## 3 Measurements and Results
### Sensor  
(1) The rising phase affected from signal reading drift of sensor:  
After turning on the sensing device, the ambient temperature around sensor will increase due to the light source heating and affected by the changes of room temperature. The increment of the ambient temperature will result in the increment of the outward radiation of sensor. Assume that the input radiation is constant; the net radiation of sensor will decrease, which means the circuit will feedback control the light source to increase the heating duty (Ratio \(\uparrow\)) to maintain the sensor and receive the average amount of thermal radiation.  
(2) The falling phase effected from signal reading drift of sensor:  
As the measuring time increases, the ambient temperature of sensor will gradually balance with the room temperature, which means the changes of the outward radiation of sensor will slow down. The net radiation of sensor will gradually insensitive to its temperature changes. Therefore, the drifting thermal radiation of the infrared light source will be the main reason for the decrease of Ratio in this phase.  
In order to analyze the changes of the operating temperature of the infrared light source caused by different heating duty, we keep the CO\({}_{2}\) concentration at 500-600 ppm and set several \(V_{th}\) (0.580, 0.680, 0.684, 0.712 V) to observe how the light source effect on the dynamic drift of Ratio.  
Besides, the dynamic drift of Ratio is also due to the temperature changes of sensor. Therefore, a thermistor is installed at the sensor to record the temperature change during the measurement. There is a certain correlation between signal reading and the temperature change before 40 min, as the drift of Ratio region shown in Figures 6 and 7.  
As shown in the Figure 8, the Ratio will change when the \(T_{sensor}\) changes, which allows us to compensate for the dynamic drift of the Ratio through changes of \(T_{sensor}\).  
In this study, we discuss the relationship between the \(T_{sensor}\) and the Ratio in the falling phase; it not only shows a good regular correlation between the \(T_{sensor}\) and the Ratio but also reveals a method of temperature compensation, as shown in Figure 8.  
We analyzed the slope in Figure 8 and figured out the temperature compensation formula as following:  
\[Ratio(new)=Ratio(old)-slope(V_{th},T_{sensor},Ratio)\times(\Delta T_{sensor}) \tag{13}\]  
where _Ratio (new)_ is temperature compensated data, _Ratio (old)_ is temperature uncompensated data, _slope (V\({}_{th}\), \(T\) sensor, Ratio)_ is variable coefficient which will change with different conditions.  
Figures 9 and 10 show two results; one is the time of dynamic drift after temperature compensation is significantly reduced from 40 min to 18 min as the drift of Ratio region after compensation and the other is that the Ratio does not change with different \(T\) sensor, which makes us to achieve the purpose of temperature compensation.  
The evaluation of temperature compensation for our proposed delta-sigma NDIR technique after 20 min is compared and is shown in Table 1. It shows that the temperature dependence of the CO\({}_{2}\) after temperature compensation is reduced from an average of 2.589% to 0.115%, which comes from the effectiveness of temperature compensation we built and it reveals our proposal architecture gives a practical application of NDIR gas concentration measurement.  
Figure 8: Relationship between Ratio and \(T\) sensor without temperature compensation.  
Figure 7: Temperature changes of sensor within 100 min.