CALCULATION OF DC CONVERTERS IN DISCONTINUOUS CONDUCTION MODE USING THE AVERAGING METHOD BASED ON LAGRANGE THEOREM

The features of calculation of output voltage ripple in dc converters with discontinuous conduction modes are considered. It is shown that the use of behaviors of charge-discharge processes of the output capacitor makes it possible to determine the parameters of voltage pulsation on it, using a mathematical model of the converter with variables averaged using Lagrange's theorems. The specified approach contributes to the significant simplification of calculations and reduction of their labor intensity. Analytical and graphical dependences of the ripple value and the ripple coefficient of output voltage of main circuits of the converters in the mode of discontinuous conduction - buck, boost and buck-boost types - were obtained. The developed analytical dependencies make it possible to effectively calculate the parameters of the converters and investigate their properties at the stage of their design, using available methods of mathematical analysis. The reliability of the obtained analytical ratios and calculation results was confirmed by simulation of converters using the PSim package. References 14, figures 4, tables 3.