## 3 Results and Discussion  
Figure 6 compares the S21 graphs of PEC and HFSS when the Rx movement distance is 0 mm. The comparison is divided into before and after impedance matching. The S21 before impedance matching was close to 0, and the PEC results were the same. After impedance matching, the resonant frequency and the maximum value of S21 for both PEC and electromagnetic simulation were 6.35 MHz and 0.86, respectively, showing identical results. As previously described, the C\({}_{\text{TX}}\) and C\({}_{\text{RX}}\) of the equivalent circuit were accurate values calculated through simulation, and C\({}_{\text{M}}\) was adjusted through the optimization process of the equivalent circuit model. Additionally, the coupler loss resistances R\({}_{\text{TX}}\) and R\({}_{\text{RX}}\) were also tuned to obtain accurate graphs.  
Figure 7 shows the maximum S21 and the magnetic and mutual capacitances as the receiving unit moves along the x-axis from \(-\)30 mm to 120 mm. The magnetic and mutual capacitances tended to remain constant when the receiving unit was within the metal plate area of the transmitting unit, between 0 mm and 90 mm. Outside this area, as inferred from Equation (1), a decrease in mutual capacitance corresponded to an increase in magnetic capacitance. Additionally, when compared with the maximum S21, the mutual capacitance showed a similar trend within the metal plate area of the transmitting unit. However, the maximum S21 sharply decreased in the regions beyond the metal plate area of the transmitting unit, between \(-\)30 mm to 0 mm and 90 mm to 120 mm.  
Figure 8 shows the results of observing the maximum value of S21 and mutual capacitance as the Rx moves between \(-\)50 mm and 50 mm along the y-axis. As the mutual capacitance approached zero, S21 decreased with a similar slope. The point where S21 approached zero can be distinguished as the null-power point. The locations where null-power points occurred were at \(-\)35 mm and 32.5 mm, and it was observed that the value of S21 recovered thereafter. Table 4 summarizes the maximum values of S21 and capacitance at key positions of the Rx along the y-axis. As noted in previous studies, null-power points tend to occur when the mutual capacitance is close to zero. However, the results presented in this study indicate that the value of S21, which had decreased in regions where the mutual capacitance was less than 0.1, also showed signs of recovery.  
As discussed in a previous study [29], this phenomenon occurs when the mutual capacitance C\({}_{\text{M}}\) formed between the transmitter and receiver converges to zero. The C\({}_{\text{M}}\) is determined by the interaction between the main coupling capacitances C\({}_{\text{23}}\) and C\({}_{\text{14}}\) and the cross-coupling capacitances. This relationship can be expressed as shown in Equation (7). The cross-coupling capacitances correspond to C\({}_{\text{13}}\) and C\({}_{\text{24}}\) in Equation (1).  
Figure 6: Comparison of transmission coefficient by impedance matching.  
In other words, when the product of the main coupling capacitances \(\rm C_{mc}\) and the product of the cross-coupling capacitances \(\rm C_{cc}\) become equal, the mutual capacitance \(\rm C_{M}\) converges to zero. Based on this principle, it can also be observed that the null-power points in Figure 8 occurred when \(\rm C_{M}\) approached zero.  
\[\rm C_{24}\cdot C_{13}=C_{14}\cdot C_{23}\leftrightarrow C_{mc}=C_{cc} \tag{7}\]