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.<
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