Mathematical modelling and analysis of transient and steady states of buck dc‐dc converter in DCM

Abstract

Purpose

The purpose of this paper is to propose a new method for mathematical modeling of the buck dc‐dc converter in discontinuous conduction mode (DCM). By using the presented modeling method, the analysis of the transient and the steady states of the buck dc‐dc converter can be performed.

Design/methodology/approach

The proposed method is based on the two Laplace and Z transforms. In the proposed method, at first, the equations of the inductor current and the capacitor voltage are obtained as the power switch is on and off. Then by using the Laplace and Z transforms, the obtained equations are solved and the relations of the inductor current and the output voltage are obtained. In the proposed method, the Laplace transform is used for determining of the general relations of the inductor current and the output voltage. Also the Z‐transform is used as a tool for determining the initial values of the inductor current and the output voltage.

Findings

The transient and the steady state response of the dc‐dc converter is analyzed by the proposed method. By using the Z‐transform, the transient response of the converter and the effect of the elements of the converter on the time constant of the transient response are investigated. In addition, the effect of the elements of the converter and the load resistance on the electrical parameters of the converter such as the output voltage ripple and the inductor current ripple are investigated.

Originality/value

The proposed method in this paper is a suitable method for mathematical modeling of dc‐dc converters. The acernote of this method is that it can be used in both transient and steady state response, analysis of the dc‐dc converters. By using the final value theorem of the Z‐transform, the steady state response of the converter is investigated. Also by using this transform, the time constants of the transient response of the converter are determined. Finally, the results of the theoretical analysis are compared with the results of simulation in PSCAD/EMTDC and also the experimental results to prove the validity of the presented subjects.

Citation

Babaei, E. and Mashinchi Mahery, H. (2013), "Mathematical modelling and analysis of transient and steady states of buck dc‐dc converter in DCM", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 32 No. 1, pp. 337-363. https://doi.org/10.1108/03321641311293920