A wireless power charging system includes an intermediate relay coil. In one aspect, a wireless power charging system is designed to charge a separate device having a receiver that includes a receiver coil. The separate device conforms to a specification for the wireless power charging system, which may be a public standard for wireless power charging systems. The wireless power charging system includes a transmitter and a relay coil resonator. The transmitter includes a driver coil that is driven by a power source. The relay coil resonator includes a relay coil that is used to inductively couple power from the driver coil to the receiver coil. The wireless power charging system is designed so that it satisfies Eqn. (11) above.