Topological formulations for the coefficient matrices of state equations for switched-capacitor networks

This paper describes new topological formulas for the coefficient matrices of the state equation for a switched-capacitor (SC) network. The topological formulas are derived from a differential state equation describing anRCnetwork with resistances(R, r)of OFF- and ON-switches, respectively. Differing from historical nodal analyses, this method is useful for the exact analysis of large scale SC networks, because the use of inverse matrices is not required and each network-construction-change in each switching time interval is disposed by a switching diagonal matrix with diagonal binary elements "1" and "0" for ON- and OFF-Switches, respectively. New characteristic matrices will be applied in order to obtain the coefficient matrices efficiently by using recursive equations, which are suitable for computer-aided analysis.