# Filament X-ray Tube Current Control Method Using Indirect Filament Temperature Estimation
## 3 Indirect Filament Temperature Estimation Algorithm
### Proposed Method  
The filament temperature is uncontrolled in the case of the existing filament heating method, which results in higher dose rates than the required value during the analysis of diseases [9]. Therefore, when operating the X-ray equipment, it is necessary to achieve a certain level of closed-loop temperature control to generate the tube current in the magnitude of the image quality [19] required for the analysis. Therefore, the temperature needs to be measured; however, the heated filament is in the vacuum of the tube and is heated at temperatures higher than 1900 K. Considering the location of the filament and the measurement temperature range, a non-contact temperature measurement method is required. However, as the voltage is high (up to 100 kV) and the vacuum tube is surrounded by insulating oil, introducing the sensors may affect the maintenance and the measurement accuracy owing to the change in emissivity. Hence, it is difficult to configure a closed-loop control considering the directly measured temperature value. To solve this problem, the temperature of the tungsten filament was derived as indicated in Equation (11), considering the change in resistivity based on the tungsten filament temperatures listed in Table 1[20]. The temperature of the current filament is indirectly estimated in Equation (11) by substituting the electrical resistivity value calculated in the digital signal processor (DSP) [21]. The temperature proportional-integral (PI) controller was constituted using the estimated filament temperature value. As the filament resistance and thermal property variation based on the temperature exhibit a non-linear relationship with the electrical input and heat generation, the PI gain was tuned considering the overshoot and rise time of the current and voltage.  
\[T=\sqrt{\frac{\rho}{7.8384\times 10^{-15}}+1.5744\times 10^{6}}-1.4788\times 10^{ 3}[\text{K}] \tag{11}\]  
The filament is composed of a tungsten wire in a spiral shape. Although the spiral fabrication generates electrical resistance and inductance components, the inductance at room temperature impedance can be ignored as it accounts for less than 0.001% of the resistance. Therefore, to indirectly estimate the temperature of the tungsten filament using Equation (11), the temperature-based changes in length and cross-sectional area of the filament were disregarded. The error between the estimated temperature and the command temperature is controlled through the PI temperature controller, and the input current required to maintain the temperature is controlled by changing the current command for each error. Therefore, it is converted into a pulse width modulation (PWM) signal through the voltage command of the inverter through the PI current controller to control the filament temperature.  
Figure 4: Conventional filament driver circuit and the control diagram.  
Figure 5 depicts the procedure for achieving an indirect temperature estimation of the filament, which can be summarized as follows:  
1. The voltage is measured at both ends of the filament;
2. The primary current of the transformer is measured for insulation;
3. The measured voltage is divided by the current to calculate the resistance of the tungsten filament. If the heating current is 0 A, the resistance cannot be calculated. Therefore, the calculation must be performed considering the resistance value obtained when the current exceeds a certain value. The heating current at this point represents the maximum heating current value on the filament datasheet, and the flowing current is limited through software;
4. The calculated resistance is converted into resistivity based on the length and cross-sectional area of the filament;
5. The temperature of the filament is estimated using the resistivity, as indicated in Equation (11).