## 1 Introduction
Third, investigations into transmission network matching [17; 18; 19; 20] seek to optimize impedance matching between various components of the transmission network, thereby reducing signal reflections and maximizing power transfer. Reference [21] presented a low-complexity analytical model for mutual inductance between coupling coils in wireless power transfer systems. The model utilized fundamental data, obtained through three-dimensional electromagnetic numerical simulations, and used a multi-objective genetic programming algorithm for optimization. This approach ensured an optimal balance between accuracy and complexity, enabling the swift and precise evaluation of coil mutual inductance under various misalignment conditions. However, the relative positions of the transmitting and receiving coils in the transmission process of the BTS are variable. The mutual inductance of the coils under driving conditions was numerically simulated, and the compensation network was optimized through the objective function of the resonant circuit [22]. In [23], the effectiveness of voltage-based  
Figure 1: Energy and data transmission of BTS. calculations in determining the equivalent mutual inductance of multiple coils aligned along the same axis was demonstrated. At a frequency of 13.56 MHz, the method produced simulation values that closely correspond to measured values. The study's experimental approach involved measuring the actual mutual inductance between coils at various distances. The results of these measurements corroborated the consistency between simulated and measured outcomes, validating the reliability of the voltage calculation method. The electromagnetic coupling process of the BTS under free space conditions has been extensively discussed and analyzed in the literature mentioned above; however, its behavior in complex application environments remains largely unexplored. While the wireless power transmission system shares some similarities with the BTS, research findings from the former are not directly applicable to the latter. This disparity arises primarily from the fact that wireless power transmission systems, predominantly used for device power supply, employ relatively stationary transmitting and receiving antennas, with transmission frequencies typically ranging from a few kHz to several hundred kHz. The frequency range differs significantly from the operating frequency of balises. Moreover, in lossy media, transmission losses far exceed those of wireless power supply systems. Additionally, when a train passes a balise, the relative position varies with the train's location, unlike that of wireless power supply systems. The transmission characteristics in water debris are one influential factor. It is difficult to accurately estimate the effect of the medium on the transmission characteristics when the balise is immersed in water. Consequently, it is necessary to establish a circuit model to analyze the transmission characteristics of the BTS. In response to the application of the BTS for underwater debris, this paper proposes a modeling method for the BTS using S-parameters. Utilizing the electromagnetic analysis and two-port network analysis, we can derive an equivalent circuit of the BTS with the frequency and conductivity of water debris taken into consideration. In this paper, measurements, simulations, and theoretical calculations have been implemented using the proposed equivalent circuit for a variety of positions between the OAU and the balise. Additionally, we analyze the power differential of the balise uplink signal in water debris environments compared to free space conditions. The remaining sections of this paper are organized as follows: In Section 2, an electrical model for the BTS in free space is established. Section 3 analyzes the magnetic field strength and transmission impedance for underwater debris. Section 4 presents the validation of the proposed electrical model through instruments and analyzes the transmission parameter characteristics that are actually measured.