Parametric Analysis of Transients in Linear Electric Circuits under DC Power Supply

Abstract

The static characteristics of loads in linear electric circuits are linear. This means that the resistances, inductances, and capacitances are constants and they do not depend on the operating mode. The transients of these circuits are always steady-states, i.e. they always tend to a certain stationary mode since the values of the currents and voltages there cannot increase indefinitely. Depending on the values of resistors, coils, and capacitors in a linear electric circuit three types of transients occur under DC sources, namely: overdamped, critically damped, and underdamped. A danger for the analyzed DC circuit is the underdamped transients. For this reason, it is necessary to determine these values of the parameters of the passive elements that lead to the threshold critically damped transients in linear electric circuit. In this paper, the sufficient condition for the occurrence of overdamped, critically damped, and underdamped transients in linear electric circuits is used. A parametric analysis of the type of transients on illustrative examples of second-order circuits (with the two conservative elements) is made. The three types of transients, varying parameters of the passive elements (resistors, coils, and capacitors), are analyzed. The present paper is an educational tool to improve students' knowledge in the field of transient responses appearing in linear circuits under constant energy sources.