Cross correlation for analogue PN measurement
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?
I seem to have almost enough heavy HP lumps to try this, but not quite
enough, hence the question!
Alan
Hi
If quadrature is the objective, just use quadrature splitters. Don’t bother with all
the PLL stuff, it just will mess everything up. The phase detector noise floor, and
loop characteristics are just the start of the mess ….
Bob
On Sep 2, 2023, at 3:17 PM, alan bain via time-nuts time-nuts@lists.febo.com 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?
I seem to have almost enough heavy HP lumps to try this, but not quite
enough, hence the question!
Alan
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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!
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.
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.
And yes, in a domestic environment my equipment tends to be offcasts
from industry, so rather older than the current generation!
Alan
On Sat, 2 Sept 2023 at 22:36, Magnus Danielson via time-nuts
time-nuts@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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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@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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