“Phantom Impedances” as an Option to Solve 3D Symmetrical Circuit Arrangements

This paper shows a new methodology to get an analytical solution for symmetrical arrangements of impedances in 3D, using a new concept named “the phantom impedance”. A great quantity of our actual power systems can be modeled as “symmetrical impedance systems”. The majority of these systems are so complex that their representation in a simple flat (2D) drawing becomes difficult, and is necessary to separate the general system in several drawings of sub-systems. For some of these systems there is no flat option to represent and solve. In other fields such microelectronics, bioengineering, biomedical sciences, etc., also we have several complex impedance systems that are not flat. In several cases, these systems are also symmetrical, at least between two points of interest. In all these cases, if we would have a simple method for the analytical solution for 3D symmetrical impedance systems, it could help enormously to improve these specific models, and to get quickly answers to complicated questions. The main goal of this paper is to bring a clear explanation of a method for this simple solution.