Characterization of MTL Hybrid Circuits with Stochastic Parameters through SDAE Approach

Abstract

The paper deals with characterization of variability of stochastic responses at hybrid circuits composed of lumped and distributed sections. The latter is formed by multiconductor transmission lines (MTL) whose parameters can vary randomly. The solution is based on the theory of stochastic differential equations (SDE), or more precisely, on stochastic differential-algebraic equations (SDAE), just due to the presence of lumped-parameter parts. The MTL is modeled by cascading generalized LRCG cells and is described by using a state-variable method. Boundary conditions are included through a modified nodal analysis (MNA) enabling to consider arbitrarily complex systems. Based on the hybrid system's resultant SDAE, the main idea is to formulate the Lyapunov-like ODE for the computation of a covariance matrix which carries information about the responses variability. To verify obtained results a statistical processing of individual stochastic trajectories is also utilized. All simulations were done in Matlab language environment.