# An Inverter Topology for Wireless Power Transfer System with Multiple Transmitter Coils
## 2 System Description and Operation
### Mode of Operation
#### 2.2.2 Detection Mode  
The detection mode serves as an approach in determining a proper transmitter coil pattern before the charging process. This mode starts with turning switches \(S_{A}\) and \(S_{B}\) on. The timing diagram and theoretical waveforms of the detection mode are depicted in Figure 6, for the case when the excitation switch \(S_{1}\) is turned on. Only the current \(I_{P1}\) flows through the transmitter coil \(L_{P1}\). Note that the detection operation is performed on each transmitter coil to collect the necessary current information for the determination of a proper coil pattern. Since the detection switches, \(S_{A}\) and \(S_{B}\), are turned on throughout the detection process, the secondary voltage \(V_{S}\) and output voltage \(V_{out}\) are essentially zero. The switching operation of each stage of the detection mode is shown in Figure 7.  
Stage 1 [\(t_{a}\)-\(t_{b}\)] in Figure 6: Both upper and lower switches, \(S_{U}\) and \(S_{L}\), are off. The input current, \(I_{in}\), is equal to the transmitter current, \(I_{P1}\), and flows in the negative direction through antiparallel diodes \(D_{1}\) and \(D_{U}\). The inverter voltage, \(V_{INV}\), is equal to the DC input voltage \(V_{in}\). The secondary current, \(I_{S}\), flows in the positive direction through detection switch \(S_{A}\) and diode \(D_{A}\).  
Stage 2 [\(t_{b}\)-\(t_{b}\)'] in Figure 6: The upper switch \(S_{U}\) starts conducting at \(t=t_{b}\). The current \(I_{P1}\) becomes positive and flows through switches \(S_{U}\) and \(S_{1}\). The secondary current, \(I_{S}\), is reduced to zero at \(t=t_{b}\)'.  
Stage 3 [\(t_{b}\)-\(t_{c}\)] in Figure 6: The switches \(S_{U}\) and \(S_{1}\) remain on, and the current \(I_{P1}\) is still positive. The negative current \(I_{S}\) flows through the switch \(S_{B}\) and diode \(D_{B}\). The switch \(S_{U}\) is turned off at \(t=t_{c}\).  
Stage 4 [\(t_{c}\)-\(t_{d}\)] in Figure 6: The lower switch \(S_{L}\) is still off. The positive current \(I_{P1}\) flows through the switch \(S_{1}\) and the antiparallel diode \(D_{L}\). The secondary current, \(I_{S}\), still flows in the negative direction.  
Figure 6: Timing diagram and theoretical waveforms of the detection mode.  
Stage 5 [t\({}_{\text{d}}\)-t\({}_{\text{d}}\)'] in Figure 6: The switch S\({}_{\text{L}}\) has been on. At t = t\({}_{\text{d}}\), the negative current I\({}_{\text{P1}}\) flows through the switch S\({}_{\text{L}}\) and the antiparallel diode D\({}_{\text{1}}\). The secondary current, I\({}_{\text{S}}\), still flows in the negative direction.  
Stage 6 [t\({}_{\text{d}}\)'-t\({}_{\text{e}}\)] in Figure 6: The current I\({}_{\text{P1}}\) flows in the negative direction through the switch S\({}_{\text{L}}\) and diode D\({}_{\text{1}}\). At t = t\({}_{\text{d}}\)', the switch S\({}_{\text{A}}\) and diode D\({}_{\text{A}}\) conduct positive current I\({}_{\text{S}}\). The lower switch S\({}_{\text{L}}\) is then turned off at t = t\({}_{\text{e}}\). The operation of one switching period is completed. The next switching cycle is repeated starting from stage 1.  
A simplified equivalent circuit for detection mode operation is shown in Figure 8. Clearly, the equivalent AC output voltage, \(\overset{\rightarrow}{V}_{out}^{ac}\), is equal to zero. The reflected impedance, \(\overset{\rightarrow}{Z}_{R}^{Detect}\), as shown in Figure 8b, is given as:  
\[\overset{\rightarrow}{Z}_{R}^{Detect}=\frac{\omega^{2}M^{2}[R_{S}-j(\omega L _{S}-1/\omega C_{S})]}{\left[R_{S}^{2}+\left(\omega L_{S}-1/\omega C_{S}\right) ^{2}\right]} \tag{9}\]  
Due to the absence of the equivalent AC resistance (\(R_{L}^{ac}\)), the reflected impedance \(\overset{\rightarrow}{Z}_{R}^{Detect}\) is significantly larger than the reflected impedance under normal operation in Equation (4). This means that the primary current (\(\overset{\rightarrow}{I}_{PT}\)) is considerably lower. With the knowledge of the current in each transmitter coil, the position of the receiver coil can be estimated, and a proper transmitter coil pattern is obtained.