Modeling Circuits With Arbitrary Topologies and Active Linear Multiports Using Wave Digital Filters

The wave digital filter (WDF) technique derives digital filters from analog prototypes that 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 paper, 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.