Probability Distribution of Transient Response of an Electric Circuit

Abstract

In this work, we explore the transient response of an electric circuit using probabilistic analysis when the precise value of the characteristic parameter of a circuit element is not known and is instead constrained to a range of values. To accomplish this, a combination of probability theory and traditional circuit analysis techniques is employed. In this approach, the circuit element’s parameter is treated as a random variable, and probability methods are used to derive the probability distribution of the voltage or current across it. To demonstrate this approach, we apply it to a resistor capacitor (RC) circuit, where the capacitance parameter of the capacitor is regarded as a random variable. We derive probability distributions for the transient voltage across the capacitor and the voltage at the output terminals to illustrate the method’s effectiveness.

Keywords

• Circuit probability distribution
• RC circuit
• transient response
• voltage random variable
• voltage prediction