Limit behavior of the magnetic coupling coefficient for mid range, near-field applications

We have derived compact algebraic bounds for the limit behavior of the magnetic coupling coefficient, κ, for axially aligned multilayer coils. These bounds are validated experimentally. We have also found an expression based on the coil geometry that captures its long-range magnetic behavior. In particular, the limit behavior of the magnetic coupling coefficient is the same for any pair of axially aligned multilayer coils when the separation distance is normalized by this expression.