The RC circuit: An approach with Fourier transforms

Abstract

In this article we shall mathematically analyse the Resistor-Capacitor (RC) circuit with the help of Fourier transforms (FT). This very general technique gives us a lot of insight into solving first order differential equations with source terms depending on time. In itself, the RC circuit is by far the most commonplace entity in modern electronics. But the method of FT is not the accepted custom for an electronic engineer, who is probably more comfortable working with complex impedances and phasors while solving problems in network analysis. In fact, what is used much more extensively is the Laplace transform. But a lot of things, (including the complex impedance itself, and some insight into complex analysis) can be understood better if we use the FT approach to solve the differential equations that come up in network analysis. The use of FT comes smoothly from first principles — precisely what we set out to demonstrate here.