An approximate analytical (structural) superposition in terms of two, or more, "alfa"-circuits of the same topology: Pt. 2 - the "internal circuit mechanism"

Abstract

This is the second part, after [1], of the research devoted to analysis of 1-ports composed of similar conductors ("f-circuits") described by the characteristic i = f(v) of a polynomial type. This analysis is performed by means of the power-law "alfa"-circuits" introduced in [2], for which f(v) ~ v^"alfa". The f-circuits are constructed from the "alfa"-circuits of the same topology, with the proper "alfa", so that the given topology is kept, and 'f' is an additive function of the connection. Explaining the situation described in detail in [1], we note and analyze a simple "circuit mechanism" that causes the difference between the input current of the f-circuit and the sum of the input currents of the f-circuits before the composition to be relatively small. The case of two degrees, f(v) = Dmv^m + Dnv^n, m unequal n, is treated in the main proofs. Some simulations are presented, and some boundaries for the error of the superposition are found. The cases of f(.) being a polynomial of the third or fourth degrees are finally briefly considered.