I. INTRODUCTION
iN a wireless power transfer (WPT) application, the need for
charging multiple receivers increases [1]–[5]. Magnetic
resonance WPT can be a good candidate for the application. In
the magnetic resonance WPT system, additional coils which are
close to a resonant coil are used for impedance matching [1],
[5]. Hence, when multiple receivers are placed on a transmitter,
cross coupling between non-adjacent coils occurs as well as
coupling between neighboring coils. In [5] and [6], a cross
coupling effect between receivers was reported. In [7], cross
coupling among relay resonators in a domino-resonator system
was analyzed. In addition to the above cross coupling, cross
coupling that is an undesired effect exists between a source coil
and receivers.
A WPT system in a few MHz is necessary to match the input
impedance to the optimal impedance (or characteristic
impedance) of the source such as a class-E amplifier [8], [9].
From the viewpoint of impedance matching, the cross coupling
may modify an optimal impedance matching condition for
maximum power transfer efficiency. In particular, when mobile
devices are close to a transmitter, the cross coupling will