Multiconductor Transmission Line System with Stochastically Affected Boundary Conditions

The paper deals with the application of stochastic differential-algehraic equation (SDAE) approach to evaluate responses of multiconductor transmission lines (MTL) with stochastically affected boundary conditions. Respective SDAEs are formulated by a modified nodal analysis (MNA) to describe lumped-parameter circuit terminating the MTL and defining the boundary conditions. These can be under stochastic affects by considering internal non-deterministic independent sources. Because of the MTL itself is described by the telegraph partial differential equations (PDE), which will be solved via an implicit Wendroff numerical scheme, the MNA SDAE will be solved via a compatible implicit Euler scheme in its stochastic version after completing the deterministic DAE with an additive noise. The MTL's responses are presented in the form of sets of individual stochastic trajectories postprocessed and completed with sample means and confidence intervals. The results were compared with those based on the MTL lumped-parameter model formed by generalized RLCG T-cells in cascade. All the simulations have been done in Matlab.