Simulation methods for multiconductor transmission lines in electronic applications

Abstract

Accurate and efficient simulation of lossy, multi-conductor transmission lines that are terminated by nonlinear circuits is necessary to design high-performance electronic circuits and packages. In this work, theoretical and practical considerations of lossy line simulation are presented. Using delay differential equations, the class of systems with "bidirectional delay" is introduced. These systems can be partitioned such that the resulting subsystems are only linked via delayed variables. It is stated in the "decoupling theorem" that the subsystems can be solved independently for a time interval, which is not longer than the shortest time delay. Circuits that contain transmission lines are shown to form systems with bidirectional delay and, consequently, can be decoupled. Using concepts derived from waveform relaxation, the decoupling is exploited to reduce the computational effort required for transmission line simulation. Moreover, an efficient method for the approximation of lossy line characteristics by rational transfer functions is presented. The method employs nonlinear minimization techniques and yields function coefficients suitable for time-domain modeling. Furthermore, the exponential wave propagation function is represented in the time domain, and discrete-time convolution is employed to calculate the transmission line response. Also described is a filtering method which considerably improves the stability of the simulation, while the deviation in the simulation results is smaller than the local truncation error. In addition, implementation of the lossy line simulator "UAFLICS" is outlined, and practical applications demonstrate the significance of coupling and loss effects.