[time-nuts] Crosscorrelation phase noise measurements

Magnus Danielson magnus at rubidium.dyndns.org
Fri Aug 3 18:17:17 UTC 2012

On 08/03/2012 04:20 AM, John Miles wrote:
> Cross correlation is one of life's few free lunches, but you do have to wait
> for it to work.  Magnus is correct in that you can get a 3 dB advantage in
> noise reduction per sweep, but that only applies to the first sweep.

Agreed. Did not mean to say anything else.

> The actual improvement in the instrument noise is related to the square root of
> the number of averages taken.  This means that a cross-correlating phase
> noise analyzer is very effective for broadband noise, where minimal
> decimation has to be done prior to the FFT.  The input buffers fill up very
> rapidly in that case, and you can get hundreds of thousands of averages in
> just a few minutes.  But measurement of low levels of 1/f^n noise close to
> the carrier can take a lot longer.

I have mostly done 1 hour measure runs, so the gain is limited.

One can view the gain for the various sections, which helps to 
illustrate the above statement.

> As an example, one customer just sent me a plot of the residual noise of a
> high-quality distribution amplifier.  The indicated PN was below -160 dBc/Hz
> at 10 Hz, but the instrument floor at 10 Hz was still -165 dBc/Hz after a
> 50-hour run!  Over that time, the 10 kHz-100 kHz FFT segment had undergone
> almost 30 million averages, improving the instrument floor in that region by
> over 35 dB.  But the segment containing 10 Hz had been averaged only 17000
> times for a 21 dB improvement.

Interesting. When more data has been received, the more interesting it 
would be to spend processing time on the closed in noise rather than 
getting more data on far out noise, as they come quickly. Pondering if 
some overlapping strategy could be be used with succsess, similar to 
what we do to ADEV and friends in the overlapping, total and theo 
strategies to improve long tau measurement quality.

> As far as concrete examples go, in addition to Magnus's suggestion of the
> NIST documents, I'd recommend this one:
> http://www.congrex.nl/EFTF_Proceedings/Papers/Session_14_Oscillators_and_Noi
> se/14_04_Bale.pdf
> Here, the authors use a pair of 1980s-vintage HP 3048A phase noise
> measurement systems with a newer signal analyzer that performs
> cross-correlation.  They are measuring additive noise from two-port devices,
> rather than oscillator noise, but the same principles apply to both.
> http://cp.literature.agilent.com/litweb/pdf/5989-1617EN.pdf
> The modern E5052A/B signal analyzers do the same thing in one box,
> basically.
> http://arxiv.org/pdf/1003.0113v1.pdf
> A good introductory article by Enrico Rubiola, with more specific math than
> the other two links.

Enrico has been using cross-correlation and averaging for quite a while, 
in combination with interferometric setups. Do read the article!

For the buffer-amplifier, they would make good use of an interferometric 
front-end to the TimePod in order to reach deeper into the noise. I 
haven't built one yet. Something to do in the fall.


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