# An Inverter Topology for Wireless Power Transfer System with Multiple Transmitter Coils
## 3 Transmitter Coil Excitation  
### Detection of Receiver Coil Position  
An important benefit of a WPT multi-coil system is the free-positioning feature, where the receiver coil can be placed freely in a designated area and may be coupled with one or more transmitter coils at a time. The coupled coil used in the proposed WPT multi-coil system is shown in Figure 9. In this work, four identical coils are adopted as multiple transmitter coils (n = 4) with a single receiver coil. The transmitter coils are arranged based on the comparative study reported in [31], where high misalignment tolerance is obtained. The mutual inductance (M) and magnetic coupling coefficient (k) between the transmitter and receiver coils are dependent on the position of the receiver coil. Theoretically, only the directly coupled transmitter coil or set of transmitter coils should be excited. For the same air gap or vertical distance between coupled coils, the magnetic coupling is maximized at the aligned position, where both coils share the same center. The coefficient k is decreased as the horizontal distance between both coils is increased. In the detection mode, the magnitude of the total primary current \(\left\langle\overrightarrow{I}_{PT}\right\rangle\) depends on the coupling coefficient as:  
\[\left|\overrightarrow{I}_{PT}\right|=\frac{\left|V_{INV}^{1}\right|}{\left[ \left(R_{PT}+\frac{\omega^{2}k^{2}L_{PT}L_{SR_{S}}}{\left[R_{S}^{2}+\left( \omega L_{S}-1/\omega C_{S}\right)^{2}\right]}\right)^{2}+\left(\omega L_{PT}- \frac{1}{\omega\mathcal{C}_{PT}}-\frac{\omega^{2}k^{2}L_{PT}L_{S}\left(\omega L _{S}-1/\omega C_{S}\right)}{\left[R_{S}^{2}+\left(\omega L_{S}-1/\omega C_{S} \right)^{2}\right]}\right)^{2}}\right]^{\left(1/2\right)} \tag{10}\]  
Then, the receiver coil position can be calculated through the total primary current obtained during the detection mode operation, as discussed in Section 2.2.2. The relationship between the total primary current and the coupling coefficient in Equation (10) is illustrated in Figure 10, using the following parameters: \(L_{PT}\) = 280 uH, \(L_{S}\) = 1.37 mH, \(R_{PT}\) = 0.33 \(\Omega\), \(R_{S}\) = 2.03 \(\Omega\), \(C_{PT}\) = 32.57 nF,  
Figure 8: Simplified equivalent circuit of the proposed system when operated in detection mode: (**a**) Overall circuit; (**b**) Reflected impedance in primary circuit.  
Figure 9: Coupled coil arrangement.  
\(C_{S}=5.4\) nF, \(f=58.51\) kHz, \(V_{in}=150\) V, and \(\alpha=126^{\circ}\). Clearly, \(\left|\overset{\rightarrow}{I}_{PT}\right|\) is decreasing as the magnetic coupling k is increased. A comparison of the transmitting current in each coil yields an approximated position of the receiver coil. For example, if the \(\left|\overset{\rightarrow}{I}_{PT}\right|\) value of transmitter coil 3 is significantly lower than the currents obtained from transmitter coils 1, 2, and 4, the receiver coil is located close to the center of transmitter coil 3, as shown in Figure 10(a). If the receiver coil is placed between coil number 3 and 4, as shown in Figure 10(b), the \(\left|\overset{\rightarrow}{I}_{PT}\right|\) values of both coils are almost identical, but substantially lower than the \(\left|\overset{\rightarrow}{I}_{PT}\right|\) value obtained from coil numbers 1 and 2 from the other end.