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

[Magnus Danielson]

Hi Erik,

How long is the measurement in time for each measurement? The time 
between each measurement is another way to answer as I suspect the 
200000 samples is done back-to-back.

Thing is, the actual digitizing of time difference has a systematic 
effect in it which is in itself problematic. It is interesting in your 
plot that the outer shape of peaks narrow down and go through zero at 
the center frequency.

If aim to measure the pulling of the reference, you should consider 
measuring the refrence oscillator output with another counter, as this 
will help to separate the effect of the input frequency offset into the 
counter you design from the pulling of the reference.

The time interval measurement input has both systematic and random 
components to them. A small frequency offset those expose the input to a 
slow phase ramp that then cycles over the interpolator's systematics. 
The period of this beat pattern then might not align up with the length 
of the measurement run, so positive and negative contributions may not 
even out, so depending on where on the cycle you measured you may get 
any range of values within the range. For odd frequencies one get 
essentially the same values but in an alternative time-order but it 
behaves about the same. Noise tends to average out smaller 
phase-differences but not larger, so it takes quite a bit of noise to 
smooth things out such that a long term average can take benefit.

This is why I am asking the questions I ask.

Cheers,
Magnus

On 2022-08-04 16:03, Erik Kaashoek wrote:
> 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
>