Series Expansion Solution for Circuit Problems

Abstract

In this chapter we assume the solution of the form of a polynomial series of the form y(t) =∑ _n a _n t ⁿ and set out to figure the series coefficients. Each of the branch currents and/or node voltages is assumed to have such a series expansion. When doing KVL/KCL we end up tying the various series coefficients and finally when we use the initial conditions were are able to calculate those iteratively. The beauty of this method is that it gives us accurate solution for small time intervals, but does need more expansion terms to predict solution at large time intervals. We apply the method on various RLC problems and obtain good match to SPICE, especially for short time scales. This method is meant to pave the way for the more efficient Fourier series method, but it stresses the idea of series summation and the idea of achieving more accurate solutions via including more series terms.