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Buck, boost, and buck-boost converters constitute large class of dc-dc converters used in practice and are interesting nonlinear dynamical systems. It has been shown earlier that various nonlinear phenomena including subharmonics and chaos can be observed in these converters. In this paper we show that with the simplifying assumption that voltage regulation is achieved in high frequency modulation, a very simple dimensionless model can be derived that explains the dynamic phenomena in both continuous conduction mode as well as the discontinuous conduction mode. Using this model, we analyze some peculiar aspects of the dynamics in discontinuous conduction mode like the occurrence of superstable orbits.

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We present the theory of border collision bifurcation for the special case where the state space is piecewise smooth, but two-dimensional in one side of the borderline, and one dimensional in the other side. This situation occurs in a class of switching circuits widely used in power electronic industry. We analyze this particular class of bifurcations in terms of the normal form, where the determinant of the Jacobian matrix at one side of the borderline is greater than unity in magnitude, and in the other side it is zero. (c) 2002 American Institute of Physics.