Nonlinear Exact Analysis and Solution of Power Stage of DC-DC PWM Boost Converter

DC-DC pulse-width modulated (PWM) converters are nonlinear systems that require control circuits to obtain the desired output voltage. These control circuits are often designed using linearized models of the converters, so modeling is a relevant topic for the design of performing closed-loop converters. In this paper, the nonlinear nature of DC-DC PWM converters operated under continuous conduction mode (CCM) is considered. It is first shown how the exact periodic solutions can be analytically computed for the nonlinear converter model in the high-frequency steady-state operating condition. Also, a nonlinear variation model, which characterizes the closed-loop dynamics, induced by perturbations of the steady state, is provided. The nonlinear models and the analytical periodic solutions are implemented in MATLAB and SIMULINK and applied to a boost converter subject to parasitic components. In particular, the behavior to step changes in duty cycle, input voltage, and load resistance are compared with the results obtained using small-signal circuit averaging techniques.