Modeling and Analysis of Switching-Mode DC-DC regulators

The nonlinear dynamics of PWM DC–DC switching regulators operating in the continuous conduction mode are investigated. A quick review of the existing analysis techniques and their limitations are first presented. A discrete nonlinear time-domain model is then derived for open-loop DC–DC converters. This model is then extended for closed-loop regulator systems implementing any type of compensation scheme. The equilibrium solutions of the closed-loop system are then identified. The eigenvalues of the Jacobian matrix evaluated at the equilibrium solution are used to assess its stability. The methods developed are used to study the dynamic behavior of a DC–DC buck regulator implementing different types of compensation design: proportional, integral, proportional–integral, and proportional–integral–derivative type feedback control. A detailed bifurcation analysis of the dynamic solutions as a design or a control parameter is changed is presented. A period-doubling route to chaos is shown to exist in voltage-mode regulators, depending on the values of the parameters of the compensator and the input voltage. A further investigation of the behavior of the converter in the instability regions was carried out to improve the understanding of this interesting behavior.