On Sun, 24 Jul 2022 08:58:10 GMT, Jan Panteltje
<pNaonStpealmtje@yahoo.com> wrote:

>On a sunny day (Sun, 24 Jul 2022 08:40:28 +1000) it happened Clifford Heath
><no_spam@please.net> wrote in
><1704967e2e98d7c6$38$2251891$26dd2c6e@news.thecubenet.com>:
>
>>On 24/7/22 05:00, Joe Gwinn wrote:
>>> I forgot to mention one thing, a way to speed initialization up:
>>>
>>> The external 1PPS pulse-train is taken as gospel. If one counts local
>>> 40 MHz oscillator cycles between any adjacent pair of 1PPS events, one
>>> will get a very accurate measurement of the local oscillator signal
>>> frequency. Knowing that it is supposed to be 40 MHz, one can compute
>>> how far off correct (as a ratio) that local oscillator is from truth.
>>> This can be used to jump far closer starting frequency to correct
>>> without waiting for convergence to get there.
>>
>>This initial measurement stands alone, not refining a previous body of
>>measurement knowledge, so it's reasonable to set the gain high. Human
>>perception does this a lot. If you hear two sounds a certain interval
>>apart, your hearing is pre-primed to expect a third at exactly the same
>>interval. If the third comes slightly early or slightly late, slightly
>>quieter or slightly louder, we jump to conclusions very quickly about
>>what's happening. Very rapid model-forming, and adapting new sensations
>>to refine the model. Very necessary for a prey animal!
>>
>>Is there a name for this idea in filter terminology?
>
>No sure, but this is related to 'the alien problem' from cryptography.
>It goes like:
>Alien comes to earh, wants to take all knowledge humans have back home.
>So he gets Encyclopedia Britannica, but it is too heavy and does not fit in his flying saucer.
>So he writes the text out as an ASCII hex number and does 1 / that number.
>then he takes a stick and puts a mark on it in that ratio
>and takes the stick back home.
>
>To say 3 ticks is all you need to convey all information in the universe
>given time has no granularity.
>The stick in that example does of course have, limited by size of atoms etc,
>But does time have granularity?
>
>I use this all the time.

Time is thought to have a granularity of sorts, about 10^-43 seconds,
which is a Planck Unit.

..<https://en.wikipedia.org/wiki/Planck_units>

Joe Gwinn

On Sun, 24 Jul 2022 16:46:15 +1000, Clifford Heath
<no_spam@please.net> wrote:

>On 24/7/22 09:08, Joe Gwinn wrote:
>> On Sun, 24 Jul 2022 08:40:28 +1000, Clifford Heath
>> <no_spam@please.net> wrote:
>>
>>> On 24/7/22 05:00, Joe Gwinn wrote:
>>>> I forgot to mention one thing, a way to speed initialization up:
>>>>
>>>> The external 1PPS pulse-train is taken as gospel. If one counts local
>>>> 40 MHz oscillator cycles between any adjacent pair of 1PPS events, one
>>>> will get a very accurate measurement of the local oscillator signal
>>>> frequency. Knowing that it is supposed to be 40 MHz, one can compute
>>>> how far off correct (as a ratio) that local oscillator is from truth.
>>>> This can be used to jump far closer starting frequency to correct
>>>> without waiting for convergence to get there.
>>>
>>> This initial measurement stands alone, not refining a previous body of
>>> measurement knowledge, so it's reasonable to set the gain high. Human
>>> perception does this a lot. If you hear two sounds a certain interval
>>> apart, your hearing is pre-primed to expect a third at exactly the same
>>> interval. If the third comes slightly early or slightly late, slightly
>>> quieter or slightly louder, we jump to conclusions very quickly about
>>> what's happening. Very rapid model-forming, and adapting new sensations
>>> to refine the model. Very necessary for a prey animal!
>>>
>>> Is there a name for this idea in filter terminology?
>>
>> There are two answers, depending on which field you mean, biology or
>> electronics.
>>
>> In biology, it has been long known that the brain creates a model of
>> the world, and keys on deviations between prediction and actual. But
>> this isn't just for expected rhythm, it's far more general and
>> flexible than that.
>>
>> With the speedup algorithm I mentioned earlier, the mechanism is
>> designed with considerable domain knowledge in hand. The primary
>> driver is to achieve robustness despite the imperfections of real
>> clocks et al. The continuous look-ahead algorithm is not flummoxed by
>> non-stationary and/or non-Gaussian probability-distributions, et al.
>
>
>> But it's more in the nature of a control system than a filter per se.
>
>A control system also models the plant, measures deviations from the
>prediction, before it applies a loop filter to decide the corrective step.
>
>That's the filter I'm referring to. It's just the same principle with
>the human system as when synchronising two clocks.

Well, yes, but we're being a bit pedantic here. The problem is that
the word "filter" can have multiple meanings. Like the low-pass loop
filter in a PLL or FLL. In the algorithm described earlier, the FLL
loop filter is implicit in the choice of look-ahead and cycle times.

Joe Gwinn

Joe Gwinn

On a sunny day (Sun, 24 Jul 2022 12:09:21 -0400) it happened Joe Gwinn
<joegwinn@comcast.net> wrote in <ugrqdhp9ldssd95u39nik1n6th9bktbs41@4ax.com>:

>On Sun, 24 Jul 2022 08:58:10 GMT, Jan Panteltje
><pNaonStpealmtje@yahoo.com> wrote:
>
>>On a sunny day (Sun, 24 Jul 2022 08:40:28 +1000) it happened Clifford Heath
>><no_spam@please.net> wrote in
>><1704967e2e98d7c6$38$2251891$26dd2c6e@news.thecubenet.com>:
>>
>>>On 24/7/22 05:00, Joe Gwinn wrote:
>>>> I forgot to mention one thing, a way to speed initialization up:
>>>>
>>>> The external 1PPS pulse-train is taken as gospel. If one counts local
>>>> 40 MHz oscillator cycles between any adjacent pair of 1PPS events, one
>>>> will get a very accurate measurement of the local oscillator signal
>>>> frequency. Knowing that it is supposed to be 40 MHz, one can compute
>>>> how far off correct (as a ratio) that local oscillator is from truth.
>>>> This can be used to jump far closer starting frequency to correct
>>>> without waiting for convergence to get there.
>>>
>>>This initial measurement stands alone, not refining a previous body of
>>>measurement knowledge, so it's reasonable to set the gain high. Human
>>>perception does this a lot. If you hear two sounds a certain interval
>>>apart, your hearing is pre-primed to expect a third at exactly the same
>>>interval. If the third comes slightly early or slightly late, slightly
>>>quieter or slightly louder, we jump to conclusions very quickly about
>>>what's happening. Very rapid model-forming, and adapting new sensations
>>>to refine the model. Very necessary for a prey animal!
>>>
>>>Is there a name for this idea in filter terminology?
>>
>>No sure, but this is related to 'the alien problem' from cryptography.
>>It goes like:
>>Alien comes to earh, wants to take all knowledge humans have back home.
>>So he gets Encyclopedia Britannica, but it is too heavy and does not fit in his flying saucer.
>>So he writes the text out as an ASCII hex number and does 1 / that number.
>>then he takes a stick and puts a mark on it in that ratio
>>and takes the stick back home.
>>
>>To say 3 ticks is all you need to convey all information in the universe
>>given time has no granularity.
>>The stick in that example does of course have, limited by size of atoms etc,
>>But does time have granularity?
>>
>>I use this all the time.
>
>Time is thought to have a granularity of sorts, about 10^-43 seconds,
>which is a Planck Unit.
>
>.<https://en.wikipedia.org/wiki/Planck_units>

Sure but there is a problem, if you scroll down on that site you find the sentence
"the Planck time is the time required for light to travel the distance of 1 Planck length in a vacuum".
That leads to a circular reasoning, as traveling half a Planck length would take half the time...
Just before that the text goes into Planck length, and says in some theories with more dimensions
that length is smaller than the fundamental Planck length
So much twenty-first century physics assumptions...
Start of big bang start of time, obvious bull.
Maybe there are a zillion bangs like there are a zillion stars and something that formed those over time.
Measurement limits like saying length in feet or whatever ...
But sure, what we can measure, being made of matter, probably has a limit.
Wait till they figure out gravity.. I still like Le Sage's model as it provides a MECHANISM for gravity.
Now they are stuck looking for dark matter..

Very interesting, physics, BTW.

On Sun, 24 Jul 2022 16:53:04 GMT, Jan Panteltje
<pNaonStpealmtje@yahoo.com> wrote:

>On a sunny day (Sun, 24 Jul 2022 12:09:21 -0400) it happened Joe Gwinn
><joegwinn@comcast.net> wrote in <ugrqdhp9ldssd95u39nik1n6th9bktbs41@4ax.com>:
>
>>On Sun, 24 Jul 2022 08:58:10 GMT, Jan Panteltje
>><pNaonStpealmtje@yahoo.com> wrote:
>>
>>>On a sunny day (Sun, 24 Jul 2022 08:40:28 +1000) it happened Clifford Heath
>>><no_spam@please.net> wrote in
>>><1704967e2e98d7c6$38$2251891$26dd2c6e@news.thecubenet.com>:
>>>
>>>>On 24/7/22 05:00, Joe Gwinn wrote:
>>>>> I forgot to mention one thing, a way to speed initialization up:
>>>>>
>>>>> The external 1PPS pulse-train is taken as gospel. If one counts local
>>>>> 40 MHz oscillator cycles between any adjacent pair of 1PPS events, one
>>>>> will get a very accurate measurement of the local oscillator signal
>>>>> frequency. Knowing that it is supposed to be 40 MHz, one can compute
>>>>> how far off correct (as a ratio) that local oscillator is from truth.
>>>>> This can be used to jump far closer starting frequency to correct
>>>>> without waiting for convergence to get there.
>>>>
>>>>This initial measurement stands alone, not refining a previous body of
>>>>measurement knowledge, so it's reasonable to set the gain high. Human
>>>>perception does this a lot. If you hear two sounds a certain interval
>>>>apart, your hearing is pre-primed to expect a third at exactly the same
>>>>interval. If the third comes slightly early or slightly late, slightly
>>>>quieter or slightly louder, we jump to conclusions very quickly about
>>>>what's happening. Very rapid model-forming, and adapting new sensations
>>>>to refine the model. Very necessary for a prey animal!
>>>>
>>>>Is there a name for this idea in filter terminology?
>>>
>>>No sure, but this is related to 'the alien problem' from cryptography.
>>>It goes like:
>>>Alien comes to earh, wants to take all knowledge humans have back home.
>>>So he gets Encyclopedia Britannica, but it is too heavy and does not fit in his flying saucer.
>>>So he writes the text out as an ASCII hex number and does 1 / that number.
>>>then he takes a stick and puts a mark on it in that ratio
>>>and takes the stick back home.
>>>
>>>To say 3 ticks is all you need to convey all information in the universe
>>>given time has no granularity.
>>>The stick in that example does of course have, limited by size of atoms etc,
>>>But does time have granularity?
>>>
>>>I use this all the time.
>>
>>Time is thought to have a granularity of sorts, about 10^-43 seconds,
>>which is a Planck Unit.
>>
>>.<https://en.wikipedia.org/wiki/Planck_units>
>
>Sure but there is a problem, if you scroll down on that site you find the sentence
> "the Planck time is the time required for light to travel the distance of 1 Planck length in a vacuum".
>That leads to a circular reasoning, as traveling half a Planck length would take half the time...
>Just before that the text goes into Planck length, and says in some theories with more dimensions
>that length is smaller than the fundamental Planck length

Well, with Planck Units, all these things are true at the same time,
and nobody knows if one causes another, or if all flow from a
currently unknown common cause. Or something.

I don't think that one can in fact move by less than a Planck length,
so in that case it is unclear if the limit is on time or on distance,
both, or something unobvious.

>So much twenty-first century physics assumptions...
>Start of big bang start of time, obvious bull.
>Maybe there are a zillion bangs like there are a zillion stars and something that formed those over time.
>Measurement limits like saying length in feet or whatever ...
>But sure, what we can measure, being made of matter, probably has a limit.
>Wait till they figure out gravity.. I still like Le Sage's model as it provides a MECHANISM for gravity.
>Now they are stuck looking for dark matter..

All that mess is the best humans have come up with so far. Stay
tuned.

>
>Very interesting, physics, BTW.

Not to mention weird.

Joe Gwinn

On Wed, 20 Jul 2022 16:20:57 -0700, John Larkin
<jlarkin@highland_atwork_technology.com> wrote:

>
>
>Suppose I have several rackmount boxes and each has a BNC connector on
>the back. Each of them has an open-drain mosfet, a weak pullup, and a
>lowpass filtered schmitt gate back into our FPGA.
>
>I can daisy-chain several boxes with BNC cables and tees.
>
>Each box has a 40 MHz VCXO and I want to phase-lock them, or at least
>time-align them to always be the same within a few microseconds,
>longterm.
>
>I could call one the leader (not "master") and make the others
>followers (not "slaves") and have the leader make an active low pulse
>maybe once a second. A follower would use her (not "his") clock to
>measure the incoming period and tweak its local VCXO in the right
>direction. That should work.
>
>Don't GPS receivers lock their 10 MHz oscillators to a 1 PPS pulse
>from the satellites?
>
>My system should work from a 1 PPS GPS pulse too, all boxes as
>followers.
>
>The PLL algorithm might be interesting.

The ultimate way to do this would be to measure the phase of the xo at
every rise of the 1 pps input, to nanosecond or picosecond resolution.
That wouldn't be hard, but it would be overkill for the requirement to
time-align power supplies.

On 2022-07-20, John Larkin <jlarkin@highland_atwork_technology.com> wrote:
>
>
> Suppose I have several rackmount boxes and each has a BNC connector on
> the back. Each of them has an open-drain mosfet, a weak pullup, and a
> lowpass filtered schmitt gate back into our FPGA.
>
> I can daisy-chain several boxes with BNC cables and tees.
>
> Each box has a 40 MHz VCXO and I want to phase-lock them, or at least
> time-align them to always be the same within a few microseconds,
> longterm.

If you only need a consensus, put the 40 mhz from the crystal onto the
BNC though some resistor, they'll sort it out, like a table full of metronoms.

If you have control loops all over the place pulling in different
directions maybe not so much.

> I could call one the leader (not "master") and make the others
> followers (not "slaves") and have the leader make an active low pulse
> maybe once a second. A follower would use her (not "his") clock to
> measure the incoming period and tweak its local VCXO in the right
> direction. That should work.
>
> Don't GPS receivers lock their 10 MHz oscillators to a 1 PPS pulse
> from the satellites?

mostlky no.

--
Jasen.

On Fri, 22 Jul 2022 09:03:16 -0400, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

>Martin Brown wrote:
>> On 22/07/2022 03:44, Clifford Heath wrote:
>>> On 22/7/22 03:10, Phil Hobbs wrote:
>>>> Gerhard Hoffmann wrote:
>>>>> Am 21.07.22 um 16:15 schrieb Phil Hobbs:
>>>>>
>>>>>> I wonder if there's an advantage to using the closure phase for an
>>>>>> array that large.  With 17 oscillators you've got 136 independent
>>>>>> phase differences, so maybe there's a way to get 22 dB instead of
>>>>>> 12 dB improvement.
>>>>>
>>>>> -v ?
>>>>>
>>>>> what do you mean with closure phase? Where do the 22 dB come
>>>>> from?
>>>>>
>>>>> The idea was simply to have all 16 regulated to the be
>>>>> synchronous and then feed them into a 16-to--1 Wilkinson
>>>>> combiner. The phase noise should average out among the
>>>>> 16 units. Just as proof of concept. The MTI-260 are quite ok,
>>>>> but with bleeding edge oscillators that could be interesting.
>>>>> In the region where you just cannot improve an oscillator.
>>>>>
>>>>>> Cheers
>>>>> Gerhard
>>>>
>>>> Sure.  Thing is, that wastes a lot of information that you could
>>>> maybe use to get 10*log(136) = 21.3 dB improvement instead of
>>>> 10*log(17) = 12.3 dB.  [136 = N(N-1)/2 when N = 17.]
>>>>
>>>> Closure is a really cute idea, which I first came across in the
>>>> context of very long baseline interferometry (VLBI) radio telescopes.
>>>> See the discussion from BEOS 3e here:
>>>>
>>>> <https://electrooptical.net/www/sed/closure.png>.
>>>
>>> Interesting, thanks.
>>>
>>> Some frequency synthesiser chips employ proprietary majick to reduce
>>> the phase noise associated with integer divide/multiply ratios.
>>> Polyphase oscillator and slipping by partial cycles I think. Perhaps
>>> they're doing something like closure against the different clock phases?
>>
>> Quite probably - it has been known for a long time in radio astronomy
>> first derived by Jennison in 1958 at Jodrell Bank for 3 antennae. This
>> is the original ground breaking paper for anyone interested
>>
>> <https://articles.adsabs.harvard.edu//full/1958MNRAS.118..276J/0000276.000.html >
>>
>>
>> (easier to understand versions exist today). WIki isn't bad:
>>
>> <https://en.wikipedia.org/wiki/Closure_phase>
>>
>> It allows you to get a good phase observable uncontaminated by the phase
>> error at each node for every distinct subset of 3 nodes. There is a
>> corresponding closure amplitude for distinct subsets of 4 nodes.
>>
>> Obviously the bigger N is the more useful observables you can get which
>> is why the big dish telescopes sometimes stay on target and in the loop
>> for perhaps longer than they really ought to in deteriorating weather.
>>
>> This book reviews most of the classical tricks used in VLBI and
>> interferometry from the period when they had just become routine:
>>
>> Indirect Imaging: Measurement and Processing for Indirect Imaging
>> Editor-J. A. Roberts
>>  0 ratings by Goodreads
>> ISBN 10: 0521262828 / ISBN 13: 9780521262828
>> Published by Cambridge University Press, 1984
>>

This proved hard to get:
..
<https://www.amazon.com/Indirect-Imaging-Measurement-Processing/dp/0521262828>
>
>The real power comes from the number of independent observables from N
>instruments going like N**2, so that you win SNR like N**2 instead of N.
>
>Quite a startling improvement for moderate-to-large N!

All very interesting. I've been digging, and came across a very
interesting article, which happens to be open-access, which is all too
uncommon.

"A geometric view of closure phases in interferometry", DOI:
<https://doi.org/10.1017/pasa.2022.6>

..<https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/geometric-view-of-closure-phases-in-interferometry/5E8A5A8D58A2FC72ADFA0587347C4DA7>

I'm still digesting it, but basically deducing the underlying geometry
allowed for some significant improvements.

Joe Gwinn

Am 25.07.22 um 18:31 schrieb Joe Gwinn:
> On Fri, 22 Jul 2022 09:03:16 -0400, Phil Hobbs

> "A geometric view of closure phases in interferometry", DOI:
> <https://doi.org/10.1017/pasa.2022.6>
>
> .<https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/geometric-view-of-closure-phases-in-interferometry/5E8A5A8D58A2FC72ADFA0587347C4DA7>
>
>
> I'm still digesting it, but basically deducing the underlying geometry
> allowed for some significant improvements.

I have not yet digested it, but can I assume that it won't help
me to create a carrier that is phase noise wise better than
averaged over 16 oscillators created equally bad?

More suitable for post-processing after-the-fact?

U. Rohde has the math for n injection locked oscillators in one
of his books, but the formulas probably fall apart when you have
to insert hard numbers for real oscillators you can buy, or build.
Methinks he is more into multiple coupled resonators.

cheers,
Gerhard

On Fri, 22 Jul 2022 20:54:49 -0500, Les Cargill <lcargil99@gmail.com>
wrote:

>Phil Hobbs wrote:
>> jlarkin@highlandsniptechnology.com wrote:
><snip>
>>>
>>> It dithers around the setpoint but nobody notices.
>>>
>
>That's what lowpass filters are for.
>
>>> This is immune to classic control theory so the concept annoys some
>>> people but it works great.
>>
>> A real old time control guy like Tim Wescott would probably be a fan
>> too--the great virtue of a bang-bang controller is that (as you say)
>> it's highly resistant to variations in the _plant_.
>>
>
>Well, yeah - it's naturally constrained. When I jack the temp target on
>the A/C here, it take 30-45 seconds to turn everything off.
>
>
>Tim used to be a lot of fun and put up with much. FWIW rbj showed up
>on Reddit and lasted a couple days.
>
>> Your furnace doesn't go nuts when you have a Christmas party, even
>> though all those people generate a lot of heat, and there's lots of
>> opening and closing of doors and ovens.
>>
>
>You're just doing trust falls with slew rate limiting. :) There's
>probably a PhD paper somewhere with a madman low-pass filtering the
>output of a bangbang with a lowpass.

We made a lot of timing modules for a big laser facility. We get a
155.52 MHz fiber data stream and lock a local VCO to that, with jitter
a couple of picoseconds. The phase detector, actually a time detector,
is an ECL d-flop in a bangbang loop.

The lowpass has switchable bandwidth, acquisition mode and track mode,
something like 8 KHz and 2 KHz.

On Mon, 25 Jul 2022 20:51:18 +0200, Gerhard Hoffmann <dk4xp@arcor.de>
wrote:

>Am 25.07.22 um 18:31 schrieb Joe Gwinn:
>> On Fri, 22 Jul 2022 09:03:16 -0400, Phil Hobbs
>
>> "A geometric view of closure phases in interferometry", DOI:
>> <https://doi.org/10.1017/pasa.2022.6>
>>
>> .<https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/geometric-view-of-closure-phases-in-interferometry/5E8A5A8D58A2FC72ADFA0587347C4DA7>
>>
>>
>> I'm still digesting it, but basically deducing the underlying geometry
>> allowed for some significant improvements.
>
>I have not yet digested it, but can I assume that it won't help
>me to create a carrier that is phase noise wise better than
>averaged over 16 oscillators created equally bad?

As you suspect, no, it won't. Only better oscillators will help.

>More suitable for post-processing after-the-fact?

The big advantage of closure-phase methods is that one can recover the
emission distribution of a very distant source by interferometry,
while ignoring various practical imperfections of radio/optical
telescope interferometers.

This works because the closure / kernel phase is an inherent property
of the source that is not affected by those practical imperfections.

This is how we image distant quasars and the event horizon of
billion-sun black holes at the center of some galaxies.

>U. Rohde has the math for n injection locked oscillators in one
>of his books, but the formulas probably fall apart when you have
>to insert hard numbers for real oscillators you can buy, or build.
>Methinks he is more into multiple coupled resonators.

Yes. The classic is a room full of pendulum clocks slipping into
synchrony. Discovered in 1666 by Christiaan Huygens, who invented of
the pendulum clock in 1657.

The only math needed is differential equations, developed a few years
later, in 1671. U. Rohde was a bit late to the party.

Joe Gwinn

Am 25.07.22 um 21:49 schrieb Joe Gwinn:

>> I have not yet digested it, but can I assume that it won't help
>> me to create a carrier that is phase noise wise better than
>> averaged over 16 oscillators created equally bad?
>
> As you suspect, no, it won't. Only better oscillators will help.

Or even more oscillators to average. :-)

Cheers, Gerhard

On Mon, 25 Jul 2022 22:16:42 +0200, Gerhard Hoffmann <dk4xp@arcor.de>
wrote:

>Am 25.07.22 um 21:49 schrieb Joe Gwinn:
>
>>> I have not yet digested it, but can I assume that it won't help
>>> me to create a carrier that is phase noise wise better than
>>> averaged over 16 oscillators created equally bad?
>>
>> As you suspect, no, it won't. Only better oscillators will help.
>
>Or even more oscillators to average. :-)

Yes, but the improvement is 5 dB per factor of ten oscillator count.
Longer integration times may be easier.

Low-noise oscillator design is a career.

Joe Gwinn

Gerhard Hoffmann wrote:
> Am 25.07.22 um 18:31 schrieb Joe Gwinn:
>> On Fri, 22 Jul 2022 09:03:16 -0400, Phil Hobbs
>
>> "A geometric view of closure phases in interferometry", DOI:
>> <https://doi.org/10.1017/pasa.2022.6>
>>
>> .<https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/geometric-view-of-closure-phases-in-interferometry/5E8A5A8D58A2FC72ADFA0587347C4DA7>
>>
>>
>>
>> I'm still digesting it, but basically deducing the underlying geometry
>> allowed for some significant improvements.
>
> I have not yet digested it, but can I assume that it won't help
> me to create a carrier that is phase noise wise better than
> averaged over 16 oscillators created equally bad?
>
> More suitable for post-processing after-the-fact?
>
> U. Rohde has the math for n injection locked oscillators in one
> of his books, but the formulas probably fall apart when you have
> to insert hard numbers for real oscillators you can buy, or build.
> Methinks he is more into multiple coupled resonators.
>
> cheers,
> Gerhard

I'm not sure--as I say, I haven't got a properly-thought-out scheme, but
it seems as though it ought to be possible to combine the measurements
to produce N-1 oscillator signals, each one N times quieter, so that
averaging _those_ would get you to the N(N-1)/2 level.

It probably needs a whole lot of phase shifters or weighted summers
(like a Wilkinson with attenuators), so it may well not be a win from a
total-hardware POV. Seems like it would be worth a bit of thought, though.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

Joe Gwinn wrote:
> On Mon, 25 Jul 2022 20:51:18 +0200, Gerhard Hoffmann <dk4xp@arcor.de>
> wrote:
>
>> Am 25.07.22 um 18:31 schrieb Joe Gwinn:
>>> On Fri, 22 Jul 2022 09:03:16 -0400, Phil Hobbs
>>
>>> "A geometric view of closure phases in interferometry", DOI:
>>> <https://doi.org/10.1017/pasa.2022.6>
>>>
>>> .<https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/geometric-view-of-closure-phases-in-interferometry/5E8A5A8D58A2FC72ADFA0587347C4DA7>
>>>
>>>
>>> I'm still digesting it, but basically deducing the underlying geometry
>>> allowed for some significant improvements.
>>
>> I have not yet digested it, but can I assume that it won't help
>> me to create a carrier that is phase noise wise better than
>> averaged over 16 oscillators created equally bad?
>
> As you suspect, no, it won't. Only better oscillators will help.

As Kipling might say, "Not so, but far otherwise."

Cheers,

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

Joe Gwinn wrote:
> On Mon, 25 Jul 2022 22:16:42 +0200, Gerhard Hoffmann <dk4xp@arcor.de>
> wrote:
>
>> Am 25.07.22 um 21:49 schrieb Joe Gwinn:
>>
>>>> I have not yet digested it, but can I assume that it won't help
>>>> me to create a carrier that is phase noise wise better than
>>>> averaged over 16 oscillators created equally bad?
>>>
>>> As you suspect, no, it won't. Only better oscillators will help.
>>
>> Or even more oscillators to average. :-)
>
> Yes, but the improvement is 5 dB per factor of ten oscillator count.
> Longer integration times may be easier.
>
> Low-noise oscillator design is a career.
>
> Joe Gwinn
>

Nah, even the simple averaging case you win SNR like N, so it's 10 dB
per decade.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

Am 26.07.22 um 14:42 schrieb Phil Hobbs:
> Joe Gwinn wrote:

>> Yes, but the improvement is 5 dB per factor of ten oscillator count.
>> Longer integration times may be easier.
>>
>> Low-noise oscillator design is a career.
>>
>> Joe Gwinn
>>
>
> Nah, even the simple averaging case you win SNR like N, so it's 10 dB
> per decade.

3 dB per doubling the # of oscs.

So, it will probably be 2 groups of 8 for my cross-correlating Timepod :-).
As I wrote, the 5.0 MHz MTI-260 were relatively cheap.

> Cheers

Gerhard, DK4XP

On Tue, 26 Jul 2022 08:05:49 -0400, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

>Gerhard Hoffmann wrote:
>> Am 25.07.22 um 18:31 schrieb Joe Gwinn:
>>> On Fri, 22 Jul 2022 09:03:16 -0400, Phil Hobbs
>>
>>> "A geometric view of closure phases in interferometry", DOI:
>>> <https://doi.org/10.1017/pasa.2022.6>
>>>
>>> .<https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/geometric-view-of-closure-phases-in-interferometry/5E8A5A8D58A2FC72ADFA0587347C4DA7>
>>>
>>>
>>>
>>> I'm still digesting it, but basically deducing the underlying geometry
>>> allowed for some significant improvements.
>>
>> I have not yet digested it, but can I assume that it won't help
>> me to create a carrier that is phase noise wise better than
>> averaged over 16 oscillators created equally bad?
>>
>> More suitable for post-processing after-the-fact?
>>
>> U. Rohde has the math for n injection locked oscillators in one
>> of his books, but the formulas probably fall apart when you have
>> to insert hard numbers for real oscillators you can buy, or build.
>> Methinks he is more into multiple coupled resonators.
>>
>> cheers,
>> Gerhard
>
>I'm not sure--as I say, I haven't got a properly-thought-out scheme, but
>it seems as though it ought to be possible to combine the measurements
>to produce N-1 oscillator signals, each one N times quieter, so that
>averaging _those_ would get you to the N(N-1)/2 level.
>
>It probably needs a whole lot of phase shifters or weighted summers
>(like a Wilkinson with attenuators), so it may well not be a win from a
>total-hardware POV. Seems like it would be worth a bit of thought, though.
>
>Cheers
>
>Phil Hobbs

Imagine a single circuit/pcb that has N crystal oscillator circuits,
injection locked and summed, in an oven.

XOs near one another, namely in the same room, like to injection lock.

jlarkin@highlandsniptechnology.com wrote:
> On Tue, 26 Jul 2022 08:05:49 -0400, Phil Hobbs
> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>
>> Gerhard Hoffmann wrote:
>>> Am 25.07.22 um 18:31 schrieb Joe Gwinn:
>>>> On Fri, 22 Jul 2022 09:03:16 -0400, Phil Hobbs
>>>
>>>> "A geometric view of closure phases in interferometry", DOI:
>>>> <https://doi.org/10.1017/pasa.2022.6>
>>>>
>>>> .<https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/geometric-view-of-closure-phases-in-interferometry/5E8A5A8D58A2FC72ADFA0587347C4DA7>
>>>>
>>>>
>>>>
>>>> I'm still digesting it, but basically deducing the underlying geometry
>>>> allowed for some significant improvements.
>>>
>>> I have not yet digested it, but can I assume that it won't help
>>> me to create a carrier that is phase noise wise better than
>>> averaged over 16 oscillators created equally bad?
>>>
>>> More suitable for post-processing after-the-fact?
>>>
>>> U. Rohde has the math for n injection locked oscillators in one
>>> of his books, but the formulas probably fall apart when you have
>>> to insert hard numbers for real oscillators you can buy, or build.
>>> Methinks he is more into multiple coupled resonators.
>>>
>>> cheers,
>>> Gerhard
>>
>> I'm not sure--as I say, I haven't got a properly-thought-out scheme, but
>> it seems as though it ought to be possible to combine the measurements
>> to produce N-1 oscillator signals, each one N times quieter, so that
>> averaging _those_ would get you to the N(N-1)/2 level.
>>
>> It probably needs a whole lot of phase shifters or weighted summers
>> (like a Wilkinson with attenuators), so it may well not be a win from a
>> total-hardware POV. Seems like it would be worth a bit of thought, though.
>>
>> Cheers
>>
>> Phil Hobbs
>
> Imagine a single circuit/pcb that has N crystal oscillator circuits,
> injection locked and summed, in an oven.
>
> XOs near one another, namely in the same room, like to injection lock.

Sure. That only gets you 10*log(N), though, AFAICT. Looking at it from
a phase noise POV, you win improved <delta phi> like sqrt(N), just as
you gain lower <delta V> by parallelling JFETs.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

On Tue, 26 Jul 2022 08:40:45 -0400, Phil Hobbs
<pcdhSpamMeSenseless@electrooptical.net> wrote:

>Joe Gwinn wrote:
>> On Mon, 25 Jul 2022 20:51:18 +0200, Gerhard Hoffmann <dk4xp@arcor.de>
>> wrote:
>>
>>> Am 25.07.22 um 18:31 schrieb Joe Gwinn:
>>>> On Fri, 22 Jul 2022 09:03:16 -0400, Phil Hobbs
>>>
>>>> "A geometric view of closure phases in interferometry", DOI:
>>>> <https://doi.org/10.1017/pasa.2022.6>
>>>>
>>>> .<https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/geometric-view-of-closure-phases-in-interferometry/5E8A5A8D58A2FC72ADFA0587347C4DA7>
>>>>
>>>>
>>>> I'm still digesting it, but basically deducing the underlying geometry
>>>> allowed for some significant improvements.
>>>
>>> I have not yet digested it, but can I assume that it won't help
>>> me to create a carrier that is phase noise wise better than
>>> averaged over 16 oscillators created equally bad?
>>
>> As you suspect, no, it won't. Only better oscillators will help.
>
>As Kipling might say, "Not so, but far otherwise."

Well, for phase noise test sets, the rule is that noise reduces as
10Log10[ Sqrt[N] ], or simply 5Log10[N], where N is the number of
correlations performed, where what's being correlated is
data-collection runs with a specified data-collection window
durations. These windows can be over time or over devices, which
should be equivalent in the noise floor.

So, getting to very low PN levels this way soon becomes impractical,
and by far the best approach is to use a better oscillator. State of
the art these days is a noise floor at around -170 dBc/Hz at 10 MHz.
As always, 1/f^a noise can be a big problem, and it doesn't average
out all that well.

We may be talking about different things.

Joe Gwinn

Lasse Langwadt Christensen wrote:
> lørdag den 23. juli 2022 kl. 03.57.33 UTC+2 skrev Les Cargill:
>> bitrex wrote:
>>> On 7/20/2022 8:22 PM, John Larkin wrote:
>>>> On Wed, 20 Jul 2022 19:32:20 -0400, Phil Hobbs
>>>> <pcdhSpamM...@electrooptical.net> wrote:
>>>>
>>>>> John Larkin wrote:
>>>>>>
>>>>>>
>>>>>> Suppose I have several rackmount boxes and each has a BNC connector on
>>>>>> the back. Each of them has an open-drain mosfet, a weak pullup, and a
>>>>>> lowpass filtered schmitt gate back into our FPGA.
>>>>>>
>>>>>> I can daisy-chain several boxes with BNC cables and tees.
>>>>>>
>>>>>> Each box has a 40 MHz VCXO and I want to phase-lock them, or at least
>>>>>> time-align them to always be the same within a few microseconds,
>>>>>> longterm.
>>>>>>
>>>>>> I could call one the leader (not "master") and make the others
>>>>>> followers (not "slaves") and have the leader make an active low pulse
>>>>>> maybe once a second. A follower would use her (not "his") clock to
>>>>>> measure the incoming period and tweak its local VCXO in the right
>>>>>> direction. That should work.
>>>>>>
>>>>>> Don't GPS receivers lock their 10 MHz oscillators to a 1 PPS pulse
>>>>>> from the satellites?
>>>>>>
>>>>>> My system should work from a 1 PPS GPS pulse too, all boxes as
>>>>>> followers.
>>>>>>
>>>>>> The PLL algorithm might be interesting.
>>>>>>
>>>>>
>>>>> It's certainly possible. However, within whatever tiny loop bandwidth
>>>>> you wound up with, the lockers would still have
>>>>>
>>>>> 20 log(40e6) = 152 dB
>>>>>
>>>>> higher phase noise than the lockee.
>>>>
>>>> GPS has that problem too.
>>>>
>>>>>
>>>>> It would be interesting to do the math to see whether it's possible to
>>>>> generate a concensus lock for the group: if you get everybody close
>>>>> enough, just sum their sine wave outputs and lock each one of them to
>>>>> that, with some bit of AC coupling or something so that they don't all
>>>>> wander together off to the edge of the tuning range.
>>>>>
>>>>> Maybe have one doing the locking with a phase shifter and the others
>>>>> with VCOs, or something like that.
>>>>>
>>>>> Definitely a partly-baked idea, but surely one could do better than
>>>>> 152 dB!
>>>>>
>>>>> Cheers
>>>>>
>>>>> Phil Hobbs
>>>>
>>>> Each box is basically a multichannel power supply, but channels can be
>>>> programmed to do stuff in timed sequences. I want different box
>>>> outputs to time align within, say, one millisecond longterm once
>>>> programs are kicked off together. So, many microseconds of equivalent
>>>> RMS phase noise is OK as long as we stay time aligned longterm.
>>>
>>> It sounds like you're looking for a protocol like DMX if what you want
>>> is to trigger sequences of events across boxes to within a millisecond,
>>> I don't understand what this lock-the-40 MHz across boxes is about.
>>>
>>> <https://en.wikipedia.org/wiki/DMX512>
>>>
>>>
>>>
>>
>> DMX for this is like hunting deer with an artillery piece. DMX is for
>> the big-ass risk scenarios in distributed topologies; this is a lot
>> less profound.
>
> ? it's a 250kbit uart on RS485, hardly rocket surgery
>

That's the physical layer; DMX is pretty holistic. I dunno - maybe
there's a COTS DMX doohickey that can be pressed into service.

--
Les Cargill

jlarkin@highlandsniptechnology.com wrote:
> On Fri, 22 Jul 2022 21:10:35 -0500, Les Cargill <lcargil99@gmail.com>
> wrote:
>
>> jlarkin@highlandsniptechnology.com wrote:
>>> On Thu, 21 Jul 2022 11:42:28 -0400, Phil Hobbs
>>> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>> <snip>
>>>> Phil Hobbs
>>>
>>> Mathematicians often like music. In my experience, music fandom is
>>> negatively correlated to engineering design skill. Different brain
>>> structure or something.
>>>
>>
>> Engineering is composition. Composition is the thin edge of the musical
>> wedge. Musicianship is different; it's pattern identification. As is
>> composition but in a different way. But it is all the same thing.
>>
>> It all depends on which wall you prefer to have your back against.
>
> I've always wondered about musicians. They have to play a piece
> hundreds of times to get it right.

Some do; some don't. Session players from back when studio time
was the dominant cost probably played the parts on a song you later
heard on the radio on the first take.

> Some have surely performed
> something thousands of times. Don't they get bored? Apparently not.
>

There's too broad a spectrum to generalize. Some forms are better for
people with mild forms of OCD.

> I design something, finish, and then want to design something entirely
> different.
>
> It depends on boredom thresholds.
>

Much does.

>>
>>> One other thing I see a lot is undue respect for standards. As in "you
>>> can't do that because it violates SCPI standards." Where are the SCPI
>>> Police when you need them?
>>
>> Over where they MATLAB.
>
> SCPI is send-and-forget. There is some query you can send to ask if
> the last command worked. And you can have an error queue that you can
> interrogate now and then for historical forensics.
>
> I told the customer that damn the specs, every command is going to
> reply with data, an error message, or "OK". They agree.
>
>

And there you go turning a perfectly good full duplex channel into a
half duplex walkie-talkie channel :)

It'll be fast enough.

--
Les Cargill

Joe Gwinn wrote:
> On Tue, 26 Jul 2022 08:40:45 -0400, Phil Hobbs
> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>
>> Joe Gwinn wrote:
>>> On Mon, 25 Jul 2022 20:51:18 +0200, Gerhard Hoffmann <dk4xp@arcor.de>
>>> wrote:
>>>
>>>> Am 25.07.22 um 18:31 schrieb Joe Gwinn:
>>>>> On Fri, 22 Jul 2022 09:03:16 -0400, Phil Hobbs
>>>>
>>>>> "A geometric view of closure phases in interferometry", DOI:
>>>>> <https://doi.org/10.1017/pasa.2022.6>
>>>>>
>>>>> .<https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/geometric-view-of-closure-phases-in-interferometry/5E8A5A8D58A2FC72ADFA0587347C4DA7>
>>>>>
>>>>>
>>>>> I'm still digesting it, but basically deducing the underlying geometry
>>>>> allowed for some significant improvements.
>>>>
>>>> I have not yet digested it, but can I assume that it won't help
>>>> me to create a carrier that is phase noise wise better than
>>>> averaged over 16 oscillators created equally bad?
>>>
>>> As you suspect, no, it won't. Only better oscillators will help.
>>
>> As Kipling might say, "Not so, but far otherwise."
>
> Well, for phase noise test sets, the rule is that noise reduces as
> 10Log10[ Sqrt[N] ], or simply 5Log10[N], where N is the number of
> correlations performed, where what's being correlated is
> data-collection runs with a specified data-collection window
> durations. These windows can be over time or over devices, which
> should be equivalent in the noise floor.

Interesting. With phase-locked sources, when you simply average the
signals directly, the flatband amplitude and phase noise amplitudes go
down like sqrt(N), i.e. the noise power goes as 1/N. It's just like
additive noise.

Inside the loop BW, things are no doubt more complicated.

There are other situations such as OTDR where the amplitude dependence
is sqrt(sqrt(N)), but that's on account of electrical power going as the
square of optical power.

>
> So, getting to very low PN levels this way soon becomes impractical,
> and by far the best approach is to use a better oscillator. State of
> the art these days is a noise floor at around -170 dBc/Hz at 10 MHz.
> As always, 1/f^a noise can be a big problem, and it doesn't average
> out all that well.
>
> We may be talking about different things.

I expect so!

Cheers

Phil Hobbs

>
>
> Joe Gwinn
>

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

On 26/07/2022 13:05, Phil Hobbs wrote:
> Gerhard Hoffmann wrote:
>> Am 25.07.22 um 18:31 schrieb Joe Gwinn:
>>> On Fri, 22 Jul 2022 09:03:16 -0400, Phil Hobbs
>>
>>> "A geometric view of closure phases in interferometry", DOI:
>>> <https://doi.org/10.1017/pasa.2022.6>
>>>
>>> .<https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/geometric-view-of-closure-phases-in-interferometry/5E8A5A8D58A2FC72ADFA0587347C4DA7>
>>>
>>> I'm still digesting it, but basically deducing the underlying geometry
>>> allowed for some significant improvements.
>>
>> I have not yet digested it, but can I assume that it won't help
>> me to create a carrier that is phase noise wise better than
>> averaged over 16 oscillators created equally bad?
>>
>> More suitable for post-processing after-the-fact?
>>
>> U. Rohde has the math for n injection locked oscillators in one
>> of his books, but the formulas probably fall apart when you have
>> to insert hard numbers for real oscillators you can buy, or build.
>> Methinks he is more into multiple coupled resonators.

Entrainment of weakly coupled oscillators at frequencies near to each
other can be quite strong (a problem if you don't want that to happen).
>
> I'm not sure--as I say, I haven't got a properly-thought-out scheme, but
> it seems as though it ought to be possible to combine the measurements
> to produce N-1 oscillator signals, each one N times quieter, so that
> averaging _those_ would get you to the N(N-1)/2 level.

I think the catch is that to do that you would have to provide hardware
to compute the cross correlation of every pair of oscillators so that
correlator complexity goes up as N(N-1)/2 too. I can't immediately see a
way to exploit this to get a better average oscillator though.
>
> It probably needs a whole lot of phase shifters or weighted summers
> (like a Wilkinson with attenuators), so it may well not be a win from a
> total-hardware POV.  Seems like it would be worth a bit of thought, though.

VLBI typically disciplines a hydrogen maser using some other long term
stable centralised terrestrial time source. Getting it just a little bit
wrong just makes the white light fringe much harder to find later. Local
clock short term stability stability is the key to it working well.

I expect they are a lot better at it by now. In my day it involved
moving around furniture van loads of tweaked VHS video tape cassettes
from the big dishes to the correlator centres.

--
Regards,
Martin Brown

On Tue, 26 Jul 2022 19:56:53 -0500, Les Cargill <lcargil99@gmail.com>
wrote:

>jlarkin@highlandsniptechnology.com wrote:
>> On Fri, 22 Jul 2022 21:10:35 -0500, Les Cargill <lcargil99@gmail.com>
>> wrote:
>>
>>> jlarkin@highlandsniptechnology.com wrote:
>>>> On Thu, 21 Jul 2022 11:42:28 -0400, Phil Hobbs
>>>> <pcdhSpamMeSenseless@electrooptical.net> wrote:
>>> <snip>
>>>>> Phil Hobbs
>>>>
>>>> Mathematicians often like music. In my experience, music fandom is
>>>> negatively correlated to engineering design skill. Different brain
>>>> structure or something.
>>>>
>>>
>>> Engineering is composition. Composition is the thin edge of the musical
>>> wedge. Musicianship is different; it's pattern identification. As is
>>> composition but in a different way. But it is all the same thing.
>>>
>>> It all depends on which wall you prefer to have your back against.
>>
>> I've always wondered about musicians. They have to play a piece
>> hundreds of times to get it right.
>
>Some do; some don't. Session players from back when studio time
>was the dominant cost probably played the parts on a song you later
>heard on the radio on the first take.
>
>> Some have surely performed
>> something thousands of times. Don't they get bored? Apparently not.
>>
>
>There's too broad a spectrum to generalize. Some forms are better for
>people with mild forms of OCD.
>
>> I design something, finish, and then want to design something entirely
>> different.
>>
>> It depends on boredom thresholds.
>>
>
>Much does.
>
>>>
>>>> One other thing I see a lot is undue respect for standards. As in "you
>>>> can't do that because it violates SCPI standards." Where are the SCPI
>>>> Police when you need them?
>>>
>>> Over where they MATLAB.
>>
>> SCPI is send-and-forget. There is some query you can send to ask if
>> the last command worked. And you can have an error queue that you can
>> interrogate now and then for historical forensics.
>>
>> I told the customer that damn the specs, every command is going to
>> reply with data, an error message, or "OK". They agree.
>>
>>
>
>And there you go turning a perfectly good full duplex channel into a
>half duplex walkie-talkie channel :)
>
>It'll be fast enough.

One might feel a little silly, having sent 14,000 commands to a box
and then discovering that the power strip is off.

Am 27.07.22 um 08:21 schrieb Anthony William Sloman:
> On Wednesday, July 27, 2022 at 12:34:40 PM UTC+10, Phil Hobbs wrote:
>> Joe Gwinn wrote:

>>>>> As you suspect, no, it won't. Only better oscillators will help.

As far as crystals go, we have reached the end.

> This might be the better oscillator.
>
> https://spectrum.ieee.org/for-precision-the-sapphire-clock-outshines-even-the-best-atomic-clocks?utm_campaign=post-teaser&utm_content=7190c3vu
>
> It's a big lump of sapphire in a pool of liquid helium. Long term stability isn't wonderful, but short term stability is uniquely good.
>
> " The team is re-engineering the device to work at 50 K by increasing the concentration of magnetic impurities in the crystal without introducing additional losses. That's a temperature that liquid nitrogen can't quite get to, but it's way easier than 6 K."
>
> Apparently the Australian Air Force has two of the 6K devices for their radar network. Probably beyond John Larkin's budget.

More on this:

<
https://scholar.google.de/scholar?q=poseidon+sapphire+oscillator&hl=de&as_sdt=0&as_vis=1&oi=scholart
>

IIRC, Poseidon Scientific Inst. , a spin-off from that
Australian univ belongs to the Microchip timing empire now.

< https://sci-hub.mksa.top/10.1109/FREQ.1995.483927 >

(shorten that ridiculous filenme)
Driscoll seems to be everywhere it is interesting.

< http://rubiola.org/ >
The entire web site is most interesting,
Alone the reference section!
In this context:

< http://rubiola.org/pdf-articles/journal/2019-UFFC--TDDS-Sapphire.pdf >

< http://rubiola.org/pdf-articles/journal/2016-JPCS-8FSM--Sapphire.pdf >

and so on.
He is also into optical oscillators .

cheers, Gerhard