  One-ports named "f-circuits", composed of similar conductors described by a
monotonic polynomial, or quasi-polynomial (i.e. with positive but not
necessarily integer, powers) characteristic i = f(v) are studied, focusing on
the 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 are
constructed 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 the
connection. 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 the
connection 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 the
independent variable as in f(.), i.e. the map of the characteristics f --> F is
close to a linear one. This unexpected result is useful for understanding
nonlinear 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 in
examples. Special topologies when the superposition must be ideal, are also
considered. In the second part [2] of the work the "circuit mechanism" that is
responsible for the high precision of the superposition, in the most general
case, will be explained.
