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

• From: David Instone <dave.instone@xxxxxxxxxx>
• To: steve weir <weirsi@xxxxxxxxxx>
• Date: Mon, 17 Jul 2006 15:31:38 +0100

```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 not an
>> 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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