Differential Coaxial Coils for Frequency-Independent Deep Magnetic Focusing on Implantable Devices

Magnetic field focusing in longitudinal direction has been a missing link for 3-D synthesized magnetic focusing (3D SMF). Deep magnetic focusing (DMF) by multiple coaxial coils, a sort of 3D SMF, is first proposed in this article, where magnetic field becomes maximum at the focal range in longitudinal direction. DMF is requisite for transcranial magnetic stimulation (TMS) and wireless power transfer (WPT). As the simplest DMF, a set of differential coils with opposite current direction is implemented. Optimum coil currents, coil radii, and coil distance are designed to provide with zero magnetic field at zero range and maximum magnetic field at a focal range. This DMF performance is found to be achieved with a penalty of peak magnetic field reduction. Experiments for the differential coils of diameters 10 and 5 cm with 3 cm gap showed 4 cm depth DMF within 6 cm diameter. Specific numbers of turns make the DMF be driven by only a single-voltage source, which is first adopted in SMF. The frequency versatile DMF characteristic is experimentally verified for 60 Hz and 40 kHz, where 27 mW is delivered to a focal point that is a demonstration for safer WPT of implantable devices.