## [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

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