Dynamic adaptation of instantaneous nonlinear bipoles in wave digital networks

Accommodating multiple nonlinearities in a modular fashion and with no use of delay elements is a relevant unsolved problem in the literature on Wave Digital (WD) networks. In this work we present a method for adapting instantaneous NonLinear (NL) bipoles characterized by monotonic increasing curves. The method relies on the fact that the characteristic of a NL bipole can be described by a line, which dynamically varies its slope and its intercept according to the actual operating point. This fact allows us to model a NL bipole as a linear real voltage generator with time-varying parameters. Dynamic adaptation makes possible to accommodate multiple nonlinearities in the same WD network, ensuring the absence of delay-free loops. We will show that diodes can be effectively modeled using the presented approach. As an example of application of our method, we present an implementation of a diode-based audio limiter.