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I've found articles that derive the shape of a mechanical capacitor plate so as to achieve linear frequency tuning for linear dial rotation as in each degree of rotation shifts the frequency the same amount.

I'm looking for how to derive the capacitance values for a binary switched array of capacitors to acheve linear tuning.

000 = all off 001 = Ca 010 = Cb

011 = Cc and so on, so that the frequency delta between 001 and 010 and so on is equal per bit.

I will set a bulk capacitance value to establish the center frequency when half the tuning capacitance is switched in. The steps would then be Cbulk, Cbulk+Ca, Cbulk+Cb, Cbulk+Ca+Cb and so on.

I am starting to think this may not be possible..

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That depends on the frequency range you're targeting. Frequency is a function of the inverse of the square root of capacitance, so you'll want to pick your endpoints first. Your description above indicates zero capacitance is one endpoint, so find the maximum capacitance you'll support, and select the others to follow an X^2 curve.

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