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 of Kirchhoff variables into pairs of 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 to as delay-free-loops. Unfortunately, this methodology can only be applied under strong linearity and topological conditions. This manuscript presents an extension of the WDF formalism involving a novel 'cross-port' vector definition of waves, whose reference resistance is a matrix of free parameters. This generalization greatly simplifies the WDF implementation of circuits with two-port elements, such as operational amplifiers. It allows us to derive wave-based descriptions of elements such as nullors, for which no scattering relation is available in the literature. Moreover, it enables a full adaptation of a wide class of two-port elements, thus avoiding the delay-free-loops that would otherwise form in traditional WDFs. This new formalism allows us to implement a wider range of circuits with two-port elements in a modular fashion, since the topology and the elements can be modeled independently.

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

Bernardini A.;Maffezzoni P.;Sarti A.
2021

Abstract

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 of Kirchhoff variables into pairs of 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 to as delay-free-loops. Unfortunately, this methodology can only be applied under strong linearity and topological conditions. This manuscript presents an extension of the WDF formalism involving a novel 'cross-port' vector definition of waves, whose reference resistance is a matrix of free parameters. This generalization greatly simplifies the WDF implementation of circuits with two-port elements, such as operational amplifiers. It allows us to derive wave-based descriptions of elements such as nullors, for which no scattering relation is available in the literature. Moreover, it enables a full adaptation of a wide class of two-port elements, thus avoiding the delay-free-loops that would otherwise form in traditional WDFs. This new formalism allows us to implement a wider range of circuits with two-port elements in a modular fashion, since the topology and the elements can be modeled independently.
adaptors
connection networks
junctions
scattering matrices
Wave digital filters
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11311/1169793
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