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Setting up the state equations of switched circuits using homogeneous models
  • Ricardo Riaza
Ricardo Riaza

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Abstract

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 = pon = 1, q = qon = 0 in the on-state and p = poff = 0, q = qoff = 1 in the off-state, whereas nonideal switches are described by nonzero values of qon 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.
15 Dec 2023Submitted to TechRxiv
22 Dec 2023Published in TechRxiv