Solution of the Cauchy Problem in Fourier Series for a Linear RC Circuit with a Resistor and Two Capacitors

Authors : Numan Özkutlu, Hafiz Alisoy, Gülizar Alisoy

Pages : 163-173

Doi:10.54370/ordubtd.1294863

View : 55 | Download : 69

Publication Date : 2023-12-31

Article Type : Research Paper

Abstract :As it is known, solutions obtained in terms of Fourier series are widely used for more detailed analysis of mathematical models defined for different engineering problems. In this study, for the mathematical analysis of transient events in active RC based linear electronic circuits, the Cauchy problem is defined and solved in terms of Fourier series. For this reason, first of all, the mathematical model needed for the mathematical definition of the investigated problem was created. Based on the defined mathematical model, a quadratic differential equation for the linear RC electric circuit is obtained and the voltage and current changes are analysed for simple special cases using the Fourier series. As a result, mathematical modelling of transient processes occurring in linear RC circuits and mathematical problems defined as the Cauchy problem for such circuits have been solved analytically. It is thought that the results of the research will contribute theoretically and practically to the solution of the problems that arise in the study and design automation of different electronic circuits containing nonlinear circuit elements.
Keywords : Elektronik, Diferansiyel Denklemler, Fourier Serileri, Matematiksel Model, RC Devre