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

Abstract

Abstract-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., opamps) 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 nonseries/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.

Linear Multistep Discretization Methods With Variable Step-Size in Nonlinear Wave Digital Structures for Virtual Analog Modeling

“…Despite voltage waves considered in this article are the most widespread in the literature on WDFs, WD structures based on alternative types of waves, such as those characterized by different units of measure [48], [57]- [59] or two free parameters per port instead of one [36], [57], have recently proved to possess peculiar interesting properties. WD models of dynamic elements based on LMSDMs and generalized definitions of waves, including the most used as particular cases, can be straightforwardly derived combining the modeling approach used in recent publications [48], [57], [58], [65] to the results presented in this manuscript.…”

“…In this Section, we briefly review how to compute the scattering matrices representing arbitrary reciprocal connection networks, i.e., topological interconnections possibly incorporating ideal transformers, in the WD domain [8], [39], [56], [57]. The reader who might be interested in the WD modeling of connection networks embedding both reciprocal and non-reciprocal linear elements, e.g., controlled sources, nullors or gyrators, is referred to [58]. In the following, we also briefly discuss the WD modeling of memoryless linear and nonlinear one-ports [1], [2].…”

22nd International Conference on Digital Audio Effects DAFx 2019 (2–6 September 2019, Birmingham, United Kingdom)

“…The final tutorial of the session, Principles of Wave Digital Filter Modeling for Virtual Analog: A Tutorial, given by Kurt Werner (SARC, Queen's University Belfast, UK), gave a comprehensive guide to the use of Wave Digital Filters. These are fundamental methods in the field of virtual analog modeling, which were described in a great level of detail, from early developments of circuit models, to recent additions such as multiple non-linearities and complex topologies [3,4].…”

Advances in Wave Digital Modeling of Linear and Nonlinear Systems: A Summary

“…Such a generalized definition was firstly presented in [35] and it proved useful for modeling WD structures based on waves with different units of measure in an unified fashion. In fact, it was used in [30] and in [16] for modeling arbitrary reciprocal and non-reciprocal multi-port WD junctions. Chapter 2 also includes the scattering relations of some fundamental circuit elements and the scattering relations of series and parallel adaptors.…”

“…Chapter 8 presents the content of the published journal article [30], where the MNAbased method, presented in [31,34] for modeling arbitrary connection networks using WD adaptors based on voltage waves, is extended in such a way that it can be applied to all mono-parametric definitions of waves using the generalized definition described in Chap. 2.…”