Knowledge Base: Coupling Factor k

By Eberhard Waffenschmidt, Philips Research. From WPC.

Depending on the distance between the transmit and receive coils, only a fraction of the magnetic flux generated by the transmitter coil penetrates the receiver coil and contributes to the power transmission. The more flux reaches the receiver, the better the coils are coupled. The grade of coupling is expressed by the coupling factor k.

The coupling factor is a value between 0 and 1. 1 expresses perfect coupling, i.e. all flux generated penetrates the receiver coil. 0 expresses a system, where transmitter and receiver coils are independent of each other.

The coupling factor is determined by the distance between the inductors and their relative size. It is further determined by the shape of the coils and the angle between them. If coils are axially aligned, a displacement causes a decrease of k. Figure 5 shows this effect for an ideal arrangement of planar coils with 30 mm diameters. It shows the measured and calculated coupling factor for parallel coils at different misalignment distances at the horizontal axis. Coupling factors in the range of 0.3 to 0.6 are typical.

Coupling factors for two planar coils with 30mm diameter

Note that a negative coupling factor means that the receiver captures the magnetic flux “from behind.

The definition of the coupling factor is given by:

It results from the general equation system for coupled inductors:

where U1 and U2 are the voltages applied to the coils, I1 and I2 are the currents in the coils, L1 and L2 are the self inductances, L12 is the coupling inductance and ω = 2πf is the circular frequency.

The coupling factor can be measured at an existing system as relative open loop voltage u: