Poul-Henning Kamp wrote: > In message <[EMAIL PROTECTED]>, "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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