Hi there,
I am looking for some advice on stability metrics for a slow oscillator.
The oscillator is used to do a measurement of another quantity which is
connected to the frequency of the Oscillator. I have taken generously
oversampled data of the oscillator voltage and now I have two
contradicting measures:
1) When I record the zero crossings and use them as phase data for the
Allan variance, the minimum is 10^-4 and it initially decays with a
slope of t^-0.5
2) On the other hand if I do least squares fits of the same data with
consecutively longer runs the reported frequency uncertainty goes down
to sigma_f/f = 10^-7. It also drops much faster with t^-1.5 wich seems
to be due to the "Cramèr-Rao lower bound" (not that I really understand
what it means), and it doesn't really go up again
It seems to be common lore that the Allan variance minimum is the best
obtainable frequency accuracy for an oscillator, but the least squares
fits seem to be much better. I have problems understanding this.
I have a mental picture that might explain this, maybe you can tell me
if it seems correct to you: Oscillators are running at a very precise
frequency much better than what our measurement devices are capable of
resolving. So the drop in the Allan variance, that is initially gained
when the measurement is longer, is actually just the reduction of the
measurement error for this precise frequency. Only when the Allan
variance goes up again, we are on a timescale over which the true
frequency of the oscillator varies.
So actually the Allan variance tells us how well we can measure the
frequency stability, but the actual frequency stability at least in the
white noise regime is much higher (several orders of magnitude). What do
you think?
Cheers,
obo
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