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Modeling >> Behavioral Models >> -2 slope from white phase noise
https://designers-guide.org/forum/YaBB.pl?num=1066269978

Message started by Yiming on Oct 15^th, 2003, 7:06pm

Title: -2 slope from white phase noise
Post by Yiming on Oct 15^th, 2003, 7:06pm

Ken,

This question might be dumb but I am somewhat confused. In the matlab script of your jitter modeling paper, you integrate the jitter using function cumsum() before you use psd() to obtain the power spectral density of phase noise. What is the theory behind the integration?

Assume the output voltage of the oscillator is x(t) = A*cos[wc*t + theta(t)] = A*cos(wc*t) - theta(t)*A*sin(wc*t), then the RMS power <x(t)^2> = A^2/2 + A^2/2 *<theta(t)^2>, where <theta(t)^2> = integral(Sphi(f), -inf, inf), and Sphi(f) is the phase noise PSD. Sphi(f) again equals to the Fourier transform of the auto-correlation function of phase noise <theta(t+tau)*theta(t)>. If the phase noise is white, it would results in Sphi(f) is white, too. ("an approach to consistent jitter modeling for various jitter aspects and measurement methods", Masashi Shimanouchi)

What am I missing here?

Title: Re: -2 slope from white phase noise
Post by Ken Kundert on Oct 16^th, 2003, 5:49pm

The VCO of Listing 16 creates a file that contains the length of each period of the VCO. Matlab reads this file in and then applies the cumsum function to compute the time at which each transition occurs. This is proportional to the phase of the VCO. The PSD function is then applied to compute the phase noise as a function of frequency.

-Ken