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

• From: "Steve Waldstein" <swldstn@xxxxxxxxxxxx>
• To: <si-list@xxxxxxxxxxxxx>
• Date: Fri, 23 Mar 2007 19:59:52 -0400

```To all,

Sorry if this is not what other think but I agree with Scott that the
Random Jitter is unbounded and that the RMS measurement represents a way
to describe its distribution if it is and only if it is Gaussian. Random
jitter does not have to be Gaussian but to simplify a lot of problems we
assume it is.

In the past people had tried to find a way to map RMS to Peak-to-Peak and
The rule of thumb developed was +/- 7 sigma. In reality this is only true
if you assume that your are concerned with an error rate of ~ 10e-12. If,
as in most modern systems you are looking for a error rate of > than 10e-12
the conversion from RMS to peak-to-peak changes. Maxim and other have
Some great app notes on converting from RMS to a error rate.

If it bounded than we assume it can be described by some deterministic
phenomena (even if we don't understand it). In this case we tend to put
it into two buckets, correlated (to something) or uncorrelated (meaning we
can't figure it out). In the past we assumed that the deterministic jitter
was only caused by duty cycle distortion (DCDj), or periodic jitter (Pj) or
even a more specific Pj called Sj (sinusoidal jitter). If it came down a
link or contained data we would also try to partition it into ISI (inter
symbol interference) or data dependant jitter (DDj). All of these are
ether correlated or uncorrelated with something but they were all bounded
because no matter how long we measured it it would not change. Random jitter
by definition will continue to "accumulate" the longer we look assuming the
probability of the event happening (no matter how low) is still > zero.

That's my two cents.

Steve Waldstein
Tundra Semiconductor

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On
Behalf Of Mark Randol
Sent: Friday, March 23, 2007 1:18 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Jitter transfer vs. accumulation

Time to get out the dictionaries.  According to mine (the before
mentioned MJSQ):

"3.5.45 jitter, random, RJ: Jitter that is characterized by a Gaussian
distribution and is unbounded."

"Because random jitter is practically measured as an RMS value (the same
as the standard deviation for a
Gaussian distribution), a seemingly small amount of RMS random jitter
corresponds to a large peak to peak value. The RMS value for random
jitter is multiplied by approximately 14 to result in a peak to peak
random jitter value that corresponds to a 10-12 bit error ratio;..."

To sum up, RJ is unbounded as the number of edges (aka samples, BER,
etc) increases, because the Gaussian distribution is unbounded at an
infinite number of samples. =20

In reality RJ is bounded because in a real system, at the grossest
level, there's not infinite time nor bandwidth.  There are other reasons
too, but those are adequate to make the point.  This makes the math
messy though, so being good engineers we 'ignore' that inconvenient
fact.  But that's not what I understood the discussion to be about.

Awaiting the deluge of 'Out of the Office' messages,
--
Mark Randol, RF Evaluation & Application Engineer
ON Semiconductor
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