## 2 System Overview and Power Channel Analysis  
The block diagram of the proposed SWIPT system is shown in Figure 1a. The system is divided into the primary and secondary side. Both sides are supplied by the DC power. The inductive link bridges the primary and the secondary sides. The information is injected into the bidirectional power transfer loop through the signal coupling transformer at both sides, which can achieve the full-duplex transmission of the signal. The schematic diagram of the proposed SWIPT system is shown in Figure 1b. The primary side and secondary side adopt the active bridges for bidirectional power transfer. \(V_{1}\) and \(V_{2}\) are the DC power supply in the primary and secondary side, respectively. The compensation structure of the circuit employs series compensation. Inductance and capacitance are connected in series in the circuit. As \(I_{p}\) and \(I_{s}\) are high-frequency currents, in order to reduce the AC resistance on the coil, the inductor coil uses multiple Litz wires. Four coupled transformers (\(T_{1}\)\(\sim\)\(T_{4}\)) are combined to form a signal modulation section and signal receiving section to complete the transmission and reception of signals. The combination of the transformers \(T_{1}\) and \(T_{4}\) is employed in backward information transfer. \(T_{3}\) and \(T_{2}\) are applied for forward information transfer. The forward and the backward information transfer frequency are 1.7 MHz and 1 MHz, respectively. Besides, \(V_{dp}\) and \(V_{ds}\) are high frequency sources of forward information and backward information transfer, respectively. \(V_{rp}\) and \(V_{rs}\) are the voltage of forward and backward information pick-up resistances, respectively. As the injected signals frequencies are different, the transmitting circuit and the receiver circuit parameters are different and this structure can realize forward and backward information transfer dependently. In order to achieve bidirectional power transmission, the SWIPT system adopts dual active full bridges. The power transfer size and direction is controlled by the three phase-shift, \(\alpha\), \(\beta\), and \(\phi\), where \(\alpha\) and \(\beta\) are half of the inter-bridge phase shift angle of the primary side and secondary sides, respectively; \(\phi\) is the phase shift angle between the primary full-bridge arms and the secondary full-bridge arms, and it can adjust power transmission direction. Figure 1: The bi-directional SWIPT system. (**a**) Block diagram. (**b**) Schematic diagram. Figure 2 shows the eight switches control signals of the dual active bridges. \(S_{1}\)\(\sim\)\(S_{4}\), \(S_{5}\)\(\sim\)\(S_{8}\) are the primary side and secondary side control signals, respectively. \(V_{p}\) and \(V_{s}\) are output three-level square wave voltage signals of the primary side and secondary side. The equivalent circuit model of the proposed SWIPT system is presented in Figure 3, where \(L_{T1}\)-\(L_{T4}\) are the equivalent inductance of the tightly coupled transformer. During power transfer, the impedance of the tightly coupled transformer inductor \(L_{T1}\)-\(L_{T4}\) are much smaller than the reflected impedance of information demodulation cells. \(V_{p}\) and \(V_{s}\) are the primary and secondary inverter output voltage. In order to simplify analysis, only the amplitude of fundamental frequency component is retained and higher harmonics are ignored. Then \(V_{p}\) and \(V_{s}\) are equivalent to:  
\[V_{p}=\frac{2\sqrt{2}}{\pi}V_{1}\ \sin\alpha,\ V_{s}=\frac{2\sqrt{2}}{\pi}V_{2} \ \sin\beta. \tag{1}\]  
Define \(V_{p}\) as the reference voltage, so the expression of the \(V_{p}\) and \(V_{s}\) is:  
\[\left\{ \begin{array}{c}\dot{V}_{p}=V_{p}\angle 0^{\circ}\\ \dot{V}_{s}=V_{s}\angle\phi\end{array} \right., \tag{2}\]  
where \(\phi\) is the phase shift angle generated between the primary side and the secondary side control signal. According to the [PERSON]'s theorem, the circuit equation is obtained. \[\left[ \begin{array}{cc}Z_{1}&-i\omega_{p}M\\ -j\omega_{p}M&Z_{2}\end{array} \right]\cdot\left[