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

[Magnus Danielson]

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

On 2022-08-03 20:58, Erik Kaashoek via time-nuts wrote:
> A well know technique for measuring phase pulling is measuring the 
> phase of two signals 0.01 Hz or less apart.
> To test if this pulling has a relevant impact on frequency measurement 
> the ratio between two 10 MHz output signals from a signal generator 
> was measured. One output signal was changed in frequency in steps of 
> 0.01 Hz between 9999999 Hz and 10000001 Hz [1]
> The plot shows the error at all measured frequencies differences (+/- 
> 1Hz in steps of 0.01 Hz) is below the accuracy target of +/- 1e-9
> Is this a relevant measurement for detecting possible interaction 
> between the two inputs of a frequency counter?
> Any suggestions for how to do a performance evaluation of a frequency 
> counter?
> [1] http://athome.kaashoek.com/time-nuts/Freq_error.PNG
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