Magnus Danielson wrote:
Steve Rooke wrote:
2009/8/6 Magnus Danielson <mag...@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.
The Hadamard processing (Dev, ModDev or Tot) gives another B term, which
considering that B is fairly small gives a drift-gain. As the series
progresses, the drift derivate dies away faster (1/t^2 rather than 1/t)
than for Allan processing so the longer time sequence used, the better
suppression of the drift mechanism (which is true for Allan processing too).
So, in this context Hadamard is better... but it still does not nail it.
It may be sufficient however. Estimating A and B and remove the trend
from the data isn't too hard.
It is an interesting exercise to estimate A and B, produce the drift
only time-series and see what Allan and Hadamard time-series for that
looks like and then compare them to the Allan and Hadamard time-series
of the raw data. Cranking out a compensated time-series and produce the
Allan and Hadamard time-series for that isn't that hard either.
Do plot the frequency or phase plot of the estimated curve along with
the actual data, along with the difference to make sure you have a good
match. This can give you a good hint that your drift estimate is either
bad or has the wrong model.
That way you can really estimate if you where drift limited or not.
Cheers,
Magnus
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