# [time-nuts] AVAR & Femtoseconds

Magnus Danielson magnus at rubidium.dyndns.org
Sun Jun 20 18:25:32 EDT 2010

```On 06/20/2010 11:53 PM, jimlux wrote:
> Robert Benward wrote:
>> Bob
>> Boy, you guys are really making me read a lot. I'm digesting Wiki
>> right now.
>>
>> I see tau, but does identifying a tau of 1E-14 allow you to say you
>> are locked to 10fs? The smallest tau I've seen in my E1938 collection
>> is 1E-1.
>>
>> Bob
>>
>
> tau is the time over which the measurement is made, typically 1 second
> or greater.
>
> loosely speaking, the 1e-14 is the average fractional deviation of
> frequency over that time period.

It is a RMS type (much like statisticians standard deviation) of
frequency stability over the "observation interval" of tau (little greek
letter looking similar but not quite like a little t, which is the real
reason for using it). Since it is a RMS type of measure, it indicates
the effective power of noise, but not what the actual deviation in
frequency will be, it's just a statistical measure. You may form a
confidence interval such as that for 99,7 % or something which forms a
scale-factor, quite similar to the use of the error function for the
Gaussian distribution.

An Allan deviation measure of 1E-14 is however not quite the same as 10
fs. Besides the units being wrong (Allan deviation is a relative and
unit-less measure, essentially Hz/Hz) the Allan variance (and hence the
Allan deviation) is a frequency stability measure, indicating the
stability of normalized frequency rather than stability of normalized
phase. The time deviation represents the stability of phase over some
observation time. Assuming the nominal frequency and linear effects
removed, then this would indicate the time error noise of the phase,
here use of seconds could be used, but it would be to stretch things a bit.

The time and frequency world has it's own qualities of noise...

Cheers,
Magnus

```