Modeling Circuits with Arbitrary Topologies and Active Linear Multiports using Wave Digital Filters

Kurt James Werner, Alberto Bernardini, Julius Smith, Augusto Sarti

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)
537 Downloads (Pure)


The Wave Digital Filter (WDF) technique derives digital filters from analog prototypes which classically have been restricted to passive circuits with series/parallel topologies. Since most audio circuits contain active elements (e.g., op-amps) and complex topologies, WDFs have only had limited use in Virtual Analog modeling. In this article we extend the WDF approach to accommodate the unbounded class of non-series/parallel junctions which may absorb linear multiports. We present four Modified-Nodal-Analysis-based scattering matrix derivations for these junctions, using parametric waves with voltage, power, and current waves as particular cases. Three derivations afford implementations whose cost in multiplies are lower than multiplying by the scattering matrix. Negative port resistances may be needed in WDF modeling of active circuits, restricting the WDF to voltage or current waves. We propose two techniques for localizing this restriction. Case studies on the Baxandall tone circuit and a "Frequency Booster" guitar pedal demonstrate the proposed techniques in action.
Original languageEnglish
Pages (from-to)4233-4246
Number of pages14
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number12
Publication statusPublished - 04 Jun 2018


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