# [SI-LIST] Re: How do two Random (Gaussian) Jitter specs add?

*From*: <art_porter@xxxxxxxxxxx>*To*: <tom_cip_11551@xxxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>*Date*: Fri, 14 Apr 2006 09:46:19 -0600

Excellent question and one that tends to drive literal thinkers crazy = until they think about it for a minute or two. If two variables have a Gaussian pdf, the standard deviation of the = combination should be the square root of the sums of the squares of the = standard deviations of the individual variables. For example if I = combine two noise sources, each having a Gaussian noise with 1 mV = standard deviation, the sum will have a standard deviation of 1.414 mV. = So, sure enough, the "P-P" value will be only 1.4 times the "P-P" of = either original signal. =20 "Peak to peak" of course depends on how long you watch, for variables = such as noise or jitter with a Gaussian pdf. To be more precise, you = could say "The probability that the noise [jitter] will exceed N mV [ps] = can be determined using the known characteristics of the Gaussian = distribution." For example 1-(1E-12) of the population should = theoretically fall within ~ +/- 7 sigma of the mean. =20 The trap you have to watch out for is, how random was the noise or = jitter? How much of the total jitter is random (unbounded) and how much = is deterministic (measure it once and you're done)? Jitter measurement = packages such as ASA's M1 (also marketed as Agilent's "Oscilloscope = Tools"), Agilent's DCA-J and EZJIT Plus, or Tektronix' JIT3 will break = down the jitter for you into random and deterministic components, and = calculate the total jitter (actually a projected total) for you based on = the probability (expressed as bit error rate) limit you choose. =20 For more background reading, I recommend = http://cp.literature.agilent.com/litweb/pdf/5988-9109EN.pdf Art Porter Agilent Technologies =20 -----Original Message----- From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] = On Behalf Of tom_cip_11551 Sent: Friday, April 14, 2006 9:08 AM To: si-list@xxxxxxxxxxxxx Subject: [SI-LIST] How do two Random (Gaussian) Jitter specs add? Hi to sll signal integrity experts. I am just a little rusty on "probability and random variables".=20 Lets say that I had a system with two or more elements that=20 generated Gaussian distribution or, random jitter, or random jitter.=20 Random jitter tends to be specifed in terms of the standard=20 deviation of the distribution. Each generator would therefore have=20 a "sigma", which is also an RMS value. If I knew the sigma of each=20 of the distributions coming from the generators, then I could=20 convert these sigma values to a peak to peak number by arbitrarily=20 assigning a desired bit error rate. The peak to peak values, as far=20 as I know, will add, linearly. However, if I wanted to stay in the statistical world, how could I=20 add the two sigma values for the two jitter generators? In my way of=20 thinking, they can not add linearly (sigma 1 plus sigma 2). Is this=20 wrong? Thank You Tom ------------------------------------------------------------------ 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: http://www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List FAQ wiki page is located at: http://si-list.org/wiki/wiki.pl?Si-List_FAQ List technical documents are available at: http://www.si-list.org List archives are viewable at: =20 http://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: http://www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List FAQ wiki page is located at: http://si-list.org/wiki/wiki.pl?Si-List_FAQ List technical documents are available at: http://www.si-list.org List archives are viewable at: http://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

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