Comprehensive closed-form analysis of bifurcation in inductive wireless power transfer systems

Abstract

An inductive wireless power transfer (IWPT) system utilizing common compensation topologiesseries (SS), series–parallel (SP), parallel–series (PS), and parallel–parallel (PP)-forms a coupled resonant system that exhibits either a single ( 𝜔0 ) or three zero phase angle (ZPA) frequencies (𝜔𝐿 , 𝜔0 , and 𝜔𝐻 ), depending on the load and coupling conditions. The bifurcation phenomenon in such systems refers to the conditional emergence of two additional ZPA frequencies ( 𝜔𝐿 and 𝜔𝐻 ) near the inherently present ZPA frequency ( 𝜔0 ) , leading to a total of those three ZPA frequencies. Exact closed-form expressions for the bifurcation criteria, the inherent ZPA frequency ( 𝜔0 ) , as well as the reflected resistance and reactance at 𝜔0 , have been extensively studied and are well-established for all four compensation topologies. However, precise closedform solutions for these parameters at the conditionally emerging ZPA frequencies ( 𝜔𝐿 and 𝜔𝐻 ) remain incomplete. In order to derive the missing closed-form solutions at the ZPA frequencies, this paper reexamines four common compensation topologies in inductive wireless power transfer (IWPT) systems. A circuit model based on mutual inductance is analyzed to establish the necessary equations for the solutions. The primary contribution of this work is to present closed-form expressions for the previously unavailable parameters at 𝜔𝐿 and 𝜔𝐻 . In this context 𝜔𝐿 and 𝜔𝐻 are formulated as functions of the circuit model parameters for all four compensation topologies. Additionally, closed-form expressions for the input resistance ( 𝑅𝑖𝑛 ) at 𝜔𝐿 and 𝜔𝐻 are derived for all topologies except the PP configuration. The closed-form bifurcation conditions are also presented as function of the circuit parameters for all four topologies. The accuracy of the extracted formulas is validated using an RF circuit simulator.