We consider the modeling of switching circuits, consisting of passive elements, independent sources, which are subject both to externally induced switches (time events) and to state events. We focus on the use of the complementarity formalism for obtaining such hybrid (actually piecewise linear) models, assuming idealized current- voltage characteristics of the diodes and switches. In particular, a coupled-inductor Boost converter is modelled as a piece-wise complementarity system. We obtained also a discrete-time model which may be used for design and simulation purposes. In order to show the good performance of the model obtained, it is compared with the model of the converter obtained from the PSIM simulation software.