# Instrumental Uncertainty of Conductance Transducers for
## 4 Experimental Results
### Linearity, Reversibility, and Repeatability  
#### 4.2.1 Long-Range Conductance Transducer (\(\pm\)400 mm)  
The conductance transducer with a measurement interval of \(\pm\)400 mm was tested, following the proposed method for the determination of linearity, reversibility, and repeatability, using the off-the-shelf power supply. During the performed tests, the average air temperature was comprised between 25.8 \({}^{\circ}\)C and 26.1 \({}^{\circ}\)C, while the relative humidity varied between 50% and 52%. The water temperature was slightly lower than the air temperature, with a minimum value of 25.3 \({}^{\circ}\)C and a maximum value equal to 25.5 \({}^{\circ}\)C. Figures 13 and 14 show the applied vertical displacement relative to the recorded input and output voltage, respectively, while Figures 15-17 represent the obtained linearity and reversibility deviations and repeatability, respectively, as a function of the output voltage. Figure 16: Reversibility deviations of the \(\pm\)400 mm conductance transducer. Figure 15: Linearity deviations of the \(\pm\)400 mm conductance transducer. Figure 13 shows that the input voltage remained stable during the test, varying between 15.0068 V and 15.0078 V, without showing correlation with the applied vertical displacement (random distribution of the experimental values for all the testing positions). With respect to the output voltage, a linear relation with the applied vertical displacement is observed in Figure 14, for the voltage measurement interval between 0.2 V and 6 V, with no significant differences between test positions. Based on these results, Figure 15 presents the corresponding linearity deviations, which can reach a maximum absolute value close to 6 mm, considering a measurement interval of \(\pm\)400 mm. These deviations show a non-random behavior, indicating that a linear calibration curve is a first approximation to the relation between the output voltage and the applied vertical displacement. In the negative part of the dimensional measurement interval, the dispersion of linearity deviation values is higher when compared to the positive region. This can be justified by reversibility, as shown in Figure 16, where the average absolute value is close to 2 mm, while in the positive region the average reversibility has a maximum value near 1 mm. A detailed observation of Figure 16 shows that reversibility deviations are mainly due to the results of the first performed test (position 0\({}^{\circ}\)), obtained for negative displacements from the half-immersion position to the full-immersion position. This shows the influence of the dry or wet condition of the transducer electrodes in the performed tests, since the first test (position 0\({}^{\circ}\)) is the only one, which starts with the half-length electrodes in a dry condition. In the remaining consecutive tests (positions 60\({}^{\circ}\) and 120\({}^{\circ}\)), the electrodes are already wet in their full-length; therefore, improving the transducer's reversibility. The transducer's repeatability (see Figure 17) is also affected by the reversibility results, having its best value in the positive region (0.05 mm), while in the negative region, the repeatability varies between 0.25 and 0.55 mm, reflecting the measurement uncertainty source related to the wet or dry condition of the electrodes during the tests. Table 1 mentions, for each tested position and for the average results, the calculated linear parameters estimates, and standard uncertainties of the calibration curve between the output voltage and the applied displacement, obtained by the application of the Least Squares Method. Figure 17: Repeatability of the \(\pm\)400 mm conductance transducer. The results presented in Table 1 show minor differences between both the estimates and standard uncertainties of the linear parameters, for all the tested positions, noticing slightly higher uncertainties in the test position 0\({}^{\circ}\), for the same reasons discussed before in this section.