[time-nuts] Frequency Ensemble

[Bob kb8tq]

Hi

The answer is (of course) yes. The somewhat more detailed answer is that it actually is a practical basement sort of thing *if* 
you have the space. I was headed off to do this and changed course. That’s just my lack of focus rather than it being an
un-doable sort of thing. What’s below is sort of a random walk through doing it. 

The first thing you need (after all the standards) is a way to do precision comparisons of all your devices. There are an infinite
number of ways to do this. Let’s say you buy 26 TICC’s to do the job ( TAPPR needs 25 ordered to get the next batch going
so that would solve two problems at once :) ). A PPS from a single source with good short term stability (maybe an OCXO) goes
into one side of all of them. A pps from a DUT goes in the other side (yes there are other ways …TAPPR needs that order ….).
You then have 26 devices each reporting how a single standard compares to the “main OCXO”. 

As. this chugs along you get a whole bunch of timestamps telling you how far your main OCXO is from each and every one of your
“standards”. Since 10 of them are GPSDO’s they likely will be doing some very similar things. For the moment let’s ignore that
and assume they are independent / uncorrelated sources. Since things like the Rb’s are free running data comes in spread out
over the second, collecting data and comparing it isn’t exact. 

Once a second, you round up all the data and make a guess about what is correct. If everything is independent and equally 
noisy and … and … and … your guess could be sqrt(N) better than any individual source. With 26 sources, you would be a bit
over 5X better than what you started with. You then diddle the EFC on an OCXO to put it inline with that estimate (yes that
may mean a 27th TICC). 

Stepping back, there was a bit of hand waving going on there : 

One assumption is that the TICC measurement noise at one second is better than the noise of the sources. That probably is 
only true at much longer time spans (say >100 seconds). You can either upgrade the measurement or accept the longer time
span. (TICC is about 1x10^-10 at 1 sec, 1x10^-12 at 100 sec, and 1x10^-13 at 1,000 sec)

The “independent / uncorrelated sources” part is very suspect with a group of (possibly same manufacture) GPSDO’s in the mix.
A burp here or there in the way GPS L1 (I’m guessing they are L1) is behaving can easily swing them all at the same time.. Things 
like temperature (Rb’s have temperature dependence) also can get into the mix. 

One alternate that might actually be easier to deal with: Run 10 free running OCXO’s and the 16 Rb’s. Add some number of 
GPS modules (with PPS outputs) to the mix. That way you will not be constantly fighting the unknown loop dynamics of the 
GPSDO’s. 

Next, somebody is likely to raise their hand and ask if the noise really *is* gaussian (and thus goes down as fast as the square root).
The same things that get into making the sources correlated (and some other things) contribute to them being non-gaussian in
this regard. Simple answer is you likely will not quite get to the 5X improvement advertised above. One thing you *can* do for 
 some effects is try to learn them via cross comparison. That gets into the guts of your software and how you decide to do this.

What the final result is at any specific tau will be very much a “that depends” sort of thing. The Rb’s have an ADEV curve that 
should drop by sqrt(tau). ( 10X better ADEV at 100X tau). Most GPSDO’s fairly flat ADEV out to some “hump” and then they
follow GPS down from that point. If you actually steer an OCXO, the control loop will get into the act as well. 

You might also look into ganging up the TICC’s to run 4 channels in one block. Unfortunately that would get the total order 
below what TAPPR needs … :) That would let you compare three standards against the master in one block and cut the 
total down to nine “pods” of two each. 

Indeed a fun project. There are a lot of papers out there on various aspects of it. Jim Barnes and David Allan authored a lot
of them, either together or independently. Since they both worked at NIST, the papers are in the public domain. 

Have fun !!!!

Bob



> On Mar 16, 2019, at 9:16 PM, Anton Moehammad via time-nuts <time-nuts at lists.febo.com> wrote:
> 
> Hi Everyone,I like to know if it possible to run let say 10 GPSDO, 16 Rb clock together and take the average to control 1 "master clock" and have better stability ?like what BIPM or NIST doing.
> I have search about ensemble system but I have no idea how much advantage I get from some clock that I already have.Thank YouAnton 
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