Allan Deviation for stability measurements on voltage references

[branadic]

Allan Deviation plot is a very common way to plot stability of oscillators in rf applications. However, people found it useful to characterize inclination sensors, MEMS or gyroscopes the same way to show their stability.
It's also a useful tool to plot stability of our voltage references unless one is able to interpret the plots. Since this is very hard this thread is about the interpretation of Allan deviation for voltage references, noise sources and all the other troublemakers like drift, random walk, temperature variations or shot noise.

First of all we need a tool to plot these charts. If you are familiar with GNU Octave you can use the script that can be found in NXP Application Note AN5087

cache.freescale.com/files/sensors/doc/app_note/AN5087.pdf

There are also scripts available for Matlab on the Mathworks website.

The easiest way is to use a tool like Plotter by Ulrich Bangert or AlaVar 5.2

To understand how the different influences display in the Allan plots I generated some noise files using GNU Octave and the ltfat-2.2.0 package. Attached are the Allan deviation for white noise, pink noise and the sum of both.

As you can see white noise gives a very clear negative slope and is unique.

Pink noise interpretation on the other hand is very hard as it strongly depends on the length of the reccord how it displays in Allan plots. It can look like random walk, but what seems to be significant for the moment is a strong negative slope on the very right side of the plot. FFT helps to identify it as pink noise. Thanks to Plotter we do have this function already implemented in here.

White noise on pink noise adds a negative slope on the left side of the Allan plot.

So what do we like to see? Well, the best result is having only white noise on our reference voltage, no drift, no temperature influence, no 1/f noise and all that stuff. Thus, the first picture with the negative slope starting at the lowest point would be best case.

Any comment and example on helping us understanding Allan Deviation Charts is welcome.

-branadic-

[thermistor-guy]

You could also try the modified Allan Deviation. It might reveal more about the noise processes in the reference:

https://en.wikipedia.org/wiki/Modified_Allan_variance
"...Its main advantage relative to Allan variance is its ability to separate white phase noise from flicker phase noise.."

David Allan's paper: http://tf.nist.gov/general/tn1337/Tn254.pdf
"...In other words, with the modified "Allan Variance" one can easily distinguish between white phase noise (a = +2) and flicker phase noise (a = +1) -- commonly occurring for the short term instabilities of quartz crystal oscillators and active hydrogen masers..."

[maxwell3e10]

Yes, Allan variance is very useful in specifying stability and is commonly used in oscillator spec sheets. In contrast, it doesn't seem to be used in specification of voltage references or meters.  As a result, the specifications are all over the place, some use rms, some p-p, some 2-min average, some 24 hour.  I don't know if that is because analog people are not familiar with Allan variance or they just try to coax the specifications to look favorable.

[thermistor-guy]

Yes, Allan variance is very useful in specifying stability and is commonly used in oscillator spec sheets. In contrast, it doesn't seem to be used in specification of voltage references or meters..."

Some researchers do use it. BIPM use it here to check the emf of a multiplexer, used to compare secondary Zener voltage references against a JJA. See figure 10 (page 15). The multiplexer's emf shows a white noise region, a flicker noise region, and a third region "probably related to temperature regulation in the laboratory".

http://www1.bipm.org/utils/common/pdf/rapportBIPM/RapportBIPM-2011-05.pdf

Very interesting. In future I want to build some JVRs (Alex Nitikin's project). Looks like Allan Deviation will come in handy for validating the builds, and for teasing out the various noise processes.

[branadic]

You could also try the modified Allan Deviation. It might reveal more about the noise processes in the reference:

https://en.wikipedia.org/wiki/Modified_Allan_variance
"...Its main advantage relative to Allan variance is its ability to separate white phase noise from flicker phase noise.."
...

The funny thing about Plotter is, you can choose between several Allan plots like modified or overlapping Allan deviation.

-branadic-

[Krytron]

Another program is TimeLab at www.ke5fx.com, its free.  Its made for a device called TimePod, but it works with other instruments and files.

A commercial program that use to be the standard is Stable32 by Hamilton Technical Services at wriley.com.

Both programs have multiple variances and work well.

[Kleinstein]

The very right end of the Allan variance plots is usually not significant. As it represents the very slow processes and thus will have poor statistics - so it is a good idea to not give much weight to the very right end (e.g. last factor of 5 in the time scale). This part is a little like the first 5 points in an FFT plot - not that significant with noise data too.

[Alex Nikitin]

Here is a plot for a 7h run of the 10V JVR measured at a reasonably constant temperature (the peak to peak variation is about 0.8ppm). I hope that I've entered the data correctly.

Cheers

Alex

P.S. - added the time series of the same run

[Jorn]

Hi Alex

Could there be a factor 10 error some where?

You seem to get 10 times lower adev that I do for a similar reference.

Time series and adev for my 10V reference below:



Regards
Jorn

[Alex Nikitin]

Hi Alex

Could there be a factor 10 error some where?

You seem to get 10 times lower adev that I do for a similar reference.

Time series and adev for my 10V reference below:



Regards
Jorn

Hi Jorn,

No error, in your case the result is in Volts, in my graphs it is a ratio (so for Volts you need to multiply it by 10V).

Cheers

Alex

[Krytron]

Stable32 was made public as of January 1, 2018.

The program for windows is available at:
https://ieee-uffc.org/frequency-control/frequency-control-software/stable-32/

Information about the program is at:  http://stable32.com/

Bill Wriley owned Hamilton Technical Services and he wrote the software.  Mr. Wriley worked on the east coast and use to designed rubidium frequency standards.  After he retired, he started Hamilton Technical Serices and wrote the program.  He has a lot of good information at his site and he has authored many technical papers concerning frequency analysis. 

I would like to thank him for his contributions and for making the program available to the public.

[texaspyro]

lulu.com sells a printed copy of the Stable32 manual for cheap... it is around 300 pages long.

[TiN]

I've played with AlaVAR freeware plotter today a bit.
Here's result, taken on xDevs.com FX ref using K2002. Graph clickable to see live JS data.



Red line is ADEV. 

PDF-report.

[Andreas]

Mhm,

y-axis is relative to range or in V?

For me something seems not to fit:
you have around 2uVpp = 0.3uVeff short term noise
and around 3uVpp = 0.5uVeff long term variation.

so I would expect 3e-8 from range or 3e-7V for tau = 2s. (1 measurement value)
Also interesting would be why the outliers have been filtered out and how much they would change the result.

with best regards

Andreas

[chuckb]

Is there a Moving Average filter running on the K2002? There seems to be about 30 seconds of filtering on the raw data.

[Kleinstein]

There is a possibility that the K2002 like some other Keithley meters use a kind of averaging for the zero readings to do AZ. This causes some correlation in the readings on the 30 s scale and some extra low frequency noise as it hinders suppression of 1/f noise. The problem is even more pronounced in the DMM7510.

[maxwell3e10]

Allan deviation is useful in understanding how the data average out over time. So its best to start with fast sampled data, at 1 NPLC or so, in order to see the transition from 1/sqrt(t) behavior to long-term drift.

[Kleinstein]

Remember that one will see a combination of the reference noise and the meters own noise. With a good quality reference the meter might have more (or similar) noise than the reference. It is at least the meter internal reference that contributes to the noise.

Using a shorter integration time can change the way the conversion is done. So averaging 10 readings at 1 PLC is not always the same as doing one measurement at 10 PLC. So it makes sense to use the mode one is interested in, if the meter itself (and not just the reference) has a significant contribution.

It is only in the range where the meter internally does averaging to simulate a long integration time, where there is a limited sense of using such a slower setting.  There is the tendency that newer meters (e.g. 3446x, DMM7510) that are good at short integration time will use averaging already early.