Calculation of Step Discontinuities in Electric Circuits: A Time-Domain Analysis

Abstract

Contribution: Two general rules for calculating, in the time domain, step discontinuities of voltages and currents in electric circuits, combining physical principles and basic mathematical treatment. The two general rules, resulting from a formal method of analysis, provide a straightforward way to update the states of a circuit, immediately after the occurrence of switching or impulsive excitation. Among its advantages, they can be used to simplify the numerical simulation of elaborate circuit topologies by avoiding approximate models of impulsive sources or switches. Background: In most engineering undergraduate textbooks, the effects of switching and impulsive sources on higher order electric circuits are usually studied for the particular case of linear time-invariant (LTI) circuits in the Laplace transform domain. This approach, however, can be time consuming and demands little reasoning on the physical principles of circuit operation. Moreover, it is not adequate for linear time-variant or nonlinear circuits. Intended Outcomes: Step discontinuities in electric circuits, caused by switching or impulsive sources, are identified and calculated through the method, allowing complete responses to be obtained afterward. Not only can the method be extended to linear time-variant and nonlinear circuits but it also has interesting consequences in numerical simulation of circuits. Application Design: An application exercise and a set of conceptual questions on the subject were proposed to electrical engineering students. Findings: The analysis of the educational experiment indicates that applying the method presented herein improves the students’ ability to obtain initial conditions of circuits, being a more straightforward and effective approach than using Laplace transform techniques.