On the chaotic and periodic behavior of the power converter Part I: the mathematical modeling

This paper is focused on the nonlinear behavior of the DC-DC converters. In the first part of this paper, the basic topologies of the DC-DC converters are analyzed and modeled. The general linear model for the Buck, Boost and Buck-Boost topologies is presented and used in the simulation performed in the second part of this paper. Also, the main tools used to study their nonlinear behavior are shown here, and applied and compared in the second part of this paper. The phase diagram, power spectrum, Poincaré map, bifurcation map, and Lyapunov exponent are briefly presented here as the most used tools to analyze the systems' stability.