## 4 Simulation Analysis  
According to Figure 4, the simulation model can be established, and the simulation parameters are: fixed inductors \(L_{0}=1.58\) mH, \(L_{\text{C1}}=10\) uH, \(L_{\text{C2}}=5\) uH, \(L_{\text{C3}}=30\) uH; the MSK signal center frequency is \(f_{0}=20\) kHz; the antenna equivalent capacitance is \(C_{a}=39.79\) nF; the antenna equivalent radiation resistance is \(R_{a}=1\)\(\Omega_{c}\) and symbol rates are 200 bps, 500 bps, 1000 bps, respectively. The simulation results are as follows. As illustrated in Figures 10(a), 10(a) and 10(a), an increase in the communication rate results in a decline of the peak voltage signal across the equivalent radiation resistance of the very low frequency antenna during traditional tuning, decreasing from approximately 40.9 V to 34.82 V. Concurrently, the fluctuations within the envelope become increasingly pronounced, with its minimum value dropping from around 38.51 V to 20.98 V. Conversely, as depicted in Figures 10(b), 10(b) and 10(b), under the SYNT-RTID synchronization control strategy, the peak voltage signal on the equivalent radiation resistance remains stable between 43.72 V and 43.93 V as communication rates rise, exhibiting both a consistent peak value and a constant envelope profile. It is evident that signals governed by the SYNT-RTID control strategy maintain significantly higher peak values compared to those observed during traditional tuning while also preserving a steady envelope. However, as illustrated in Figures 10(b), 10(b) and 10(b), the signal experiences a period of detuning. This phenomenon arises from the fact that, according to the previously described control strategy flowchart, real-time impedance measurement necessitates a certain \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{\(f_{0}\)} & \multicolumn{1}{c}{\(15\) kHz} & \multicolumn{1}{c}{\(20\) kHz} & \multicolumn{1}{c}{\(25\) kHz} & \multicolumn{1}{c}{\(30\) kHz} \\ \hline
100 bps & 19 & 7 & 4 & 3 \\
200 bps & 37 & 15 & 9 & 5 \\
300 bps & 57 & 24 & 13 & 7 \\
400 bps & 75 & 32 & 17 & 9 \\
500 bps & 94 & 40 & 21 & 12 \\
600 bps & 113 & 48 & 25 & 14 \\
700 bps & 133 & 56 & 29 & 17 \\
800 bps & 151 & 64 & 33 & 19 \\
900 bps & 170 & 72 & 37 & 21 \\
1000 bps & 189 & 80 & 41 & 23 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Inductance values \(\Delta L/\)uH corresponding to different Baud rates and center frequencies. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{\(f_{0}\)} & \multicolumn{1}{c}{\(15\) kHz} & \multicolumn{1}{c}{\(20\) kHz} & \multicolumn{1}{c}{\(25\) kHz} & \multicolumn{1}{c}{\(30\) kHz} \\ \hline
600 bps & 2.887 & 1.616 & 1.031 & 0.714 \\
700 bps & 2.897 & 1.620 & 1.033 & 0.716 \\
800 bps & 2.906 & 1.624 & 1.035 & 0.717 \\
900 bps & 2.916 & 1.628 & 1.037 & 0.718 \\
1000 bps & 2.926 & 1.632 & 1.039 & 0.719 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._duration; during this time, both the amplitude and phase of the signal do not exhibit abrupt changes when out of tune but instead undergo gradual variations. Consequently, only those impedance measurements taken after stabilization of amplitude and phase yield accurate results. At this juncture, the controller within the tuning control unit will issue corresponding enable control instructions to the logic gate unit. Upon receiving these enable instructions, the logic gate unit is primarily governed by code word sequence signals and subsequently outputs tuning control signals to the switching device. Following initial impedance measurement, which identifies necessary enabling for specific logic gates, subsequent controls are predominantly managed by code word sequence signals; thus, ensuring that at this stage, the signal remains consistently in resonance with a stable envelope. Figure 11: Time domain waveforms of the voltage signals at both ends of the R\({}_{\text{a}}\) under different tuning modes when the communication rate is 200 bps. (**a**) Fixed tuning; (**b**) when the SYNT-RTID synchronous control strategy is used.