[SI-LIST] Re: Jitter transfer vs. accumulation

 
 
I think it is valuable to generalize the discussion a bit.   Once again,
going back to Stochastic processes, RMS, mean, variance, peak-peak etc.,
are all ways for estimating the parameters of a random variable
describing a random process.   Depending on the process, some estimators
work, some don't.
 
For a Gaussian jitter process, lets say a fictional PLL with no DJ, only
Random Jitter exactly described by a Gaussian probability density
function, the variance and sample mean, along with RMS are good
estimators of the  process.  "Good" implies that the estimators will
converge on the universe population of all of the jitter events as the
sample size goes toward infinity.    In other words, collect a lot of
samples, make your calculations, and you have a very good description of
your system.  "Good" means the estimators are unbiased and converge.
An example of a non-convergent estimator is:
 
Now, make peak-peak jitter measurements of this process for one clock
cycle.    This estimator, peak-peak jitter, is not a good estimator of
the process since it continues to increase since the process is Gaussian
and collecting more samples digs deeper into the tails of the
distribution.    The process is by definition unbounded.
 
Applying estimators to describe a process infers confidence, and
confidence intervals are established accordingly.  Agilent has written a
few very good app notes on their fast BERT seach methods that utilize
confidence intervals for doing BER work on a channel.
 
Add DJ to the last PLL example, so that you now have a jitter process
with DJ and RJ.   DJ is described by a bounded PDF, where RJ is
unbounded, we now a random process defnined by several pdf's one of them
describes the DJ the other 2 the RJ tails.  A new set of estimators is
required that can deal with both RJ and DJ.    The Dual-Dirac model
accounts for both and is very useful to build a simple set of estimates
where you have both DJ and RJ.   Our Staff Research Scientist, Ransom
Stephens has done a lot of really good work in this area (Teraspeed
Consulting LLC).
 
In the PLL case, the system is typically stationary.   Stationarity
implies that the statistics or estimators dont change over a different
interval for which they are measured.     For example, I measure 1000
cycles in 2 minutes and obtain a mean frequency of 100MHz, if I
remeasure the 1000cycles over another 2 minute interval and obtain
101MHz, the system may not be stationary.   An example of a PLL with
non-stationary statistics with significantly large charge pump leakage
generating a frequency spur that results in some very defined peak-peak
DJ, where the temperature varies randomly and is not controlled.  The
leakage is temperature dependent, alters the jitter picture, you now
have a non-stationary system.       
 
My comment to George is that a free-running VCO is a non-stationary
process, not that the RJ RMS is unbounded over a certain interval.
Since the VCO is not stationary, the mean frequency of the VCO does not
have an average value that is meaningful and the RMS jitter is not
independent of the time interval it is measured over.    The
autocorrelation record of the VCO jitter increases showing the as we
increase the measurement interval the RMS jitter increases versus
interval length.   I am not stating that the RJ RMS measured over any of
those intervals is unbounded however.   The RJ RMS estimate is bounded
over every measurment interval, but again, for the VCO it increases as
the time interval increases.    
 
In other words, the RJ RMS is bounded over a defined measurement
interval, but the RJ RMS increases versus the interval length.
 
 
 
 
 
 
 
 
 
 
 
 
 
Alfred P. Neves      <*)))))><{ 


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-----Original Message-----
From: Scott McMorrow [mailto:scott@xxxxxxxxxxxxx] 
Sent: Friday, March 23, 2007 9:59 AM
To: Vinu Arumugham
Cc: George.Tang@xxxxxxx; Alfred P. Neves; weirsi@xxxxxxxxxx;
si-list@xxxxxxxxxxxxx
Subject: Re: [SI-LIST] Re: Jitter transfer vs. accumulation


Vinu

I would agree, and would claim that the RMS value is a scalar
representation of an unbounded phenomena (the 1-sigma value of the
statistics), when we view it w.r.t. a true Gaussian distribution.  The
jitter itself is unbounded.

I suspect that we have a nomenclature issue.  I would claim, however,
that the measured RMS jitter value (not the actual) will change over
time as additional samples are taken, and better statistical confidence
is obtained.  The RMS jitter value is then a bounded number which
describes an unbounded process.

But I'm just a hack engineer. WTF do I know?


Scott


Scott McMorrow

Teraspeed Consulting Group LLC

121 North River Drive

Narragansett, RI 02882

(401) 284-1827 Business

(401) 284-1840 Fax



http://www.teraspeed.com



TeraspeedR is the registered service mark of

Teraspeed Consulting Group LLC


Vinu Arumugham wrote: 

May be we need to clear up the terminology/definitions.

By RMS jitter I think George is referring to RJ rms or the 1-sigma value
of the gaussian. This I think is bounded as George has repeatedly
stated.
The peak-peak RJ of course is unbounded and depends on the number of
samples. I think George has referred to this as phase jitter.

Comments from Steve and Alfred seemed to suggest that the RJ rms, the
1-sigma of the gaussian itself is unbounded.
Steve, Alfred could you please clarify if that is what you
meant/observe?

Thanks,
Vinu



Scott McMorrow wrote: 

George



I have a quick question.  You said:



"The VCO RMS jitter is bounded, and so is the PLL RMS jitter.  The RJ

distribution takes on a true Gaussian waveform."



My meager understanding of this is that Rj is by definition unbounded.
And the presence of a true Gaussian distribution (when all other
deterministic components have been subtracted out) is an indication of
this unboundedness. And yes, theoretically it will approach infinity at
infinite time. However, because the random component is so low, it
"seems" to be bounded within a specific BER confidence level.  Which is
why we have repeatability in measurements.  My contention is that Rj is
much smaller than most people believe or are able to measure, and that
it is low probability deterministic noise components that dominate the
jitter spectrum. Unfortunately, these can also tend to have
near-gaussian distributions, mucking up the measurement apparatus.



If what I say above is correct, then what you describe above is truly
unbounded jitter, taking on a Gaussian distribution.



Do you agree?





best regards,



Scott









Scott McMorrow

Teraspeed Consulting Group LLC

121 North River Drive

Narragansett, RI 02882

(401) 284-1827 Business

(401) 284-1840 Fax



http://www.teraspeed.com



TeraspeedR is the registered service mark of

Teraspeed Consulting Group LLC





  

  

    

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