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One-ports named "f-circuits", composed of similar conductors described by amonotonic polynomial, or quasi-polynomial (i.e. with positive but notnecessarily integer, powers) characteristic i = f(v) are studied, focusing onthe algebraic map f --> F. Here F(.) is the input conductivity characteristic;i.e., iin = F(vin) is the input current. The "power-law" "alfa-circuit"introduced in [1], for which f(v) ~ v^"alfa", is an important particular case.By means of a generalization of a parallel connection, the f-circuits areconstructed from the alfa-circuits of the same topology, with different "alfa",so that the given topology is kept, and 'f' is an additive function of theconnection. We observe and consider an associated, generally approximated, but,in all of the cases studied, always high-precision, specific superposition.This superposition is in terms of f --> F, and it means that F(.) of theconnection is close to the sum of the input currents of the independent"alfa"-circuits, all connected in parallel to the same source. In other words,F(.) is well approximated by a linear combination of the same degrees of theindependent variable as in f(.), i.e. the map of the characteristics f --> F isclose to a linear one. This unexpected result is useful for understandingnonlinear algebraic circuits, and is missed in the classical theory.  The cases of f(v) = D1v + D2v^2 and f(v) = D1v + D3v^3, are analyzed inexamples. Special topologies when the superposition must be ideal, are alsoconsidered. In the second part [2] of the work the "circuit mechanism" that isresponsible for the high precision of the superposition, in the most generalcase, will be explained.

An approximate analytical (structural) superposition in terms of two, or  more, "alfa"-circuits of the same topology: Pt.1 - description of the  superposition