# Filament X-ray Tube Current Control Method Using Indirect Filament Temperature Estimation
## 4 Experiments  
To validate the effectiveness of the proposed filament temperature control method, we performed a comparison experiment using the setup depicted in Figure 6. As the proposed temperature estimation algorithm requires highly accurate measurements of the voltage and current authorized to the filament from the filament heating circuit (Figure 5), verification experiments were conducted at the measurement points. Figures 7 and 8 illustrate the waveforms obtained from the verification experiment of the measurement points of the voltage and current authorized to the filament, respectively. Figure 7 depicts the primary and secondary voltages and the root-mean-square (RMS) conversion results of the 1:1 transformer depicted in Figures 4 and 5. Herein, an additional 3.5 V voltage drop was observed between the primary and secondary windings of the transformer, which represents the measurement point of the voltage authorized to the filament. This implies that the primary winding of the insulating transformer is inaccurate. Figure 8 illustrates the results of the current measurements on the primary and secondary windings of a 1:1 insulating transformer. The blue and green waveforms denote the currents on the primary and secondary windings, respectively. As the RMS values of the primary and secondary winding currents coincide at 98%, the results verify that the filament heating current can be measured on both the primary and secondary windings. Therefore, based on the values measured on the secondary winding, we determined that the voltage must be authorized to operate the proposed algorithm. Moreover, the current value measured  
Figure 5: Filament driver circuit and control algorithm of the proposed method. at the primary winding is used for the operation of the proposed temperature estimation algorithm, similar to the conventional current control method. Figure 6: Experimental setup for comparison of the conventional current control with the proposed temperature control. Figure 7: Primary winding and secondary winding voltage results of the filament in the insulating transformer. (Note: \(V_{p}:1\)st wind voltage, \(V_{s}:2\)nd wind voltage, \(V_{prms}:1\)st wind voltage rms value, \(V_{srms}:2\)nd wind voltage rms value). To estimate the temperature using the measured heating voltage and current values and to verify the accuracy, stability, and repeatability of the controller, experiments were repeated 10 times for a total of 5 reference temperatures from 1700 to 2100 K with a difference of 100 K. Figure 9 shows the results of five waveforms of a reference temperature, estimated temperature and temperature error at each reference. Table 2 shows the results of displaying the maximum and minimum temperature error value, reference temperature, average temperature, and average error to show the accuracy of temperature control for each reference. Figure 8: Primary winding and secondary winding current results of the filament in the insulating transformer. (Note: \(I_{p}:1\)st wind current, \(I_{s}:2\)nd wind current). Figure 9: _Cont._  
As a result of temperature control, the overall average error was 3.1 K, and the repeatability and stability were verified. Furthermore, we performed an experiment to verify whether the magnitude of the tube current and estimated temperature value in the X-ray tube change over time using the aforementioned heating method. The results were compared with those obtained from the control-based conventional heating method. This experiment used an anode voltage of 15 kV, wherein few X-rays were generated. The  
Figure 9: Reference temperature, estimated temperature, and temperature error waveforms for temperature references of **(a)** 1700 K, **(b)** 1800 K, **(c)** 1900 K, **(d)** 2000 K and **(e)** 2100 K.  
**Author Contributions:** Conceptualization, H.-L.Z. and J.-J.J.; methodology, H.-L.Z. ; software, H.-L.Z. and J.-J.J.; validation, H.-L.Z. and J.-J.J.; formal analysis, J.-J.J.; investigation, H.-L.Z. and J.-J.J.; re-sources, H.-S.M.