[time-nuts] Re: Can the ADEV of a GPSDO output ever be lower than the minimum of the ADEV of the internal oscilator and the ADEV of the GPS PPS?

[Attila Kinali]

On Fri, 29 Apr 2022 16:53:58 +0200
André Balsa <andrebalsa at gmail.com> wrote:

> Mathematically, no, a GPSDO cannot have a lower uncertainty (ADEV) than the
> minimum observable uncertainty (ADEV) of the combined oscillator
> (disciplined clock) and PPS (disciplining clock) from the GPS receiver.
> Unless there is some magic trick to remove the uncertainty in a clock that
> I am not aware of. ;)

This is not quite true. 

Keep in mind that the *DEV metrics all implicitly assume that the noise
is Gauss distributed and has a PSD of the form of 1/f^a, a ∊ [0,4]
and a high-frequency cut-off. The moment you leave this relatively
restrictive class of functions you have to validate that the *DEV metric
you are using is still producing what you think it does. One common function
for which we have done this are quadratic functions (with noise), also
known as "linear frequency drift". But we have done so for a scant few
other functions.

If you have read my mail a few days ago, then you might have noticed that
few oscillators we have actually fit into this class. And the "worse" they
are, the less they fit. An OCXO can have sudden phase and frequency jumps.
Not to mention its temperature dependency which will lead to some phase
function which looks noise like, even slightly self-similar (another
characteristic of 1/f^a noise), but actually isn't. There is some periodic
behaviour in it, at different repetition rates, together with linear,
quadratic and cubic components. Go to a TCXO or even a simple XO and
things get even worse.

I can't go into the mathematical details as I don't have nearly enough
knowledge about the nitty gritty stuff of *DEV. But we have people here
who know way more than I do, who could chip in.

As for the case at hand. There has been a plot of the TCXO's free running
behaviour earlier. In which one could see that the TCXO had some quite
distinct frequency steps, presumably from the temperature compensation.
Between these the phase was pretty stable. Which means the ADEV gets
detoriated by the frequency steps and doesn't see these "flat" portions
inbetween, not to mention it breaks with the assumption which ADEV is
built upon. Now, if the control loop hits a sweet spot where the loop
compensates these frequency steps quickly but without degrading the 
"flat" portions inbetween, then the ADEV of the combined TCXO + PPS + control loop
could indeed be lower than the individual components. But without a closer
look at what happens to the phase, it is hard to tell whether this is a
genuine effect of the control loop, an artifact of the simulation or simply
a bug somewhere.

			Attila Kinali


PS: Please, for the sake of all that is ticking, whenever you post an *DEV plot,
add error bars. *DEV are statistical figures. And like all statistical figures
they have an uncertainty. Without the error bars it is hard to judge whether the
values are statistically significant or just some randomly thrown dice because
of not enough data.

-- 
In science if you know what you are doing you should not be doing it.
In engineering if you do not know what you are doing you should not be doing it.
        -- Richard W. Hamming, The Art of Doing Science and Engineering