Electromagnetic resonance coupling involves creating an
LC resonance, and transferring the power with
electromagnetic couplings without radiating electromagnetic
waves. Hence, the magnetic coupling and electric coupling
can be represented as mutual inductance and mutual
capacitance respectively as shown in Fig. 2.
Zsource in Fig. 2 represents the characteristic impedance, and
Zload is the impedance of the load. In this system, they are
both considered to be the same at Z0, 50Ω the default
characteristic of most high frequency systems. The ohm loss
and the radiation loss of the antennas are represented by R. In
this paper, the power is transferred via magnetic coupling.
Therefore the coupling can be represented by mutual
induction Lm.
Next the resonance frequency is calculated based on the
equivalent circuit. To satisfy the resonance condition, the
reactance of Fig.2 must be 0, as in equation (1). The condition
in equation (1) can be satisfied by two resonant frequencies as
calculated in equation (2) and (3). The coupling coefficient k
can be calculated from equation (2) and (3) to become
equation (4)