Simulation of stochastic responses at multiconductor transmission lines with fluctuating parameters

The paper deals with a method for the simulation of stochastic responses at multiconductor transmission lines (MTL) with fluctuating parameters via theory of stochastic differential equations (SDE). The MTL responses are formed by the sets of stochastic trajectories completed by corresponding sample means and confidence intervals. The MTL model is based on a cascade connection of generalized RLCG networks and a state-variable method is used to formulate basic MTL´s model equations. The boundary conditions are folded in via a modified nodal analysis (MNA) enabling to consider an MTL as a part of arbitrarily complex lumped-parameter circuits. Finally, a vector stochastic differential-algebraic equation (SDAE) is formulated, and the implicit Euler numerical scheme consistent with the Itô stochastic calculus used. To partly verify the results deterministic responses were stated via other methods and compared with mean values of stochastic ones. All simulations were performed in Matlab^®.