[SI-LIST] Re: Rx Eye Mask width, BER, and Jitter
- From: Conrad Herse <herse@xxxxxxxxxxxxxxxxxx>
- Date: Tue, 22 Jun 2010 07:53:52 -0500
Thanks everyone for the replies, I found them most helpful. I think
Wolfgang was able to articulate my question better than I, it's what he
referred to as condition "(b)": receiver strobe jitter. I was trying to
directly use the Rx jitter tolerance to calculate receiver strobe jitter
to scale the eye mask.
I need to study the math examples provided a little more carefully and
review some data sheets again. I'll follow up if I have more questions.
Thanks!
Conrad Herse
Vinu Arumugham wrote:
> 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> |
>>
>>
>>> --------------------------------------------------------------------------------------------------------------------------------------------------|
>>>
>> |------------>
>> | To: |
>> |------------>
>>
>>
>>> --------------------------------------------------------------------------------------------------------------------------------------------------|
>>>
>> | |
>>
>>
>>> --------------------------------------------------------------------------------------------------------------------------------------------------|
>>>
>> |------------>
>> | Cc: |
>> |------------>
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>>
>>> --------------------------------------------------------------------------------------------------------------------------------------------------|
>>>
>> |si-list@xxxxxxxxxxxxx |
>>
>>
>>> --------------------------------------------------------------------------------------------------------------------------------------------------|
>>>
>> |------------>
>> | Date: |
>> |------------>
>>
>>
>>> --------------------------------------------------------------------------------------------------------------------------------------------------|
>>>
>> |06/21/2010 04:50 PM |
>>
>>
>>> --------------------------------------------------------------------------------------------------------------------------------------------------|
>>>
>> |------------>
>> | Subject: |
>> |------------>
>>
>>
>>> --------------------------------------------------------------------------------------------------------------------------------------------------|
>>>
>> |[SI-LIST] Re: Rx Eye Mask width, BER, and Jitter |
>>
>>
>>> --------------------------------------------------------------------------------------------------------------------------------------------------|
>>>
>> |------------>
>> | Sent by: |
>> |------------>
>>
>>
>>> --------------------------------------------------------------------------------------------------------------------------------------------------|
>>>
>> |si-list-bounce@xxxxxxxxxxxxx |
>>
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>>> --------------------------------------------------------------------------------------------------------------------------------------------------|
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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
