Systematic derivation of reference circuits for wave digital modeling of passive linear partial differential equations

Finding an appropriate reference circuit, is an integral part of numerical integration using wave digital (WD) concepts. We show an approach for the systematic derivation of a canonical internally passive electrical circuit from a class of linear partial differential equations (PDEs). We present two methods to transform this circuit into a reference circuit, having a one-to-one corresponding wave digital structure. As an example, we deduce a reference circuit for a wave digital algorithm from Maxwell's equations and depict simulation results.