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LF Crystal Tester: 60 kHz Resonator Frequency Distribution

Histogramming all 50-ish resonator frequencies shows reasonably good distributions:

Notably, there’s no obvious suckout in the middle, as with those eBay Hall-effect sensors.

60 kHz Resonant Frequencies - CX 24 pF - histogram

60 kHz Resonant Frequencies – CX 24 pF – histogram

I don’t know what to make of the difference between the parallel series-capacitor and basic serial resonant frequencies for each tuning fork:

60 kHz Resonant Frequencies - CX 24 pF - delta histogram

60 kHz Resonant Frequencies – CX 24 pF – delta histogram

Perhaps each resonator’s frequency depends on its (laser-trimmed) tine mass and follows a more-or-less normal distribution, but the parallel-serial difference series capacitor changes the frequency based on (well-controlled) etched dimensions producing quantized results from three different masks / wafers / lots, with the motional inductance and capacitance incompletely modeling the physics?

For reference, the resonators look like this:

Quartz resonator - detail

Quartz resonator – detail

Producing the histograms uses the LibreOffice frequency() array function, which requires remembering to whack Ctrl-Shift Enter to activate the function’s array-ness.

[Update: Faceplant about “parallel” resonance, which is actually the shifted resonant peak due to the 24 pF series cap. Apparently I typo-ed the second histogram subheading and ran with the error; the figures are now correct.]

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