resonator does not include a capacitor, the characteristics of the
open-ended coil and the pitch in between the two coil layers
make up for the capacitance. Hence, along with the inductance
from the length of the coils, the resonator is represented as a
series set of lumped inductor L and capacitor C [18].
Zsource in Fig. 2 represents the characteristic impedance of
the source, and Zload is the impedance of the load. In this paper,
they are both set to be Z0; 50 Ω is the default characteristic of
most high-frequency systems. R represents the ohm loss and
radiation loss of the resonators.
The resonance frequency of the resonator pair can be calculated
based on the equivalent circuit. To satisfy the resonance
condition, the reactance of Fig. 2 must be zero (1). This can
be satisfied by two angular resonance frequencies as shown in
(2) and (3). The subscripts “m” and “e” in these two equations
represent the two angular resonance frequencies where the
magnetic and electric wall is formed at the plane of symmetry,
respectively. The magnetic field in the former is strong at the
center of the coils, while the latter has strong magnetic fields
at the edge of the coils. Both these frequencies allow highefficiency
WPT through MRC [24]. The coupling coefficient
k can be derived from (2) and (3) into (4)