# [time-nuts] ADEV from phase or frequency measurement

Magnus Danielson magnus at rubidium.dyndns.org
Sat Mar 1 08:25:49 EST 2014

```Volker,

On 01/03/14 12:15, Volker Esper wrote:
> Hello dear fellow time-nuts,
>
> I stumbled over a question that may sound stupid to you:
>
> Is the usual ADEV plot the result of a phase or a frequency measurement?
>
> I get totally different results when comparing a phase and a frequency
> measurement of the same source. Or am I doing something totally wrong?

The core of the ADEV is the square of the second degree derivate of
phase, where the phase measures are tau seconds away from each other.

You can use frequency measures, but it is likely that the start-point of
the next measure is not the end point of the previous frequency measure.
you need to use the dead-time bias function to compensate for this
effect. This was explained by Dave Allan in his Feb 1966 article, as the
2-point dead-time free variance was the unification of a large range of
different measures, and he supplied the bias functions to unify them.
Now that there was one variance to forge them all, they kept referring
to it as Allan's variance and well, it's now history.

Another aspect is that your counter may do some "smart" filtering on the
measures it makes. This reduces the bandwidth of the counter as the
averaging removes noise. This also causes low-tau values that has
white-phase noise to be lower than expected. This "improvement" is
however not helping you to get better ADEV, it just fools you, as the
ADEV of white phase noise will depend on the measurement bandwidth,
known for a long time but ignored my many measurement setups.

I've tried to cover these topics on the Allan Variance Wikipedia article.

I would avoid using frequency measures from counters if phase measures
can be made, as you can avoid both these issues rather than requiring to
measure their effect and compensate for it. It is tricky to maintain
valid numbers that way.

There are cases where ADEV is better calculated from frequency measures,
so it is a valid tool, but care always needs to be taken to make sure
the numbers remains scaled properly.

Cheers,
Magnus
```