[time-nuts] Phase noise from Allan Deviation ?

Magnus Danielson magnus at rubidium.dyndns.org
Mon Dec 14 20:19:33 EST 2015


On 12/14/2015 07:04 AM, Richard (Rick) Karlquist wrote:
> 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.

1976 PTTI paper by Fischer:

1977 PTTI paper by Chi (Fischer being adviser):

1978 PTTI paper by Fischer:

Things have happen since those papers, in many ways.

> 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


Other tutorials is at:

In particular, check out Francois Vernottes presentation:
He covers a lot of ground there, and in the end he also covers 
curve-fitting to estimate noise levels.

> 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!

Indeed. However, one has to be careful with ones methods, or one will 
not estimate the noise-levels properly. Regardless if you use the 
frequency method or time method, doing meterologically sound and 
traceable measurements remains a difficult task indeed.


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