[time-nuts] Allan Variance with an HP53132a counter

[Gilles Clement]

Hi, 

I am new to this list and have been following it for a while with great interest. I am afraid I am getting contaminated with the "TN" virus… !

I developed a home-brewed OCXO crystal oscillator disciplined with a long wave radio station signal (162 kHz). Its working quite well with a long term stability that is « probably » better than 10E-8 which I am actually looking forward to better understand. I am considering using an HP53132 counter for this purpose, although I understand that it may not be the most recommended approach….

Please find hereafter the rationale: 
- The HP53132 implements a triangular averaging algorithm (Delta averaging) in its standard frequency or period measurement mode of operation 
- This feature provides a pretty high resolution (up to 0.5*10E-12 if I am correct) which should be appropriate at least to get a first idea of the oscillator performance
- But it comes with the drawback that an Allan Variance computed directly from such frequency (or period) readings, would be distorted with respect to the "standard" Allan Variance (which assumes a PI averaging instead of a Delta averaging algorithm to compute the fractional frequencies)
- However, from the Australian paper titled : « Considerations on the Measurement of the Stability of Oscillators with Frequency Counters » I noticed that:
When I look at OCXO crystals oscillator stability discussions in the literature, White Frequency, Flicker Frequency and Random Walk Frequency seem to be the dominant noise factors considered (ex: in phase noise spectral density graphics)
The distortion from Allan Variance to Delta Variance is limited for White Frequency, Flicker Frequency and Random Walk Frequency noises (though it can be several orders of magnitudes for White Phase and Flicker Phase noises)
Moreover formulas are provided in the paper to evaluate the amount of such distortions. The impact appears to be a simple multiplier of 1.33, 1.30 and 1.15 for the three corresponding noises, the slopes of the curves are not impacted (i.e: tauE-1 ; tauE+0 and tauE+1)
- So the idea is the following: start with a simple bench test, reading the standard mode of Periods measurement, calculate the "naive" Triangular Variance from these data, identifying the noise types (according to the slope of the curve sections), and applying the corresponding offset correction, hopefully leading to an estimate of the "standard" Allan Variance.  
- This approach would have the great advantage to be simple and cost effective, as one can find nowadays second hand 53132’s at reasonable cost even with the (mandatory) OCXO option.  

Comments welcomed, 
Best, 
Gilles.