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Message started by sj156.lim on Sep 17^th, 2023, 8:43pm

Title: Questions about Accumulating Jitter
Post by sj156.lim on Sep 17^th, 2023, 8:43pm

Dear all,

I am reading a guide document called "Modeling Jitter in PLL-based Frequency Synthesizers" in the Analysis menu
And I have two questions as below.

Question 1.
There is the following sentence on page 12.
"For systems that exhibit simple accumulating jitter, each transition is relative to the previous transition, and the variation in the length of each
period is independent, so the variance in the time of each transition accumulates"

In this part, It is said each transition is related to the others,
On the contrary, I do not understand how the variation in the length of each period becomes independent, can it be explained??

Question 2.
On page 12,
I don't understand how Equations (34) and (35) came out, can anyone explain how Jk is induced ?
I thought it was like the following, is the following equations wrong?

Jk =√(var(ti+k -ti))
= √(var[jacc(ti+k)-jacc(ti)+k∙T])
= √(var[jacc(ti+k)-jacc(ti)])

J = √(var[jacc(ti+1)-jacc(ti)])

And, I don't understand why T goes into jacc in J = √(var[jacc(ti+T)-jacc(ti)])---(35).

Thanks in advance
Jin

Title: Re: Questions about Accumulating Jitter
Post by Ken Kundert on Sep 19^th, 2023, 12:00am

As for question 1, the origin of simple accumulating jitter is a white noise source. A white noise source is uncorrelated. Thus the value at any instant is uncorrelated with the value at any later instant. The length of a cycle is related to the noise from the white noise source. Thus, the length of any particular cycle is independent of (uncorrelated to) the length of any previous cycle. The accumulating nature of simple accumulating jitter comes from the fact that the cycles follow one after another, thus the start of one cycle is delayed or advanced by the variation in the preceding cycle. This is referred to as a random walk.

The situation is analogous to a person that, starting from the origin, repeatedly flips two coins to determine whether to take one step either north, south, east or west during each interval. The motion on each interval is independent (uncorrelated to) the motion on the prior interval, yet the man slowly drifts from the origin because each of the steps accumulate.

As for questions 2, J from (35) is the variation in the length of one cycle. Since the variation of each cycle is independent, the total variation in k adjacent cycles is J√k, which is (34).