Measurement uncertainty of a noisy reference - Page 1
Forum section: electronics / general

author: splin
author_rank: Frequent Contributor
timestamp: February 10, 2018, 01:40:38 am
content: 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?

author: montemcguire
author_rank: Regular Contributor
timestamp: February 10, 2018, 02:38:31 am
content: 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.

author: Andreas
author_rank: Super Contributor
timestamp: February 10, 2018, 07:02:45 am
content: 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 repeatableAttached 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 deviationto 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 regardsAndreas

author: Kleinstein
author_rank: Super Contributor
timestamp: February 10, 2018, 09:20:25 am
content: 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.