Mathematical model for studying frequency response of a buck-boost DC/DC converter

Bryansk State Technical University, Bulvar 50-let Oktyabrya, Bryansk, 241035, Russia

^* Corresponding author: mail@ahaos.ru

Published online: 10 March 2025

Abstract

The paper is devoted to the development of a high-speed nonlinear dynamic mathematical model of a direct inverting voltage converter designed to remove its low-signal frequency response, namely: open loop transmission coefficient, input conductivity, output resistance of the converter. The study focus is a direct inverting voltage converter with output voltage feedback having a proportional regulator in the loop stabilization circuit and generators of sinusoidal measuring effects as part of the circuit. The paper gives a mathematical model of the converter which is a system of differential and nonlinear transcendental equations. The proposed model belongs to numerical and analytical ones, where at certain time intervals processes are described by a system of linear differential equations. This approach allows to significantly speed up the calculation of frequency response of the converter in comparison with standard software using numerical integration methods. The paper gives the results of calculating the frequency response and compares with the results obtained using verified software. The analysis shows the correctness of the developed mathematical model. The proposed approach has not been considered before, and the use of a nonlinear mathematical model allows to take into account the nonlinearity of the object under study.