[ntp:questions] NTP phase lock loop inputs and outputs?

David L. Mills mills at udel.edu
Fri May 30 15:06:07 UTC 2008


Bill,

No. You are averaging an average. You are trying to bait me with further 
discussion. I am done.

Dave

Unruh wrote:

> "David L. Mills" <mills at udel.edu> writes:
> 
> 
>>Bill,
> 
> 
>>Read it again. Judah takes multiple samples to reduce the phase noise, 
>>not to improve the frequency estimation.
> 
> 
> Dave: The frequency estimate is done by subtracting two phase
> determinations. Thus the phase noise enters the frequency determination. By
> reducing the phase noise you reduce the frequency noise as well. I think
> you need to read it again, but us just telling the other to read properly
> will not help. 
> 
> The frequency estimate is obtained in NTP and in his procedure by making
> phase measurements. 
> f_i= (y_i-y_{i-1})/T
> If y_i=z_i+e_i where z_i is the "true" time and e_i is a gaussian random
> variable, then delta f_i= sqrt( <e_i^2>+<e_{i-1}^2>)/T
> By reducing <e_i^2> you reduce delta f_i. And as you point out, you can
> reduce <e_i^2> by making a bunch of measurements. Those measurements can be
> all done at the end points or spread over the time interval T. The latter
> is not quite as effective in reducing delta f_i since many of the
> measurements do not have as long a "lever arm" as if they were all at the
> endpoints, and that is why uniform sampling is about sqrt(3) worse than
> clustering at the end points. But in either case, the more measurements you
> make the more you reduce the uncertainty in the frequency estimate. 
> 
> Anyway, at this point everyone else has enough information to make up their
> own mind. 
> 
> 
> 
> 
>>Dave
> 
> 
>>Unruh wrote:
> 
> 
>>>You must have read a different paper than that one. I found it (through our
>>>library) and it says that if you have n measurements in a time period T,
>>>the best strategy is to take n/2 measurements at the beginning of the time
>>>and n/2 at the end to minimize the effect of the white noise phase error on the
>>>frequency estimate. That is perfectly true, and gives an error which goes
>>>as sqrt(4/n)delta/T rather than sqrt(12/n)(delta/T) for equally spaced
>>>measurements (assuming large n) T is the total time interval and delta is the std dev of each phase measurement . But it certainly does NOT say that if you have n
>>>measurements, just use the first and last one to estimate the slope. 
>>>
>>>If you have n measurements, the best estimate of the slope is to do a least
>>>squares fit. If they are equally spaced, the center third do not help much
>>>(nor do they hinder), but a least squares fit is always the best thing to
>>>do. 
>>>
>>>
>>>"David L. Mills" <mills at udel.edu> writes:
>>>
>>>
>>>
>>>>Bill,
>>>
>>>
>>>>NIST doesn't agree with you. Only the first and last are truly 
>>>>significant. Reference: Levine, J. Time synchronization over the 
>>>>Internet using an adaptive frequency locked loop. IEEE Trans. UFFC, 
>>>>46(4), 888-896, 1999.
>>>
>>>
>>>>Dave
>>>
>>>
>>>>Unruh wrote:
>>>
>>>
>>>>>"David L. Mills" <mills at udel.edu> writes:
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>>Bill,
>>>>>
>>>>>
>>>>>>Ahem. The first point I made was that least-squares doesn't help the 
>>>>>>frequency estimate. The next point you made is that least-squares 
>>>>>>improves the phase estimate. The last point you made is that phase noise 
>>>>>
>>>>>
>>>>>No. The point I tried to make was the least squares improved the FREQUENCY 
>>>>>estimate by sqrt(n/6) for large n, where n is the number of points (assumed
>>>>>equally spaced) at which the phase is measured. I am sorry that the way I
>>>>>phrased it could have been misunderstood.
>>>>>
>>>>>
>>>>>The phase is ALSO improved proportional to sqrt(n)
>>>>>. 
>>>>>This assumes uncorrelated phase errors dominate the error budget. 
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>>is not important. Our points have been made and further discussion would 
>>>>>>be boring.
>>>>>
>>>>>
>>>>>Except you misunderstood my point. It may still be boring to you. 
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>
>>>>>>Dave
>>>>>
>>>>>
>>>>>>Unruh wrote:
>>>>>>
>>>>>>
>>>>>>
>>>>>>>"David L. Mills" <mills at udel.edu> writes:
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>>Bill,
>>>>>>>
>>>>>>>
>>>>>>>>If you need only the frequency, least-squares doesn't help a lot; all 
>>>>>>>>you need are the first and last points during the measurement interval. 
>>>>>>>
>>>>>>>
>>>>>>>Well, no. If you have random phase noise, a least squares fit will improve
>>>>>>>the above estimate by roughly sqrt(n/4) where n is the number of points.
>>>>>>>That can be significant. It is certainly true that the end points have the
>>>>>>>most weight ( which is why the factor of 1/4). Ie, if you have 64 points,
>>>>>>>you are better by about a factor of 4 which is not insignificant. 
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>>The NIST LOCKCLOCK and nptd FLL disciplines compute the frequency 
>>>>>>>>directly and exponentially average successive intervals. The NTP 
>>>>>>>>discipline is in fact a hybrid PLL/FLL where the PLL dominates below the 
>>>>>>>>Allan intercept and FLL above it and also when started without a 
>>>>>>>>frequency file. The trick is to separate the phase component from the 
>>>>>>>>frequency component, which requires some delicate computations. This 
>>>>>>>>allows the frequency to be accurately computed as above, yet allows a 
>>>>>>>>phase correction during the measurement interval.
>>>>>>>
>>>>>>>
>>>>>>>He of course is not interested in phase corrections. 
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>>Dave
>>>>>>>
>>>>>>>
>>>>>>>>Unruh wrote:
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>>David Woolley <david at ex.djwhome.demon.co.uk.invalid> writes:
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>Unruh wrote:
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>>I do not understand this. You seem to be measuring the offsets, not the
>>>>>>>>>>>frequencies. The offset is irrelevant. What you want to do is to measure
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>Measuring phase error to control frequency is pretty much THE standard 
>>>>>>>>>>way of doing it in modern electronics.  It's called a phase locked loop 
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>Sure. In the case of ntp you want to have zero phase error. ntp reduces the
>>>>>>>>>phase error slowly by changing the frequency. This has the advantage that
>>>>>>>>>the frequency error also gets reduced (slowly). He wants to reduce the
>>>>>>>>>frequency error only. He does not give a damn about the phase error
>>>>>>>>>apparently. Thus you do NOT want to reduce the frequecy error by attacking
>>>>>>>>>the phase error. That is a slow way of doing it. You want to estimate the
>>>>>>>>>frequency error directly. Now in his case he is doing so by measuring the
>>>>>>>>>phase, so you need at least two phase measurements to estimate the
>>>>>>>>>frequency error. But you do NOT want to reduce the frequency error by
>>>>>>>>>reducing the phase error-- far too slow. 
>>>>>>>>>
>>>>>>>>>One way of reducing the frequency error is to use the ntp procedure but
>>>>>>>>>applied to the frequency. But you must feed in an estimate of the frequecy
>>>>>>>>>error. Anothr way is the chrony technique. -- collect phase points, do a
>>>>>>>>>least squares fit to find the frequency, and then use that information to
>>>>>>>>>drive the frequecy to zero. To reuse past data, also correct the prior
>>>>>>>>>phase measurements by the change in frequency.
>>>>>>>>>(t_{i-j}-=(t_{i}-t_{i-j}) df
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>(PLL) and it is getting difficult to find any piece of electrnics that 
>>>>>>>>>>doesn't include one these days.  E.g. the typical digitally tuned radio 
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>A PLL is a dirt simply thing to impliment electronically. A few resistors
>>>>>>>>>and capacitors. It however is a very simply Markovian process. There is far
>>>>>>>>>more information in the data than that, and digititally it is easy to
>>>>>>>>>impliment far more complex feedback loops than that.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>or TV has a crystal oscillator, which is divided down to the channel 
>>>>>>>>>>spacing or a sub-multiple, and a configurable divider on the local 
>>>>>>>>>>oscillator divides that down to the same frequency.  The resulting two 
>>>>>>>>>>signals are then phase locked, by measuring the phase error on each 
>>>>>>>>>>cycle, low pass filtering it, and using it to control the local 
>>>>>>>>>>oscillator frequency, resulting in their matching in frequency, and 
>>>>>>>>>>having some constant phase error.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>>the offset twice, and ask if the difference is constant or not. Ie, th
>>>>>>>>>>>eoffset does not correspond to being off by 5Hz. 
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>ntpd only uses this method on a cold start, to get the initial coarse 
>>>>>>>>>>calibration.  Typical electronic implementations don't use it at all, 
>>>>>>>>>>but either do a frequency sweep or simply open up the low pass filter, 
>>>>>>>>>>to get initial lock.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>And? You are claiming that that is efficient or easy? I would claim the
>>>>>>>>>latter. And his requirements are NOT ntp's requirements. He does not care
>>>>>>>>>about the phase errors. He is onlyconcerned about the frequency errors.
>>>>>>>>>driving the frequency errors to zero by driving the phase errors to zero is
>>>>>>>>>not a very efficient technique-- unless of course you want the phase errors
>>>>>>>>>to be zero( as ntp does, and he does not). 
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>




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