Vector Wave Digital Filters and Their Application to Circuits With Two-Port Elements

Wave Digital Filters (WDFs) turn circuits into networks of input-output relationships that can be computed in an explicit fashion. This is done through a linear port-wise mapping Kirchhoff variables pairs incident-reflected waves introducing one scalar free parameter per port, called reference port resistance. Parameters are then used to eliminate the implicit equations relating wave variables, referred as delay-free-loops. Unfortunately, this methodology only applied under strong linearity and topological conditions. manuscript presents extension WDF formalism involving novel “cross-port” vector definition waves, whose resistance matrix parameters. generalization greatly simplifies implementation with two-port elements, such operational amplifiers. It allows us derive wave-based descriptions elements nullors, for which no scattering relation available literature. Moreover, it enables full adaptation wide class thus avoiding delay-free-loops would otherwise form traditional WDFs. new implement wider range modular fashion, since topology modeled independently.