[time-nuts] TIC resolution impact on GPSDO's performance

Dr Bruce Griffiths bruce.griffiths at xtra.co.nz
Mon Dec 25 00:02:58 EST 2006


Poul-Henning Kamp wrote:
> In message <000001c72769$8363beb0$03b2fea9 at athlon>, "Ulrich Bangert" writes:
>
>   
>> For the most of you it will already now be kind of evident that the
>> crossing point defines the magical value that we have to set the loop
>> time constant to but this fact can be formulated with a bit more of
>> scientifical preciseness: At no observation time tau will it be possible
>> to have an ADEV at the OUTPUT of the standard that is lower then BOTH
>> Allan plots at this tau.
>>     
>
> This is not true in general, but does hold true for the example you
> have chosen.  The exact requirement for truthfullness is that the
> noise-processes of your two sources must be uncorrelated.
>
>   
>> What if we had not used the sawtooth corrected values but the raw 1pps
>> phase data?
>>     
>
> Your black line is bogus in the usual "teacher's bad example way".
>
> We know that the hardware PPS signal from gps is phasemodulated
> with a +/- N ns signal which has a box distribution and upper
> frequency limit of 2 Hz and which, subject to temperature stability
> and hanging bridges, has no significant frequency components below
> < 1/500s.
>   
How can this be true?
The PPS output rate is 1Hz!
Are you saying there is significant wideband noise on the 1 PPS output?
Is that lower frequency limit 0.002Hz?
> It follows readily for this, that only teachers trying to show a
> bad example would use the PPS signal for tau > 500 second without
> filtering the higher frequencies out, one way or another.
>
> (In the initial capture phase, no filtering should be used to get
> the best possible frequency response of the PLL, in the "grab" phase
> where the integrator is clamped, a simple exponential average should
> be used.  Once lock has been aquired, linear regression offers a
> useful zero-latency filtering model.)
>
> Your black line should have reflected this.
>
>
> But your further argument has trouble as well.
>
> No causal algorithm can allow you to implement:
>
> 	if (tau < N)
> 		use OCXO
> 	else
> 		use GPS
>
> For some interval of tau, both sources will affect the result, if
> you do post-factum disciplines (ie: paper clocks) you can do it a
> lot closer to optimal, but the statistics gets increasingly nasty
> and the age of your data will approach infinity as the fidelity
> increases.
>
> But most fatal to your message: you look at the wrong kind of stats
> for this particular kind of discipline.
>
> When you discipline an frequency source (OCXO, Rb, Cs) to a phase
> source (GPS, Loran-C, WWV, DCF77, NTP etc), you have to decide for
> which parameter you (optimize your) discipline:
>
> 	Minimum phase offset.
> 	Minimum frequency offset.
> 	Best phase stability.
> 	Best frequency stability.
> 	Best holdover performance in phase.
> 	Best holdover performance in frequency.
>
> All I have heard about here so far, is the first and a few cases
> of the second kind, and neither of those shows their performance
> particularly well on an ADEV plot.
>
> And most amateurs even forget to deal with quartz frequency jumps
> and other 'point-like' upsets.
>
> The theory behind a PLL is really no different from a PID temperature
> regulation, and I highly recommend people read up on those because
> they are generally explained much better than when PLL's are the
> subject.
>
> Before you get any good ideas: note that our measurement noise
> (jitter/resolution) only for very long tau permits meaningful use
> of the D(ifferential) term.  It is possible to use a hysteresis on
> the D term to catch frequency jumps in the xtal, but it is of dubious
> advantage compared to just detecting and resetting the PLL).
>
> A less significant difference from PID regulations is higher order
> integrals:  They are not useful for temperature regulation, but if
> you want to get really nasty with your PLL, you can add another
> term to model the frequency drift, and another one to model the
> change in frequency drift and another one to model the change in the
> change of the frequency drift and ... (you get the idea).
>
> Be aware that floating point is necessary and that rounding errors
> will mess you up if you are not very careful with your sums and
> differences.
>
> I can highly recommend writing a small program or big spreadsheet
> to simulate a PLL so you can play with the coefficients and get a
> feel for the dynamics by watching plots of the phase and frequency
> deltas and ADEV etc.
>
> Merry X-mas!
>
> Poul-Henning
>
>   
Bruce



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