[time-nuts] Method for comparing oscillators

[Steve Rooke]

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?

Cheers,
Steve

> 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
>
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-- 
Steve Rooke - ZL3TUV & G8KVD
A man with one clock knows what time it is;
A man with two clocks is never quite sure.