Comparative study of the time-domain methods for the computer aided analysis of microwave circuits

Three time-domain methods are widely used: the finite difference time domain method (FD-TD), the transmission line matrix method (TLM) and the spatial network method (SN). The authors have conducted a global comparative analysis of the FD-TD, TLM and SN methods. The results of the investigation are summarized. The three methods prove formally equivalent in application to the analysis of linear microwave circuits of arbitrary complexity. The objective of the study is to extend the theorem of formal equivalence of FD-TD and TLM to nonlinear applications. In principle, the time-domain algorithms enable unified full-wave simulation of microwave circuits incorporating lumped nonlinear elements. They propose a nonlinear modification of FD-TD, and investigate its relationship to two nonlinear modifications of TLM due to Johns and O´Brien (1980) and Voelker and Lomax (1980). They also determine general criteria for stable and accurate incorporation of an arbitrary nonlinear element into a linear FD-TD (or TLM) model