Electrical characteristics for triangular resistors–capacitors–inductors network designed on two coats

Abstract

SummaryThis work deals with a theoretical study of a triangular electrical lattice built on two layers. First, the auxiliary source notion is introduced for characterizing the potential difference over each electrical element, then the mathematical formalism of the Wave Concept Iterative Process (WCIP) method is developed and adapted to the studied circuit. The method is based on the concept of the incident and reflected waves which are defined from the current and voltage at each branch of the circuit. Two relations connecting the waves are established into two definition domains: a spectral domain using the Kirchhoff laws and the auxiliary source connections and another spatial domain defining the boundary conditions and the circuit design. Hence, a system of two equations is obtained, and it is resolved by an iterative process; the transition between the two domains is ensured by the fast Fourier transform and its inverse. Moreover, the equivalent impedance between the feeding source and the nodes of the bottom layer has been calculated. Among the numerical simulation methods, this method has demonstrated its performance for analyzing various designs of the networks including resistors–inductors (RL), resistors–capacitors (RC), and resistors–capacitors–inductors (RLC) circuits excited by a lumped voltage source. The effect of the circuit parameters on the electrical currents and equivalent impedance has been studied.