## 3 DT Model of the Electromagnetic Coupling Process of the BTS
### Equivalent Model of Passive Balise Transmitting Current  
Depending on the balise energy source, the \(i_{1}\) in (13) changes accordingly. The LEU provides the current on the active balise transmitting antenna, so the current intensity can be kept constant during communication. However, the passive balise uses the received tele-powering signal as the energy source, and the magnitude of the transmitted current is affected by the received magnetic flux, which changes with the longitudinal displacement between antennas. In order to accurately describe the change of the uplink signal transmitting current intensity of the passive balise with the magnetic flux intensity of the received downlink RF power signal, the input-output characteristics of the passive balise need to be modeled. Directly building such a model is a difficult task for balise, whose internal conversion circuits contain nonlinear devices. Fortunately, the SUBSET-085 test specification proposes a black-box test method for balise input-output characteristics. According to the balise input-output characteristic curve, the equivalent current model of the balise can be obtained by curve fitting. When the train passes through the passive balise, the current on the balise transmitting antenna is determined by the magnetic flux \(\phi_{\rm d}\) passing through the balise receiving antenna and the input-output characteristics of the balise:  
\[\phi_{\rm d}=M_{\rm d}i_{\rm d}. \tag{14}\]  
\(M_{\rm d}\) is the mutual inductance between the onboard tele-powering transmitting antenna and the balise receiving antenna, which can be calculated by referring to (1). The excitation current \(i_{\rm d}\) is an adjustable constant provided by the BTM. The balise input-output characteristic is determined by its internal conversion circuit and needs to meet the requirements of the SUBSET-036 functional interface specification [1], as shown in Figure 6.  
The abscissa represents the magnetic flux of the tele-powering signal received by the balise. The ordinate represents the current on the balise transmitting antenna, which comes from the received magnetic flux processed by the internal conversion circuits. The relevant parameter requirements of the reduced size balise in SUBSET-036 specification are shown in Table 1.  
Figure 6: Balise input-output characteristics. We can fit the curve in Figure 6 with a univariate nonlinear regression model:  
\[i_{\phi}=a_{\phi}+b_{\phi}\phi_{\mathrm{d}}+\frac{c_{\phi}}{{\phi_{\mathrm{d}}}^{ 2}}+\frac{d_{\phi}}{{\phi_{\mathrm{d}}}^{6}}, \tag{15}\]  
In (15), \(a_{\phi}\), \(b_{\phi}\), \(c_{\phi}\), and \(d_{\phi}\) are all constants, \(\phi_{\mathrm{d}}\) represents the magnetic flux, and \(i_{\phi}\) represents the current on the balise transmitting antenna. According to Figure 6, the balise uplink current is positively correlated with the magnetic flux passing through the balise receiving antenna, but it is a nonlinear relationship. An accurate balise input-output characteristic curve is the basis for establishing the uplink current model of the passive balise. Fortunately, a method to measure this input-output characteristic curve of balise has been proposed in [2]. Furthermore, this test is also a necessary part of the functional test of the balise. Therefore, a simplified method is to attain the balise input-output characteristic curve through testing and use (15) to fit the curve, omitting the modeling of the complex conversion circuits inside the balise. According to the requirements of the balise input-output characteristic test in the test specification, a certain type of passive balise was tested. The connection block diagram of the test equipment and the test layout are shown in Figures 7 and 8, respectively. The test program and procedures were consistent with the requirements in the specification. It is worth noting that in this test, the vertical distance between the test antenna and the balise was 220 mm.