Buck DC-DC converter: Mathematical modeling and transient state analyzes

In this paper, a new method is proposed for mathematical modeling of buck dc-dc converter in continuous conduction mode (CCM). In this method, firstly, the differential equations of inductor current and capacitor voltage are obtained according to the equivalent circuit of the converter and then using Laplace and Z transforms the differential equations are solved and the relations of inductor current and output voltage are obtained. In this method Laplace transform is used to determine the general relations of inductor current and output voltage and Z-transform is used to determine the initial conditions of current and voltage. After that, the transient state response of inductor current and output voltage of buck dc-dc converter are analyzed using the obtained mathematical model. Then the effects of converter´s components and load resistance on the transient response are analyzed. Finally, the results obtained from the theoretical analysis are compared with the simulation results through PSCAD/EMTDC to verify the analysis.