# A Novel Bidirectional Wireless Power Transfer System for Mobile Power Application
## 2 Analysis of Proposed Circuit Topology  
The proposed bidirectional wireless power transfer circuit with primary side and secondary side circuits is shown in Figure 3. Both the primary side and secondary side circuits can be the transmitter (\(T_{X}\)) or receiver (\(R_{X}\)). In the proposed topology, there is a boost inductor, an active switch, as well as a resonant capacitor and resonant coupled inductor in both the primary side and secondary side. The primary side circuit and secondary side circuit are designed to be symmetric to each other. However, the power direction is controlled by the switching duty ratios \(D_{1}\) and \(D_{2}\) of switch 1 and  
Figure 1: Full-bridge bidirectional wireless power transfer Electric Vehicle (EV) charger system. Figure 2: Bidirectional wireless power transfer for mobile power application. switch 2. While switch 1 is active and switch 2 is idle, the power flow is controlled from \(T_{x1}\) to \(R_{x1}\). While switch 2 is active and switch 1 is idle, the power flow is controlled from \(T_{x2}\) to \(R_{x2}\). Therefore, the energy can be transferred easily from primary side to the secondary side or from secondary side to the primary side. For convenient explanation of how the circuit works, assume that the primary side is the transmitter and the secondary side is the receiver. The active switches are assumed to be ideal active switches with anti-paralleling body diode. To illustrate the circuit operation, the key waveforms of the proposed bidirectional wireless power transfer system during one switching period are shown in Figure 4 and the circuit operation can be divided into four states to explain and discuss. (1) State 1 (\(t_{0}\leq t<t_{1}\)): In this mode, as shown in Figure 5, the switch \(S_{1}\) is turned on and switch \(S_{2}\) is turned off as be a diode. Switch current \(i_{ds1}\) is increasing. Inductor \(L_{1}\) is magnetized by the input voltage \(V_{1}\) so as to increase the inductor current \(i_{L1}\). The capacitor \(C_{1}\) resonates with the coupled inductor \(L_{r1}\). The resonant current \(i_{L1}\) is changed from positive to negative and produces the magnetic  
Figure 4: The key waveforms of the proposed bidirectional wireless power transfer system during one switching period. Figure 3: Proposed bidirectional wireless power transfer circuit. vector potential \(\overset{\rightarrow}{A}_{1}\) through the primary side plane coil, i.e., the transmitter. The magnetic vector potential \(\overset{\rightarrow}{A}_{1}\) is transmitted to the secondary side plane coil, i.e., the receiver and generates a resonance between the \(L_{r2}\) and \(C_{2}\) so as to release energy to the inductor \(L_{2}\) and load. The equivalent circuit equations can be described as Equations (1)-(6). \[L_{1}\frac{di_{L1}}{dt}=v_{1}, \tag{1}\]  
\[L_{r1}\frac{di_{Lr1}}{dt}+M\frac{di_{Lr2}}{dt}=-v_{C1}, \tag{2}\]  
\[C_{1}\frac{dv_{C1}}{dt}=i_{Lr1}, \tag{3}\]  
\[C_{2}\frac{dv_{C2}}{dt}=i_{Lr2}, \tag{4}\]  
\[L_{r1}\frac{di_{Lr1}}{dt}+M\frac{di_{Lr2}}{dt}=-v_{C2}, \tag{5}\]  
Figure 1:0  
where \(M\) is the mutual inductance and determined by the magnetic vector potential \(\overset{\rightarrow}{A}_{1}\) and \(\overset{\rightarrow}{A}_{2}\). Therefore, the mutual inductance can be expressed as \(M=\frac{\mu_{0}N_{1}N_{2}}{4\pi}\oint\oint\frac{d\overset{\rightarrow}{I}_{1 }\cdot d\overset{\rightarrow}{I}_{2}}{R}\). \(N_{1}\) and \(N_{2}\) are the numbers of turns of the primary and secondary side, respectively. \(\overset{\rightarrow}{I}_{1}\) and \(\overset{\rightarrow}{I}_{2}\) indicate the flux direction of coil 1 at primary side and coil 2 at secondary side, respectively. \(R\) is the distance between the primary-side and secondary-side windings. (2) State 2 (\(t_{1}\leq t<t_{2}\)): In this mode, as shown in Figure 6, switch \(S_{1}\) is turned on and switch \(S_{2}\) is turned off. Switch current \(i_{ds1}\) is increasing. Inductor \(L_{1}\) is magnetized by the input voltage \(V_{1}\) so as to increase the inductor current \(i_{L1}\).