The wireless power transfer circuit that is used by Qi and several other companies is a subclass of a class of converters called “resonant converters”. These types of converters convert a DC voltage into an AC switched waveform using an “inverter”, pass that waveform through a “resonant tank” (the name used for the resonant elements in this type of converter) to step up or step down the AC voltage, then rectify that AC voltage into a output DC voltage that has been stepped up or down in the final “rectifier” stage. Each of these stages is shown in the figure below. Oftentimes you’ll have a filter at the output of the rectifier to smooth the output voltage.
The trick to making a resonant converter wireless is to find a way to incorporate circuit elements into your resonant tank that do not require physical contact. In practice, the solution is to use two plates of a capacitor, or two coils of a transformer, separated by some distance.
Resonance occurs in circuits when you have a combination of inductors and capacitors being excited by a sinusoidal signal at a particular frequency. The resonant frequency, or frequencies when using more than two inductors or capacitors, is dependent on the value of those inductors and capacitors. The two coils we use in the transmitter and receiver form a loosely coupled transformer. The loosely coupled transformer can be modeled as two inductors and an ideal transformer. The two inductors model the "leakage inductance", or the inductance caused by the magnetic field lines produced by one coil that do not pass through the other coil. A circuit model of the transformer is shown in the figure below, which was taken from a fantastic book on electromagnetic machines by Fitzgerald and Kingsley, called “Electric Machinery”. Now, with a model of the receiver and transmitter coils in terms of inductances, we are now free to choose our combination of capacitors to be used on the transmitting and receiving side to tune to the resonant frequency we desire.
Another interesting note is that the resonant frequency tends to shift as the load at the output changes. The figure below is from yet another fantastic book on power electronics called “Fundamentals of Power Electronics” by Erickson and Maksimovic. It shows how a resonant converter transfer function (defined by the ratio of output voltage to input voltage) changes as the load (represented by Q here, which is a normalized version of the load resistance) changes.
There are additional considerations that must be taken into account when designing a resonant converter. These include the input impedance and output load characteristics of the resonant tank. The input impedance can help achieve “soft switching” on the switching stage that converts the input DC voltage to an AC voltage. This helps to improve efficiency by reducing the switching losses experienced in this first stage. The output load characteristic is another important design element, as it allows the load being powered at the output of the converter to receive the voltage it needs as it varies the amount of power being drawn from the converter.
By designing a resonant converter with the input impedance, resonant tank frequencies, and output load characteristic all in mind, one can achieve high efficiency power transfer with the convenience of wireless power transfer.