Transformations of Passive Linear One-Port Networks with Equal Branch Impedances from 3D Half-Cube Schematic to an Equivalent Impedance

Analysis of complex linear electric circuits with only one voltage source is simplified if equivalent transformations of the corresponding circuits are applied. After these transformations, a circuit with a simpler structure is obtained, but the values of all currents in its branches and of all voltages in it do not change. Normally, in analysis, the 3D electric circuit is presented as a graphical 2D schematic. In this study, transformations of a complex electric circuit with a 3D circuit to look like a half-cube are suggested. Each branch of the analyzed circuit includes only passive elements (resistors, coils, and capacitors) and all branches' impedances are equal. Thus, there is no possibility of the appearance of phenomenon serial and/or parallel resonances in the considered electric circuit. Three basic cases of power supply between pairs of nodes in the circuit are considered. Thus, the initial circuit is replaced with a passive linear one-port network including only one impedance. Equivalent passive linear one-ports and Delta-Star transformations were used. All proposed equivalent transformations are applicable for both DC and AC power supplies. The paper finishes with concluding remarks about the advantages of these transformations to simplify the analysis of the linear electric circuit studied.