| This paper focuses on the frequency splitting and bifurcation phenomena that appear in the wireless power transfer systems. These two phenomena are analyzed for different possible configurations of the magnetically coupled circuits of the system, through electric circuit methods and mathematical calculus. Considering two printed spiral coils with similar geometrical properties, the study started with a calculus of the splitting frequency. It was made for the series-series connection, but also for series-parallel, parallelseries and parallel-parallel connections. The graphical representations of the load voltage as function of the frequency revealed that this phenomenon is visible only for the series-series and series-parallel connections; even if one or two peaks appear in all cases they are not directly connected to the frequency splitting phenomena, respectively to the spitting factor. The bifurcation phenomenon is analyzed starting from the bifurcation equation defined for the input admittance of the wireless power transfer system. The four types of configurations are analyzed from the graphical representations of the imaginary part of the admittance as function of the frequency. Because an important factor in the frequency splitting and bifurcation phenomena appearance is the ratio between the input resistance and the load resistance, in the last part of the paper the splitting coupling factor as function of the input resistance – load resistance ratio is depicted. The paper brings new contributions in the field through a comparative study on the frequency splitting and bifurcation phenomena for all the four types of configuration of the wireless power transfer systems. Through mathematical calculations, formulas for estimating the frequency (angular frequency) of occurrence of each phenomenon are obtained. The results are validated by comparative simulations related to a system of identical spiral coupled coils. The results of the analysis were commented comparatively and some conclusions could be drawn. |
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