[time-nuts] Frequency Stability Analyzer - ZCDs

[Bob kb8tq]

Hi

Assuming we are still talking about a test instrument that needs to handle a variety of levels
and a range of frequencies, the 6957 is probably as good as anything. 

With a “full up” Collins style circuit, you very much need to optimize for a specific input. 
Change that and you change the circuit. 1 MHz, 10 MHz, and 100 MHz will each “want”
a very different set of parts. Change levels 10:1 and that has an impact ….

Even if you *do* get a circuit up and running, take a look at the TC of the caps in all those
filter stages. Matching all that up for a valid test is going to be a bit hard. You have a wide
range of values and (likely) a range of capacitor types. Not an easy problem to solve without
ovenizing the whole beast. Do that and you no longer have a “simple” box … (and no guarantee
a basic oven will solve the problem …)

Bob

> On Jul 27, 2019, at 6:32 AM, Magnus Danielson <magnus at rubidium.se> wrote:
> 
> 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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