So what precisely is the counting algorithm used in HP53310? I try to figure out by applying a 10 MHz signal with a 500 Hz square wave frequency modulation. The counter is set to auto sampling with manual sampling interval of 100 usec. The data looks like this:
![](https://www.eevblog.com/forum/metrology/hp53310a-and-other-counter-allan-deviation/?action=dlattach;attach=705294)
You can see that each transition is 2-3 points wide. Also note that even though the period of 2 msec is a multiple of the sampling interval of 100 usec, the transition points don't line up, so each sampling interval is not precisely 100 usec, only on average so.
The counter can produce a nice histogram of the data, like this:
![](https://www.eevblog.com/forum/metrology/hp53310a-and-other-counter-allan-deviation/?action=dlattach;attach=705300)
To get the counting weight from it, one has to first do a cumulative integral of the histogram, then exchange x and y axes of the plot, and then calculate the derivative. The result looks like this:
![](https://www.eevblog.com/forum/metrology/hp53310a-and-other-counter-allan-deviation/?action=dlattach;attach=705306)
I was surprised when this nice plot appeared, it's like decoding a secret message!
So the counting method is a truncated Lambda scheme. It uses a total of 3 times the specified sampling time interval t. Zero crossings at times from -1.5 t to -0.5t are subtracted from the ones from 0.5 t to 1.5 t and averaged together. The difference between every pair of zero crossings is 2 t. One can show that this is the most efficient simple accumulation scheme. The fractional frequency uncertainty is given by dt/(2 t)/sqrt(f t), where dt is the uncertainty of a simple pulse width measurement. If one scales to the total measurement time, the traditional lambda scheme gives a prefactor of sqrt(8 ), truncated lambda gives sqrt(6.75) and optimal linear fitting gives sqrt(6).
Looking at the plot from previous post, one would expect the simple gate time measurement with uncertainty 10
-9/tau to translate into 1.6x10
-13/tau
3/2 for the enhanced scheme at 10 MHz. Instead, we measure almost exactly a factor of sqrt(2) more, 2.2x10
-13/tau
3/2. This persists for all frequencies, so apparently HP53310 measures every other zero crossing. This would make sense based on careful reading of the datasheet. In the +TI Fast histogram mode it can make measurements at 2.5 MHz. Since each TI measurement requires 2 zero crossings, it implies that 5 MHz is the maximum zero crossing measurement rate.
So HP53310 implements a very efficient counting scheme and can measure zero crossings at a rate up to 5 MHz. But it counts only every other zero crossing. Also the time interval value is misleading, the total measurement time for each point is equal to 3 times time interval setting.