[time-nuts] Frequency Stability Analyzer - ZCDs

[Attila Kinali]

On Sat, 27 Jul 2019 18:21:50 +1200 (NZST)
Bruce Griffiths <bruce.griffiths at xtra.co.nz> wrote:

> The LTC6957 is a better choice for squaring up sinewaves:
> http://www.ko4bb.com/getsimple/index.php?id=phase-noise-and-other-measurements-with-a-timepod

If you want to have a single component ZCD, then I agree.
Otherwise, a multi-stage Collins like ZCD can perform better.
Especially, if the input waveform has known properties, then
the multi-stage approach can properly optimize for those.

> Comparators are almost always noisier.
> Oliver Collins wrote a paper on optimising such sine to square converters.
> I extended the analysis to allow optimisation when the input noise of the 
> cascaded stages arent equal.

There is one important point with Collins' analysis that hardly gets
mentioned: His analysis assumes that the output signal of a stage is
trapezoid. While this is true for high gain settings, it is not for
low gain settings. Ie in his example with 6 stages, the first three stages
have a total gain of 23, ie the signal has still significant curvature.
Thus Collins' analysis the noise contribution of these three stages contains
significant erros. See the attached paper for details.

Additionally, in a multi-stage ZCD, it is very important to keep the
duty cycle at 50%, as otherwise the even harmonics give rise to an increase
of flicker noise due to noise up- and down-conversion. See [1] for details.

			Attila Kinali

[1] "A Physical Sine-to-Square Converter Noise Model", by Attila Kinali. 2018.
http://people.mpi-inf.mpg.de/~adogan/pubs/IFCS2018_comparator_noise.pdf

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