A unified set-theoretic approach to the analysis of PWL resistive circuits and composite N-ports

We consider the search for all DC solutions of resistive Piecewise-Linear (PWL) circuits and the analysis of the characteristics of resistive PWL composite $N$-ports. These problems are unified from a theoretical and operating point of view by introducing the so-called $N$-augmented circuit, obtained from the $N$-port by closing its ports with $N$ norators. Set-theoretic approach is used to describe the properties of the $N$-augmented circuits leading to the formulation of a general DC analysis algorithm, based on Linear Programming techniques. The examples at the end of the paper show some practical and efficient application of the general DC analysis algorithm.