# Instrumental Uncertainty of Conductance Transducers for
## 4 Experimental Results
### Linearity, Reversibility, and Repeatability
#### 4.2.2 Short-Range Conductance Transducer (\(\pm 140\) mm)  
The conductance transducer with a measurement interval of \(\pm 140\) 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 \(24.7\,^{\circ}\)C and \(25.1\,^{\circ}\)C, while the relative humidity varied between \(45\%\) and \(47\%\). The water temperature was slightly lower than the air temperature, with a minimum value of \(24.5\,^{\circ}\)C and a maximum value equal to \(24.7\,^{\circ}\)C. Figures 18 and 19 show the applied vertical displacement relative to the recorded input and output voltages, respectively, while Figures 20-22 represent the obtained linearity and reversibility deviations and repeatability, respectively, as a function of the output voltage. Figure 19: Relation between the output voltage of the \(\pm\)140 mm conductance transducer and the applied vertical displacement. Figure 20: Linearity deviations of the \(\pm\)140 mm conductance transducer. Figure 18 shows that the input voltage remained stable during the performed test, varying between 15.0041 and 15.0052 V, with no signs of 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 19, for the voltage measurement interval between 0.5 and 10 V, with no significant differences between test positions. Based on these results, Figure 20 presents the corresponding linearity deviations, showing a cyclical variation between 2 and \(-\)4 mm, considering a measurement interval of \(\pm\)140 mm. In the same way as the case of the long-range transducer (see Figure 15 in Section 4.2.1), this systematic behavior shows that the linear calibration curve is a first approximation to the relation between the output voltage and the applied vertical displacement. The highest linearity deviation was obtained in the 60\({}^{\circ}\) test position, for the extreme positive vertical displacement, which is close to the transducer's operational limit. Figure 21: Reversibility deviations of the \(\pm\)140 mm conductance transducer. Figure 22: Repeatability of the \(\pm\)140 mm conductance transducer. With respect the reversibility results (shown in Figure 21), the same cyclical variation seen in the linearity deviations, is also noticed but with a reduced magnitude, close (in average) to \(\pm\)0.5 mm. The highest reversibility absolute deviations (near 1 mm) were obtained in the first tested position (0\({}^{\circ}\)), confirming the influence of the wet or dry electrodes condition in the obtained results, as seen in the case of the long-range transducer (see Section 4.2.1). The transducer's repeatability (see Figure 22) is also affected by the reversibility results, having its best value in the positive region, below 0.10 mm (ignoring the result obtained for the extreme positive vertical displacement, close to the transducer's operational limit).In the negative region, the repeatability reaches a maximum value of 0.17 mm, reflecting the measurement uncertainty source related to the wet or dry condition of the electrodes during the tests. Table 2 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. The results presented in Table 2 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 60\({}^{\circ}\), which can reflect the effect of some perpendicularity deviation between the transducer's electrodes and the water surface in this position.