Analyzing Electric Circuits with Computer Algebra

Abstract

This report shows how starting from classic electric circuits embodying commonly electric components we have reached semi-complicated circuits embodying the same components that analyzing the signal characteristics requires a Computer Algebra System. Our approach distinguishes itself from the electrical engineers’ (EE) approach that relies on utilizing commercially available software. Our approach step-by-step shows how Kirchhoff’s rules are applied conducive to the needed circuit information. It is shown for the case at hand the characteristic information is a set of coupled differential equations and that with the help of Mathematica numeric solutions are sought. Our report paves the research road for unlimited creative similar circuits with any degree of complications. Occasionally, by tweaking the circuits we have addressed the “what if” scenarios widening the scope of the investigation. Justification of the accuracy of our analysis for the generalized circuits is cross-checked by arranging the components symmetrizing the circuit leading to an intuitively predictable reasonable result. Mathematica codes are embedded assisting the interested reader in producing and extending our results.