Abstract:Summary
This paper deals with an RLC circuit network with triangular or hexagonal grid. It is about a planar equilateral triangular grid where the passive (resistor, capacitor, and inductor) or active (voltage source for example) components are located at the sides or/and at nodes attached to the ground. The planar graph is oriented by three main direction vectors phase shifted to 60° degrees. The wave concept iterative process (WCIP) method was employed to the theoretical formulation of the problem. In the fo… Show more
“…To overcome some drawbacks of the previous works and to improve the circuits design, we recently reformulated and adopted the Wave Concept Iterative Process (WCIP) method [29][30][31][32][33][34] into rectangular and triangular approaches, that facilitate problem solving of RLC circuits with rectangular 35 and triangular topologies, 36 respectively.…”
The paper presents a theoretical study of a rectangular electrical network 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 method is developed and adopted to the studied circuit. The used 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 defining the boundary conditions and the circuit design. Hence a two equations system 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 performances for analyzing various designs of the networks including RL, RC and RLC circuits excited by a lumped voltage source. The effect of the circuit parameters on the electrical currents and equivalent impedance has been studied.
“…To overcome some drawbacks of the previous works and to improve the circuits design, we recently reformulated and adopted the Wave Concept Iterative Process (WCIP) method [29][30][31][32][33][34] into rectangular and triangular approaches, that facilitate problem solving of RLC circuits with rectangular 35 and triangular topologies, 36 respectively.…”
The paper presents a theoretical study of a rectangular electrical network 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 method is developed and adopted to the studied circuit. The used 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 defining the boundary conditions and the circuit design. Hence a two equations system 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 performances for analyzing various designs of the networks including RL, RC and RLC circuits excited by a lumped voltage source. The effect of the circuit parameters on the electrical currents and equivalent impedance has been studied.
“…To overcome some insufficiencies of the techniques presented, we recently formulate the Wave Concept Iterative Process Method (WCIP) should be adjusted to the examination of the electrical network circuits with triangular [33][34][35] and rectangular topologies. 36 In the literature, the WCIP method has demonstrated its potential, capacity, and efficiency to resolve several microwave problems with regard to the antennas conception, [37][38][39] the electromagnetic scattering, [40][41][42] and the microwave circuit design.…”
Section: Introductionmentioning
confidence: 99%
“…To overcome some insufficiencies of the techniques presented, we recently formulate the Wave Concept Iterative Process Method (WCIP) should be adjusted to the examination of the electrical network circuits with triangular 33–35 and rectangular topologies 36…”
This 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-capacitorsinductors (RLC) circuits excited by a lumped voltage source. The effect of the circuit parameters on the electrical currents and equivalent impedance has been studied.
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