[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?

[Magnus Danielson]

Hi,

On 2022-05-09 15:05, Attila Kinali wrote:
> 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.

OK, so I'll give it a shot. This works better on whiteboard.

ADEV and friends is not the most direct approach when discussing locked 
oscillators, you need to understand it in terms of phase-noise and then 
you can map that to ADEV and friends.

As you build a PLL, you will low-pass filter the reference with the loop 
bandwidth, and you will highpass the noise of the steered oscillator. A 
PLL will have the unfortunate property of jitter peaking, so you will 
have gain in excess of 1 at the PLL resonance frequency. This 
jitter-peaking will occurr for both the reference noise and the 
oscillator noise, and it will then add up together. You can approximate 
what this will do, but the ADEV and friends will see the energy added 
both from both reference and oscillator, as well as the colouring of the 
jitter peaking. The disturbance of the peak at the PLL natural/resonance 
frequency will for the ADEV be quite similar to adding a sine frequency 
of the same frequency as the PLL natural frequency, and thus causing the 
ADEV and friends to see an additional peaks on top of the underllying 
noise slopes.

Trouble is, at the cut-over frequency you will get a slight peaking 
however you go, and your ADEV will suffer accordingly. What you can do 
is to keep the damping factor high, and thus jitter peaking low. That helps.

You never "win" this game, you only limit your losses.

>
> 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.
A step in phase or frequency will "kill" your ADEV plot. You learn to 
set things up to avoid outliners when using TimeLab. The raised floor 
from it will take a long time to average out.
>
> 			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.

+1: This is in line with what IEEE Std 1139 recommendations. Actually, 
there is more things to include, including bandwidth, number of samples, 
any removal of linear drift etc.

Cheers,
Magnus