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

In this work, the use of magnetic induction (MI) 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 and 100 m, the optimum frequency of operation decreases from 8000 down to 80 Hz. Experiments are performed in air and 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 m, 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.