calcul_3eme_ordre - return the zeros and the pole of a third order digital PLL type 2
[tau1,tau,tau2] = calcul_3eme_ordre(fn,phi,kv,icp,N)
- fn : real. natural cut-off frequency of the open-loop transfert function [Hz]
- phi : real. phase margin at the cut-off frequency [rad]
- kv : real. local sensitivity of the oscillator [Hz/V]
- icp : real. maximum charge pump output current [A]
- N : integer. feedback divider value
- tau1 : real. zero of the transfert function of the filter (s)
- tau : real. firt pole of the transfert function of the filter (s)
- tau2 : real. second pole of the transfert function of the filter (s)
Computation of poles and zeros of a third order pll type 2 are made with the open loop transfert function of the loop :
where
is the transfert function of the direct gain and
is the feedback gain.
At the frequency cut-off
of the open loop transfert function :
and then
//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
IRCOM Group
Alan Layec
- 1
- U. Rhode, Digital PLL Frequency Synthesizers.Prentice Hall, 1983.