[time-nuts] Measurements - Phase vs TDEV vs ADEV/MDEV

[Magnus Danielson]

Attila,

On 02/20/2016 07:22 PM, Attila Kinali wrote:
> Moin,
>
> We are building here some clock synchronization system and have done
> some measurements. I am trying to do some sanity checks, but I am
> not sure whether what I am interpreting into the data is actualy true.
> Hence I would like to ask for your help.
>
> Our system consists of nodes that send out a pulse at a rate of 20kHz
> to every other node. This pulse is used to synchronize the phase of
> the pulses using a TDC implemented into a FPGA (based on the OHWR TDC core
> from CERN[1]). From the self-calibration and the timing estimates we got
> from the synthesizer, we guestimate that the largest bin is approximately
> 140ps in size.
>
> Our measurements have been done using an SR620 with an trigger signal
> generated by one of the nodes with a rate of 10Hz, about 5us before
> the pulse. The output pulse of one node was connected to the start
> input and another to the stop input. (see picture)
>
> Looking at the phase data, you can see that jitter of the pulses
> of two nodes is <+/-170ps, with the average being pretty much in a window
> that is samler than +/-70ps.
>
> For the other *DEV plots, I also added measruements of the Teensy 3.1
> oscillator stabilty that I got from Jim Lux a while ago. There are
> two traces, one is the raw data and another one with the temperature
> dependence removed using a linear fit. As the oscillator we used is
> an  I expect our stability to be better, but not
> a too big difference (at most an order of magnitude at 1s).
>
>
> The TDEV we get for 0.1s is 4.6e-11 and for 1s it's 1.3e-11, going nicely
> down as an (almost) straight line until about 100s (we have a longer
> measurement that shows us that long term effects do not kick in until >100s).
>
> The ADEV starts at 8.0e-10 @0.1s passes by 7.8e-11 @ 1s and goes
> down as a straight line. The straight line is to be expected, as
> the two nodes are phase "locked", hence their frequency error
> averages out over time.
>
>
> My interpretation of the TDEV is, that it's the 1sigma error of the interval
> in seconds, when measuring a period of tau. And for the ADEV it's the 1sigma
> error of the fractional frequency deviation when measuring the frequency.

Yes. This is a good approximation for scale.

> So, my assumption was that ADEV*tau is approximately the 1sigma error in
> seconds I would get when measuring a time interval of tau. But looking at this
> data, this doesn't hold true for my clock sync system, but matches the
> Teensy oscillator data quite well. Yes, TDEV is derived from MDEV and
> not from ADEV. But what creates this big difference?

The additional filtering of the MDEV compared to ADEV. Also, there is a 
sqrt(3) scaling factor to make TDEV align up. If you look at the slope 
to the left, you see the 1/tau slope in ADEV, but as you multiply by tau 
you expect the TDEV to be flat, but it has a 1/sqrt(tau) curve, this is 
due to the MDEV having a 1/(tau*sqrt(tau)) for white phase-noise and 
thus the expected TDEV becomes 1/sqrt(tau).

Now, there is somewhat of an optical solution going on, so comparing the 
slopes makes it a bit difficult. Comparing the MDEV and TDEV plots, 
there is an equal distance between the time-system and Teensy plots, 
with about 3 decades at 10 s.

As the filtering kicks in from different starting points (100 ms and 1 
s) that in itself can make comparisons look a little bit odd.

I often flip between ADEV/MDEV/TDEV to avoid misinterpreting the plots, 
and illustrate different aspects. The TDEV plot also gives me some good 
hint about the time-instability issues rather than frequency 
instability. Not the best tool, but a hint.

> Also, extrapolating the Teensy oscillator ADEV back to 0.1, it seems
> like the clock sync generates a synchronity that is two orders of
> magnitude better than what the cheap crystals of the Teensy do.
> I would expect the ASVTX-09 to be better (it's a TCVXO after with
> a phase noise spec of <-135dBc at 1kHz and a temp dependence <2.5ppm over
> operating range) and also the clock sync to have an effect. But getting
> two orders of magnitude improvement seems to be too much. Hence I am
> not sure whether the measurement setup we had is flawed and gives
> us better numbers than we actually achieve.

Since it's a white-noise limit, somewhere along the time you could have 
a slew-rate limitation going. Sine into a comparator behaves like that.
Look at the TADD-2 input for instance, where you linearly gain yourself 
out of slew-rate limits before hitting the comparator. Do you measure 
the ASVTX-09 direction? Did you know that I've yet to see a counter that 
handles this correctly?

Hint, the Abracon ASVTX-09 datasheet:
http://www.abracon.com/Oscillators/ASVTX-09.pdf
says Output type: Clipped Sine.
Thus, you don't have good slew-rate to start with. There is nothing 
wrong with a clipped sine on the output, and it looks like a nice little 
toy there, but for white noise you won't get it's noise performance 
unless you at least attempt to handle it correctly.

So, I just think you measured the white-noise limitation of your Teensy. 
You should be able to get much better performance out of that oscillator.

As for your timing system, you see only your white noise. You measure 
the relative time between the nodes, which is relevant in itself, and in 
there you should only expect white and flicker noises, as well as 
systematic noises. I would pull the complete data from the TDCs and 
process that for systematics.

For absolute stability, you should use a start or stop timer from 
another source. Maybe measure the 10 Hz output against the counter 
time-base would do it. Then it would be more comparable to your teensy.

Also, as you have an idle counter, you can use it's time-base output 
instead of the teensy. You can also use the 1 kHz output on the front.

> Any help in clarifying these points and correcting my interpretations
> are very much appreciated.

Hope I got you started.

Cheers,
Magnus

> 				Attila Kinali
>
>
> [1] http://www.ohwr.org/projects/tdc-core/wiki
>
>
>
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