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Using COMP to measure a capacitive sensor?

We have been using nRF52832 and nRF52840 processors in our board for a few years happily. Now we are evaluating a new type of sensor (confidential) that behaves like a variable capacitor. There are various solutions to measure a capacitor value, but all require external circuit. I'm trying to see if there is a way to use just the nRF52 (and a few passives) to do this. The PIC family of processors use a component called CTMU that can be used to accurately measure capacitors just using a known resistor.

In reading more, the CTMU is a current source and a comparator used to measure the capacitance. I was wondering if there's any way to use the COMP to measure a capacitance, using either a method similar to the CTMU or using it as an oscillator and measuring the frequency. But, while there are a lot of notes about capacitive sensing for buttons, I could not find anything on measuring capacitances.

Is this something that could be done? If so, any pointer to get started would be welcome (we are still using the nRF5 SDK, given our long codebase investment)

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