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

[Poul-Henning Kamp]

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.

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

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