2}}}
$

File content


//Calcul_3eme_ordre - Scilab function - 
//Return the zeros and the pole of a third order digital PLL type 2
//Based on the Rhode's Model
//13 octobre 2003 - IRCOM GROUP - Author : A.Layec
function [tau1,tau,tau2]=calcul_3eme_ordre(fn,phi,kv,icp,N)
  wn=2*%pi*fn;
  tau2=(-tan(phi)+1/cos(phi))/wn;
  tau1=1/(wn*wn*tau2);
  tau9=(kv*icp/(2*%pi))/(N*wn*wn);
  tau=tau9*sqrt((1+wn*wn*tau1*tau1)/(1+wn*wn*tau2*tau2));
  c0=(tau2/tau1)*((kv*icp/(2*%pi))/(wn*wn*N))*sqrt((1+(wn*tau1)^2)/(1+(wn*tau2)^2));
  c1=c0*((tau1/tau2)-1);
  r1=tau1/c1;
endfunction

See Also

Authors

IRCOM Group Alan Layec

Bibliography

1
U. Rhode, Digital PLL Frequency Synthesizers.Prentice Hall, 1983.