[time-nuts] Method for comparing oscillators

[Magnus Danielson]

Steve Rooke wrote:
> 2009/8/6 Magnus Danielson <magnus at rubidium.dyndns.org>:
>> Ulrich Bangert wrote:
> ...
>>> Well, stability over time is what exacly is displayed in a
>>> tau-sigma-diagram
>>> of an oscillator. Since only a few words before he is saying that he is
>>> NOT
>>> intersted into Allan Deviation plots, then he is perhaps interested into
>>> something else?
>> Yes. Sigma-Tau plots of the Allan Deviation fame (with friends) addresses
>> the instability of the noise part of things. For crystal oscillators and
>> other non-atomic oscillators "linear" factors in frequency drift is not best
>> specified, described or measured using that method, which was invented
>> purely to be able to handle the phase noise side of things, not the slow
>> frequency drift.
> 
> For these sorts of measurements on drifting oscillators would it not
> be prudent to use the Hadamard Deviation?

Hadamard Deviation does not fully cancel the non-stable drift.

Just do the math... d(t) = AB/(B*t+1) and derive and you get what 
infects the Hadamard Deviation, i.e.

             AB^2
d'(t) = - ---------
           (B*t+1)^2

So, regardless of which of the Allan Dev friends we have, identifying 
drift mechanism, cancel that out of the data before Allan Dev friend 
processing is the propper way to do it. Hadamard gets you closer in a 
one-step process. I have also played with tricks to calculate the 
constant drift in parallel with building the quadrature for Allan Dev 
and it works out fine too. Gets some of the job done, but drift 
post-processing remains an issue that needs to be handled to get propper 
data out of the measurements. Just cancelling the average drift as 
modeled as a constant drift gets part of the job done, regardless if 
done separate or through Hadamard Deviation.

Cheers,
Magnus