Simulation of multiconductor transmission lines with random parameters via stochastic differential equations approach

This article addresses a method for the simulation of multiconductor transmission lines (MTLs) with fluctuating parameters based on the theory of stochastic differential equations (SDEs). Specifically, confidence intervals of an MTL model’s stochastic responses are effectively evaluated. First, the MTL’s deterministic model with lumped parameters, based on generalized Π sections connected in cascade, is formulated and described through a state variable method, which results in a vector ordinary differential equation (ODE) in the time domain. A vector SDE is then developed by incorporating the respective stochastic processes into its deterministic counterpart. Next, the first two moments of the stochastic processes are calculated via the solution of respective Lyapunov-like ODEs, to assess expectations and the variances of stochastic responses, and also to determine relevant confidence intervals. A statistical processing of individual stochastic trajectories is used to validate the results.