[time-nuts] Re: Testing frequency pulling on a DYI counter

[Magnus Danielson]

Erik,

Good job there. I suspected that the actual frequency pulling, if any, 
was very low.

Yes, numerical issues in linear regression can be painful.

In the accelerated method I developed, you can engineer the values to 
avoid major numerical issues. Also, you are not the first to have seen 
such issues. This is done first-degree by making sure that things is 
accumulated without making any roundings, and secondly by choosing the 
number of samples just right to make the unavoidable final division not 
too terrible to the end result.

It's well known that you get fractional issues too.

Cheers,
Magnus - tired after driving 600+ km

On 8/4/22 20:04, Erik Kaashoek wrote:
> Bob, Magnus,
>
> Using a second counter (my famous Picotest U6200A) locked to the 
> reference output of the DIY counter and measuring the output of the 
> signal generator and also set to gate of 10 s it is confirmed that the 
> frequency pulling (if any) is below 1E-11 (not more digits on the 
> display of the U6200A)
> Generator is set to 10.000,000,000,2 MHz and is measured as such by 
> the U6200A
> As there seems to be no frequency pulling I went back to the 
> simulation of the linear regression algorithm and discovered that when 
> there is a integer  divide/multiply relation between the internal 
> reference and the measured frequency the regression looses some accuracy.
> For sure if the reference is close to an integer multiple of the 
> measured frequency (10 Mhz measured -> 200 MHz reference) the 
> regression collapses completely in accuracy. I hoped that by creating 
> a fractional relation this collapse would not happen at 10 MHz but is 
> still there, although much smaller. For this test I'm using a "div 3 
> times 64 e.g. 213.333,333,333,333... MHz" internal reference frequency 
> derived from the external 10MHz reference. Ton van Baak warned me 
> against using fractional relations in a counter but otherwise it is 
> impossible to measure a 10 MHz input signal with any accuracy without 
> a HW time to digital as the interpolation no longer works. I can 
> switch dynamically to 200 MHz or 245 MHz reference and these produce 
> much much worse results.
> I realize this test only measures if the TCXO used as reference in the 
> DIY counter does not show frequency pulling but it does not show if 
> the PLL used to convert the 10MHz to 213.333333333... MHz for the 
> internal counters shows any frequency pulling.
> NOt
> Erik.