[time-nuts] Frequency Stability Analyzer - ZCDs

[Magnus Danielson]

Hi,

On 2019-07-27 12:07, Attila Kinali wrote:
> 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.
The LTC6957 is a multi-stage device with only 4 different bandwidths to
optimize for, so you can do better. It may however be good enough for
many purposes.
>
>> 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.

The trapetzoid model is a simplification which is better than sine or
square, but not perfect.

Another thing with Bruce noticed was that it assumed the same noise from
all op-amps, but you can choose different op-amps with different noise
and slope-rates and then you need different formulas, which Bruce produced.

>
> 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.

This effect has been seen by NIST for dividers, which made them conclude
one needs to end with a divide by 2.

Cheers,
Magnus

> 			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
>
>
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