## 3 Synchronous Control Strategy Based on Real-Time Impedance Detection  
Basic condition: The high level of the control signal corresponds to the high frequency point \(f_{h}\) of the MSK signal, and the low level corresponds to the low frequency point, \(f_{I}\), of the MSK signal. The system is resonant at high frequency by adjusting the fixed  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**A** & **B: Symbol Signal** & **C: Controller Signal** & **D** & **E** & **F** \\ \hline
1 & 0 & 1 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Logic truth table.  
Figure 5: Logic control unit diagram (A is a fixed logic instruction, D and E are the outputs of XOR and AND gates, respectively, and F is the final control instruction output by the logic control unit.).  
tuning inductor, \(L_{0}\), and the initial state of the power electronic switches at both ends of the controlled inductor is conduction.  
Figure 6 shows the flow of synchronous control strategy based on real-time impedance detection (hereinafter referred to as SYNT-RTID synchronous control strategy). The calculation process of the controlled inductance, \(\Delta L\), is as follows [16].  
\[Z=\frac{\overset{\bullet}{U}}{\overset{\bullet}{I}}=\frac{U\angle\varphi_{u}}{ L\angle\varphi_{i}}=|Z|\angle\varphi_{Z}=z\angle\varphi_{Z} \tag{3}\]  
\[Z=\frac{\overset{\bullet}{U}}{\overset{\bullet}{I}}=R+j(\omega L-\frac{1}{ \omega C}) \tag{4}\]  
\[\omega L-\frac{1}{\omega C}=z\sin\varphi_{Z} \tag{5}\]  
\[L=\frac{z\sin\varphi_{Z}}{\omega}+\frac{1}{\omega^{2}C} \tag{6}\]  
\[\Delta L=\frac{\text{Im}[Z]}{\omega}=\frac{z\sin\varphi_{Z}}{\omega} \tag{7}\]  
As shown in Figure 6, after \(\Delta L\) is obtained, the appropriate combination of controlled inductors is selected by the table look-up method. Each \(\Delta L\) corresponds to a group of controlled inductor combinations, and each controlled inductor corresponds to the control port of a controller to ensure that the controller can control the corresponding number of inductors.  
Figure 6: Flowchart of synchronous control strategy based on real-time impedance detection.  
The actual accuracy of the inductor is difficult to reach the accuracy of the theoretical value. At the same time, considering the cost, the accuracy of the inductor should also be controlled within a reasonable range. The VLF communication system is a narrowband system, and the accuracy of the inductor has a great impact on the system. We mainly discuss the influence of the inductor accuracy on the power factor angle, \(\varphi\), and the antenna radiation efficiency of the antenna feeder system.  
For the convenience of discussion, in this section, the antenna equivalent capacitance is \(C_{a}=~{}39.79\) nF, the antenna equivalent radiation resistance is \(R_{a}=1~{}\Omega\), the MSK signal center frequency, \(f_{0}\), are 15 kHz, 20 kHz, 25 kHz, and 30 kHz, respectively, and the symbol rate, \(R_{B}\), is 200 bps, 300 bps, 500 bps, 700 bps, and 900 bps. \(L_{0}\) is the amount of tuning inductance required by the antenna fed system at frequency \(f_{h}\) resonant, and \(L_{l}\) is the amount of tuning inductance required by the antenna fed system at frequency \(f_{l}\) resonant, and \(\Delta L=L_{l}-L_{0}\). The heat loss is ignored in this paper.