Download Wave Digital Filter Adaptors for Arbitrary Topologies and Multiport Linear Elements
We present a Modified-Nodal-Analysis-derived method for developing Wave Digital Filter (WDF) adaptors corresponding to complicated (non-series/parallel) topologies that may include multiport linear elements (e.g. controlled sources and transformers). A second method resolves noncomputable (non-tree-like) arrangements of series/parallel adaptors. As with the familiar 3-port series and parallel adaptors, one port of each derived adaptor may be rendered reflection-free, making it acceptable for inclusion in a standard WDF tree. With these techniques, the class of acceptable reference circuits for WDF modeling is greatly expanded. This is demonstrated by case studies on circuits which were previously intractable with WDF methods: the Bassman tone stack and Tube Screamer tone/volume stage.
Download Resolving Wave Digital Filters with Multiple/Multiport Nonlinearities
We present a novel framework for developing Wave Digital Filter (WDF) models from reference circuits with multiple/multiport nonlinearities. Collecting all nonlinearities into a vector at the root of a WDF tree bypasses the traditional WDF limitation to a single nonlinearity. The resulting system has a complicated scattering relationship between the nonlinearity ports and the ports of the rest of the (linear) circuit, which can be solved by a Modified-NodalAnalysis-derived method. For computability reasons, the scattering and vector nonlinearity must be solved jointly; we suggest a derivative of the K-method. This novel framework significantly expands the class of appropriate WDF reference circuits. A case study on a clipping stage from the Big Muff Pi distortion pedal involves both a transistor and a diode pair. Since it is intractable with standard WDF methods, its successful simulation demonstrates the usefulness of the novel framework.