Generalized adaptors with memory for nonlinear wave digital structures

The problem of modeling a nonlinear resistor in the Wave Digital domain can be seen as that of applying to its nonlinear characteristic the affine transformation that maps Khirchhoff variables into wave variables. When dealing with nonlinear elements with memory, such as nonlinear capacitors and inductors, the above approach cannot be applied, as affine transformations are memory less. In this paper, a new approach is proposed for modeling nonlinear elements with memory in the wave domain. The method we propose defines a more general class of wave variables and adaptors with memory that, under some conditions, can incorporate the "memory" of a nonlinear circuit and allow us to treat some nonlinear elements with memory as if they were instantaneous.