Analytical calculation of the self-resonant frequency of biomedical telemetry coils

Inductive link is commonly used in biomedical telemetry as a method to wirelessly transmit power and/or data, where coil is very critical to achieve high efficiency. One of the most important but often ignored parameters of the coils is the self-resonant frequency. Due to the fact that the parasitic capacitances are functions of the geometry and winding sequence of the coil, it is very difficult to calculate the self-resonant frequency. The lack of knowledge about the self-resonant frequency greatly limits the design efficiency, especially when the target operating frequency is high, on the order of tens of MHz. This paper presents an analytical model to calculate the self-resonant frequency of multiple-layer coils. A general model of coils to calculate the total parasitic capacitance is given first and then an analytical equation for self-resonant frequency is obtained. The experimental measurement results demonstrate that the equation can accurately predict the self-resonant frequency, therefore can be used for guiding the coil design.