# [time-nuts] How can one measure ADEV of a good oscillator?

Tom Van Baak tvb at LeapSecond.com
Mon Dec 1 17:05:00 EST 2014

```> I think I have a flaw in my understanding of this.
>
> How can something like an SR620 measure the ADEV of an oscillator,  if the
> oscillator is of a similar or better than the reference fed into the SR620?

The key is to realize that all measurements are actually just comparisons: the instrument itself has no knowledge if the REF or your DUT is the better frequency source.

If you use a SR620 to measure a TCXO then you are [mostly] measuring the DUT.
If you use a SR620 to measure a cesium then you are [mostly] measuring the REF.

I say "mostly" because no frequency standard is perfect, and the instrument itself contributes noise to the measurement. So strictly speaking, any measurement is always the sum of REF noise, instrument noise, and DUT noise. Never assume any of these are zero.

> I see plots of ADEV  for hydrogen masers, but I can't understand how this
> can be measured from the phase data unless the reference is better than the
> DUT, which is not going to be possible with a good hydrogen maser.

You measure a good hydrogen maser with a better hydrogen maser, or with another good hydrogen maser.

The same is true if all you have a couple of OCXO.

> I was thinking it might be possible if one has 3 oscillators and 3 time
> interval counters to perhaps solve 3 simultaneous equations. I can't prove
> that, but it seems intuitively correct.

Correct. That's what we do. And you can use more than 3 if you want.

> Also I have seen graphs of both Allan variance and Allen deviation.  Both
> are typically 10^-12 for a decent oscillator, but given the variance and
> standard deviation are related by a square root, they can't both be around
> 10^-12.  I would expect to see values of 10^-6 or 10^-24, but I don't see
> such dramatic differences from 10^-12.

In the 70's it was common to [incorrectly] call it Allan variance. These days it is [correctly] called Allan deviation, or root Allan variance. Note that it's also called the two-sample variance/deviation, especially by mathematicians.

> If I see numbers around 10^-12 on an OCXO,  is that the Allen variance or
> Allen Deviation?

It's Allan deviation. Not Allen. Not variance.

/tvb

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