Measurement uncertainty of a noisy reference

[splin]

How accurately can a reference which has 1/f noise be measured, assuming a hypothetical noise and drift free measurement system?

Take the example of the LTZ1000 with 0.1Hz to 10Hz noise of 1.2uV p-p and a 1/f corner frequency around 1.3Hz. Averaging measurements over ever longer periods doesn't help much, if at all, once you get into the 1/f region. It also becomes difficult (impossible?) to distinguish between low frequency noise and drift.

So what is the relationship between uncertainty and noise levels and particularly 1/f noise?

What for example would be the best uncertainty that could be stated for short term (ie. a few hours at most) measurements of an LTZ1000 (again ignoring the errors/uncertainties in the measuring system itself), and what would the optimum measurement time be?

When recording measurements over very long periods to determine drift, how can you ever be sure (to a defined confidence level) that what looks to be a systematic drift is not just random, very low frequency noise?

[montemcguire]

Averaging a number of shorter measurements reduces their uncertainty, but does not necessarily add in lower frequency (drift) components. For example, the simple way to highpass a 0.1Hz measurement is to measure over 10 seconds. Averaging 10 of these however is not the same as a 100 second measurement, and does not introduce components below 0.1Hz, it just reduces the uncertainty.

[Andreas]

Hello,

I would do a allan deviation diagram.
There you see quickly what number of values you have to average to get "best stability"
So the lowest uncertainity which you can get.
Of course in a real world you will have to repeat the allan deviation several times since it variese with environment conditions.

But in your case you have a drift free measurement system so it should be very repeatable   

Attached a example from my ADC#21.
The one is freshly after it has been built + calibrated so the drift is still large showing in rising standard deviation
to 0.5 uV for longer integration times due to drift.
(x-axis in minutes, y-axis in mV after 2:1 divider).

The other is after some months of operation showing that the best stability (standard deviation) of 0.25 uV in 5V range can be obtained by averaging around 200-300 measurement (1 minute) values.
(x-axis in raw measurements, y-axis again in mV after 2:1 divider).

with best regards

Andreas

[Kleinstein]

Drift can be seen as a special type of low frequency noise. So there is not much to separate drift and very low frequency noise - these are more like different ways to look at it.

The noise if called 1/f noise - however in a well behaved part the f^-n  part is not with n at exactly 1 but a little less (e.g. 0.9), if the part is well behaved. So things get a little (but not very much) better when averaging over very long times.

The Allan variance plot is a good way to look at the data. If there are additional variations going up faster than 1/f the minimum will give a limit for possible accuracy.