Electric Circuit Analysis with Laplace Transform in MATLAB

Abstract

Electrical circuits are fundamental components in various engineering and technological applications. Their analysis often involves solving differential equations describing the current and voltage's time- varying behavior. For circuits containing inductors and capacitors, these equations can be complex due to the energy storage properties of these components. The Laplace transform offers a powerful mathematical tool to simplify such problems by converting differential equations into algebraic equations in the -domain. This project explores using the Laplace transform to analyze an RLC series circuit subjected to a step voltage input. The study aims to understand the transient and steady-state behaviors of the circuit by deriving the governing equations in the Laplace domain, solving for current and voltage, and transforming the results back to the time domain. MATLAB, a widely used computational software, was utilized for symbolic computation, numerical simulation, and graphical results representation. The methodology involved defining the circuit parameters, formulating the Laplace transform equations, and using MATLAB's Symbolic Math Toolbox to solve for the time-domain current. The theoretical analysis was validated through MATLAB simulations, which provided insight into the oscillatory transient response and eventual steady-state behavior.