[time-nuts] Plot phase noise spectrum from DMTD measurement?

[John Miles]

> Ok some cool advice - this thread is an interesting thought exercise. I'm
> going to think about it a some more, but it seems, in comparison at least,
> the loose phase-lock technique remains the simplest. Provided you have a
> low-frequency spectrum analyser handy.

It would be a better idea from the standpoint of VCO modulation bandwidth as
well.  If you measure PN by looking at the tuning voltage in the tight-PLL
configuration, you'll probably be limited to offsets of a few kHz before the
response rolls off.

> The sound card idea is clever as well - however, I'd assume one needs to
> measure the ADCs clocking oscillator offset, since that will be apparent
> when plotting the beat frequency phase (what I mean is that sampling will
> then look like another mixing process). What I usually due is  to
> clock the
> sampling system off a clock that's correlated to the clock under
> test. This
> resolves that issue.

Sound cards will usually end up running within 1 Hz of the desired sampling
rate, but it's important to pick a sampling rate that's native to the
hardware, or the driver will resample the data.  On Windows, many drivers
for popular sound cards rely on some imprecise resampling code that
apparently was distributed by Microsoft in the DDK.  Stick with 44100 or
48000 Hz, or you'll be lucky to land within a few dozen Hz in some cases.

Warren's been getting some really nice ADEV plots from a tight PLL sampled
with a USB sound card, running a quick and dirty command-line utility I put
together to acquire the data and downsample it.  I'll post the next build on
my web page if anyone else is interested in playing with it.

> However, I'd like to experiment with the cross-correlation idea,
> since I've
> got a setup that will lend itself perfect to that. Maybe I could
> save myself
> some time, with clever post-processing.
>
> Can anyone recommend a fundamental text on the cross-correlation
> technique?

The easy way out is to look for a dual-channel FFT analyzer or one of its
successors.  The HP 3562A and 3563A models are pretty affordable these days,
and they've been used in a number of papers on cross-correlation
measurements of various types of noise.  SRS also sells some nice
multichannel analyzers.

If you're looking to write your own processing code, you should search for
information on 'cross spectrum' as well as 'cross correlation' techniques,
because the former is the correct term for the scenario where the sampled
data from both channels is already time-aligned.  For its part, the cross
spectrum is just a $5 mathematical buzzword for the vector length between
the corresponding output bins of two FFTs, obtained by multiplying one array
by the complex conjugate of the other.  When averaged over time, the real
component of the cross spectrum will converge to the common signal at the
ADC inputs.  Unlike the DUT signal, the ADCs' noise contribution is randomly
distributed in phase space.  It will converge to zero when averaged and fall
out of the measurement... at least to the extent that the channels are truly
uncorrelated.

Unwanted channel correlation is one of several reasons to use a lab-grade
FFT analyzer instead of a sound card for multichannel measurements.  At a
minimum it would be better to use two USB sound cards and run them from a
common clock.

Enrico Rubiola's "The cross-spectrum experimental method" is a good survey
of the basic principles (http://arxiv.org/abs/1003.0113); also see
http://tycho.usno.navy.mil/ptti/ptti2001/paper42.pdf and Walls's original
"Cross-correlation phase noise measurements" paper, as well as the various
white papers at aglient.com and symmetricom.com.

Rubiola's material is the most helpful I've found, really.  I've been doing
a lot of R&D in this area lately, and I've found that most DSP textbooks are
too far removed from real applications (no pun intended) to be of much use.
The math is not rocket surgery, but you couldn't tell that from a survey of
the academic literature.

-- john, KE5FX