## 3 Signal Path Modeling and Analysis
### Forward Information Transfer Channel Analysis  
The circuit model of the forward signal transmission channel is shown in Figure 5a. For the forward information transfer, the information is injected into the power carrier on the primary side. The information is emitted by the high-frequency source \(V_{dp}\) and amplified by the \(LC\) resonant circuit. Then, the power and the information carrier transmit through the common inductive link from the primary side to the secondary side. On the receiver side, the \(LC\) circuit is tuned in the forward information transfer frequency to select and amplify the high-frequency carrier signal while attenuating the strength of other carriers.  
In order to enhance the forward and backward information transmission and the strength of reception, the transmitting and receiving modules are resonant at the information carrier frequency. The angular frequencies of the forward or backward information transmission are \(\omega_{dp}\) and \(\omega_{ds}\), respectively.  
The equivalent circuit of the signal coupling transformer is shown in Figure 5a, where \(R_{md1}\)\(\sim\)\(R_{md4}\) are the core loss resistance, \(L_{md1}\)-\(L_{md4}\) are the mutual inductance, \(L_{k1}\)-\(L_{k4}\) and \(L_{dk1}\)-\(L_{dk4}\) are the leakage inductance of the four tightly coupled transformers, \(R_{k1}\)-\(R_{k4}\) and \(R_{kd1}\)-\(R_{kd4}\) are leakage resistance. According to Figure 5a, the equivalent impedance of the signal receiver network is  
\[Z_{T1}(\omega)=\frac{1}{\frac{1}{\gamma\omega L_{md1}}+\frac{1}{\kappa_{md1}} +\frac{1}{j\omega L_{kl1}+R_{kd1}+1/(j\omega C_{d1}+1/R_{d1})}} \tag{10}\]  
\[Z_{T2}(\omega)=\frac{1}{\frac{1}{j\omega L_{md2}}+\frac{1}{\kappa_{md2}}+\frac {1}{j\omega L_{k2}+R_{k2}+1/(j\omega C_{d2}+1/R_{d2})}} \tag{11}\]  
Figure 5: Forward information transfer channel. (**a**) Simplified schematic of the forward transmission channel. (**b**) Bode plot of the forward information transmission.  
The coupled inductance at transmitter side is ignored because its inductance is much smaller than the coil inductance. Thus, the secondary side impedance \(Z_{s}(\omega)\) is:  
\[Z_{s}(\omega)=j\omega L_{2}+\frac{1}{j\omega C_{2}}+R_{2}+Z_{T2}(\omega)+j\omega L _{k2}+R_{k2}+j\omega L_{T4} \tag{12}\]  
The impedance of the secondary side reflected in the primary side is:  
\[Z_{rs}(\omega)=\frac{\omega^{2}M^{2}}{Z_{s}(\omega)} \tag{13}\]  
The primary side impedance is equivalent to:  
\[Z_{p}(\omega)=j\omega L_{1}+\frac{1}{j\omega C_{1}}+R_{1}+j\omega L_{k1}+R_{k 1}+Z_{T1}(\omega)+Z_{rs}(\omega) \tag{14}\]  
The gain of the information demodulation voltage at the secondary side is:  
\[G_{T2}(\omega)=\frac{V_{rp}}{V_{T2}}=\frac{1/(j\omega C_{d2}+1/R_{d2})}{j \omega L_{kd2}+R_{kd2}+1/(j\omega C_{d2}+1/R_{d2})} \tag{15}\]  
The gain of the tight coupled transform \(T_{3}\) is:  
\[G_{T3}(\omega)=\frac{V_{T3}}{V_{dp}}=\frac{1/(1/j\omega L_{md3}+1/R_{md3})}{j \omega L_{kd3}+R_{kd3}+\frac{1}{j\omega C_{d3}}+\frac{1}{1/j\omega L_{md3}+1/R _{md3}}} \tag{16}\]  
So the forward information transmission gain \(G_{fd}\) (\(\omega\)) is:  
\[G_{fd}(\omega)=\frac{V_{rp}}{V_{dp}}=\frac{Z_{T2}(\omega)}{Z_{p}(\omega)}\cdot \frac{j\omega M}{Z_{s}(\omega)}\cdot G_{T2}(\omega)\cdot G_{T3}(\omega) \tag{17}\]  
The bode plot of different carrier frequencies \(G_{fd}\) (\(\omega\)) is shown in Figure 5b. There exist three extreme points in this figure, where the low-frequency point A is the power carrier frequency and the higher gain frequency point B is the forward information carrier transmission frequency 1.7 MHz. Another extreme point C is the backward information transmission channel point.