[time-nuts] Phase noise from Allan Deviation ?

Richard (Rick) Karlquist richard at karlquist.com
Mon Dec 14 01:04:08 EST 2015

```On 12/13/2015 7:15 PM, Tom McDermott wrote:

> It brings up a question:  Is it possible to estimate the phase noise of that
> internal crystal from the ADEV measurements?  There are a bunch of
> papers that go the other way:  from Phase Noise to Adev.   Searching
> brings up only one paper that goes from ADEV to Phase Noise but it's text
> does not seem to be readily available.  It apparently models the oscillator
> as a couple of well known error models.
>
> -- Tom, N5EG]

In general, you cannot determine phase noise from ADEV,
even though you can determine ADEV from phase noise.
This is just a mathematical reality.

Mike Fischer (of HP) presented papers at the 1977 and
1978 that show conversions between PN and ADEV for
individual noise processes, where each process has a
specific slope of amplitude vs frequency.  The only
time you can go from ADEV to PN is if you can isolate
a process.

In the specific case of crystal oscillators, in general,
they follow a flicker noise of frequency process model
close to the carrier (within 100 Hz).  You can often
assume that ADEV is dominated by this process and therefore
translate it to an equivalent PN.  The way to tell if
ADEV is dominated by this process is that it will be
independent of tau, for tau of 0.1 sec or less.

On the IEEE UFFC site, there is a tutorial on crystal oscillator
design by Mike Driscoll (you don't have to be a member to
access it).  I believe this covers this topic.  You go
from ADEV to "frequency noise" and then to phase noise

You can "practice" this calculation on any crystal oscillator
that has published ADEV and phase noise.   It is of course
extremely easy to screw it up :-)   What I have found
is that most crystal oscillators seem to obey the flicker
model.

I have been able to measure flicker noise on crystals that
were not installed in an oscillator, and then install them
in an oscillator and the ADEV turned out to be what
was predictable from the phase noise.  It really works!

Rick Karlquist N6RK

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