For the wireless power systems regulated by the Wireless Power Consortium (WPC), magnetic power transfer can be achieved using a simple transformer. Traditional transformers typically consist of a single physical structure where two coil windings are wrapped around a magnetic core material. The magnetic core has a much higher permeability than air (see Figure 1). Due to the use of high-permeability materials in traditional transformers, most of the magnetic flux generated by one coil couples with the other coil. The degree of coupling is measured using the coupling coefficient (k-value), which ranges from 0 to 1.

 

Figure 1. Traditional Transformer with a Single Physical Structure

A dual-coil transformer is defined by the following three parameters:
L11 represents the self-inductance of coil 1.
L22 represents the self-inductance of coil 2.
L12 represents the mutual inductance between coils 1 and 2.
The coupling coefficient between the two coils can be expressed as :
 

Figure 2. Ideal Model of a Traditional Transformer

Using the coupled inductors shown in Figure 2, the ideal transformer can be modeled. By applying the voltage and current relationships of these inductors, the wave equation for this dual-coil transformer can be derived.
 

Figure 3. Cantilever Model of a Traditional Transformer

For the convenience of circuit analysis, the model in Figure 2 can be represented using a cantilever model, as shown in Figure 3. In this representation, the magnetic coupling and mutual inductance are simplified into leakage inductance and magnetizing inductance. Through this circuit realization, we can understand the physical nature of this coupling. For an ideal transformer, the turns ratio can be calculated using the following equation:
 

In a strongly coupled system, the leakage inductance percentage of the magnetizing inductance is very small, so this parameter can be neglected when calculating the first approximation. Besides high coupling, the series resonant capacitors used in the Qi standard system also reduce the impact of leakage inductance. Therefore, the first approximation of the voltage gain from the primary coil to the secondary coil is: 
 

The transformer in a Qi standard system is composed of two separate physical components :
The transmitter (Tx) and the receiver (Rx), each with its own isolated coil. When the Tx and Rx are in proximity, they form a coupled inductance relationship, which can be simply modeled as a dual-coil transformer using an air core (see Figure 4). The shielding materials at both ends serve as a magnetic flux shortcut, ensuring that the magnetic flux exists between the two coils. Figure 5 shows a 2D simulation of the magnetic field lines during typical operation.
 

Figure 4. Simplified Inductive Coupling Transformer Using an Air Core

Figure 5. Simulated Magnetic Field Distribution with Current Flowing Through the Coils

In a typical Qi standard system, the coupling coefficient (k) is significantly lower than in traditional transformers. The coupling coefficient for traditional transformers ranges from 0.95 to 0.99, meaning 95% to 99% of the magnetic flux couples to the secondary coil. However, for Qi standard systems, the coupling coefficient ranges from 0.2 to 0.7, meaning 20% to 70% of the magnetic flux is coupled. In most cases, Qi standards employ a series resonant capacitor on the Tx and Rx to mitigate this low coupling issue. This capacitor can compensate for the resonant leakage inductance.