[time-nuts] Phase noise from Allan Deviation ?

[Magnus Danielson]

Tom,

On 12/14/2015 04:15 AM, Tom McDermott wrote:
> I've constructed a homebrew setup to measure time intervals using a
> software defined radio.  Basically a single-channel downconversion to
> about one hertz, then count samples from the SDR clock to time stamp
> the zero crossings.  This is done in gnuradio and saved to a file for
> post processing. The resolution is theoretically good, but the accuracy
> is unknown.
>
> The result produces ADEV vs. Tau charts with reasonably sane looking
> results.
> The 'unknown' is a Rubidium oscillator locked to CDMA pilot (TS2700),
> and the internal crystal oscillator in the SDR radio as the reference.
> Thus, ADEV probably is mostly measuring that internal crystal rather than
> the TS2700.  Later on a GPSDO will be tried as the reference clock to
> see if the Adev results are better.

You will see the SDR clock noise, as it most likely will dominate.

> 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.

Yes.

Allan Deviation was invented in order to reliably estimate the strengths 
of the different noise-types and separate them. Today we can do this in 
the phase-noise domain, but that was hard to do in the 60thies so they 
had to use counters.

Look at the Allan Deviation wikipedia article, where I have included the 
formulas for various forms of noises and their ADEV curve. These are the 
formulas you need.

In order to separate white phase noise from flicker noise, ADEV isn't a 
good tool, so you need to use the MDEV instead. David Allan recommends 
MDEV for this purpose, as the lack of separation was nagging him and it 
took some additional 15 years before the problem was solved.

In order to estimate the noise levels, you do a curve fit of the AVAR or 
MVAR to the noise-slopes. I recommend the writings of Francois Vernotte. 
He has study the field and understood the matching process needed.

As always, remember that the system bandwidth B will be important to the 
estimation of the noise-level of a source. The sigma-counters for 
instance have much lower system bandwidth to reduce the white phase 
noise, but as you estimate you will can get the wrong estimated value 
unless you use the correct value. For omega-counters, Vernotte showed 
how the proper formulas to be used looks, great work there. The PDEV is 
so far the optimum processing-tool, but MDEV (which is easier to get 
right) is not far behind. No one using omega-counters can get the PDEV 
right to this day, but we are discussing how to correctly remedy that.

Cheers,
Magnus