[SI-LIST] Re: Rx Eye Mask width, BER, and Jitter
- From: Vinu Arumugham <vinu@xxxxxxxxx>
- To: Conrad Herse <herse@xxxxxxxxxxxxxxxxxx>
- Date: Mon, 21 Jun 2010 15:45:39 -0700
Conrad,
Here's another way of performing the calculation:
For simplicity assume entire RX jitter contribution is RJ.
LinkRJ12 = 1 - DJ = 0.7UI
That's the total RJ contribution from the TX and RX at BER of 1e-12.
TXRJ12 = 0.5UI at BER of 1e-12.
RXRJ12 = sqrt (LinkRJ12^2 - TXRJ12^2) = 0.49UI at BER of 1e-12.
TXRJrms = 0.5/14=0.036 UI
RXRJrms = 0.49/14=0.035 UI
TXRJ15 = 0.036*15.883=0.57UI at BER 1e-15.
RXRJ15 = 0.035*15.883=0.56UI at BER 1e-15.
LinkRJ15 = sqrt(0.57^2+0.56^2)=0.8UI at BER of 1e-15
To operate these TX and RX on a link at a BER of 1e-15, you would have
to reduce the LinkDJ to 1 - LinkRJ15= 1 - 0.8UI = 0.2UI.
RX Jitter tolerance can then be specified as:
RJ = 0.57UI
DJ = 0.2UI
TJ = 0.77UI
BER = 1e-15.
Thanks,
Vinu
wolfgang.maichen@xxxxxxxxxxxx wrote:
> Hello Conrad,
> maybe rephrasing the problem helpf. Let's see if I understood your goal:
>
> - You have a receiver that can liver with an eye opening of 0.2 UI (i.e.
> works correctly if no transition falls into the center 20% of the eye).
>
> - That means total allowed jitter is Tj = (1 - 0.2) UI = 0.8 UI
>
> - Specification further says that out of that total number, max. 0.3 UI
> can be Dj and max. 0.5 UI can be Rj.
>
> It does not seem to me that so far this is dependent on the BER at all.
>
> What can the random jitter of the input signal be so we get BER=1e-15
> instead of BER=1e-12 based on the input signal alone?
>
> BER=1E-12 --> Q = approx. 14 --> Rj (input signal) = 0.5 UI / Q = 0.036 UI
> RMS
> BER=1E-15 --> Q = approx. 16 --> Rj (input signal) = 0.5 UI / Q = 0.031 UI
> RMS
>
> The 0.2 UI required eye opening is not affected by the required BER at
> all. What does change is simply the allowed Rj RMS value (must be smaller
> for smaller BER - no surprise here).
>
>
> However, one thing we did not take into account so far is that the
> receiver will have some internal jitter (strobe jitter) as well. In
> addition the receiver will have some static strobe placement error (i.e.
> the strobe may on average happen at 0.55 UI instead of in the center at
> 0.5 UI). The resulting BER of the received signal is affected by the
> combination of input signal jitter (which is limited by the Rj, Dj and Tj
> specs above), the receiver jitter, and the receiver strobe placement
> error.
>
> Unfortunately, from the available data only the first contributor is
> known. My calculation above basically assumes that the BER is solely given
> by the input signal, with the receiver being perfectly jitter- and
> skew-free. So without further knowledge or assumption about the receiver
> one cannot get a definitive answer.
>
> So let's make some assumptions:
>
> For example, lets assume that the receiver strobe is perfectly placed in
> the center, and the receiver only exhibits random jitter (which is a very
> idealistic assumption). On the other hand, assuming receiver jitter to be
> pure Rj is the most conservative assumption (will overestimate total
> jitter) when extrapolating to lower BERs. So the conclusions below will
> give a conservative estimate.
>
> If the receiver had a 0.2 UI RJ (@ BER 0.2 US this Rj(receiver) = 0.2/14 =
> 0.014 UI RMS), then the BER of the received signal would actually be
>
> Rj(received signal) = approx. BER(input signal) + BER(receive strobe) =
> 1E-12 + 1E-12 = 2E-12
>
> That's clearly not what the spec says (it says that with an input signal
> jitter of 0.3 UI Dj and 0.5 UI Rj you get BER = 1E-12, not 2E-12). So my
> conclusion is that the receiver actually must have much less Rj than
> 0.2/14 UI (i.e. the receiver BER contribution must be negligible compared
> to the input signal BER). How much, that I can't tell from the data. Which
> also means, the available information is not sufficient to answer the
> question. But a reasonable assumption would be that it is at least one
> order of magnitude smaller (i.e. < 1E-13).
>
> But what we CAN say is that in order to get BER=1E-15 in a similar way
> than 1E-12, we need two things:
>
> (a) - have drive signal at BER=1E-15, and
> (b) - have receiver strobe BER << 1E-15
>
> Condition (b) will require the eye opening of the input signal to be
> larger than 0.2 UI (so the receive strobe has more "room" to jitter around
> without causing errors). Is this what you were looking for? Assuming
> BER(receiver) was <1E-13 and we want to keep the same ratio between the
> receiver strobe BER and the input strobe BER (>= 1 order of magnitude),
> then the receiver strobe BER should be <1E-16.
>
> Once you know what (b) yields, you can the calculate the new input signal
> requirements. You can caculate by which factor to enlarge the required eye
> opening with those two numbers (BER before 1E-13 for 0.2 UI opeing, BER
> after 1E-16 for xy UI eye opening --> solve for xy). E.g. assume you find
> that you now need xy = 0.3 UI eye opening, then the new spec for the input
> signal would be:
>
> Tj = (1 - 0.3) = 0.7 UI
> Dj = 0.3 UI (let's use the same we had before)
> Rj = (0.7 - 0.3) = 0.4 UI @ BER 1e-15
>
> --> Rj = approx. 0.4 / Q = 0.4 / 16 = 0.025 UI RMS
>
> So in fact we have TWO new values in order to go from BER 1E-12 to 1E-15:
>
> (1) required eye opening 0.3 (instead of 0.2) (this would be your "growing
> the receive eye)
> (2) maximum signal Rj = 0.025 UI RMS instead of 0.036 UI RMS
>
> Wolfgang
>
>
>
>
>
>
>
>
> James.Mueller@xxxxxxxxxx
> Sent by: si-list-bounce@xxxxxxxxxxxxx
> 06/21/2010 02:18 PM
>
> To
> Conrad Herse <herse@xxxxxxxxxxxxxxxxxx>
> cc
> si-list@xxxxxxxxxxxxx, si-list-bounce@xxxxxxxxxxxxx
> Subject
> [SI-LIST] Re: Rx Eye Mask width, BER, and Jitter
>
>
>
>
>
>
> As the bit error ratio you require gets lower, the Tj your Rx needs to
> tolerate will increase for a given specified Dj and rms jitter. Likewise
> the eye opening will shrink. I'm not sure why you say you expect the "min
> required eye to grow". The Tj tolerance grows so that the eye opening
> "tolerance" shrinks, e.g. the Rx needs to be able to tolerate a smaller
> eye
> opening width in the incoming signal. I'm not sure I'm helping, I think
> part of this is semantics or definitions.
>
> Jim
>
>
>
> James J Mueller
> LeCroy Corporation
> Cell phone: 914-522-8555
>
>
>
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> |Conrad Herse <herse@xxxxxxxxxxxxxxxxxx> |
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> |si-list@xxxxxxxxxxxxx |
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> |06/21/2010 04:50 PM |
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> |[SI-LIST] Re: Rx Eye Mask width, BER, and Jitter |
>
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>
>
>
> Hi Jim,
>
> Maybe this is what's confusing me. The receiver specifies a jitter
> *tolerance*. From this an Rx minimum eye width can be determined. I
> would expect the min required eye width to *grow* when going to
> BER=1e15, since the receiver must *tolerate* more jitter. Making the min
> Rx eye mask smaller at BER=1e-15 doesn't seem correct, it implies the Rx
> jitter tolerance increases at 1e-15. Again, I'm referring to the Rx
> jitter tolerance and what the receiver requires, I understand that the
> actual eye size at the receiver will decrease when more jitter is
> budgeted into the system.
>
> Thanks,
>
> Conrad Herse
>
>
>
> James.Mueller@xxxxxxxxxx wrote:
>
>> Hi Conrad,
>>
>> When you went to calculate the mask size at BER= 1E-15, you added the
>> additional rms jitter contribution instead of subtracting.
>>
>> Jim
>>
>>
>>
>> James J Mueller
>> LeCroy Corporation
>> Cell phone: 914-522-8555
>>
>>
>>
>>
>>
>
>
>> From: Conrad Herse <herse@xxxxxxxxxxxxxxxxxx>
>>
>
>
>
>
>> To: si-list@xxxxxxxxxxxxx
>>
>
>
>
>
>> Cc: herse@xxxxxxxxxxxxxxxxxx
>>
>
>
>
>
>> Date: 06/21/2010 03:41 PM
>>
>
>
>
>
>> Subject: [SI-LIST] Rx Eye Mask width, BER, and Jitter
>>
>
>
>
>
>> Sent by: si-list-bounce@xxxxxxxxxxxxx
>>
>
>
>
>
>>
>>
>>
>> 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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Other related posts:
- » [SI-LIST] Rx Eye Mask width, BER, and Jitter- Conrad Herse
- » [SI-LIST] Re: Rx Eye Mask width, BER, and Jitter- Marty Bewildered
- » [SI-LIST] Re: Rx Eye Mask width, BER, and Jitter- James . Mueller
- » [SI-LIST] Re: Rx Eye Mask width, BER, and Jitter- Conrad Herse
- » [SI-LIST] Re: Rx Eye Mask width, BER, and Jitter- Conrad Herse
- » [SI-LIST] Re: Rx Eye Mask width, BER, and Jitter- Murphy, Martin
- » [SI-LIST] Re: Rx Eye Mask width, BER, and Jitter- James . Mueller
- » [SI-LIST] Re: Rx Eye Mask width, BER, and Jitter- wolfgang . maichen
- » [SI-LIST] Re: Rx Eye Mask width, BER, and Jitter- T.K. Jeon
- » [SI-LIST] Re: Rx Eye Mask width, BER, and Jitter - Vinu Arumugham
- » [SI-LIST] Re: Rx Eye Mask width, BER, and Jitter- Marty Bewildered
- » [SI-LIST] Re: Rx Eye Mask width, BER, and Jitter- Conrad Herse
