A wireless power transmission system has a wireless power receiving device that can be charged using multiple different types of wireless power transmitting devices. The different types of wireless power transmitting devices have power transmitting coils that exhibit different levels of magnetic coupling with the power receiving coil of the wireless power receiving device. The wireless power receiving device may include capacitors, resistors, and/or other loading circuits that can be independently switched into use depending on the level of magnetic coupling that is detected, on a rectified voltage level, on the size of the output load, and/or on information conveyed during handshaking operations to present a desired impedance adjustment at the power receiving coil so that data signal can be properly conveyed between the power receiving device and the power transmitting device.