Mathematical Modelling of Buck Converter

A dc converter is a lossless dc transformer that must supply regulated outputted voltage under varying load and input voltage condition. Also the converter values changes with time, temperature and pressure. Hence to control the output voltage, detailed understanding of the dynamic behaviour, transient response and small signal characteristics of the converter is required, which can’t be understood by the physical model of the converter. So the mathematical modelling of the dc-dc converter is a way to model them as time independent systems, defined by a unified set of differential equations, capable of representing circuit waveforms. Therefore, it can be a convenient approach for designing controllers to be applied to switched converters. This paper derives the mathematical modelling of a pulse width modulated (PWM) open loop buck converter operating in continuous conduction mode (CCM) and presents its verification by simulation in SIMULINK. The parasitic resistance of reactive elements is included in the circuit model in order to avoid the problem of inconsistent initial condition. (Abstract) Keywords-state space modelling, buck converter, Simulink, Differential Equations __________________________________________________*****_________________________________________________