## 2 Structure and Modeling of the Proposed System  
### Structure of the Proposed System  
The transmission circuit structure of the traditional amplitude modulated signal and power synchronous transmission system is shown in Figure 1a. The DC-DC modulation circuit is composed of a voltage source, a switch tube \(S_{\text{d}}\), a diode \(\text{D}_{\text{d}}\) and an inductor \(L_{\text{d}}\). MOSFET \(\text{S}_{\text{1}}\)-\(\text{S}_{\text{4}}\) (\(\text{S}_{\text{1}}\) and \(\text{S}_{\text{2}}\) are leading leg, \(\text{S}_{\text{3}}\) and \(\text{S}_{\text{4}}\) are lagging leg) and diode \(\text{D}_{\text{1}}\)-\(\text{D}_{\text{4}}\) form a full-bridge inverter circuit. The primary transmitting circuit and the secondary receiving circuit are consistent with Figure 1b. The DC-DC circuit \(L_{\text{d}}\) has the function of filtering, limiting the signal transmission baud rate and bit width. The structure of MASK modulated power and information synchronous transmission system based on PSFB is shown in Figure 1b. The DC-DC modulation circuit is removed, which makes the whole system structure simpler. At the same time, the influence of passive devices on the system is reduced, and the baud rate is improved. Without \(L_{\text{d}}\) filtering, higher bit width data can be transmitted. The transmitting circuit consists of transmitting coil \(L_{\text{p}}\), its parasitic resistance \(R_{\text{p}}\) and compensating capacitance \(C_{\text{p}}\). The receiving circuit includes a power-receiving part and an information-detecting part. \(L_{\text{S}}\), \(R_{\text{S}}\) and \(C_{\text{S}}\) are the inductance, internal resistance and compensation capacitance of the receiving coil of the power-receiving part. The information detection part demodulates the signal with DSP through demodulation circuit. The output waveform of the full-bridge inverter during normal operation is shown in Figure 2. The DSP generates four pulse width modulation signals (\(U_{\text{S1}}\)-\(U_{\text{S4}}\)) for MOSFET drive signals. The dotted lines are \(U_{\text{S4}}\) and \(U_{\text{S3}}\), and \(\alpha\) is the phase shift angle. \(U_{\text{p}}\) is the output voltage waveform of the full bridge inverter. \(I_{\text{p}}\) is the primary current waveform. Figure 1: System structure diagram: (**a**) Traditional amplitude modulation transmission circuit; (**b**) structure diagram of MASK modulation power and information synchronous transmission system based on PSFB. Figure 2: Inverter working waveform. The time domain expression of inverter output voltage \(U_{\text{P}}\) is:  
\[U_{\text{P}}(\varphi) \begin{cases}U_{\text{d}}&,\quad\varphi\in(0,\pi-\alpha]\\ 0&,\quad\varphi\in(\pi-\alpha,\pi]\\ -U_{\text{d}}&,\quad\varphi\in(\pi,2\pi-\alpha]\\ 0&,\quad\varphi\in(2\pi-\alpha,2\pi],\end{cases}  \tag{1}\]  
where \(U_{\text{d}}\) is the DC voltage source voltage. The Fourier series expansion of Equation (1) can be obtained:  
\[U_{\text{P}}(\varphi)=\sum_{k=1}^{\infty}\frac{4U_{\text{d}}}{k\pi}\cos\left( \frac{k\alpha}{2}\right)\sin\left(k\alpha+\frac{k\alpha}{2}\right). \tag{2}\]  
Therefore, the kth harmonic effective value of the inverter output voltage is:  
\[U_{\text{Pk}}=\frac{2\sqrt{2}}{k\pi}U_{\text{Li}n}\abs{\cos\frac{k\alpha}{2}} \text{, }k=1,3,5\ldots\text{.} \tag{3}\]  
From Equation (3), it can be seen that when the input voltage is constant, the output voltage can only consider the fundamental wave due to the addition of the resonant compensation capacitor \(C_{\text{P}}\) at the transmitter. As the phase shift angle increases, the output fundamental component will continue to decrease to zero. By controlling the phase shift angle between the leading leg and the lagging leg of the PSFB, the effective value of the inverter voltage output by the system is changed. The electric power is transmitted to the receiving coil through the transmitting coil, so as to adjust the power coupled to the receiving coil and make the receiving voltage change linearly with the phase shift angle.