Time-domain variability analysis of general linear systems terminated with nonlinear devices

In this paper, a new approach for the time-domain variability analysis of general linear systems terminated with nonlinear devices is presented. A deterministic, stable and passive model of the stochastic system under study is built starting from the Polynomial Chaos (PC) coefficients of the system's scattering parameters, and by means of the Galerkin projection (GP) method and the Vector Fitting (VF) algorithm. This model is then converted into an equivalent circuit via a suitable synthesis technique. The nonlinear terminations with stochastic input and output signals are also represented by SPICE-compatible equivalent models, based on the stochastic testing (ST) method. Finally, the equivalent models for both the linear and nonlinear parts are suitably connected and analyzed with a standard circuit simulator. Only a single time-domain simulation is necessary to compute the PC model of the port voltages and currents. The proposed approach, which is applicable to any passive system describable with a scattering representation, is here validated against state-of-the-art techniques based on the simulation of a distributed transmission-line network with diodes and nonlinear drivers.