Measuring Capacitive Pressure Sensor with an MFIA Impedance Analyzer

March 11, 2024 by Meng Li

In our previous blog post, we have shown how to use an MFIA Impedance Analyzer to measure and model the impedance of a piezoelectric material. An interesting finding is that the measured impedance as well as the derived capacitance varies based on a sample's direction. For instance, when the sample stands vertically without facing gravity on the main axis, we observe a very different impedance response. In other words, the impedance is a function of the applied stress, and this effect can be used to sense the pressure. We shall explore more in this blog post, and discuss how to measure and understand the effect properly.

setup capacitive pressure sensor

Figure 1. Sketch showing a 2-terminal impedance measurement setup of our capacitive pressure sensor. Note that the dielectric diaphragm in the middle (highlighted in orange stripes) can attach to a 3rd electrode as a reference, but is not used in our blog post. Other capacitive sensors might also have a different design.

We connect a capacitive pressure sensor in a 2-terminal configuration to an MFIA Impedance Analyzer, as illustrated in Figure 1, and then measure its impedance in a wide frequency range from 1 Hz to 5 MHz as shown in Figure 2. We see that the impedance decreases linearly with frequency, and that the derived capacitance using Cp||Rp model stays roughly constant below 100 kHz. Above 100 kHz, the parasitic inductance starts to play a role so that the derived capacitance increases. In the scope of this blog post, we ignore this parasitic effect coming mainly from the long cables in the measurement setup, and focus below 100kHz only. 

It is important to note that the pressure sensor as our device-under-test (DUT) in this blog post is almost purely capacitive, hence different from a piezoelectric scenario mentioned in the previous blog post. In the latter case, there are resonance frequencies where the DUT becomes more sensitive (to the pressure). To make better use of piezoelectric sensors, we must determine their characterization frequencies first. In contrast, capacitance pressure sensors are easier to use and require no knowledge of frequency dependency in advance.

full sweep of impedance

Figure 2. LabOne Sweeper screenshot showing the measured impedance (upper chart) and the derived capacitance (lower chart) of our capacitive pressure sensor between 1 Hz and 5 MHz. Note that the capacitance is constant before reaching 100 kHz.

For completeness, we measure the capacitances at different loading conditions between 1 kHz and 1 MHz, as illustrated in Figure 3. The load is added by placing 2 CHF coins piece by piece on top, each weighing 8.8 g nominally. At the first glance, we see a non-linear effect straightaway. The first 2 CHF coin creates a bigger capacitance change at 390 fF, whereas the third 2 CHF only adds a capacitance as small as 16.8 fF. This capacitance is very small, but we can still resolve it clearly, thanks to the high (sub fF) precision of the MFIA.

fine sweeps

Figure 3. LabOne Sweeper screenshot showing the derived capacitances of the capacitive pressure sensor at different loads. Red: 0 g, orange: 8.8 g, blue: 17.6 g, and green: 26.4g. The load is added by placing 2 CHF coins consecutively on top of the sensor. 

To delve deeper, we calculate the capacitance averaged between 1 kHz and 100 kHz, and plot the result in Figure 4. We observe that the 'absolute' capacitance has a linear trend on the inverse load. This is because the bending of the sensor dielectric diaphragm is proportional to the pressure, yet inversely proportional to the capacitance (considering a parallel-plate capacitor model). This explains the non-linearity in Figure 3. Some capacitive pressure sensors may have a 3rd electrode connected to the diaphragm as a reference, which enables the measurement of the 'relative' differential capacitance. In doing so, it is possible to remove the capacitance background (in our case, the ~20 pF floor) and improve the measurement precision (in our case, the 16.8 fF part). Nonetheless, the relationship between the load and the differential capacitance will become more complicated, which requires extra calibration during manufacturing. 

capacitance versus inverse load

Figure 4. Derived capacitance plotted against inverse load placed on top of our capacitance pressure sensor. A linear fit is also shown in a solid line to highlight the linear relationship between the two.

Conclusion

In this blog post, we have explained the impedance measurement of a capacitive pressure sensor. This type of pressure sensor is easier to use than piezoelectric sensors, yet reveals a non-linear relationship between the measured capacitance and the actual load. Thanks to the high precision of the MFIA Impedance Analyzer, we can still resolve the tiny capacitance change on the sensor without using a differential setup. 

If you are interested, please get in touch with us to set up a demo.