Analysis of higher-order electrical circuits with noisy sources via stochastic differential equations approach

The paper presents an unconventional technique for the analysis of higher-order electrical circuits excited from the sources with randomly varying voltages based on the stochastic differential equations (SDE) approach. The voltage and current responses of the electrical circuits are computed and represented in the form of mean values with particular confidence intervals to provide an estimate of the results. The method is applied to analyze responses of circuit models of optional orders, consisting of a cascade connection of the RLGC networks. To develop the model equations the state-variable method is used, afterwards a corresponding vector SDE is formulated and a stochastic Euler numerical technique utilized. To verify the results the deterministic responses are also computed by the help of the PSpice simulator or the numerical inversion of Laplace transforms MATLAB^® procedure, in both cases removing a random term from the drive source.