## 2 Analysis of a New Active Quench Detection Method for High-Temperature Superconducting Magnets
### Simulation Results  
Figure 4 shows the equivalent circuit for the simulation of the proposed quench detection method.  
Figure 3: Equivalent circuit to explain the quench detection method.  
Figure 2: Equivalent circuit of the proposed quench detection method.  
Electromagnetic force (EMF) and noise signals were applied to the input source of the rotor coil where the EMF signal is the alternating field component generated by the interaction between the rotor and stator coil. The resonance frequency of the circuit was tuned to the EMF signal frequency. A noise signal is an unpredictable noise component in an industrial environment or measurement system. The quench was assumed to occur after 60 s based on the voltage signal measured at \(R_{ext}\). The quench was generated by heating of the nichrome wire of the heater trigger. The stator coils tested in the simulation were ins and not-insulated (NI) coils, respectively.  
Table 1 shows the specifications of the simulation parameters and Figure 5 shows results of the FFT analysis of the voltage signal measured at \(R_{ext}\) using the INS coil. As shown in Figure 5, although the amplitude of the EMF and the noise signal are the same value at the input source, the amplitude of these signals measured in \(R_{ext}\) are not the same after performing the FFT analysis. This is because the resonant frequency of the circuit is tuned to the frequency of the EMF signal, so the maximum value of the transfer function curve appears at the resonant frequency of the circuit (Figure 6).  
Figure 4: Equivalent circuit of the simulation for verification of the proposed quench detection method.  
Therefore, the amplitude of all other components decreases, except the signal corresponding to the resonance frequency [16; 17]. However, unlike the result for the INS coil, the noise signal is not filtered using the NI coil, as shown in Figure 7. Therefore, as can be seen in Figure 8, to confirm the reason why the noise signal was not filtered, an equivalent circuit analysis was performed. Figure 9 shows the equivalent circuit using the INS and NI coil. As shown in Figure 9, when the stator coil is NI, there is \(R_{R}\), which is the contact resistance between turns of the coil. Moreover, the amplitude of \(R_{R}\) is several m\(\Omega\), so that the combined resistance is decreased compared with that of the INS coil. The band-width of the transfer function is inversely proportional to the amplitude of the resistance, therefore, the noise signal was not filtered when the NI coil was used as the stator coil.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Parameters** & **Values** \\ \hline \multirow{3}{*}{V\({}_{\text{AC}}\)} & EMF & Peak [V\({}_{\text{peak}}\)] & 0.5 \\  & & Frequency [Hz] & 45.42 \\ \cline{2-3}  & Noise & Peak [V\({}_{\text{peak}}\)] & 0.5 \\  & Frequency [Hz] & 20 \\ \hline \multirow{3}{*}{V\({}_{\text{AC}}\)} & R\({}_{\text{div}}\) [k\(\Omega\)] & 1 \\  & R\({}_{\text{R}}\) [m\(\Omega\)] & 0.4 \\ \cline{1-1}  & R\({}_{\text{ext}}\) [\(\Omega\)] & 5 \\ \cline{1-1}  & Id\({}_{\text{C}}\) [A] & 70 \\ \cline{1-1}  & R\({}_{\text{0}}\) [m\(\Omega\)] & 10 \\ \cline{1-1}  & L\({}_{\text{B}}\) [mH] & 11.4 \\ \cline{1-1}  & L\({}_{\text{INS}}\) [mH] & 0.123 \\ \cline{1-1}  & L\({}_{\text{NI}}\) [mH] & 0.125 \\ \cline{1-1}  & Mutual inductance & 0.04 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specifications of the simulation parameters and values.  
Figure 5: FFT analysis results using the insulated (INS) coil.  
Figure 6: Transfer function shape of the resonant circuit using the INS coil.