ensemble oscillators for better stability
I think the key is to always obtain the best oscillator/s possible.
Combining oscillator for lower Phase Noise does work but with
diminishing returns. If I am not mistaken 2 perfectly matched phase
locked oscillators can theoretically lower Phase Noise 3dB, four can
lower Phase Noise another 3dB etc. Dual oscillators in Cross Correlated
measurements will also produce a 3dB theoretical reduction in a Phase
Noise measurement system.
Thomas Knox
Date: Sat, 29 Dec 2012 23:33:52 +0100
From: magnus@rubidium.dyndns.org
To: time-nuts@febo.com
Subject: Re: [time-nuts] ensemble oscillators for better stability
Tom,
On 29/12/12 18:11, Tom Van Baak wrote:
Corby,
So that's an interesting experiment. I think the key is keeping them
in tight phase so that what you gain in combined performance is still
better than what you lose with the additional mixing electronics.
If you just mixup, then you do not need to lock them up. You only need
that if you add them up in a power-combiner.
A couple of comments that come to mind.
- This was a topic some years back -- for internal use, hp tightly
combined multiple 10811 oscillators so that the net phase noise or
short-term performance was significantly better than any one of the
constituent oscillators.
Care to share a reference on that? It would be interesting to see how
they did it and how well they where doing it.
- It would be nice to be able to extend this to more than 2
oscillators, in such a way that you gain by sqrt(N) without
corresponding losses due to increased noise.
Using the mix-up strategy would be possible. Also, for three sources you
would get back to your starting frequency easily on the second mixer. A
mix-up strategy would allow to mix 5 and 10 MHz sources, but
unfortunately that would give the 10 MHz sources twice the weight of 5
MHz sources. The free-running measure and locked additive strategies
does not have that drawback.
- You already realize that being able to keep coherence between the
standards as long as possible is highly desirable.
It depends on what strategy you try to achieve.
- Consider that none of the UTC(k) timing labs use your technique.
The reason is that it's far easier to compare N frequency
standards in near-realtime (like every second or every 100 s,
etc.) combining the measurement numbers than it is to combine
the actual electrons coming out of the frequency standards in
realtime.
Also, they do not need the high-frequency phase noise benefit. If they
need low phase-noise, an active H-maser is used.
Another benefit of not locking the standards is that you can observe
them undisturbed by a control-loop, which make things easier for what
they try to achieve.
So this is one reason why I keep encouraging those of you building
amateur, inexpensive, high-resolution, multi-port phase comparators.
It is indeed an interesting thing do to. To benefit it needs to have
many channels, say 8 or so. Preferably expandable further as you have
more sources to look at and form an ensemble of.
If you had a couple of these comparators you'd simultaneously
measure each of your 5065A and perhaps several other standards all
using a common reference. It wouldn't really matter which standard
was the reference, since the data is all pair-wise relative.
As you compare many sources, doing M-cornered hat stuff becomes
possible, and you can get some confidence in the absolute phase-noise of
all involved sources.
It's trivial to create an ensemble in software, based on multiple
phase measurements that arrive by spi or gpib or rs232. With that
calculated mean phase you can then ex post facto apply a correction
to each of the oscillators in the ensemble. It's like sawtooth
correction; you take the pulse as you see it, but you apply a
freshly calculated correction factor.
A note on ensembles is that NTP actually features ensemble calculations,
as it is able to estimate the noise, do weighting of various sources
etc. Inspired by the work done at NIST. I'm not completely sure that NTP
will work well with unlocked frequency sources, but I mention it so
people can look in their NTP books and read up a bit.
The main point is that the past noise of a source is used to calculate
the weight it can have in order to form the optimum stability. This is
how the national labs create their time-scales, and then how EAL is
built for maximum frequency stability, then being corrected into the TAI
for phase stability and then synthesized into UTC to form a stable GMT
replacement.
Once you have started to walk on the ensemble path, you are not that far
off from looking at doing a full-blown time-scale.
Cheers,
Magnus
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Tom Knox wrote:
Dual oscillators in Cross Correlated
measurements will also produce a 3dB theoretical reduction in a Phase
Noise measurement system.
Since when?
Its way better than that.
I routinely achieve a PN floor below -170dBc/Hz (I don't have an OCXO
with a phase noise floor below ~ -175dBc/Hz) using a pair of oscillators
each having a PN floor (~ -150dBc/Hz) well above that
Bruce
and not having a -175dBc/Hz reference, how you can tell that your dual
-150dBc/Hz performs like a -170dBc/Hz?
Moreover: what is the physical principle that can explain this? Injection
locking? Average in the power summer? Taking hundreds or thousands
oscillators it seems possible to reach astonishing levels...
On Sun, Dec 30, 2012 at 10:44 AM, Bruce Griffiths <
bruce.griffiths@xtra.co.nz> wrote:
Tom Knox wrote:
Dual oscillators in Cross Correlated
measurements will also produce a 3dB theoretical reduction in a Phase
Noise measurement system.
Since when?
Its way better than that.
I routinely achieve a PN floor below -170dBc/Hz (I don't have an OCXO with
a phase noise floor below ~ -175dBc/Hz) using a pair of oscillators each
having a PN floor (~ -150dBc/Hz) well above that
Bruce
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Azelio Boriani wrote:
and not having a -175dBc/Hz reference, how you can tell that your dual
-150dBc/Hz performs like a -170dBc/Hz?
You can't.
Moreover: what is the physical principle that can explain this? Injection
locking?
Not injection locking just the magic of cross corrrelation.
Only the phase noise that is common to both measurement channels
remains after sufficient averaging.
Average in the power summer? Taking hundreds or thousands
oscillators it seems possible to reach astonishing levels...
Bruce
On Sun, Dec 30, 2012 at 10:44 AM, Bruce Griffiths<
bruce.griffiths@xtra.co.nz> wrote:
Tom Knox wrote:
Dual oscillators in Cross Correlated
measurements will also produce a 3dB theoretical reduction in a Phase
Noise measurement system.
Since when?
Its way better than that.
I routinely achieve a PN floor below -170dBc/Hz (I don't have an OCXO with
a phase noise floor below ~ -175dBc/Hz) using a pair of oscillators each
having a PN floor (~ -150dBc/Hz) well above that
Bruce
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Bruce,
The Tsc5125A and miles Timepod show a phase noise floor 3dB above the noise floor of the two oscillators (if two are used with identical noise floors).
Your oscillators are better than you think, or your equipment is not calibrated.
Btw: that result IS what you want, why would you want that measurement to show better results than what your DUT can provide??
Now the tester may recognize that IT by itself could do better with better reference and DUT, and thus may also show a lower instrument noise floor, but that cannot be reached with a noisy reference no matter how long you average.
It would be nice if that worked, then we all could use $10 TCXOs instead of $1000 Wenzel references.
A cross correlated measurement usually treats the DUT and REF identically, so if one is way more noisy than the other one, the noisier one will be the noise floor shown.
Bye
Said
Sent From iPhone
On Dec 30, 2012, at 1:44, Bruce Griffiths bruce.griffiths@xtra.co.nz wrote:
Tom Knox wrote:
Dual oscillators in Cross Correlated
measurements will also produce a 3dB theoretical reduction in a Phase
Noise measurement system.
Since when?
Its way better than that.
I routinely achieve a PN floor below -170dBc/Hz (I don't have an OCXO with a phase noise floor below ~ -175dBc/Hz) using a pair of oscillators each having a PN floor (~ -150dBc/Hz) well above that
Bruce
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and follow the instructions there.
and not having a -175dBc/Hz reference, how you can tell that your dual
-150dBc/Hz performs like a -170dBc/Hz?
Moreover: what is the physical principle that can explain this? Injection
locking? Average in the power summer? Taking hundreds or thousands
oscillators it seems possible to reach astonishing levels...
Good questions! Phase noise (and AM noise for that matter) is considered to
be a "stationary process," meaning that its statistical properties are
expected to remain the same from one measurement period to the next. If the
quantity you're trying to measure is both random and stationary, then it's a
good candidate for measurement by averaging.
To take advantage of the stationary property of phase noise, you start by
measuring the spectral density of the DUT noise with two independent FFT
measurements based on the output of two independent phase comparators. The
DUT is fed to both of the comparators' input channels with a splitter, while
their references come from two independent oscillators. With repeated
measurements, the average of the two FFT output arrays will converge on the
spectral characteristics that are common to both channels.
The key idea is that because the two references have nothing in common,
their phase and amplitude contributions are as likely to be positive as
negative at any given instant, and will average to zero. Since the FFT bins
contain complex 2D quantities (I and Q), what actually happens is that the
inner product between the two vectors approaches the correct value when
averaged over time.
So, given a stationary noise process, you are not limited to the usual
sqrt(N) improvement in statistical fidelity, where N is the number of
references that contribute to the measurement. All you have to do is let
the measurement run longer with N=2. The measurement floor will improve in
proportion to sqrt(M), where M is the number of averages taken with your
pair of independent references.
Cross correlation (the process I just described) sounds like a free lunch,
and it is -- but only for stationary processes. When measuring a source's
frequency stability or phase drift, you can't rely on the statistics to
remain the same from one block of data to the next, since observing how the
underlying process changes over time is the whole idea. So you can only
improve stability measurements by increasing N, not M. (In a limited sense
ADEV can be 'backed out' of a cross-correlated phase noise measurement, but
only to the extent that the short term statistical properties are
stationary.)
For further reading and less hand waving, see the Agilent E5052A/B
literature, the TSC 5120A-01 manual and white paper by Sam Stein, and Enrico
Rubiola's book/website.
-- john
Miles Design LLC
On Sun, Dec 30, 2012 at 10:44 AM, Bruce Griffiths <
bruce.griffiths@xtra.co.nz> wrote:
Tom Knox wrote:
Dual oscillators in Cross Correlated
measurements will also produce a 3dB theoretical reduction in a Phase
Noise measurement system.
Since when?
Its way better than that.
I routinely achieve a PN floor below -170dBc/Hz (I don't have an OCXO
with
a phase noise floor below ~ -175dBc/Hz) using a pair of oscillators each
having a PN floor (~ -150dBc/Hz) well above that
Bruce
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Bruce,
The Tsc5125A and miles Timepod show a phase noise floor 3dB above the
noise floor of the two oscillators (if two are used with identical noise
floors).
Bruce is actually talking about a semi-undocumented trick with the TimePod
that allows it to act like an E5052 or TSC 5120A-01 with two internal
references. Basically, you remove the SMA jumpers from the TimePod's input
jack panel and feed two independent reference sources that are very close to
the same frequency to the Ch0 IN and Ch2 IN jacks. Then you connect your
DUT to the REF IN jack, and flip the channel equations from "0-1" and "2-3"
to "1-0" and "3-2" to reverse the roles of the input and reference sources.
That allows the cross-correlation algorithm that normally removes the ADC
noise from a PN measurement to remove the uncorrelated noise from your two
references as well. It's a nifty technique, but it is important that the
two references be close to the same frequency for various reasons, some of
which I haven't adequately investigated. So it falls into the "Unsupported
technique/Use at your own risk" category.
It would be nice if that worked, then we all could use $10 TCXOs instead
of
$1000 Wenzel references.
That's basically how the E5052A/B and TSC 5120A-01 work -- if you look at
their phase noise floor specs, they are much better than what can be
obtained from any one reference source. The E5052A/B instruments actually
use the technique to remove the noise from two VHF-microwave downconverters.
That was my original intent in adding those SMA jacks -- see
http://www.miles.io/timepod/VHF_test_jig.jpg and
http://www.miles.io/timepod/VHF_example_400_MHz.png , where a pair of HP
8662A synthesizers is used to downconvert a much quieter 400 MHz source for
measurement at 9 MHz.
In principle you can indeed use a pair of $10 TCXOs as references to measure
arbitrarily low-noise DUTs, but you may need to run the measurement for days
or weeks. Measurement time is the price of the free lunch in this case.
-- john
Miles Design LLC
John,
If the math works out, then I guess it must work.. If one has the time to wait..
Bye,
Said
Sent From iPhone
On Dec 30, 2012, at 16:23, "John Miles" jmiles@pop.net wrote:
Bruce,
The Tsc5125A and miles Timepod show a phase noise floor 3dB above the
noise floor of the two oscillators (if two are used with identical noise
floors).
Bruce is actually talking about a semi-undocumented trick with the TimePod
that allows it to act like an E5052 or TSC 5120A-01 with two internal
references. Basically, you remove the SMA jumpers from the TimePod's input
jack panel and feed two independent reference sources that are very close to
the same frequency to the Ch0 IN and Ch2 IN jacks. Then you connect your
DUT to the REF IN jack, and flip the channel equations from "0-1" and "2-3"
to "1-0" and "3-2" to reverse the roles of the input and reference sources.
That allows the cross-correlation algorithm that normally removes the ADC
noise from a PN measurement to remove the uncorrelated noise from your two
references as well. It's a nifty technique, but it is important that the
two references be close to the same frequency for various reasons, some of
which I haven't adequately investigated. So it falls into the "Unsupported
technique/Use at your own risk" category.
It would be nice if that worked, then we all could use $10 TCXOs instead
of
$1000 Wenzel references.
That's basically how the E5052A/B and TSC 5120A-01 work -- if you look at
their phase noise floor specs, they are much better than what can be
obtained from any one reference source. The E5052A/B instruments actually
use the technique to remove the noise from two VHF-microwave downconverters.
That was my original intent in adding those SMA jacks -- see
http://www.miles.io/timepod/VHF_test_jig.jpg and
http://www.miles.io/timepod/VHF_example_400_MHz.png , where a pair of HP
8662A synthesizers is used to downconvert a much quieter 400 MHz source for
measurement at 9 MHz.
In principle you can indeed use a pair of $10 TCXOs as references to measure
arbitrarily low-noise DUTs, but you may need to run the measurement for days
or weeks. Measurement time is the price of the free lunch in this case.
-- john
Miles Design LLC
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Said,
On 31/12/12 03:36, Said Jackson wrote:
John,
If the math works out, then I guess it must work.. If one has the time to wait..
It does work. Tried it with a handfull of BVAs and the graphs make sense.
Want quieter oscillators now.. :)
Cheers,
Magnus