[time-nuts] 1 pps Accuracy in two locations

[Attila Kinali]

On Wed, 4 Dec 2019 09:40:34 -0000
<martyn at ptsyst.com> wrote:

> I'm always being asked to provide equipment that can produce two 1 pps
> outputs aligned to each other to within a few ps.
> 
> These two 1 pps pulses are not in the same location and could be 100 metres
> to a few km away.

As others have written, getting down to a few ps is not feasible, at least
not with the amount of money your customers are likely willing to pay.
To get down to these levels you will need to pull fibres from one location
to another and using special circuitry to activly compensate variation
in length due to temperature changes and vibration, even for burried fibres.
Just to put into perspective what your customers are asking for: in 1ps
light travels 300µm in vacuum/air or ~150µm in fibre/coax. This means,
to get better than 10ps, you have to control the length of everything down
to better than 1mm. Thermal expansion coefficient is somewhere between
1e-6 to 1e-4 for solids. Assuming you have 1e-6 and want to bridge 1km
you would need to keep the temperature of the whole fibre stable to 1°C
in order to keep the timing variation due to length change below 10ps.
And that's not yet accounting for changes in refraction index (i.e. speed
of light) due to temperature changes or a myriad other effects that you
will have to deal with.

Even white rabbit, which is probably the most advanced system you will
likely get your hands on (does two-way timing to compensate for length
of fibre and length variation), gives you about 200ps of uncertainty
from one node to the next (but <10ps rms jitter). Each WR switch/node
costs ~3k€ so isn't exactly cheap either, but you get GBit ethernet
ontop of the time transfer as well.

> So they are asking for two of my GNSS frequency standards with 1 pps
> outputs.

State of the art time transfer using GPS, I am aware of, is what BIPM has
demonstrated two years ago using iPPP and, IIRC a base line of a few 100km
of 200ps uncertainty. But that's using calibrated GPS receivers in a
temperature controlled environment with lots of post-processing.
I.e. it's not real-time. For shorter baselines, I expect the uncertainty
to come down a bit. But I would not assume for it to go below 100ps without
verifying first, even at very short baseliens of a few 10s of meters.

If you have money to spare and line of sight between the locations,
you could employ something like the NIST free space laser system
https://www.nist.gov/programs-projects/optical-two-way-time-frequency-transfer
But beware: it uses multiple frequency combs which cost as much as a very
nice car. Each of them. But they get to sub-100fs stability, which means
you could get to low-ps uncertainty, if done correctly.

Rule of thumb: if you need time transfer better than 1ns you need to think
about what you are doing, even within the same room. If you leave the
building, going below 1ns is going to be hard. Doing better than 1ns within
a neighborhood, while possible, will need some serious equipment and proper
planing. Any factor of 10 better will drive up your cost by a factor 100 to
1000.

Rule of thumb #2: if you need to control lengths to better than 10µm, your
mechanics guy will throw a fit as he will most likely be unable to manufacture
to that precision, unless you are building something tiny.

			Attila Kinali 

-- 
Science is made up of so many things that appear obvious 
after they are explained. -- Pardot Kynes