Investigation of a Heterogeneous RLC Lattice with Triangular Topology, Excited by a Lumped Voltage Source

Abstract

Heterogeneous triangular network composed of resistors, capacitors and inductors gives a genuine electrical model for analyzing many engineering and physical problems. Here, we discuss various designs of RLC electrical circuits possessing a triangular topology. The theoretical formulation uses the WCIP technique. The proposed method rests on the definition of the incident and reflected waves from the voltage and current on each circuit branch. The use of the auxiliary source concept makes the execution of the employed technique simple and increments the capacity and effectiveness of the strategy for treating more intricate circuits. The mathematical formulation is subdivided into two definition domains: a spatial domain expresses the network architecture and imposes the boundary conditions, and a spectral one which characterizes the periodicity laws and describes the coupling of the electrical elements. The relationships formulated are resolved by an iterative process where the spectral and spatial equations are repeated up to the convergence. In numerical example, the results obtained by the WCIP method, for a resistors network of triangular topology, show good conformance with the analytical solutions. The method has also demonstrated its performances for investigating various designs of heterogeneous RLC lattice with triangular topology including the heterogeneous RL, RC and RLC circuits, perturbed RC circuits and a composite RLC circuit excited by vertical and horizontal lumped sources.