Fractional Order Modelling of DC-DC Boost Converters

This paper presents a fractional order modeling and analysis method for a DC-DC Boost converter in discontinuous conduction mode (DCM) by using circuit averaging method. First, an equivalent averaged circuit model for the fractional order Boost converter in DCM operation is proposed. Then at the second stage, the corresponding DC circuit model is obtained by averaged circuit model. Finally, the transfer function of the duty cycle to the output voltage and also the transfer function of the input voltage to the output voltage in DCM operation are derived from the corresponding small signal equivalent circuit model. Simulation results are presented to show the correctness of the proposed method. These simulation results indicate that the fractional order model has a specific significance for the performance of the DC-DC converter.