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

*From*: istvan novak <Istvan.Novak@xxxxxxx>*To*: George.Tang@xxxxxxx*Date*: Fri, 23 Mar 2007 07:45:35 -0400

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 > > > ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: http://www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List technical documents are available at: http://www.si-list.net List archives are viewable at: http://www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu

**Follow-Ups**:**[SI-LIST] Re: Jitter transfer vs. accumulation***From:*Tang, George

**References**:**[SI-LIST] Re: Jitter transfer vs. accumulation***From:*Tang, George

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