Structure of the Solution-Space and Homologous Time Constants Solution of Resonant Inductive Coupling Circuits

Abstract

In a previous study, we obtained the general solution for resonant inductive coupling by mixing factors of eigenstates, and we derived power transmission and power reception formulas for inductive coupling coils. Numerical calculation results in the time and frequency domains always satisfy energy conservation requirements. We thus obtained a number of interesting results. However the expression of the general solution is too complicated to predict the behavior of the solution. Therefore, in this study, we will obtain an understandable expression of the general solution by restricting mixing factors to real numbers. This restriction is identical to the “Homologous Time Constants” condition, which states that time constants of the primary circuit and secondary circuit must be equal.