The wave concept iterative process (WCIP) method for electrical circuit network with triangular and hexagonal topology

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 formulation, the potential difference across each circuit component is represented by an auxiliary source defined in the spectral domain. The proposed theory is developed into two definition domains: a spectral domain in which periodicity and coupling between the circuit components are defined and a spatial domain describing the network topology and imposing the continuities conditions (Kirchhoff laws). The transition between the spectral and spatial domain is ensured by the so‐called fast hexagonal Fourier transform. Numerical applications demonstrate the ability of the method for solving the inhomogeneous triangular lattices. Various conceptions have been proposed including an RL, RC, and RLC triangular network circuit, a perturbed triangular RLC circuit, and a triangular circuit excited by many lumped sources.

Design and analysis of two layers RLC network of rectangular topology by wave concept iterative process method

“…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.…”

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

“…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.…”

“…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…”