Wireless power transmission uses a pair of magnetically-coupled coils, each in series with a capacitor. The self-inductance and mutual inductance of circular coils can be estimated from the geometry. For two identical coils at axial distance , the mutual inductance is given by , while their individual self-inductances are the same: . Applying these in the equivalent circuit, it is possible to analyze the frequency characteristics of the system.
Assuming a constant voltage source with impedance , the frequency characteristic of currents in two coils can be obtained by applying harmonic analysis. The coil distance , capacitances and , and output resistance are variable parameters. The frequency characteristics of input and output powers determine and . As you can see by changing the parameters, the frequency characteristics are sensitive to these parameters.
There are four candidates for resonance frequencies: , , , . These are indicated by vertical lines in the graphics. The displayed frequency range is set so as to include these frequencies. The following tendencies are noticed in the frequency characteristics.
1. When , two peaks appear around the above resonance frequencies (Snapshot 1).
2. When , can differ from for small , resulting in the two-peak profile (Snapshot 2).
3. When and is large, all three resonance frequencies are similar, resulting in the one-peak profile, especially for larger output resistance (Snapshot 3).
An example of the electromagnetic field around the two coils is displayed in the companion Demonstration: "Electromagnetic Field In Wireless Power Transmission."
 J. Garnica, R. A. Chinga, and J. Lin, "Wireless Power Transmission: From Far Field to Near Field," Proceedings of the IEEE, 101(6), 2013 pp. 1321–1331. doi:10.1109/JPROC.2013.2251411.
 J. D. Jackson, Classical Electrodynamics, 3rd ed., New York: Wiley, 1999.