Alfred and Art, Ok, I get the flicker noise, johnson noise part. However, from a practical point of view, how does one isolate the true = unbounded random jitter from the bounded uncorrelated jitter using any = testing equipment in a running system environment ?=20 Is crosstalk the only source of BUJ ?=20 How about phase noise induced by PLLVDD or SSO or core activities to the = Tx/Rx PLL (almost sounds like crosstalk isn't it ?) -----Original Message----- From: Alfred P. Neves [mailto:al.neves@xxxxxxxxxxx] Sent: Monday, March 26, 2007 2:08 PM To: Chris Cheng; si-list@xxxxxxxxxxxxx Subject: RE: [SI-LIST] Bounded vs Unbounded jitter (was : Jitter transfer vs. accumulation) When I was doing a lot of applications work in the jitter area this concept was troubling to many engineers. I did some research on this issue and have some results to share. BTW, there is an entire section 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=3DX1+X2+...Xn... =20 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 that as 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.=20 The practical aspect of these concepts is selecting a suitable noise source for generation of jitter for RX tolerance testing. I like to use peak/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=3D0) 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 making BER measurements down to 10E-12. You have to use a very good quality noise source to create very high peak/RMS jitter accordingly. =20 Alfred P. Neves <*)))))><{ =20 Hillsboro Office: 735 SE 16th Ave. Hillsboro, OR, 97123 (503) 679 2429 Voice (503) 210 7727 Fax =20 Main Corporate office: Teraspeed Consulting Group LLC=20 121 North River Drive=20 Narragansett, RI 02882 (401) 284-1827 Business (401) 284-1840 Fax=20 http://www.teraspeed.com =20 Teraspeed is the registered service mark=20 of Teraspeed Consulting Group LLC =20 -----Original Message----- From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On Behalf Of Chris Cheng Sent: Monday, March 26, 2007 12:24 PM To: si-list@xxxxxxxxxxxxx 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 = =3D PLL, I propose starting this bounded vs. unbounded jitter discussion in =3D this thread instead. Thanks in advanced, Chris -----Original Message----- From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of art_porter@xxxxxxxxxxx Sent: Monday, March 26, 2007 11:36 AM To: steven@xxxxxxxxxxxxxxxxxxxx; si-list@xxxxxxxxxxxxx Subject: [SI-LIST] Re: Jitter transfer vs. accumulation Here is a thought experiment that helps me think about "random" jitter, =3D =3D3D which I first encountered when thinking about noise in the = ancient days =3D =3D3D when most digital hardware was so slow we didn't have to worry about =3D3D jitter.=3D3D20 Could the TIE of a transition ever reach 1000 years? If you argue that = =3D =3D3D it could, postulate a condition under which it could do so. (If = the PDF =3D =3D3D is truly normal and unbounded, then of course it = could.)=3D3D20 Or think about some other randomly distributed parameter, such as =3D3D heights of people. As you look at a larger and larger sample of =3D3D individuals, the PDF gets more and more normal looking. But has there = =3D =3D3D ever been a 0.0005-inch tall adult human being, or a 700-foot tall =3D3D adult? The normal distribution works fine as a mathematical = insight into =3D =3D3D physical processes such as jitter or noise, as long as = you don't force =3D =3D3D your thinking out of some normal range of bounds, = such as the mass that =3D =3D3D can be supported by a skeleton and = musculature, or the height to which =3D =3D3D the heart can pump blood.=3D3D20 The central limit theorem reminds us that many phenomena appear Gaussian =3D =3D3D only because they are an accumulation of the effects of a = large number =3D =3D3D of non-random processes. I suspect the same is true of = most jitter in =3D =3D3D the real world.=3D3D20 Art Porter=3D3D20 Agilent Technologies =3D3D20 -----Original Message----- From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] =3D =3D3D On Behalf Of Steven Kan Sent: Monday, March 26, 2007 11:56 AM To: si-list@xxxxxxxxxxxxx Subject: [SI-LIST] Re: Jitter transfer vs. accumulation > From: "Alfred P. Neves" <al.neves@xxxxxxxxxxx> > 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 =3D3D 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 = =3D3D finite=3D3D20 samples may be a "best fit" with the Gaussian, can we = really say that =3D =3D3D any=3D3D20 process is truly unbounded when applied to real-world phenomena that =3D3D occur=3D3D20 in real-world products? If = I apply the constraint that I need to examine =3D =3D3D a=3D3D20 given = process over the life of the product (or the life of the user or =3D =3D3D = the=3D3D20 life of the Earth), does that then put bounds the process(es) and =3D the=3D3D20 resulting statistics? I can see the argument from the math side, e.g. "unbounded 'by =3D3D definition'",=3D3D20 but do the 'definitions' include practical constraints? My empirical gold-bar ratio is still zero.=3D3D20 ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List technical documents are available at: http://www.si-list.net List archives are viewable at: =3D3D20 //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu =3D3D20 ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List technical documents are available at: http://www.si-list.net List archives are viewable at: =3D20 //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu =3D20 ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List technical documents are available at: http://www.si-list.net List archives are viewable at: =20 //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu =20 ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List technical documents are available at: http://www.si-list.net List archives are viewable at: //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu