[time-nuts] frequency stabilty question

[Magnus Danielson]

Hi Bob,

On 16/08/11 18:20, Bob Camp wrote:
> Hi
>
> This brings in another subtle but significant issue.
>
> We talk about the ADEV being done as the standard deviation of the frequency
> differences, but often that's not what's done. Even with zero dead time,
> there's another bit of magic in there. Drift is removed before the samples
> are used.
>
> Oddly there are multiple approaches to drift removal. It comes as no
> surprise that the more aggressive the drift removal, the better looking the
> result. If you are looking at ADEV, it's always worth asking if (and how)
> the drift was removed.

Indeed. Some (incorrectly) beleive that Hadamard deviation does this. 
Well, Hadamard will cancel linear frequency drift, i.e. f = f_0 + D*t 
but any other drift function will not be fully cancelled. Crystals for 
instance can be found to better match

f = f_0 + A ln (B*t)

Now, toss the Hadamard on that it will make it's third difference on the 
phase and consume the first degree drift, but the higher parts of the 
logarithm expression will still be there. This can be seen as a rising 
slope at higher taus. Sure, the Hadamard will remove much of the first 
degree effect, but for best result use propper higher degrees matching 
and remove the systematic effects such that only noise effects remains. 
Hadamard is however powerful to provide a preview while collecting data. 
For very low rate aging it can also be useful.

In general, ADEV is nice for noises, but fails to give you propper 
feeling of systematic effects, which is best treated in their own 
problem domain. A linear drift can be illustrated with ADEV, but ADEV 
will display it with a bias of 1/sqrt(2) so the composite is actually 
not trustworthy.

Also, you need to check the frequency and phase plots to learn what is 
causing unexpected results. When using TimeLab, the wrapped and 
unwrapped phase and the frequency plots all needs to be checked as they 
highlight different errors. Thermal variations and its systematic effect 
isn't best treated by ADEV for instance.

> Of course there's also pre-filtering as a function of Tau, but that's even
> more exotic.

... and complex.

There are many aspects to correct measurements.

I think I covered some of them in the Allan Deviation article.

Cheers,
Magnus