[time-nuts] Allan deviation and modified Allan deviation

Tom Van Baak (lab) tvb at leapsecond.com
Mon Feb 18 18:27:32 EST 2013

I often plot both ADEV and MDEV, too. The difference between them indicates the amount of white phase noise there is in the measurement (the sum of DUT and REF and phase meter). You'll see for some standards, especially at longer tau, there is little or no difference. 

Right, MDEV is almost always less, since it artificially "removes" noise. Of course the noise is still there in the electrons, but it is not reported by this statistic. However, the sometimes legitimate reason for doing this is two-fold:

First, an MDEV plot allows one to distinguish white from flicker phase noise types; something plain ADEV cannot do (both noise types show up as slope -1 with ADEV). As such, MDEV is a more powerful noise diagnostic than ADEV. But you can't necessarily treat the numbers as true, live performance. In order for MDEV to do its magic it must (mathematically) remove noise that you know is there.

Second, there are some cases where the user plans to use the oscillator in a system that removes white noise by averaging against an equal or better standard. In this case it's nice to know ahead of time how much white noise there is to remove; so using MDEV is more informative than ADEV.

For example, if you plan to compare two cesium time standards by collecting long-term data, then post-averaging, and plotting time stability once an hour or day, then MDEV is fair game. But if you plan to use the standard for any sort of real-time system then ADEV comes closer to representing the actual frequency stability that you will see.

MDEV tells you how little instability you would have left after you squeeze out all the white noise. Every orange has juice inside, but to measure juice or pulp you destroy the original orange.

Note a similar thing happens with ADEV and HDEV. If you plan to use an oscillator in a system that methodically removes linear frequency drift (like a smart GPSDO) then HDEV is a better (cheaper) indicator than ADEV.

In summary, use the measurement statistic (and bandwidth) in the lab that best matches how the oscillator will actually be used in real life. 
I too would like to compare records made over many years. One problem is that phase meters can have different bandwidths and so, especially at short term, it's hard to know how much of the reported [in]stability is due to the DUT or REF or the filtering before, in, or after the phase detector itself. Most meters have a tau- or noise- dependent bias.

/tvb (iPhone4) SF

On Feb 18, 2013, at 11:59 AM, cdelect at juno.com wrote:

> Ok I've been plotting my oscillators for years using Allan Deviation.
> That way all my records can be compared easily.
> Is there any advantage to using Modified Allan Deviation?
> It seems to give a better stability plot but that just seems to be
> cheating!
> If I plot both ways what do the differences mean?
> Thanks,
> Corby
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