Setting Up the State Equations of Switched Circuits Using Homogeneous Models

This paper discusses a new modeling framework for switched circuits. The core idea is to avoid the distinction between the topologies defined by the short-and open-circuits corresponding to the on-and off-states of each ideal switch. We treat both cases in a uniform manner by describing Ohm's law in terms of a single variable u, via the relations i = pu , v = qu . The parameters p and q describe the state of the switch, either ideal or nonideal. An ideal switch is described by the values p = p(on)= 1, q = q(on )= 0 in the on-state and p=p(off)=0, q=q(off)=1 in the off-state, whereas nonideal switches are described by nonzero values of q(on) and/or p(off) . Regardless of the number of switches, all working states of a given circuit can be described by means of a single model which, in essence, may be set up by conventional methods. This avoids the need to draw different schematics and write down a variety of models depending on the state of each switch, as it is almost invariably done when modeling switched circuits. We use this framework to address the state-space formulation problem for switched circuits. The results are then applied to the analysis of several DC-DC power converters and a multilevel inverter.