## 4 Experimental and Simulation Results and Discussion  
In this section, we compare and analyze the VNA measurement results, HFSS simulation results, and PEC analysis results of the underwater stacked CPT coupler. Figure 8 shows the \(S_{21}\) parameters obtained using three methods when the distance \(d\) between the transmitter and receiver is 20 mm. As mentioned before, all the circuit components used in the PEC analysis are measured values of passive components and coupler configurations in an RLC meter, so they reflect the non-ideal characteristics of the components. Nevertheless, the HFSS electromagnetic simulation results show very similar trends to the PEC analysis results, which indicate that the simulation was properly performed. However, the actual measurement results using the VNA show relatively low resonant frequency and \(S_{21}\), which are different from the other two analysis results. The reason  
Figure 8: Transmission coefficient of underwater stacked CPT coupler (at d = 20 mm). Figure 7: The electric field attenuation of various types of water from 0 to 300 mm. why the VNA actual measurement results are different from the other two analysis results is because of the additional parasitic resistance and parasitic capacitance that occurred during the fabrication of the underwater stacked CPT coupler. Parasitic resistance and parasitic capacitance can occur during the soldering process of the components of the LCL-matching circuit and the SMA connector. Therefore, the simulation for the characteristic analysis of the underwater stacked CPT coupler is to be replaced by PEC analysis. The PEC analysis results include the non-ideal characteristics of the real coupler structure in the RLC meter measurement and are also reliable because they are almost identical to the HFSS electromagnetic simulation results. Figure 9 shows the change in coupler equivalent components when the distance \(d\) between the transmitter and receiver is swept from 10 mm to 200 mm. Since the transmitter and receiver have the same specifications, the sizes of \(C_{1}\) and \(C_{2}\) are the same. When the distance between the transmitter and receiver is 10 mm, \(C_{1}\) and \(C_{2}\) have a low value of about 5.8 pF, but sharply increased to about 10 pF until 50 mm. After 50 mm, it shows a gradual decrease to 200 mm. In the case of \(C_{m}\), however, it has the highest value of about 6.4 pF at 10 mm, but exponentially decreases to about 0.2 pF until 100 mm. After 100 mm, \(C_{m}\) is close to 0, and the coupling between the transmitter and receiver almost disappeared. \(R_{w}\) is the parameter that was most sensitive to water shaking during the measurement process of the RLC meter. Unlike the capacitance component of the coupler, it shows relatively unstable variation. \(R_{w}\) has a maximum value of 14 ohm at 20 mm, and gradually decreases to about 10 ohm as the distance between the transmitter and receiver increases. These variations in coupler equivalent components indicate why stacked CPT couplers have difficulty operating underwater. \(R_{w}\) in the air with the same configuration is about 0.1 ohm, which is low enough to ignored, but the \(R_{w}\) of the stacked CPT coupler operating underwater has a high resistance of about 11 ohm or more, which is less than 50 mm where the transmitter and receiver have relatively high coupling coefficients. Most of the \(C_{1}\) and \(C_{2}\) components are self-capacitance components, and the resistance of about 10 ohm connected in series with \(C_{1}\) and \(C_{2}\) is fatal to the performance degradation of the stacked CPT system underwater. Despite the optimal matching, the reason why the stacked CPT has a low \(S_{21}\) parameter of about 0.7 at 20 mm is largely due to the influence of the \(R_{w}\) component. In addition, the \(C_{m}\) of the stacked CPT operating in water can enhance the main coupling capacitance due to the high permittivity but can also enhance the cross-coupling capacitance.