Fast simulation and sensitivity analysis of lossy transmission lines by the method of characteristics

In this paper we use the method of characteristics to derive a new simulation model of lossy transmission lines, and we present the sensitivity analysis in the time domain. The simulation model is as fast as the recursive convolution model based on moment matching and Pade' approximation, but does not have the stability problem. The sensitivity analysis model is particularly useful for transmission line circuits containing nonlinear elements, and is believed to be the first time domain model. Both the simulation and sensitivity analysis models are applicable to uniform and nonuniform transmission lines with arbitrary nonzero initial states. Also we show that any nonlinear circuit element has a very simple linear model in sensitivity analysis. Furthermore, we demonstrate that for any circuits, the modified nodal admittance (MNA) matrices in simulation and in sensitivity analysis equations are the same, therefore no LU decomposition is needed in sensitivity analysis. The contributions in this paper have been implemented into a general-purpose program CSSC (Circuit Simulation and Sensitivity Analysis with Characteristics) which shows excellent accuracy and efficiency in both simulation and sensitivity analysis of transmission line circuits.