# An Inverter Topology for Wireless Power Transfer System with Multiple Transmitter Coils
## 2 System Description and Operation
### Mode of Operation
#### 2.2.1 Normal Mode Operation  
The normal mode operation is initiated when the detection switches, \(\mathrm{S_{A}}\) and \(\mathrm{S_{B}}\), are turned off. The timing diagram and theoretical waveforms for the case when the excitation switch \(\mathrm{S_{1}}\) is turned on are depicted in Figure 3. Only transmitter coil number 1 (\(\mathrm{L_{P1}}\)) is energized. If two or more coils  
Figure 1: Overall block diagram of the proposed system. Figure 2: Circuit configuration of the proposed system. are energized at the same time, a parallel connection of the energized coils is formed. The resulting circuits of each stage are shown in Figure 4.  
Figure 3: Timing diagram and theoretical waveforms of the normal mode. Stage 1 [t\({}_{a}\)-t\({}_{b}\)] in Figure 3: Both upper and lower switches, \(S_{U}\) and \(S_{L}\), are off. The transmitter current \(I_{P1}\) 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, where diodes \(D_{R1}\) and \(D_{R4}\) are turned on. The secondary voltage (\(V_{S}\)) is identical to the DC output voltage (\(V_{out}\)). Stage 2 [t\({}_{b}\)-t\({}_{b}\)] in Figure 3: The upper switch \(S_{U}\) starts conducting at t = t\({}_{b}\), and the current \(I_{P1}\) starts flowing in the positive direction through switches \(S_{U}\) and \(S_{1}\). The secondary current, \(I_{S}\), flows in the positive direction and reduces to zero at t = t\({}_{b}\). Stage 3 [t\({}_{b}\)-t\({}_{c}\)] in Figure 3: The current \(I_{P1}\) still flows in the positive direction through the switches \(S_{U}\) and \(S_{1}\). At t = t\({}_{b}\), the secondary current \(I_{S}\) starts flowing in the negative direction through diodes \(D_{R2}\) and \(D_{R3}\). The secondary voltage \(V_{S}\) becomes negative with opposite polarity to the output voltage (\(-V_{out}\)). The upper switch \(S_{U}\) is turned off at t = tc. Stage 4 [t\({}_{c}\)-t\({}_{d}\)] in Figure 3: 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 inverter voltage \(V_{INV}\) is equal to zero. The secondary current, \(I_{S}\), still flows in the negative direction through diodes \(D_{R2}\) and \(D_{R3}\). Stage 5 [t\({}_{d}\)-t\({}_{d}\)] in Figure 3: The lower switch \(S_{L}\) starts conducting at t = t\({}_{d}\), and the current \(I_{P1}\) starts flowing in the negative direction through the switch \(S_{L}\) and the antiparallel diode \(D_{1}\). The secondary current, \(I_{S}\), still flows in the negative direction. Stage 6 [t\({}_{d}\)-t\({}_{e}\)] in Figure 1:0 The current \(I_{P1}\) flows in the negative direction through the switch \(S_{L}\) and diode \(D_{1}\). At t = t\({}_{d}\), the secondary current, \(I_{S}\), starts flowing in the positive direction through \(D_{R1}\) and \(D_{R4}\). The secondary voltage \(V_{S}\) is changing from negative to positive value. At t = t\({}_{e}\), the lower switch \(\mathrm{S_{L}}\) is turned off. The operation of one switching period is completed. Then, the switching operation is repeated, starting from stage 1. From fundamental harmonic approximation (FHA), a simplified equivalent circuit of the system under the normal mode of operation is shown in Figure 1:1 The fundamental component of the inverter voltage (\(V_{INV}\)) is denoted by \(V_{INV}^{1}\), and its amplitude can be expressed as:  
Figure 1:2  
The operating angular frequency is denoted by \(\omega\). \(\mathrm{L_{PT}}\) and \(\mathrm{R_{PT}}\) represent the equivalent self-inductance and winding resistance of multiple transmitter coils, regardless of the number of coils connected in parallel. The total compensation capacitance in the primary circuit is defined as \(\mathrm{C_{PT}}\).