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Modeling >> Behavioral Models >> Some doubts in modeling jitter
https://designers-guide.org/forum/YaBB.pl?num=1212724241

Message started by pkd on Jun 5^th, 2008, 8:50pm

Title: Some doubts in modeling jitter
Post by pkd on Jun 5^th, 2008, 8:50pm

Hi!
I have read from some books that, phase noise causing jitter is modeled as 1/f (pink) Gaussian noise. Suppose you consider that ϕ is a random variable having Gaussian pink distribution. Then, the sine wave plagued with phase noise is given by y(t)= Asin(ωt+ϕ). Implementing the above process in a digital computer, typically it would be done as follows: y_n=y(nT_s )= Asin(2πf/f_s n+ϕ), where n=0,1,2,…, and f_s=1/T_s .
The question is how often should ϕ be sampled. Should ϕ by ϕ_n, meaning that ϕ is sampled at every step of n, or is it sampled once every cycle? But the problem is doing this way; the waveform becomes discontinuous at the edges of the cycles.

Our question is more clearly explained in the attached document:

The code used to generate the above plot is given below:
fs=100; % [color=#990000]100 samples per cycle
y=zeros(10*fs,1);
for n=1:10 % sampling phase noise once every cycle
y((1:fs+1)+(n-1)*fs)=sin(2*pi*[0:1/fs:1]+randn); % randn is white Gaussian random variable
end[/color]

Title: Re: Some doubts in modeling jitter
Post by Stefan on Jun 6^th, 2008, 3:43am

Think of phase noise in terms of random frequency deviation between periods, not phase deviation itself.
Check the papers section of designers guide for some literature.

Title: Re: Some doubts in modeling jitter
Post by Visjnoe on Jun 10^th, 2008, 5:01am

Dear,

you can model phase noise by adding a (random) phase signal to your ideal phase (2*pi*Fnom*t). You evaluate the phase of your signal every period of Fnom.
If we call the phase at a certain time nT phi_real[nT] and the ideal phase at that time phi_ideal[nT] , than the phase noise equals:

phasenoise = phi_real[nT]-phi_ideal[nT] (in radians)

If you want to convert to jitter, you multiply this number by T/(2*pi)

Regards

Peter