Evaluation of Responses in MTL Model Excited from Multiple Stochastic Sources

Abstract

The paper presents a technique for simulation of stochastic responses and their statistical characteristics in multiconductor transmission lines (MTL). The method follows a theory of stochastic differential equations (SDE) and relevant numerical techniques for their solution. The MTL’s model, formed via generalized sections in cascade, is designed to cover various situations at stochastic and/or deterministic excitations. In this way both the noisy pulses driving MTL’s terminal ports and effects of possible unwanted disturbances along the MTL’s wires are allowed to be simulated. First the state-variable method is applied to derive a deterministic description, then voltage stochastic variations are incorporated to define the vector linear SDE. To obtain the characteristics of stochastic responses, firstly the set of trajectories is statistically processed, while a weak stochastic backward Euler scheme, consistent with the Itô stochastic calculus, is applied. Finally, a method of direct calculation of variances, based on the solution of relevant Lyapunov-like differential equations, is used with advantage. All the simulations were performed in the Matlab language environment.The paper presents a technique for simulation of stochastic responses and their statistical characteristics in multiconductor transmission lines (MTL). The method follows a theory of stochastic differential equations (SDE) and relevant numerical techniques for their solution. The MTL’s model, formed via generalized sections in cascade, is designed to cover various situations at stochastic and/or deterministic excitations. In this way both the noisy pulses driving MTL’s terminal ports and effects of possible unwanted disturbances along the MTL’s wires are allowed to be simulated. First the state-variable method is applied to derive a deterministic description, then voltage stochastic variations are incorporated to define the vector linear SDE. To obtain the characteristics of stochastic responses, firstly the set of trajectories is statistically processed, while a weak stochastic backward Euler scheme, consistent with the Itô stochastic calculus, is applied. Finally, a method of direct calculation of variances, based on the solution of relevant Lyapunov-like differential equations, is used with advantage. All the simulations were performed in the Matlab language environment.