What is the source of the output impedance equation for inverting switched-capacitor converters?
The equation in the LM2664 and similar data sheets is specific to all switched-capacitor inverters with a four switch topology, which is basically all of them. The equation was derived from the capacitor characteristics and the average switch resistance assuming around 50% duty cycle, which is how all of the inverters now operate. All the inverter data sheets should have this equation somewhere but some people write it in a slightly different form, which can be confusing. Assuming all four switches are identical, the output impedance of an inverting switched capacitor converter is: Rout = approx. 2 x Rsw + 2/(fosc x C1) + 4 x ESRc1 + 4 x ESRc2, where Rsw is the sum of the four switch on-resistances, fosc is the switching frequency, C1 is the capacitance of the central capacitor, and ESRc1 and ESRc2 are the series resistances of C1 and C2.
