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

TL;DR

This paper analyzes the internal circuit mechanisms of similar polynomial-conductance circuits using power-law 'alfa'-circuits, revealing small differences in input currents and establishing error bounds for superposition.

Contribution

It introduces an approximate analytical superposition method for 'alfa'-circuits of the same topology, including error analysis and simulation results.

Findings

The difference between the input current of the combined circuit and the sum of individual currents is small.

Error bounds for superposition are established through analysis and simulations.

The approach extends to polynomial f(v) of third and fourth degrees.

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.