A Unified Treatment of Deterministic and Random Transients in Electrical Circuits

The continuity of capacitor voltages and inductor currents, well-known from the deterministic case, cannot be directly applied if the initial conditions are random. In this paper, new continuity relations for probability densities, mean values, correlation and covariance functions of the state variables are introduced. These continuity relations can be used for a global characterization of random transients. New formulas for initial condition and forced components of transient statistical moments are also presented. These formulas offer a direct approach for random transient analysis. Deterministic transients can be regarded as particular, degenerated, random transients. On this basis, one can develop a unified treatment of deterministic and random transients in electrical circuits. This unified framework is certainly an advantage, not only in teaching activities related to transient phenomena. Key-Words: Electrical circuit, Initial condition, Random transients, Statistical moments, Continuity relations