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I am trying to build an LC meter using the Arduino platform. It's based on this tutorial here.

Specification: 10nH to 1000nH, 1uH to 1000uH, 1mH to 100mH and capacitance from 0.1pF up to 900nF.

However, I am unsure which prescaler to use for the timer. If I'm not mistaken the timer affects how accurately the frequency is measured, thereby affecting the measured inductance /capacitance. How can I choose a suitable one?

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I take it that you are trying to develop from scratch some Arduino firmware that duplicates the PIC firmware that comes with the kit. With no more detail than that, I can only answer your question in general terms.

To get the maximum resolution for your L or C measurement, you need to have a largest possible number of significant bits in your frequency measurement. This means that the time period over which you're counting needs to be comparable to the time it takes the counter to overflow, without actually letting it overflow. Since the frequency, and therefore the overflow time, is the unknown in this project, your firmware will have to do a search, trying different intervals (or different prescaler values) until it finds the best one.

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