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

[Erik Kaashoek]

Hi Magnus,
The measurements uses least square processing over 200000 samples per 
measurement
As you proposed a high resolution scan was made showing the pulling to 
be indeed in the order of the delta to the reference frequency [1]
But its not a constant pull and the measured frequency sometimes jumps 
back to the correct frequency or even to the opposite side.
The bandwidth of the variations (2E-10) is too constant not to be based 
on some underlying phenomena still to be investigated, especially above 
the reference frequency.
Please keep in mind this is still measured using prototype HW using long 
connecting wires.
Hope this improves when done on a PCB.
Erik.
[1] http://athome.kaashoek.com/time-nuts/Freq_error_fine.PNG

On 4-8-2022 10:46, Magnus Danielson via time-nuts wrote:
> Hi Erik,
>
> Be aware that frequency pulling of the oscillator is not the same 
> phenomena as exposing non-linearity in time-interval measurement. The 
> later being more complicated by presence of noise. This nonlinearity 
> is actually a bit of a complex animal. I would not use the term 
> frequency pulling to describe the overall phenomena. If you see the 
> same pattern of deviation at some other frequency the actual frequency 
> pulling would be much less. Consider for instance 15000001 Hz.
>
> First of all you need to consider that you will have noise causing 
> your frequency estimates to spread out. The four classical noises of 
> oscillators will cause a Gaussian distribution on frequency estimates. 
> In itself it has zero mean contribution, but as one makes limited 
> length measure there will be a residual offset here or there, which 
> jumps around in Gaussian shape.
>
> The frequency flicker modulation as converted into flicker frequency 
> readings isn't strictly Gaussian, but good enough that we can use it 
> as an approximation.
>
> Frequency pulling of the counters reference oscillator would pull it 
> towards the frequency of the other signal, so if you use a higher 
> frequency the reference would go higher. Observing this in the noise 
> variations require a bit of patience, but it possible, so that the 
> confidence interval around the average is tight enough that you see 
> the change. As we measure the external frequency it would mean that we 
> would see it count the assigned signal lower. This would work if we 
> can maintain stability of the oscillators well enough that they have 
> not glided towards each other, which they naturally also could do.
>
> So, there is a bit of careful measurements to be done before claiming 
> frequency pulling.
>
> Naturally, using accelerated least square processing for frequency 
> estimation is recommended. Helps to surpress noise.
>
> Cheers,
> Magnus