[time-nuts] Cross-correlatiion workshop at EFTF-IFCS-2017

[Magnus Danielson]

Fellow time-nuts,

I thought that I should write a few lines about the EFTF-IFCS, so a good 
start would be the Cross-correlation workshop which is about addressing 
the complexities of the cross-correlation measurement and achieving 
stable and proper measurements. This session was curated by Prof. Enrico 
Rubiola of femtosecond and Craig Nelson of NIST.

OK, for those that don't know about the issue, let me get a quick 
explanation here. For a long time cross-correlation have been a 
technique to remove the internal noise of two, by feeding the source 
into two channels using a power-splitter, and then each channel add its 
noise which is uncorrelated. The cross-correlation of the channels then 
sees the common signal and as one average over multiple spectrums the 
uncorrelated signals average out. Sounds splendid, but trouble showed up 
on the horizon when they had trouble getting stable readings from 
measurement to measurement as the noise starts to reach the thermal 
noise floor. Some measurements where about 20 dB below the noise floor, 
some where about the noise floor, but there was a dip in the response.
As one look closer on historic measurements using cross-correlation it's 
been there for ages, since the measurement method started to be used. 
Looking closer on it, it looks like the thermal noise flips from 300 K 
to -300K and the "dip" is where the noise goes through zero. Oups!

In 2015 there was a similar workshop, at that workshop Joe Gorin 
contributed an explanation for where the anti-correlated noise was 
generated. In a Wilkinson splitter, the power is divided into two ports. 
However, to achieve isolation between the ports, a resistor of twice the 
impedance is needed, i.e. 100 Ohm. It just happens that the noise that 
generates is two times the noise of the source, and it is completely 
anti-correlated, thus subtracting. OK, great, now we know why it breaks 
this way. What to do about it? At NIST Archita Hati and Craig Nelson 
where pulling their hair and at the FSM8 conference in Potsdam, Archita 
presented a poster which was interesting exercise in failure to solve 
the problem with a whole range of splitters, including a Wilkinson where 
they out of desperation had pulled the resistor, and still it was 
problematic. During late evening discussions over wine at FSM8 we had 
the most interesting discussions. Good teachings where had for everyone 
involved.

At EFTF 2016 in York, I met with Craig and Archita to discuss some 
ideas, which they tried and found useful and presented by Archita at 
IFCS 2016 in New Orleans a month later. My contribution was to ask about 
what isolation gives us, and it turns out that lack of isolation causes 
channel noise to back-propagate and reach the other channel, being now 
correlated noise between the channels and then acting as correlated 
noise, with a complex response after FFT depending on the delay between 
the channels. Given that the source noise pops up on the real axis due 
to equal distance to the channels, insertion of variable delays allows 
one to steer the vector of the channel noise onto the imaginary axises 
where it as a secondary effect collapses as they cancel. Sound great 
huh? Yeah, in theory, but it is hard to balance this to maintain the 
full property for the length of the full measurement, but at least some 
attempt on it.

Now, with that back-story it was time for another workshop on 
cross-correlation at the EFTF-IFCS-2017 in Besancon. Enrico asked for my 
contribution, so I volunteered to contribute. We ended up being some 
30-40 people in the room, with people like Dave Leeson present.

A variety of presentations where made, illustrating the width of 
different insights. NoiseXT showed a source that could generated AM and 
PM noise, in hope that it could prove useful in provoking different 
scenarios and be useful to illustrate AM-to-PM conversion for instance.
Jason Breibarth of Hollingsworth presented an array of cases where 
AM-to-PM was evident. Enrico presented an approach to estimate the 
removed noise and simply add it back. Mike Driscoll discussed the 
potential of doing a different approach with mixers for higher amplitude 
level. Sam Stein made some good comments about how their equipment was 
built and pointed out some difficulties they had ran into, such as the 
cross-AVAR needed to avoid the flipping sine. Also, the data as 
presented out for post processing is a different decimation path than 
what is used for internal processing since, well, it was difficult to 
have them so close.

As for myself, I made the point that even with ideal splitter, isolation 
is broken when noise from channels is reflected on the source, as some 
sources have far from flat 50 Ohm impedance, something that is known to 
be the case for some sources being troublesome to measure. Similar to 
the other cross-talk problem, it will create a partial collapse of the 
spectrum. My slides can be sent if anyone cares to have them, I will 
upload them to my server.

As of this day, there is no real answer of how to do all this, we have 
multiple research groups and vendors seriously scratching their head on 
this one, but it is really amazing to be sitting on on this as 
observations and solutions are being tried. We now know better that we 
have a myriad of issues causing phase-noise readings to be of the mark, 
and some claim to be even non-physical. So, there is real research being 
done in what we used to consider a well-researched area, namely 
phase-noise measurements. This is one tough cookie to crack.

Hope it was an interesting read.

Cheers,
Magnus