[SI-LIST] Re: Jitter transfer vs. accumulation

George,

I have been following with great interest the discussion on jitter. 
I need to admit that I did my PhD on stochastic processes in
precision measurements many years ago, so my math has become
rusty.  For this reason I will leave the details to those who practice
them today. 

However, I have a question to you about the applications.  If I am
not mistaken, in your arguments you assume that the power going
to the VCO and PLL circuit is clean, or at least clean enough that
power-supply modulation can be neglected.  Does this mean that
for chips that you design the customers get a specification regarding
how clean the supply rail needs to be going to the analog pins?

Regards,

Istvan Novak
SUN Microsystems


Tang, George wrote:

>Alfred,=20
>
>See comments in [[[[[ ]]]]]. =20
>
>George=20
>
>
>-----Original Message-----
>From: Alfred P. Neves [mailto:al.neves@xxxxxxxxxxx]=20
>Sent: Wednesday, March 21, 2007 11:07 PM
>To: weirsi@xxxxxxxxxx; Tang, George; si-list@xxxxxxxxxxxxx
>Subject: RE: [SI-LIST] Re: Jitter transfer vs. accumulation
>
>George,
>
>
>  
>
>>{{{{{Alfred made the initial postulate that open-loop VCO has rms=20
>>jitter governed by his funny equation Y=3DmX + b, where Y is the rms=20
>>jitter, X is the time duration of measurement, and m > 0.  This shows=20
>>that as time goes to infinity, the rms jitter of the open-loop VCO also
>>    
>>
>
>  
>
>>goes to infinity.
>>    
>>
>
>No George, this is not what I said.  It is the autocorrelation record of
>the VCO that increases linearly on a log-log plot, where the axis are
>log(RMS jitter) and log(time interval length), where this is not to be
>confused with an RMS jitter or whether it is bounded or not. =20
>
>[[[[[Amazing.  If your autocorrelation record for the open-loop VCO
>looks like Y=3DmX + b, you have either invented a random-noise-free
>environment (congratulations to you,) or your environment is so bad that
>it is completely dominated by deterministic modulation so you cannot
>take clean measurements at all.  My guess is that the latter case is the
>truth.  ]]]]]]]=20
>
>
>I already
>provided numerous references regarding this and can also provide
>numerous measurements for several VCO's to illustrate VCO RMS jitter
>characteristics versus measurement interval.  We have used this analysis
>100's of times for closed (and open loop) PLL analysis to determine the
>PLL loop bandwidth and peaking in the PLL loop response. =20
>
>[[[[[Like I said before, we do not see this problem in our measurements.
>The VCO RMS jitter is bounded, and so is the PLL RMS jitter.  The RJ
>distribution takes on a true Gaussian waveform.  In addition to that, we
>test our communication channels (including TX, RX, &PLL) for weeks with
>no errors.  All our measurements fairly closely match up with the system
>BER predicted by the model simulation.  We do not see the problems that
>you are fighting with.  ]]]]]=20
>
>
>You can also
>use this analysis to analyze jitter problems like spurious response due
>to charge pump leakage, power supply junk like switching noise or HF
>digital, XTALK in the substrate, SSO, and jitter multiplication from PLL
>to PLL.  The basis for this analysis is work by John McNeil in
>collaboration with Analog Devices in the mid 90's - have you read the
>reference already provided, I can send you a copy if need be?   I didn't
>originate the concept, just use the practical elements to analyze PLL's
>and VCO's.  Before you belittle this, become dismissive, or make any
>more personally targeted comments it may behoove you to do a bit of
>homework.   And once again, you are asked to significantly raise the
>level of your professionalism in your communications.  =20
>
>  
>
>>He further claimed that with the feedback loop of=20
>>the PLL, the rms jitter became bounded.  You don't think Alfred was=20
>>crazy enough to make the mistake of comparing phase jitter of VCO to=20
>>the RMS jitter of the PLL, do you?  That will be comparing apples to=20
>>bananas, let alone oranges
>>    
>>
>
>No, I did not say this either.  The reference was regarding the
>autocorrelation record, NOT any comment regarding characteristics of VCO
>RMS jitter.  A VCO has certain properties:   It has poor frequency
>stability, it is temperature sensitive, it is not WSS (wide sense
>stationary), it has a LOT of low frequency jitter due to numerous 1/f
>noise sources, it also has unbounded RMS jitter, but the estimate of the
>RMS jitter is difficult to measure since:   Measure the RMS of a VCO
>over a certain time T, remeasure the RMS jitter later over the same time
>interval and you will arrive at a different RMS number since it is not a
>stationary process.   Sample size really has little to do with this.
>BTW, do you have data on "stable" VCO's in terms of PPM frequency drift
>versus time, after you claim the temperature stabilizes in 1-2 hours.
>
>[[[[[If the RMS RJ of the VCO is unbounded, the closed-loop PLL will
>never be fully stable since the feedback has finite correction
>capability.  The only way the PLL can be fully stable is that the RMS
>jitter of the VCO HAS TO BE BOUNDED.  We measure the PLL for say 20
>minutes on day one and another 20 minutes on day 2 and day 3, and the
>Peak-to-Peak jitter and RMS jitter for each day matches the results of
>the other days down to 0.1ps range.  To say that the VCO and/or the PLL
>has unbounded RMS jitter will be a tough tough sell, since you will
>never be able to get this kind of repeatability otherwise.  ]]]]]]=20
>
>
>NOW, place the VCO into a PLL loop that is locked on a stable input
>signal, the VCO accumulated phase jitter  is shaped by the PLL loop
>response.  The RMS RJ jitter measured (using some RJ-DJ extraction) will
>be unbounded  - by definition.   =20
>
>[[[[[Why?  What equipment do you use to give you such results? ]]]]]
>
>The resulting PLL accumulated jitter,
>phase jitter, or autocorrelation record will not continue to increase
>past a value related to the PLL loops bandwidth, however (assuming the
>loop is stable).  =20
>
>
>[[[[[Phase jitter is bounded??  What equipment shows that! ]]]]]]
>
>This is due to the intrinsic PLL loop gain. =20
>
>[[[[[No, you are wrong, again.  Even when the PLL is in the locked
>operation, the feedback can only correct the VCO jitter within the loop
>bandwidth.  Beyond that, the feedback cannot do anything, period.  When
>the overall PLL output RMS jitter is measured to be bounded across all
>frequencies, then the VCO RMS jitter *must also be bounded across all
>frequencies*. =20
>
>On the other hand, phase jitter for a locked PLL is unbounded due to
>probability of random events.  ]]]]]
>
>
>My point is that the way to deal with both VCO's and the VCO-PLL
>integrated loop is with autocorrelation analysis.  We have addressed a
>lot of data recovery issues, PLL and VCO design issues using these
>methods, solved a lot of problems.   Unfortunately, these methods are
>not used that heavily (there is one exception in the industry however),
>but we see value in the approach especially in regard to Chris's initial
>email where you want to analyze peaking and jitter multiplication from
>TX to RX, including models of the reference PLL or oscillator and signal
>path.
>
>[[[[[I do not doubt the validity of autocorrelation theories, but I
>highly suspect that you have valid data to support your claims.
>Especially when your environment gives you data in the form of Y =3D mX =
>+
>b.  ]]]]]
>
>
>
>Alfred P. Neves      <*)))))><{
>
>=20
>Hillsboro Office:
>735 SE 16th Ave.
>Hillsboro, OR, 97123
>(503) 679 2429 Voice
>(503) 210 7727 Fax
>=20
>Main Corporate office:
>Teraspeed Consulting Group LLC=20
>121 North River Drive=20
>Narragansett, RI 02882
>(401) 284-1827 Business
>(401) 284-1840 Fax=20
>http://www.teraspeed.com
>=20
>Teraspeed is the registered service mark=20
>of Teraspeed Consulting Group LLC
>=20
>
>
>-----Original Message-----
>From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
>On Behalf Of steve weir
>Sent: Wednesday, March 21, 2007 8:29 PM
>To: Tang, George; si-list@xxxxxxxxxxxxx
>Subject: [SI-LIST] Re: Jitter transfer vs. accumulation
>
>
>George, thanks for the reply.
>At 05:02 PM 3/21/2007, you wrote:
>  
>
>>Steve,
>>
>>Please see comments in {{{{{ }}}}} below.
>>
>>
>>George
>>
>>
>>snip
>>-----Original Message-----
>>From: steve weir [mailto:weirsi@xxxxxxxxxx]=3D20
>>Sent: Tuesday, March 20, 2007 4:10 AM
>>To: Tang, George; Alfred P. Neves; Chris Cheng; si-list@xxxxxxxxxxxxx
>>Subject: Re: [SI-LIST] Re: Jitter transfer vs. accumulation
>>
>>George, please correct me if I am wrong, but I believe:
>>
>>1) That the inverter gain K is both temperature and supply voltage=20
>>dependent.
>>
>>{{{{{True, not a function of time. }}}}}
>>
>>    
>>
>Good.  Then do we also agree that when the supply voltage and=20
>temperature both vary with time that the gain does as well?  If not why?
>
>
>  
>
>>2) That even in an isothermal, constant supply, and zero noise =
>>    
>>
>Vref=3D20=20
>  
>
>>environment, running open-loop that in the limit any single VCO=3D20=20
>>output interval can vary from epsilon*ring_stages to approximately=3D20 =
>>    
>>
>
>  
>
>>Vcc/Vths_nom*UI*ring_stages.
>>
>>{{{{{You CANNOT rewrite the laws of physics with your funny formula.=20
>>The input sensitivity (in mV) is not proportional to VCC voltage nor=20
>>inversely proportional to Vth.  Throwing such formulae around does not=20
>>fool people into believing you.  }}}}}
>>    
>>
>
>George there is no attempt to "fool people".  Please keep the=20
>discussion on a professional level.
>
>The minimum period for one inverter in the presence of a large enough=20
>shot noise pulse is the inverter minimum delay time epsilon, is it not?
>An arbitrarily large noise shot pulse can only defer a transition by=20
>a maximum amount of time.  If you object to the approximation of=20
>Vcc/Vths I am open to discussion of alternative approximations.
>
>
>  
>
>>Maybe I don't understand what you mean by
>>
>>"My assertion is that when temperature,
>>voltage, low noise level and fixed noise frequency parameters are all=20
>>in steady-state condition, the open-loop VCO output jitter shall be=20
>>constant."
>>
>>{{{{{The output RMS jitter shall be constant.  When we talk about PLL=20
>>or VCO jitter, we usually talk about the RMS jitter.  Phase jitter is=20
>>meaningless unless you specify the sample size.  }}}}}
>>
>>
>>That sounds like Dj induced from power supply feedback.
>>
>>
>>{{{{{Whatever the cause, the result is the same.  }}}}}
>>    
>>
>
>OK I think we agree there is a big difference between peak jitter and=20
>RMS jitter.  So, I think we can put that aside and concentrate on RMS
>jitter.
>
>
>  
>
>>My interpretation is that even in this pristine environment of a=3D20=20
>>perfect power supply the oscillator exhibits unbounded Rj.  If it =
>>    
>>
>is=3D20
>
>  
>
>>bounded, what limits it?
>>
>>{{{{{Alfred made the initial postulate that open-loop VCO has rms=20
>>jitter governed by his funny equation Y=3DmX + b, where Y is the rms=20
>>jitter, X is the time duration of measurement, and m > 0.  This shows=20
>>that as time goes to infinity, the rms jitter of the open-loop VCO also
>>    
>>
>
>  
>
>>goes to infinity.  He further claimed that with the feedback loop of=20
>>the PLL, the rms jitter became bounded.  You don't think Alfred was=20
>>crazy enough to make the mistake of comparing phase jitter of VCO to=20
>>the RMS jitter of the PLL, do you?  That will be comparing apples to=20
>>bananas, let alone oranges.
>>
>>My claim is that both VCO rms jitter and PLL rms jitter are bounded,=20
>>and the closed-loop feedback circuit simply attenuates the open-loop=20
>>rms jitter.  Both circuits have unbounded phase jitters.  }}}}}
>>    
>>
>
>So it sounds to me that we agree that Rj is unbounded.  My experience=20
>agrees with Al's assertion that due to Rj, RMS jitter does creep=20
>upwards with time.  This is the evil of the 1/f noise corner=20
>exhibited by every DC amplifier I have encountered.  If noise density=20
>/ square root frequency were the RMS value wouldn't creep.  What is
>wrong here?
>
>I have to agree with you that an indefinite divided by a definite is=20
>still indefinite.  Al will have to address whether he was saying that=20
>feedback bounds peak jitter, and if so why.
>
>
>
>  
>
>>In my world, ( which may be perverse ) the only way that we get to=3D20 =
>>    
>>
>
>  
>
>>bound Rj is to bound the number of UIs, and we don't get to do =
>>    
>>
>that=3D20=20
>  
>
>>until we close the feedback loop.
>>
>>
>>{{{{{Sorry, another funny theory of yours.  RJ is a statistical=20
>>probability.  Bounding the number of UIs does not bound the=20
>>peak-to-peak RJ.  Closing the feedback loop does not bound RJ p-p. =20
>>}}}}}
>>
>>    
>>
>
>I acknowledged that I mispoke on this in my private e-mail to=20
>you.  The likelihood that an event outside some magnitude will occur=20
>shrinks with reduced exposure.  Applying feedback cannot reduce the=20
>limit which remains indefinite.  It does however effectively reduce
>sigma.
>
>  
>
>>In my mind this goes back to=3D20
>>Chris' issue which is that from the loop cut-off up to 1/UI the =
>>    
>>
>VCO=3D20=20
>  
>
>>accumulates phase error based on thermal, power supply noise, and=3D20=20
>>reference voltage noise disturbances with little or no=3D20 =
>>    
>>
>attenuation.
>
>  
>
>>It is only well within the closed loop B/W that=3D20 feedback =
>>    
>>
>diminishes=20
>  
>
>>those error terms WRT the apparent reference=3D20 timing source.  Is =
>>    
>>
>this
>
>  
>
>>incorrect?
>>
>>
>>{{{{{No.  Phase jitter is always accumulated regardless open-loop or=20
>>closed-loop.  Closing the loop does attenuate the phase error within=20
>>the bandwidth, but RMS RJ does not go to zero.  }}}}}
>>
>>    
>>
>
>We agree that feedback cannot drive jitter to zero.  I remain at odds=20
>with your blanket assertion that phase jitter accumulates in a closed=20
>loop as well as an open loop.  Jitter is a noise term, and all my=20
>references state that a feedback loop works to reduce noise terms of=20
>the elements within the loop.  Do you have a reference as to why this=20
>would not be so in this situation?
>
>It appears we agree that the loop acts to reduce phase error which is=20
>what we care about and where Chris' complaint came from.  We appear=20
>to also agree that as we slide down the GBW curve the amount of=20
>correction shrinks.  Do we agree that well above the 0db crossing the=20
>loop does almost nothing to adjust the VCO phase to match the=20
>incoming data stream?  If we agree then I think Chris' point is=20
>made.  If we don't, I would like to know why.  It may be for the=20
>particular standards that Chris is unhappy about that other concerns=20
>drove the cut-off frequencies selected.  But from the narrow=20
>perspective of the PLL bandwidth impact on CDR function I see his point.
>
>  
>
>>If so, why?  Absent feedback, I=3D20
>>expect the each inverter in the oscillator to exhibit 1/f noise =
>>    
>>
>like=3D20
>
>  
>
>>any other amplifier no matter how clean the power supply is.  Do =
>>    
>>
>you=3D20
>
>  
>
>>agree?  If not, why?
>>
>>{{{{{Sure.  But with feedback, the same is still true that the random=20
>>noise is still present.  That is not the point of the argument.  }}}}}
>>
>>    
>>
>
>I am not sure if we agree that feedback attenuates all types of noise.
>Do we?
>
>
>  
>
>>I agree that designing a stable VCO and feeding it with clean low=3D20=20
>>impedance power are important towards achieving low jitter.  But I=20
>>am=3D20 having difficulty following the apparent idea that achieving=20
>>those=3D20 goals eliminates jitter components as opposed to reducing =
>>    
>>
>them
>
>  
>
>>to=3D20 small values.  Is there a conflict between semantics of "very=20
>>small"=3D20 and "zero"?
>>
>>
>>{{{{{I never said that jitter can be eliminated.  I only said that RMS=20
>>jitter is bounded for both VCO and PLL.  Alfred made the assertion that
>>    
>>
>
>  
>
>>VCO has unbounded rms jitter, but PLL has bounded rms jitter.  The=20
>>funny equations you guys put out do not help with your arguments at=20
>>all. }}}}}
>>
>>    
>>
>
>Al is very capable and knowledgeable in this area.  I do not speak=20
>for him.  It would be a lot easier to reach a common understanding if=20
>you could tone down the open hostility.
>
>
>  
>
>>Regards,
>>
>>
>>Steve.
>>    
>>
>snip=20
>
>  
>

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