*4.4. Curvature Test*

The sensitivity to curvature of the capacitive sensors is shown in Figure 13 for a variety of pressures. The curvature clearly influences the sensor capacitance when subject to pressure. The sensitivity of the sensor was found to be 0.0812 pF/mmHg and 0.106 pF/mmHg for radii of curvature of 19.9 mm and 39.9 mm, respectively. From the bladder test, the sensitivity on a flat surface (infinite radius) is 0.100 pF/mmHg. As shown in this figure, the sensor sensitivity decreases as the radius of the curvature decreases, i.e., the sensor is more curved. This sensitivity to curvature may potentially impose limitations in the sensor calibration when mounted on a flexible object of variable curvature, such as a calf muscle. This can be mitigated if the sensor is securely placed against a rigid plate of fixed curvature attached to the user. The sensors may then be calibrated where the plate closely fits a person's local body shape during in-situ measurements. Of course, a rigid plate changes the pressure loading experienced by the compression user.

**Figure 13.** Pressure vs sensor capacitance for various radii of curvature.

#### *4.5. Thermal and Humidity E*ff*ects*

As shown in Section 4.2, an o ffset of up to 2 pF was observed between several test runs, which relates to a 20 mmHg variation across the pressure range for these tests. This is a significant source of error, particularly for the smaller pressure values. It is reasoned that the mechanical setup of the fixture should be tolerant to changes in orientation due to the conformity of the air bladders employed in the bladder test. To further examine the source of this o ffset value shown in Figure 10, the e ffect of temperature and humidity is studied.

In initial testing in the mass test setup, the temperature of the sensor was allowed to settle at a temperature of 29 ◦C and the test was performed. The temperature was then dropped to 26 ◦C and the mass test was repeated twice over an approximately two-hour period. As shown in Figure 14, there is a notable o ffset with the change in temperature. Like the bladder test results shown in Figure 10, the sensitivity of the sensor is the same despite the o ffset. This o ffset is termed the no-load o ffset.

**Figure 14.** Capacitance vs applied pressure for various temperatures.

Further tests were performed to characterize the offset by measuring the capacitance under the no-load condition while varying temperature and humidity. The sensor was placed on a Peltier module, which acts as a hot/cold plate in order to control the sensor temperature. The capacitance was then measured at several ambient humidity and temperature values, as shown in Figure 15. Using the experimental results shown in this figure, the sensor's temperature sensitivity, or thermal coefficient, was found to be approximately −0.38 pF/◦C, and the humidity sensitivity was measured to be −0.345 pF/%RH. This relates to approximate pressure errors of 4 mmHg/◦C and 4 mmHg/%RH. These tests indicate that both the temperature and humidity have noticeable effects on the sensor's output. Thus, the variances in the bladder test results are likely attributed to the differences in the temperature and humidity conditions during these tests. It was noted, however, that the ambient conditions were not recorded prior to bladder testing.

**Figure 15.** No load capacitance versus temperature and humidity.

The mathematical proof shown below explains the reason behind the offset created by temperature. It should be noted that it may be assumed that the permittivity remains fairly constant for the given temperature range. This is ultimately the reason for the sensitivity (slope of the pressure-capacitance plot) remaining unchanged for various temperatures. Therefore, assuming ε*r* remains constant, any change in temperature, *T*, results in changes of thickness, length and width of the dielectric layer as shown below:

$$\mathbb{C}\_{T\_0} = \varepsilon\_r \varepsilon\_0 \frac{lw}{d} \to \mathbb{C}\_T = \varepsilon\_r \varepsilon\_0 \frac{l(1 + a\Delta T)w(1 + a\Delta T)}{d(1 + a\Delta T)} = \varepsilon\_r \varepsilon\_0 \frac{lw(1 + a\Delta T)}{d} = \mathbb{C}\_{T\_0}(1 + a\Delta T) \tag{2}$$

$$C\_T = C\_{T\_0} + C\_{T\_0} \alpha \Delta T \tag{3}$$

Here, *CT* is the capacitance for temperature T, and *CT*0 denotes the capacitance for temperature *T*0. The above equation shows that a given temperature change, Δ*T*, results in a constant offset *CT*0<sup>α</sup>Δ*<sup>T</sup>* compared to its reference value at *T*0. Therefore, with permittivity constant, the pressure-capacitance relation has the same slope for all temperature values, and the temperature change only causes a capacitance offset. It should also be noted that the DEAP material has a negative coefficient of thermal expansion which results in a negative offset upon an increase of temperature as shown in Figure 15.

#### *4.6. Pneumatic-Based Sensor Comparison*

The results of the pneumatic sensor comparison tests are plotted in Figure 16. The linear sensitivity value obtained during the bladder test was used to calibrate the StretchSense sensor, since those test conditions were most-similar to the cylindrical test bed setup. The results show that the PicoPress exhibits an average error of +/− 6.38 mmHg. Meanwhile, the StretchSense sensor exhibits an average error of +/− 8.03mmHg. The error is calculated by averaging the sum of the sensor calibration error and twice the standard deviation for each pressure value. As described in earlier sections, these errors include the influence of hysteresis, measurement noise, curvature and biases in calibration. Decreasing the capacitive sensor footprint can help to reduce curvature sensitivity.

**Figure 16.** Experimental comparisons of StretchSense and PicoPress sensors.

From the tests performed, recorded sensor sensitivities and errors have been grouped in Table 2 for reference. The sensitivity and error are both seen to vary depending on the testing method implemented. The piston test reported the lowest sensitivity, and the pneumatic sensor comparison test returned the largest error observation. As a result, to perform a conservative characterization of similar sensors in the future, the piston and pneumatic sensor comparison tests should be used to determine sensor sensitivity and error, respectively.


**Table 2.** Sensor sensitivity and error values for each test.
