[SI-LIST] Re: Rx Eye Mask width, BER, and Jitter

  • From: Marty Bewildered <martym777@xxxxxxxxx>
  • To: si-list@xxxxxxxxxxxxx
  • Date: Mon, 21 Jun 2010 18:14:02 -0700 (PDT)

Lately there seem to be some confusion about what Rj is ... and believe me, it 
is only a convention.
If I read the version of the dual Dirac equation correctly ... then you are 
calling Rj something it is not.

Rj is the (1-sigma) of the Gaussian part of the jitter ... and is the 
equivalent rms for a perfect Gaussian ... at least in 
the (oversimplified) DD model.  Some people seem to be trying to change the 
definition (from MJSQ)
and that is not a very good idea, because it leads to exactly this kind of 
misunderstanding. 

The model says: Tj is Dj plus a function of BER times Rj.  (see numerous 
references) ...  The function of BER
is the "confidence interval" for a confidence level of 1-BER. 

This function of BER evaluates to (approx) 14 for BER = 1e-12 and 15.9 for BER 
= 1e-15 (numbers
to which you refer below). 

Some people are calling Rj the product of this function and the Gaussian 
"sigma" which is Rj. The SAS spec
violently breaks the standard definition of Rj in this regard, and I hope not 
too many people will follow suit. 

> The 0.2 UI was a fabricated number for this example, it could be 
> anything. However, more importantly the 0.2 UI is a *receiver eye width* 
> derived from an Rx jitter *tolerance*, not a margin. I would expect the 
> required Rx eye mask width to *increase* and my receiver jitter 
> tolerance to *decrease* for a higher BER. Jitter will increase at a 
> higher BER, 
but won't the receiver require a wider eye mask at a higher 
> BER too?

So 0.21 is your "margin" and 0.79 is your tolerance ... is that what you mean? 
You need to conform to
a mask width of 0.21 UI (that's your margin) and you can tolerate up to 0.79 UI 
of Tj. And if you insist on a lower BER 
(thus a higher confidence level) you expect the margin to decrease (because 
your expectation is more
stringent) and the tolerance (in UI) to increase for the same margin.  The sum 
of the margin and tolerance is 1UI ... no?

Of course that's now how it really works. When we make the BER lower (more 
stringent) and we need to meet the
same tolerance (for Tj), the Rj needs to be smaller so the Tj figure does not 
exceed the tolerance. 

The mask (if you insist on a mask) must be smaller for a lower BER ... and is 
related to margin, not tolerance.
Is it possible you mean 1e-15 is larger than 1e-12? Because it's clear the 
margin is less  for 1e-15 than for
1e-12 ... but only for the same Rj. 

I think a good part of the confusion is in the fact that a more stringent (not 
higher) BER "requires" a lower Rj
and Dj combination. It does not "imply" it. To meet the more demanding 1e-15 
BER, you better have a lower Rj. 
It doesn't automatically meanyou "do" have a better Rj. 

And for the record, when I hear things like Rj = 0.72 UI ... I shudder.  
People/committees that roll-in the confidence
interval (in N sigma) to the Rj figure, are missing the whole point of having 
an Rj figure and a dual-Dirac
model. It's so you can scale the contribution of Rj to a given BER ... and not 
have to work backwards from some
assumption about what BER was used to roll-it-in, and then forwards again to 
answer questions like yours.

see:

’Jitter analysis: The dual-Dirac model, RJ/DJ, and Q-scale’, White paper by 
Ransom Stephens, 31st December,
 2004, Agilent Technologies. www.agilent.com

MJSQ: Methodologies for Jitter and Signal Quality Specification is a document 
written as part of the INCITS project 
T11.2. http://www.t11.org/index.htm. Reference made to Rev 14, 9th June 2004.


DesignCon 2007. A Comparison of. 
Methods for. Estimating Total Jitter. Concerning Precision, Accuracy
and Robustness,  Martin T Miller, PhD, Chief Scientist at LeCroy Corp,
http://www.designcon.com/infovault/results.asp?BROWSE_ID=3





----- Original Message ----
From: Conrad Herse <herse@xxxxxxxxxxxxxxxxxx>
To: si-list@xxxxxxxxxxxxx
Sent: Mon, June 21, 2010 1:39:08 PM
Subject: [SI-LIST] Re: Rx Eye Mask width, BER, and Jitter

Marty,

Thanks for the comments. My comments below:

Marty Bewildered wrote:
> My first comment is Rj is not a function of BER, Tj is ... or more directly 
> Jrms ... is a function of BER

Isn't Jrms basically 1 sigma (std dev), and Q is some number of sigmas 
to get to a target BER (or am I missing something)? Rj is derived from 
Jrms and the target BER Q, which then is included in Tj.

> Second comment ... if your margin at 1e-12 is 0.2UI, you're in big trouble at 
> 1e-15.

The 0.2 UI was a fabricated number for this example, it could be 
anything. However, more importantly the 0.2 UI is a *receiver eye width* 
derived from an Rx jitter *tolerance*, not a margin. I would expect the 
required Rx eye mask width to *increase* and my receiver jitter 
tolerance to *decrease* for a higher BER. Jitter will increase at a 
higher BER, but won't the receiver require a wider eye mask at a higher 
BER too?

Thanks,

Conrad

> Basically your Tj is getting bigger than 1UI ... so all the numbers don't 
> make sense anymore.

Conrad Herse

> 
> 
> 
> ----- Original Message ----
> From: Conrad Herse <herse@xxxxxxxxxxxxxxxxxx>
> To: si-list@xxxxxxxxxxxxx
> Cc: herse@xxxxxxxxxxxxxxxxxx
> Sent: Mon, June 21, 2010 12:40:13 PM
> Subject: [SI-LIST] Rx Eye Mask width, BER, and Jitter
> 
> Hello experts,
> 
> I've been working on trying to scale receiver eye mask widths to 
> different bit error rates. There is something which is puzzling me which 
> I'm hoping someone can clear up for me.
> 
> I've been studying the dual-Dirac jitter model given by the formula:
> 
> Tj = Dj + 2Q * Jrms
> 
> where Q is a constant from the Complimentary Error function for a given 
> BER (2Q*Jrms = Rj at a specific BER). So if I have a receiver with the 
> following jitter tolerance spec:
> 
> Tj = 0.8 UI
> Dj = 0.3 UI
> Rj = 0.5 UI
> BER = 1e-12
> 
> then, given 2Q = 14 for BER = 1e-12:
> 
> Jrms = 0.5 / 14 = 0.036 UI
> 
> The Rx eye mask width would be:
> 
> 1 - 0.8 = 0.2 UI
> 
> If I want to scale the Rx eye mask width to BER=1e-15 I would expect I 
> need to *grow* the eye mask width by Jrms.
> 
> Given that 2Q = 15.883 at BER = 1e-15, then my new eye mask width would be:
> 
> 0.2 + (15.883 - 14) * 0.036 = 0.268 UI
> 
> So far so good, assuming I did this correctly. Here's what puzzles me, 
> if I adjust my Rx jitter tolerance to accommodate the new Rx eye mask:
> 
> Tj = 1.0 - 0.268 = 0.732 UI
> Dj = 0.3 UI
> Rj = 0.732 - 0.3 = 0.432 UI
> BER = 1e-15
> 
> and recalculate Jrms:
> 
> Jrms = 0.432 / 15.883 = 0.027 UI
> 
> The Jrms number has changed, I wouldn't expect this to happen simply 
> because I'm extrapolating to a different BER. Can someone please 
> straighten me out?
> 
> Thanks!
> 
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