A unifying network approach for circuits simplification and equivalent resistances, capacitors and inductors evaluation

Abstract

It is proposed a network approach for electric circuits simplification, that through a unified systematic procedure allows simplifying circuits of any complexity, and evaluation of the equivalent resistances, capacitors and inductors. Circuits to be simplified are characterized by their nodes, and by the elements of different types (resistances, capacitors and inductors) connecting each pair of nodes. Once that information organized in the matrix form, circuit simplification is straightforward based on the simplification conditions, which are key elements of the proposed approach. Simplification process evolves eliminating nodes from the original circuit, node by node, and evaluating the equivalent element types connecting the remaining nodes, up to the required simplification level. The key elements of the simplification procedure are the same for all the element types. For circuits with elements of different types simplification can be made in a segregated way, each time for one element type, or simultaneously for all the element types. The simplification procedure can be used with pencil and paper, or easily programmed for automatic and fast circuits simplification. Use of the proposed approach is illustrated through some appealing examples.