Symbolic linear mathematica based technique for piecewise linear circuits

This paper is intended to show an approach to directly translate linear methods to PWL circuit problems. The basic idea is to hide the non-linearity to the linear method, so that the user can handle the PWL problem as if it was a linear one. So doing writing equations for a PWL circuit can be extremely simple and fast, since the PWL formulation becomes a linear formulation. Moreover, since it is possible to use usual linear solvers the solution is improved as well. This approach is based first on symbolic formulation and calculations, then on rules application, which deliver to the symbolic processor the task to deal with the PWL aspects of the problem. A Mathematica procedure dedicated to this aim will be suggested, together with a practical example where a four-diode rectifier is handled as a linear circuit.