Mathematical model of a DC/DC converter based on SEPIC topology

Objectives. A DC/DC converter based on SEPIC topology is a unipolar electronic device which converts an input positive voltage into a stabilized output voltage of the same polarity. It also has the ability to regulate polarity both below and above the input voltage. The aim of the paper is to analyze the DC/DC converter in its both operation phases, as well as to draw up equivalent circuits and obtain characterizing differential equations using Kirchhoff’s rules for each phase. Each system of differential equations is reduced to Cauchy equations, in order to be further transformed into a limiting continuous mathematical model. Each system of equations is converted into a matrix form and subsequently combined into a single matrix system.

Methods. The construction of a limiting continuous mathematical model was accomplished using Kirchhoff’s rules. Multisim software was used for the computer simulation, thus enabling the calculated results of direct currents and voltages to be compared to those of the simulation.

Results. Results show that the phase coordinates of the mathematical model tend towards the values of real currents and voltages of the converter at a switching frequency higher than 200 kHz. Fairly good agreement is established between the calculated values of currents and voltages and the values obtained by simulation (with varying fill factor and switching frequency).

Conclusions. The resulting limiting continuous mathematical model of the DC/DC converter based on SEPIC topology allows for an estimation of the dependence of the currents flowing through the inductor windings and the voltages across the capacitors on a number of parameters. The limiting continuous mathematical model of the DC/DC converter based on SEPIC topology is the basis for its circuit design and physical-and-mathematical analysis.

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