[time-nuts] Re: Underlying math of cross-correlation PN Test Sets

[Magnus Danielson]

Hi,

On 2022-04-25 01:57, Joseph Gwinn wrote:
> I'm digging into the basic math of how cross-correlation phase noise
> test sets (like the 53100A) work, so I'm looking for good articles on
> the complex-exponentials math.
>
> One item of interest is the effects of imperfections in the power
> dividers that make a pair of perfect copies of the reference signal
> in a residual-PN setup.  I gather from Walls 1992 that the limit on
> cancellation of signal-source PN is the imperfect isolation of the
> power divider.
>
> I'm more interested in clarity of exposition and the physics than in
> solid walls of pure math.

I recommend you to look at the NIST T&F archive on the topic. Also their 
AM and PM calibration document.

The field have developed over the years, covering a range of aspects, 
including 2014 article describing the noise cancelling errors and 2016 a 
proposal for how to address that.

The 2014 paper (David Howe, Craig Nelson and Archita Hati) is a good 
paper as it sums thing up. The 2016 paper provide new hints in addition.

Quick explanation: you cross-correlate with two independent channels, so 
only the DUT noise correlate. Averaging on the complex outputs of the 
FFT based cross-correlation output removes the channel noises. Your 
result will be on the real axis and your imaginary axis should be a 
small vector of noise. When the real axis goes negative, as it does when 
reaching thermal noise level, do not believe the measurement.

Cheers,
Magnus