Some properties of series-parallel nonlinear resistive circuits

In a linear series-parallel circuit having a unique independent source, the polarity of a branch voltage depends only on the polarity of the source voltage. This dependence is given by the Duffin´s rule (R. J. Duffin, 1965). Here, this rule is extended to some classes of nonlinear series-parallel resistive circuits containing one or many independent sources. This rule is used to prove some new properties of these circuits: bounding regions and slope bounds for transfer characteristics, modification of the driving-point characteristic produced by some modifications of branch characteristics, monotone sensitivity with respect to many branches, and concavity of the driving-point characteristic in terms of the branch characteristic´s concavities