[time-nuts] Method for comparing oscillators

[Magnus Danielson]

Ulrich Bangert wrote:
> Warren and John,
> 
> my point has not been to judge who has to be interested in what. My point
> has only been to use the right terms for it. Let me give an example: John
> uses the term
> 
>> ...but I am more concerned with ... and stability over time
> 
> 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.

As for frequency drift, it has been shown that using a model of

f(t) = A*ln(B*t+1)

or for some cases

f(t) = A*ln(B*t+1) + C*ln(D*t+1)

best models the frequency drift properties. Notice that the drift rate 
is not constant but rather

d(t) = AB / (B*t + 1)

This is not very well handled by the Allan Deviation calculations, so it 
needs to be estimated and removed from the data before hitting the Allan 
Deviation core.

Estimating A and B is fairly trivial if assuming t = 0 for the first 
drift sample and then let t be tau for the next drift sample.

Once stable values for A and B is established, the drift properties can 
be scetched out into the future.

As for the drift chaning direction, this comes from the case when A and 
C has different signs. All this is covered in literature.

For a complete picture of frequency stability, "linear" or mechanical 
changes, environmental changes and noise values all needs to be 
combined. Just looking at the Allan Deviation plot is as foolish as just 
looking at the frequency drift. The experienced designer may however 
know for which tau-range either of them is expected to dominate, and 
thus cheat a bit in the analysis.

Cheers,
Magnus