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

Sun Sep 3 16:09:13 UTC 2023

Dear Alan,

On 2023-09-03 10:44, alan bain via time-nuts wrote:
> Thank you - that is basically a complete answer to my question within
> hours of my having asked it and the four papers fill in even more
> detail. The power splitter point is very interesting.

Happy to help you along the path.

Notice how you can use audio cards for low noise ADC if you have no 
DC-blocking. That work if you do not need wide-band beyond 10 kHz or so.

> Also take the point about the full cross spectrum - the imaginary part
> is going to be the quadrature part so a good approximation to the
> noise spectrum.
Yes. You do cross-correlation as a time-inversed convolution, but as you 
convert that to frequency you achieve the time-inversion through 
inversion of the imaginary part before multiplication 
component-per-component. Also, this then is the form you want things 
anyway, so it is just to average over N samples for each complex 
component. Look at how noise reduces on imaginary axis to see how your 
result stabilizes on the real axis. Quite beutiful.
>
> And yes, in a domestic environment my equipment tends to be offcasts
> from industry, so rather older than the current generation!

I conclude too that my laboratory is built out of offcast from industry. 
Very much so. My humble lab builds on slowly accumulating things that work.

I was able to be given a RF-generator from work. It filled no real 
purpose for them, but for me, so as we moved, they needed to downsize 
and the "Instrument storage room" changed name to "Magnus room". A few 
pieces was taken out, and quite a bit of stuff pushed in. The 
RF-generator naturally had a PSU that died. I was able to locate a NOS 
PSU with perfect match, and after that I got a working RF-generator 
again, for the cost of the PSU and transport.

Similarly, I was able to locate a R&S SMA-100A generator local at dirt 
low price, mostly because the seller did not want to botter with ebay. 
It has unfortunately not the frequency tuning needed to be useful, 
despite being a marvel in so many other aspects. I suspect I will have 
to use a separate OCXO and tune using that to get that feed. If there is 
a decent way to upgrade the SMA-100A I would love to do that.

A pair of HP70420A and a HP89410A for cross-correlation and I think you 
see where this is going.

To go full interferometric cross-correlation I need to add steerable 
delays, and the three Colby DL-10A that I found cheap in the US have all 
been converted to 230 VAC and work just fine. Needs a bit of cable 
cutting and just a few lines of code. Oh, and I need to use one 
generator to inject calibration signal. Will be fun.

Cheers,
Magnus

>
> Alan
>
>
>
>
> On Sat, 2 Sept 2023 at 22:36, Magnus Danielson via time-nuts
> <time-nuts at lists.febo.com> wrote:
>> 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
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