Improved Neural Network Modeling of Circuit Elements With Biparametric Wave Digital Filters

Recent studies have demonstrated the effectiveness of combining Wave Digital Filters (WDFs) with Neural Networks (NNs) for modeling nonlinear circuits. In this context, an NN is used to approximate the scattering equations of nonlinear elements and is connected to a WDF-based linear network representing the rest of the circuit. However, the adaptation condition required to obtain a fully explicit structure can lead to unfavorable parameter values, which can heavily distort the representation of the nonlinear characteristic in the wave domain. This issue becomes particularly critical when modeling hysteresis (or other nonlinearities exhibiting memory), as the transformed characteristic may hinder accurate learning by collapsing the different branches of the hysteresis loops onto each other. In this work, we propose the use of Biparametric Wave Digital Filters (BWDFs) to overcome these limitations. By exploiting the additional degrees of freedom offered by the biparametric formulation, a more suitable wave domain representation of the nonlinearity can be obtained, thereby easing the NN modeling task. Furthermore, we show that this approach can be integrated into existing WDF structures with minimal modifications, making its adoption straightforward even in the case of complex circuits.