Modelagem matemática utilizando transformadas de Laplace e séries de Fourier para descrever circuitos elétricos e suas aplicações

Abstract

The objective of this work is to use differential equation methods to solve circuits with a high degree of complexity, in a didactic and understandable way. In this way, mathematical tools such as Laplace transforms will be approached, exploring their properties as zeros and poles and analyzing the transient regimes that are defined in a short period of time, as well as the permanent regime that there will be no changes in their state. The second analysis is the use of the Fourier series whose function is defined as a series of sines and cosines, where the first term of the series is the CC component and the second component of the series is CA, in this way, we define the harmonic components of the system. After this analysis, a circuit will be implemented that can describe these mathematical concepts. RLC‘s circuits are used, as well as the introduction of operational amplifiers, in order to describe the mathematical concepts, that is, applied electronics concepts will be used, in order to guarantee that the mathematical concepts can be implemented and circuits will be used as filters, oscillators and differential pairs. Finally, it will be used in the circuits and computer and laboratory simulations will be carried out, in order to prove all the concepts that will be explored throughout the project.