## [SI-LIST] Re: Fibre channel interconnect margins

• From: steve weir <weirsi@xxxxxxxxxx>
• To: David Instone <dave.instone@xxxxxxxxxx>
• Date: Mon, 17 Jul 2006 07:36:51 -0700

```David, the issue here is one of:

1)  I have a physical phenomenon, what is it, and how does it affect
my circuit?  AND
2)  How can I test to see how this phenomenon affects my circuit?

In the case of 1) we are interested in the behavior over a very long
period of time and over many events.  2) imposes an economic
practicality that implores upon us to find a way to predict 1) from
necessarily truncated results.  That practical test consideration
does not cause the natural process to truncate.

Regards,

Steve.
At 07:31 AM 7/17/2006, David Instone wrote:
>Steve, and list
>  Lets try this another way.  The original statement that started
> all this was:
>>I suppose we're way off in the weeds, here, but is the noise actually
>> >unbounded? Or does it just behave in a Gaussian-like manner
>> within the realm
>> >of times/rates that matter for shipping product?
>My take on this is that in real world circuits the jitter, or the
>effects of the noise, is bounded and only behaves in a Gaussian like
>manner within limits.
>Why do I say this?  Well if I want to produce a signal with random
>jitter, ie as per definition unbounded and Gaussian, then I buy a
>noise source add its output to my perfect un-jittered signal using a
>limiting amplifier and I get a signal with 'Random Jitter'.  Well
>for a start I have to pay around \$5000 to get a noise source that
>stands half a chance of actually being Gaussian down to just  +/- 7
>sigma and even then unless the waveform I'm adding it to has the
>right shape it's still not going to produce truly Gaussian
>jitter.  So back to reality, is my 50c IC with \$50 PSU really going
>to have truly Gaussian unbounded jitter out to infinity, or even +/-
>7sigma, when my lab source is struggling to do +/- 7 sigma? Not a
>chance in hell, well maybe 1 in infinity.
>
>So the spec says RJ is unbounded and Gaussian, nice, convenient and
>simple.  But what does it mean in practice?  Could it mean that
>within the limits of your measurement, and also the ability of the
>jitter producing mechanisms in your product, that the jitter
>approximates a Gaussian curve, I believe so.   Now I'm going to risk
>diverting the thread again.  A Gaussian curve is a mathematical
>function that best fits naturally occurring events that seem to be
>random.  Does this force randomly occurring events to fit a Gaussian
>curve out to infinity? Dave
>
>
>steve weir wrote:
>>David, I did not regard it as an attack just an opinion that is
>>different and worth discussing.
>>
>>The basis of our disagreement appears to be in the definition of
>>bound.  I look at things from the standpoint of electrical noise.
>>Time interval in a timing circuit is the result of the magnitude of
>>some electrical quantity, and is always causal, each event defining
>>a new interval follows the previous.  This means that noise
>>effectively multiplies the interval by some factor   1/oo <= K <=
>>oo.  Jitter is still unbounded, but every incremental interval has
>>a positive duration.
>>
>>So far we have been talking about noise in the oscillator itself.
>>
>>Now, let's see what a PLL does to this quagmire.  If noise hammers
>>the VCO then the PLL feedback loop applies gain to divide the
>>effect of the noise.  If we still believe in infinity, infinity
>>divided by anything is still infinity.  In practice will the
>>oscillator stop for an unlimited time?  It will only when it
>>fails.  On the other end, two successive pulses can occur
>>essentially on top of each other.
>>
>>A receiver PLL will take a finite amount of time to realign within
>>a fixed amount of phase to the jittered stream for the case of the
>>oscillator event, and will take a different, much longer amount of
>>time to align to the short term frequency offset that noise in the
>>PLL error amplifier causes.  The phase error between the source
>>stream and the recovered clock in the latter case generally follows
>>a classic 2nd order step response.  The golden PLL is a PLL with
>>specific frequency response and damping.  Even if we have a PLL
>>that uses N=1, the PLL only starts correcting after a timing error
>>is already apparent.  For a timing error of sufficient magnitude
>>data moves outside the timing window, a data recovery error is
>>guaranteed, and no PLL is going to prevent that.  A nasty little
>>problem that gets into systems is power supply noise coupled into
>>the VCO and/or error amplifier by one means or another.  For
>>systems with high Ns it can get really ugly.
>>
>>On a slightly different tack, for a PLL using a PFD, the unit
>>interval is that at the phase comparator input which is VCO/N or
>>Fref.  Noise whacking the error amplifier will push the VCO off
>>frequency until new information arrives to get it back.  If the
>>noise jumps the VCO up it can take up to VCO/N cycles before we
>>start correcting.  If noise slows the VCO down, it will take at
>>least one cycle of Fref to get it back.
>>
>>So, I think the only place that we are having any semantic trouble
>>is on the notion of unbounded noise.  While we likely will never
>>see such a thing, the math really does tell us that an interval can
>>go virtually to zero 1/oo, or last forever.  I think the important
>>part of this concept is that it says that random noise ( jitter )
>>will create data errors sooner or later.  And I think doubt about
>>that is where the discussion began.  The tough issue is finding the
>>actual random jitter.  The value is often way overestimated because
>>deterministic jittter that we have difficulty correlating gets
>>incorrectly classified as RJ.  People turn the crank on the math
>>and conclude that their links are 10E-12 or 10E-14 when they are
>>really more like 10E-20 from an RJ standpoint.
>>
>>Regards,
>>
>>
>>Steve.
>>At 06:35 AM 7/4/2006, David Instone wrote:
>>>Steve,
>>>  Firstly, my initial response was in support of Alan's posting
>>> of FC and other serial standards. FC defines random jitter in FC-PI-3 as
>>>>jitter, random (RJ): Jitter that is characterized by a Gaussian
>>>>distribution. Random jitter is
>>>>defined to be the peak-to-peak value for a BER of 10-12, taken to
>>>>be approximately 14 times
>>>>the standard deviation of the Gaussian distribution.
>>>
>>>
>>>  So lets look at it both ways
>>>>That means that any single incremental interval can never have
>>>>jitter of more than -(1UI-epsilon).
>>>If that jitter is all Gaussian then hasn't it been truncated, or
>>>do we have to say that it's not RJ because it's bounded?
>>>
>>>
>>>>If on the other hand we want to integrate phase compared to some
>>>>distant fixed timing reference, then a stream can theoretically
>>>>precess total time interval error by an unbounded amount.
>>>FC measures jitter against a timing reference derived from a
>>>golden PLL.   If over any finite period of time the RJ causes the
>>>frequency as seen by the PLL to change then the PLL will move the
>>>VCO, thus creating a limit to the max observed RJ.  If the RJ is
>>>distributed so that the frequency does not have to change then the
>>>'single incremental interval' effect will apply.
>>>  Have we not then got a jitter distribution that is Gaussian in
>>> form but with limits to the maximum deviations?
>>>
>>>Regards
>>>Dave
>>>
>>>steve weir wrote:
>>>>David,
>>>>
>>>>I would just like to make certain that we are talking along the
>>>>same lines here.  The operation of the oscillator, no matter what
>>>>its construction is causal.  So the closest that any two events
>>>>can occur is epsilon.  That means that any single incremental
>>>>interval can never have jitter of more than -(1UI-epsilon).
>>>>
>>>>If on the other hand we want to integrate phase compared to some
>>>>distant fixed timing reference, then a stream can theoretically
>>>>precess total time interval error by an unbounded amount.
>>>>
>>>>Regards,
>>>>
>>>>
>>>>Steve.
>>>>At 03:10 AM 7/4/2006, David Instone wrote:
>>>>>Steve,
>>>>>   I didn't disallow an infinite time between events.  I allow
>>>>> for the time between events to be between 0 and infinity, but not
>>>>> negative.
>>>>>Thus if I'm measuring the time between edges and my reference I
>>>>>can measure an infinite time between my reference and a
>>>>>following edge but never more than 1 UI between the last edge and my
>>>>>reference.
>>>>>That last edge could of course be from a edge that should have
>>>>>occurred an infinite amount of time in the future, but from the
>>>>>point of view of the measurement it's only 1 UI early.
>>>>>Regards
>>>>>Dave
>>>>>
>>>>>
>>>>>steve weir wrote:
>>>>>>David, I disagree.  It does not change causality.  It changes
>>>>>>the incremental delay between two events.  Imagine for a moment
>>>>>>that we have a simple relaxation oscillator as the basis of our VCO.
>>>>>>In the presence of an infinitely large noise pulse, which is
>>>>>>the limit for random noise, it takes an infinite amount of time
>>>>>>for the ramp to reach the threshold.  The next cycle will not
>>>>>>begin untilt he current cycle completes.  It may sound like
>>>>>>something from Douglas Adams, but it really is mathematically
>>>>>>and physically sound.
>>>>>>
>>>>>>Regards,
>>>>>>
>>>>>>Steve.
>>>>>>At 01:50 AM 7/4/2006, David Instone wrote:
>>>>>>>Because it makes for a nice simple clean definition.  However,
>>>>>>>I believe you have to take the real world into consideration.
>>>>>>>Allowing the RJ to be really unbounded means that each edge in
>>>>>>>a bit stream could be advanced or delayed by an infinite amount.
>>>>>>>Taken to extremes this means that  the order of  edges  could
>>>>>>>be reversed.
>>>>>>>This is obviously absurd, the measured time between edges can
>>>>>>>reduce until it is zero, it cannot go negative.  The time
>>>>>>>between edges can of course go to +ve infinity, but that isn't
>>>>>>>a bit error, the system has failed or been switched off.
>>>>>>>steve weir wrote:
>>>>>>>>RJ really is unbounded by definition.
>>>>>>>>
>>>>>>>>Steve.
>>>>>>>>At 09:46 AM 7/3/2006, Steven Kan wrote:
>>>>>>>>
>>>>>>>>>>Date: Fri, 30 Jun 2006 21:48:56 -0700
>>>>>>>>>>From: Alan.Hiltonnickel@xxxxxxx
>>>>>>>>>>Subject: [SI-LIST] Re: Fibre channel interconnect margins
>>>>>>>>>>
>>>>>>>>>>In fact, I think that companies DO ship products that toss a random
>>>>>>>>>>error approximately every 10e-xx or so. Why? Because the statistical
>>>>>>>>>>theory behind those errors is that random/Gaussian noise is, by
>>>>>>>>>>definition, unbounded - errors are a fact of life, even if the error
>>>>>>>>>>rate is very low.
>>>>>>>>>I suppose we're way off in the weeds, here, but is the noise actually
>>>>>>>>>unbounded? Or does it just behave in a Gaussian-like manner
>>>>>>>>>within the realm
>>>>>>>>>of times/rates that matter for shipping product? I suppose
>>>>>>>>>if I sat in my
>>>>>>>>>chair for long enough, a truly unbounded system might cause
>>>>>>>>>a gold bar to
>>>>>>>>>pop into existence on my desk, but my empirical GBR (gold-bar rate) is
>>>>>>>>>currently 0.
>>>>>>>>>
>>>>>>>>>------------------------------------------------------------------
>>>
>>
>>
>
>--
>Dave Instone
>Oxford Semiconductor Ltd
>25 Milton Park
>Abingdon
>Oxon ox14 4ea
>UK
>www.oxsemi.com
>+44 (0)1235 824963
>
>

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