## 3 Modular Modeling for BTM System
### Modeling of Sensitive Equipment Module
#### 3.3.2 T for BTM System with F1 or F3  
The relationship between Signal Noise Ratio (SNR) and Bit Error Rate (BER) of BTM signal \(S_{u}\) could be calculated by Equation (15). According to European standard SUBSET 036, the BER of BTM system should be below \(10^{-6}\) when BTM system carries out F1 [7] and F3 function. Thus, the SNR of output signal \(S_{u}\) should be larger than 13.5 dB according to BER of BTM system of Figure 15. That means, in function F1 and F3, the BTM should receive correct data when the SNR of \(S_{u}\) is larger than 13.5 dB. And if the SNR of \(S_{u}\) is lower than 13.5 dB, the BTM will fail to start or report erroneously localization of a balise even balise missing. Thus, the critical condition \(T\) could be set at SNR = 13.5 dB.  
Figure 14: Magnitude-frequency characteristic of filter amplifier circuit.  
Significantly, the useful signal levels are different in these two functions, as shown in Figure 16, thus the sensitive disturbance levels should be calculated separately.  
For a certain type of BTM system, the maximum electrical level of the test data received by BTM is 57.76 dB\(\mu\)V at 4.512 MHz and 56.43 dB\(\mu\)V at 3.95 MHz during \"on-line transmission self-test\" processing, shown in Figure 16a. It is the useful signal level in the self-test function. For \"Data Reception Function\", the maximum signal level received by BTM is 77.76 dB\(\mu\)V, shown in Figure 16b.  
To validate sensitive equipment module, field tests are carried out, shown in Figure 17. The differential-mode disturbance at the input of BTM is tested by the spectrum analyzer when the train stops and runs. For this train, the exhaust system locates near the on-board antenna of BTM. It may produce disturbance. In the test, when the train is running normally, BTM system could normally operate. If the train is going to run and the exhaust system power on initially, BTM system cannot start and the train cannot run either. However, if shutting down the exhaust system and making the BTM system start first, the train could start to work successfully. The disturbance at the input of BTM is shown in Figure 18. When the exhaust system works, the disturbance level is 58.59 dB\(\mu\)V at 3.95 MHz and 47.19 dB\(\mu\)V at 4.512 MHz. If the exhaust system is powered off, the disturbance level is around 40 dB\(\mu\)V at both 3.95 MHz and 4.512 MHz for this field test.  
Figure 16: The signal received by on-board antenna: (**a**) The electrical level of self-test data; (**b**) The electrical level of balise message.  
Figure 15: Relationship between SNR and BER of BTM signal.  
Based on the BTM signal level in Figure 16 and the disturbance level in Figure 18, the phenomenon could be explained by the modeling of sensitive equipment module.  
When the exhaust system starts before the BTM system, the SNR is \(-2.16\) dB at 3.95 MHz and 10.57 dB at 4.512 MHz. They all smaller than the critical condition \(T\) (SNR = 13.5 dB). Thus, the on-line transmission self-test fails and BTM system will not start. As a result, the train cannot operate either.  
When BTM system starts first without exhaust system, the noise is low, and the smallest SNR is 16.43 dB at 3.95 MHz (the disturbance source level is 40 dB\(\mu\)V when exhaust system is powered off). Comparing to the critical condition \(T\), the BTM system will pass on-line transmission self-test and start normally. During Data Reception function, the BTM useful signal is much higher than the noise. When the exhaust system started, the smallest SNR is 19.17 dB which is still larger than 13.5 dB. Therefore, the train could continue to operate normally.  
Therefore, the model analysis could predict the EMS of BTM system well.