[time-nuts] Re: Cross correlation for analogue PN measurement

[Magnus Danielson]

Alan,

On 2023-09-02 21:17, alan bain via time-nuts wrote:
> I have been curious as to whether it is possible to reduce the noise
> floor below that of the reference oscillator when doing a PN
> measurement HP3048 style if the DUT feeds a power splitter which feeds
> two identical PLLs locking (separate) low phase noise oscillators in
> quadrature (e.g. two copies of the 8662A + 11848A setup) with the two
> phase detector outputs feeding Ch1 and Ch2 respectively of the dynamic
> signal analyser, but with the latter set to compute the cross spectrum
> (which the old 3562A can do).
>
> Clearly one needs to repeat the process multiple times and average. If
> the two reference oscillators are assumed uncorrelated to the DUT and
> each other (maybe they need to live in separate racks - or piles - to
> avoid vibration coupling) then this cross spectrum reduces to the
> power spectrum of the DUT noise.  Clearly the two oscillators need
> independent time bases - not a connection to the house 10MHz standard,
> but that's probably fine as the phase lock loop would normally tweak
> the EFC of the reference in each synthesiser.
>
> The cross correlation approach seems used commonly in the digital
> domain as part of IQ type analysers, but does it work in the purely
> analoge one or does some other factor appear and become the dominant
> one and wipe out the gains?

What you describe is the classical cross-correlation setup. It works, to 
a limit. Your limit will be at and near the thermal floor. If you don't 
go near, you will stay just fine.

The trouble you will end up with is the noise-cancellation that occurs, 
causing a collapse of the noise spectrum. [1]

The culprit is the power-splitter. [2] [3]

This is a hard problem, of which one solution was presented by NIST an 
independent researcher. [4] Other solutions have been put forward by 
Rubiola. There is pro and cons about either solution.

Much of this research was done with somewhat more modern equipment than 
you describe, but the basic technique remains the same. The HP89410A 
with cross-correlation option is a step forward. Later Agilent solutions 
uses a digitizing board and let the computer do the FFT and 
cross-correlation.

As you process, I strongly suggest you follow Prof Rubiolas 
recommendation over wine at the 8FSM in Potsdam, is to _not_ do the 
absolute function on the output of the cross correlation. This way you 
can observer the noise on the imaginary axis and as you come to the 
cross-correlation cancellation, you can observe the result from the DUT 
change sign as it goes from positive to negative. This helped me to 
understand the processing and it inspired the work in [4].

What modern digital sampling avoids, is a myriad of noise folding issues 
etc. Just sampling the mixer signals rather than use 
zero-cross-detectors resolves some of the issues. Claudio Colosso have 
written fantastic work on these issues. The continuation is that this is 
the way forward, and it really is. Extremely sharp guy. His tutorials on 
new methods is fantastic.

So, I do encourage you to try it out. Just learn where the limits are 
and not overbeleive potential results.

> I seem to have almost enough heavy HP lumps to try this, but not quite
> enough, hence the question!
Cheers,
Magnus

[1] https://tf.nist.gov/general/pdf/2697.pdf

[2] https://tf.nist.gov/general/pdf/2844.pdf

[3] https://tf.nist.gov/general/pdf/2828.pdf

[4] https://tf.nist.gov/general/pdf/2853.pdf