Abstract
This paper develops an analytical method for modeling the inductor currents and capacitor voltages (ICCV) of a generic DC-DC converter system. The purpose of the designed methodology is to propose a new generalized modeling technique for DC-DC converter systems that accurately models the transient behavior of those systems. The modeled converter is assumed to operate over some number of circuit stages. Each circuit stage can be separately modeled as a linear time-invariant (LTI) system that is solved through the uni-lateral Laplace transform. Furthermore, the initial conditions (ICs) of these LTI systems are related through different algebraic expressions and discrete-time difference equations that originate from the continuity of the ICCV with respect to time. These discrete-time difference equations are then solved with the uni-lateral Z-transform to determine the ICs of the ICCV at each switching period. The generalized theoretical analysis is applied to the study of the transient behavior of the buck-boost converter across various different circuit parameters. This analysis justified with laboratory experimentation of the buck-boost converter, and the transient behavior of the buck-boost converter is compared for each experimental parameter set. The experimental results and the theoretical analysis provide very similar results across the different converter parameters.