A combinatorial method for computing bounds on solutions of active non‐linear resistive networks

Let \cal N be a consistent connected network including independent voltage and current sources, positive linear resistors, multiterminal weakly no‐gain non‐linear resistors and equal numbers of nullators and norators, U(\cal N) a voltage appearing between a distinguished pair of nodes and I(\cal N) a current flowing in a distinguished branch in an equilibrium state of \cal N. It is proved that, under conditions detailed in the paper, U(\˜cal N¹)≤ U(\cal N) ≤ U(\˜cal N²) and I(\overline \cal N^\raise1pt1) ≤ I(\cal N) ≤ I(\overline \cal N^\raise1pt2) where \˜cal N¹,\˜cal N²,\overline \cal N^\raise1pt1, and \overline \cal N^\raise1pt2, are networks derived from \cal N by replacing non‐linear resistors by open‐ and/or short‐circuit structures. An earlier combinatorial method of estimating solutions of non‐linear resistive networks is extended to cover networks including active elements. The method is tested on simple examples of active diode‐transistor circuits.