Simulation of single and coupled transmission lines using time-domain scattering parameters

A new method of transient analysis and simulation of interconnects is introduced. The presented approach permits calculation of scattering parameters of lossy nonuniform transmission lines and n-wire lossy coupled uniform lines directly in the time domain. In both cases, the procedure is the same. First, the partial differential equations are converted to integral telegrapher's equations, using the method of characteristics. Next, these integral equations are solved by the method of successive approximations, and infinite series expansions of scattering parameters in the time domain are obtained. The terms of the series expansions are expressed by elementary functions. The infinite series obtained are generally fast convergent and can be truncated after a few first terms, with the small relative truncation error previously defined. The number of terms in the truncated series can be determined on the basis of transmission line parameter values and the assumed relative truncation error. Finally, test examples for single and n-wire coupled line are presented. Simulation time and memory occupation are very small.