Modeling Time-Varying Reactances using Wave Digital Filters

Olafur Bogason; Kurt Werner
DAFx-2018 - Aveiro
Wave Digital Filters were developed to discretize linear time invariant lumped systems, particularly electronic circuits. The timeinvariant assumption is baked into the underlying theory and becomes problematic when simulating audio circuits that are by nature time-varying. We present extensions to WDF theory that incorporate proper numerical schemes, allowing for the accurate simulation of time-varying systems. We present generalized continuous-time models of reactive components that encapsulate the time-varying lossless models presented by Fettweis, the circuit-theoretic time-varying models, as well as traditional LTI models as special cases. Models of timevarying reactive components are valuable tools to have when modeling circuits containing variable capacitors or inductors or electrical devices such as condenser microphones. A power metric is derived and the model is discretized using the alpha-transform numerical scheme and parametric wave definition. Case studies of circuits containing time-varying resistance and capacitance are presented and help to validate the proposed generalized continuous-time model and discretization.