I have seen circuits involving crystal oscillators connecting two capacitors between each of the crystal legs and ground. I would like to know how to design the value of these capacitors for different crystal frequencies.
Answer
The frequency is irrelevant, what matters is the load capacitance of the crystal. It's specified by the crystal manufacturer.
Most MCUs use a Pierce oscillator with two feedback capacitors, which are effectively in series, although they look as though they might be in parallel. You therefore need to select the capacitors that, in series, and accounting for some stray capacitance, give the required crystal load capacitance. Most MCU manufacturers have application notes on capacitor selection, as do most crystal suppliers. Here is a typical example.
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