[SI-LIST] Re: Bounded vs Unbounded jitter (was : Jitter transfer vs. accumulation)

 My view on this is that you don't actually need a gaussian source for Rx
jitter tolerance testing.  Simply generate some short term DJ that occurs at
sufficiently random times that the SERDES can't 'predict' it or be biased to
one side of the bit period.  Increase the amplitude of this DJ until you get
errors for virtually every occurrence.   This very rapidly gives you the
width of your short term error window.  You then need only reduce the amount
of this DJ  until  the errors occur  within  your required BER over a
sufficient length of time to account for the real RJ events inside your
receiver
Regards
Dave Instone
+44 (0)1235 824963
OXFORD SEMICONDUCTOR LIMITED 25 MILTON PARK ABINGDON OXFORDSHIRE OX14 4SH
Registered in England no 2733820 Registered Address: As above 
Alfred P. Neves wrote: When I was doing a lot of applications work in the
jitter area this concept was troubling to many engineers. I did some
researchon this issue and have some results to share. BTW, there is an
entiresection on Central Limit Theorem in the book "Probability and Random
Processes for Electrical Engineering" Alberto Leon-Garcia that I referenced
before. First, the Gaussian probability density function (pdf) is used to
model many processes which is justified by the Central Limit Theorem. It is
also important to differentiate that although the Guassian pdf used to model
the process is unbounded by definition, the actual process itself may not be
actually unbounded, here is an example why: Consider the simple case of
measuring the Johnson noise across a simple resistor. The noise across the
resistor is modeled using a Gaussian process. The Central Limit theorem
states that given a sequence of random variables, X1, X2, etc., to Xn with
finite mean u and finite variance sigma-squared and let Sn be
Sn=X1+X2+...Xn... Sn would be the total Thermal or Johnson noise modeled
across the resistor. X1, X2... is the contribution of each charged particle
random motion in the resistive material. The theorem specifically states
thatas n becomes large, it "approximates" a Gaussian random variable. n, in
this case and most practical cases is not infinite since there are countable
number of charged particles, but as n---> infinity, or the resistor size
approaches infinitely large in the limit, the "approximation" to Gaussian
distribution fit to thermal voltage noise becomes better. There are,
however,a finite number of charged particles, so at some point the model
breaks down for a finite size resistor with a countable number of charged
particles. The practical aspect of these concepts is selecting a suitable
noise source for generation of jitter for RX tolerance testing. I like to
usepeak/RMS ratio to describe how deep the tails of a process modeled with
Gaussian pdf is. To my knowledge at this date, the only 2 groups of people
who have generated either a jitter source, or a noise source with tested
"random-ness" or very high peak/RMS ratio is Agilent and Noisecom . Noisecom
actually specifies a Peak/RMS ratio (or peak/1sigma where mean=0) to their
noise source. Agilent specifically tested their jitter generation tool,
measuring the quality of the random-ness or peak/RMS factor. An interesting
application of this is that you need greater than 7 peak/RMS ratio for
makingBER measurements down to 10E-12. You have to use a very good quality
noise source to create very high peak/RMS jitter accordingly. Alfred P.
Neves<*)))))><{ Hillsboro Office: 735 SE 16th Ave. Hillsboro, OR, 97123
(503)679 2429 Voice (503) 210 7727 Fax Main Corporate office: Teraspeed
Consulting Group LLC 121 North River Drive Narragansett, RI 02882 (401)
284-1827 Business (401) 284-1840 Fax http://www.teraspeed.com[1] Teraspeed
isthe registered service mark of Teraspeed Consulting Group LLC
-----OriginalMessage----- From: si-list-bounce@xxxxxxxxxxxxx[2]
[mailto:si-list-bounce@xxxxxxxxxxxxx[3]] On Behalf Of Chris Cheng Sent:
Monday, March 26, 2007 12:24 PM To: si-list@xxxxxxxxxxxxx[4] Subject:
[SI-LIST] Bounded vs Unbounded jitter (was : Jitter transfer vs.
accumulation) Art, I like your 700 ft tall adult. :-D In an effort to focus
the original message to bandwidth trade-offs in = PLL, I propose starting
this bounded vs. unbounded jitter discussion in = this thread instead.
Thanksin advanced, Chris -----Original Message----- From:
si-list-bounce@xxxxxxxxxxxxx[5] [mailto:si-list-bounce@xxxxxxxxxxxxx[6]]On
Behalf Of art_porter@xxxxxxxxxxx[7] Sent: Monday, March 26, 2007 11:36 AM
To:steven@xxxxxxxxxxxxxxxxxxxx[8]; si-list@xxxxxxxxxxxxx[9] Subject:
[SI-LIST] Re: Jitter transfer vs. accumulation Here is a thought experiment
that helps me think about "random" jitter, = =3D which I first encountered
when thinking about noise in the ancient days = =3D when most digital
hardware was so slow we didn't have to worry about =3D jitter.=3D20 Could
theTIE of a transition ever reach 1000 years? If you argue that = =3D it
could, postulate a condition under which it could do so. (If the PDF = =3D
istruly normal and unbounded, then of course it could.)=3D20 Or think about
some other randomly distributed parameter, such as =3D heights of people. As
you look at a larger and larger sample of =3D individuals, the PDF gets more
and more normal looking. But has there = =3D ever been a 0.0005-inch tall
adult human being, or a 700-foot tall =3D adult? The normal distribution
works fine as a mathematical insight into = =3D physical processes such as
jitter or noise, as long as you don't force = =3D your thinking out of some
normal range of bounds, such as the mass that = =3D can be supported by a
skeleton and musculature, or the height to which = =3D the heart can pump
blood.=3D20 The central limit theorem reminds us that many phenomena appear
Gaussian = =3D only because they are an accumulation of the effects of a
large number = =3D of non-random processes. I suspect the same is true of
most jitter in = =3D the real world.=3D20 Art Porter=3D20 Agilent
Technologies =3D20 -----Original Message----- From:
si-list-bounce@xxxxxxxxxxxxx[10] [mailto:si-list-bounce@xxxxxxxxxxxxx[11]] =
=3D On Behalf Of Steven Kan Sent: Monday, March 26, 2007 11:56 AM To:
si-list@xxxxxxxxxxxxx[12] Subject: [SI-LIST] Re: Jitter transfer vs.
accumulation From: "Alfred P. Neves" <al.neves@xxxxxxxxxxx>[13] Subject:
[SI-LIST] Re: Jitter transfer vs. accumulation Date: Sat, 24 Mar 2007
09:48:38 -0700 This estimator, peak-peak jitter, is not a good estimator of
the process since it continues to increase since the process is =3D Gaussian
and collecting more samples digs deeper into the tails of the distribution.
The process is by definition unbounded.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ IANAE, but I've been thinking about
this for awhile now. Though our =3D finite=3D20 samples may be a "best fit"
with the Gaussian, can we really say that = =3D any=3D20 process is truly
unbounded when applied to real-world phenomena that =3D occur=3D20 in
real-world products? If I apply the constraint that I need to examine = =3D
a=3D20 given process over the life of the product (or the life of the user
or= =3D the=3D20 life of the Earth), does that then put bounds the
process(es) and = the=3D20 resulting statistics? I can see the argument from
the math side, e.g. "unbounded 'by =3D definition'",=3D20 but do the
'definitions' include practical constraints? My empirical gold-bar ratio is
still zero.=3D20
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