Impedance Matching Through a Reconfigurable Relay Coil Achieving Maximum Wireless Power Transfer Under Variations of Coupling Coefficient and Load Resistance

In this work, a 6.78 MHz three-coil wireless power transfer (WPT) system was presented, which consists of a transmitter (TX) coil, a reconfigurable relay coil (RRC), and a receiver (RX) coil. We analytically derived the critical coupling boundary and impedance matching (IM) condition in the strong-coupling regime for the first time. Under the variation of either coupling coefficient
$\boldsymbol {k}$
or load resistance
$\boldsymbol {R}_{\text {L}}$
, we proposed to achieve the IM condition on both TX and RX sides by adjusting the RRC’s inductance through electronically selecting its constituting loops. This eliminates the coupling tuning related with the mechanical position change. To obtain the optimum loop inductance in the RRC, we simply measured the voltage and current on the TX side without requiring information of
$\boldsymbol {k}$
or
$\boldsymbol { R}_{\text {L}}$
. This eliminates the RX-to-TX communication link. We implemented a prototype WPT system by including a class-D power amplifier (PA) and a rectifier, and the effectiveness of IM was verified under variations of
$\boldsymbol {k}$
and
$\boldsymbol {R}_{\text {L}}$
. Compared with the system without IM, the transmission ratio
$\boldsymbol { S}_{{21}}$
and load power
$\boldsymbol {P}_{\text {Load}}$
were respectively increased from 66.5 % to 77.9 % and 4.2 W to 10.2 W at
$\boldsymbol {k} = 0.15$
and
$\boldsymbol {R}_{\text {L}} = 20~\Omega $
. Furthermore, the performance improvement of our system for the wireless charging of multiple RX coils was demonstrated.