A Model of the Magneto-Inductive Link With Relays to Cross the Air–Water Interface

In this work, the use of magnetic induction to cross the air-water boundary is investigated. An analytical expression is derived for the magnetic field in air from a coil underwater and is validated with simulation results that also include the effect of the front-end. Specifically, the ratio of the induced voltage of the receiver over transmitter current is maximized for a given distance between small coils with a radius of 6.5 cm and it is found that an optimal frequency exists: for a distance between 10 to 100 meters, the optimum frequency of operation decreases from 8000 Hz down to 80 Hz. Experiments are performed in air as well as in sea-water tanks to verify the mutual inductance and end-to-end attenuation. The experiments agree with the theory for distances up to 1.6 meters, after which a noise floor is reached. To increase the range, the use of passive repeaters is studied and a relay coil that transfers the energy to a receiver inside a magnetic shield is analyzed. When configured correctly, this relay can significantly enhance the receiver output voltage, as demonstrated through simulations, potentially increasing it by up to tenfold.