In a course of digital electronics, our Professor wanted to give us just an introduction to charge pumps. Here the basic topology:
Then he says that the circuit behaves like a bucket brigade chain: a charge packet is transferred by Vdd to CP1 (when CK' is high), then from CP1 to CP2 (when CK is high), and so on and, finally, from CPN to CS. At each transfer step, the voltage of the charge packet is increased. At each clock cycle, Vout is increased until the steady state is reached.
From a conceptual point of view it is clear to me up to now. But then he calculates the dc voltage gain as follows:
Question: why does he say that "each capacitor CPi is charged to the voltage across the preceding capacitor plus Vck"?