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

From: "T.K. Jeon" <tkjeon@xxxxxxxxxxx>
To: Conrad Herse <herse@xxxxxxxxxxxxxxxxxx>, "si-list@xxxxxxxxxxxxx" <si-list@xxxxxxxxxxxxx>
Date: Mon, 21 Jun 2010 15:16:54 -0700

Hi Conrad,

The rx jitter tolerance mask usually shows a diamond shape. So let's say a 
vertex of left extreme is X1, then X1=DJ/2+Q*Jrms, hence, the right extreme is 
1-X1. This tells the width of the tolerance mask gets narrower as Q is 
increased. 

From your example, the width is 0.2UI and 0.12UI for BER of 1E-12 and 1E-15, 
respectively. In the case of 1E-15, RJ becomes 0.58UI(0.88-0.3), therefore Jrms 
didn't change.

TK

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] On 
Behalf Of Conrad Herse
Sent: Monday, June 21, 2010 12:40 PM
To: si-list@xxxxxxxxxxxxx
Cc: herse@xxxxxxxxxxxxxxxxxx
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!

-- 
Conrad Herse

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References:
- [SI-LIST] Rx Eye Mask width, BER, and Jitter
  - From: Conrad Herse

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

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