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Comment by michaelt | Hacker News Reader

I looked into the sensing mechanism used by these cheap digital verniers [1] - which involves overlapping capacitive plates.

What I couldn't figure out was how precisely the sensing worked, because it looked like it would have to measure capacitance at the femtofarad levels, and nothing I had access to could measure a capacitance that small - or monitor the sensing process without adding enough capacitance to mess it all up. It also looked like it'd be really sensitive to the distance between the plates, but it didn't seem to control that particularly precisely.

If anyone here knows how they measure such small capacitances and how control for the distance between the plates, I'd be fascinated to hear more about it!

[1] https://www.mjt.me.uk/posts/digital-vernier-teardown/

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You measure discharge times repeatedly ensuring the capacitor is never fully charged. Presuming you know the impedance, temperature and charge voltage you can get very precise. It's a frequency counter after all.

Distance control is sort of weak which is why these are no good against vibration.

Another way is to use contact resistance with very accurate bridge temperature corrected voltmeter. More expensive. Essentially a potentiometer. Dimensionality is less important, but contact still is. To do that you need a high-ish impedance wiper you can slide over.

So I think you don't need to measure the capacitance per se. Instead you use the capacitances to make a series of (AC) voltage dividers. The lines that are individually broken out (call these the vernier lines) will have different degrees of coupling to the sense node, depending on the caliper position. Assume the capacitance of the sense node is fixed. The controller pulses each vernier line in sequence and measures the sense node in turn. The higher the capacitance of a given vernier line, the more voltage will couple across to the sense node. The highest pulse tells the controller which vernier position it's in, so the absolute voltage levels don't matter, conceptually speaking.

As for the distance between plates, a caliper ought to be made to a high degree of repeatability. PCB thickness not so much though, probably 10%? To first order capacitance goes as ~1/d. But again, the measurement is relative, not absolute. As long as all the capacitances are affected by the same distance factor, the scheme still works.

Anyway, that's an informed guess based upon those scope shots.

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