[time-nuts] A simple sampling DMTD

Sun Nov 3 00:41:08 UTC 2019

Dear all,

Attila got me thinking with his remark:

I am a bit astonished by the high noise level you have. I would have
> expected
> this to yield something below 1ps, judging from what we got from what
> Nicolas
> acheived in his work on the sine exitation based TIC[1].

...and I realised that I'm expressing the error wrong. What I had
calculated was the standard deviation of the entire signal (noise +
drift/wander). For short time periods I do get sub-ps noise levels, even
without correcting for LF/DC errors.

It may make more sense to look at the Allan deviation. I've used tvb's
adev1 tool ( http://www.leapsecond.com/tools/adev1.htm ), with a manual
correction to accommodate the 10sps data. To investigate the effect of high
pass filtering and attenuating even-order harmonics, I've generated
1001-point high pass and band pass FIR filters with GMeteor (
http://gmeteor.sourceforge.net/ ; the odd size of 1001 points being the
largest size I could reliably get the program to generate filter solutions
for); the BPF was generated to have nulls at 20, 40, 60 and 80Hz. 10MHz was
generated with an 10811 that had been powered up for three days after
having been in storage for over a year, its output fed to a Mini-Circuits
ZFSC-2-1 splitter, connected to the DMTD with two 3in semi-rigid cables.
The test was run for 175k seconds (just over 2 days) in a very much
non-temperature controlled attic. The resulting ADEV can be found at
http://www.lartmaker.nl/time-nuts/DMTD%20self-noise%20ADEV.pdf ; the
measured time difference between the channels is
http://www.lartmaker.nl/time-nuts/DMTD%20self-noise.png ; the input
spectrum of channel 1 with and without the filters is
http://www.lartmaker.nl/time-nuts/DMTD%20self-noise%20input%20spectrum.pdf

For tau=1s the Allan deviation without any filtering is 9.5E-13. High pass
filtering to eliminate LF noise and drift improves this to 4.6E-13; adding
bandpass filtering yields 3.2E-13. Out to 1000s the adev decreases linearly
with tau, after that performance degrades (further testing in a temperature
controlled room should show whether this is intrinsic or not).

As the high pass filtering seems to have the largest impact, I plan to
implement this first (still based on averaging over a single period
centered around the rising flank of the sine; the on-board processor
doesn't have enough horsepower to run a 1001pt FIR at 2ksps). Next I want
to add code to phase lock the on-board VCTCXO to the reference input, this
should also make it easy to implement a notch filter to eliminate (even)
harmonics. After that I want to see if I can get a computationally
efficient arcsin/arctan applied to the data, to make it easier to extend
the number of samples used by the ZCD without running into linearity
issues. Meanwhile I'm working on a daughterboard with twin Lattice iCE40
FPGAs.

Any suggestions so far?

To be continued,

JDB.

On Tue, Oct 22, 2019 at 12:33 AM Jan-Derk Bakker <jdbakker at gmail.com> wrote:

> Dear Attila,
>
> Thank you for your feedback, replies inline:
>
> On Tue, Oct 15, 2019 at 6:01 PM Attila Kinali <attila at kinali.ch> wrote:
> [snip]
>
>> The biggest change I would make, would be to use a higher sampling
>> frequency and use an FPGA with a CORDIC as phase detector. Especially
>> as your goal is to measure the phase difference of a distribution system,
>> where the frequency of both inputs is exactly the same.
>>
>
> That's the next step (after I've taken this 8-bit processor as far as it
> can go). I'm working on a daughterboard with dual Lattice iCE40 UltraPlus
> FPGAs, picked mainly because an open toolchain is available, but also for
> their price and QFN48 package options (which I've not found in any other
> FPGA family of similar density).
>
> (note that for my purposes I do need to DMTD different frequencies, in
> particular the 10MHz system master clock vs the slaved 50MHz clocks on the
> individual SDR boards in the phased array).
>
>
>> The reason for this is rather simple. You are using a LMS fit over
>> 32 samples around the zero crossing of a 10Hz signal with a ~10MHz
>> sampling clock. This means you have just a few samples over what would
>> be otherwise possible.
>>
>
> It's not quite that bad, as the double CIC decimator already performs
> quite a bit of averaging/filtering. The LMS fit is over 32 samples out of
> 200 per period (after the CIC). I expect the largest improvement to come
> from the increase in input sample rate.
>
>
>> The other advantage is, that you operate close to the 1/f corner
>> frequency,
>> Ie the effect of 1/f noise hits you (almost) fully. Sampling the full
>> sine wave instead gives you the ability to work far away from the 1/f
>> corner and thus greatly reduces the effect of 1/f noise.
>>
>
> This is definitely true, and at the moment my largest source of errors. As
> an intermediate step I'm considering shifting the beat frequency up some
> (say to 40...50Hz) and then I/Q demodulating in software.I expect this will
> make the filtering of LF noise easier.
>
> If you are interested, I have a parametrizable CORDIC core written
>> in VHDL ready for use.
>
>
> Thank you' I may take you up on that. So far I've been looking at the
> (Verilog) CORDIC code in the Ettus USRP sources.
>
> [snip]
>
> > I've been running some tests with a 10MHz sine wave from an Abracon
>> AOCJY1
>> > OCXO into a resistive divider, feeding both channels of the DMTD through
>> > identical SMA cables (Amphenol 135101-07-M0.50). At the ADC input this
>> > yields a -12dBFS sine wave (PSD of the beat note:
>> >
>> http://www.lartmaker.nl/time-nuts/PSD%20of%20AOCJY1%20into%20the%20LTC2140.pdf
>> > ). Over a 34000s measurement period the ZCD as described upthread (least
>> > squares fitting of the 32 samples nearest the zero crossing of the
>> rising
>> > flank, but without DC/drift correction) shows a time difference of 6.3ps
>> > between the two channels, with a standard deviation of 1.6ps (full plot:
>> >
>> http://www.lartmaker.nl/time-nuts/DMTD%20Time%20between%20zero%20crossings%20with%20resistive%20divider%20(no%20offset%20correction).pdf
>> > ).
>>
>> I am a bit astonished by the high noise level you have. I would have
>> expected
>> this to yield something below 1ps, judging from what we got from what
>> Nicolas
>> acheived in his work on the sine exitation based TIC[1].
>
>
> This is actually better than I had expected, given the drift/LF noise I
> get from the LTC2140 (
> http://www.lartmaker.nl/time-nuts/LTC2140-14%20drift.pdf ). As I've
> mentioned upthread I'm looking for a robust way to cancel this drift; my
> best plan so far is to calculate the signal average between subsequent
> _falling_ edges, and to use this to get the zero level for the rising edge.
> (This is a problem which I would expect to have a closed form solution,
> even when the period of the sine is not an integer multiple of the sampling
> rate. Alas, my undergrad-level math seems to be failing me, so I'm
> resorting to the blunt instrument of numerical approximations. I hope to
> have more time for this in a week or two; in the meantime I'm very open for
> hints.)
>
>
>> BTW: you want to keep even harmonics as low as possible, as these lead
>> to increase of 1/f noise in the system (see [3] for an explanation)
>>
>
> Thanks, that's good to keep in mind. What I've shown is the unfiltered
> output of the OCXO under test; I've not attempted to do any analog
> filtering on this.
>
> Sincerely,
>
> JDB.
>