Dynamic characterisation of a linearised transfer function of non-ideal buck converters

The inherent nonlinear behaviour of DC-DC power supplies complicates the task of working out their linear models, which are essential for a model-oriented control. In a model-oriented control design approach, the accuracy of the plant model directly influences the performance of the control system as the plant parameters tend to be linked to the gains of the controllers. This paper presents a dynamic analytical model of a DC-DC buck converter based on small signal analysis with a closed loop control. The small signal model is used to analyse the small deviations around the steady-state operating point of a buck converter leading to an accurate modelling of the closed loop converter parameters. A complete state-space analysis is undertaken where the output voltage to duty ratio transfer function for a non-ideal buck converter including the parasitic elements is developed.