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If I understand this correctly, on a touch screen, you have a a grid based system where the rows and columns are either driving or receiving. When you touch the screen a mutual capacitance arises between the driving and receiving node. How exactly does that capacitance get read out into an (x,y) coordinate on the screen? To be more specific, once the mutual capacitance is induced, how is the signal read out, what does it go through to translate into an x,y position?

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Your understanding is not correct. There is always capacitance between the TX and RX, regardless of whether there is a touch. When there is a touch, the capacitance actually decreases.

To sense a touch, the capacitance at each intersection is measured. Loosely speaking, the measurement is done by sequentially applying a voltage on the TX lines and checking the voltage on the RX lines. A larger capacitance will charge and discharge more slowly.

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