Force-sensing capacitor

A force-sensing capacitor is a material whose capacitance changes when a force, pressure or mechanical stress is applied. They are also known as "force-sensitive capacitors". They can provide improved sensitivity and repeatability compared to force-sensitive resistors[1] but traditionally required more complicated electronics.[2]

Operation principle

Typical force sensitive capacitors are examples of parallel plate capacitors. For small deflections, there is a linear relationship between applied force and change in capacitance, which can be shown as follows:

The capacitance, ${\displaystyle C}$, equals ${\displaystyle \varepsilon A/d}$, where ${\displaystyle \varepsilon }$ is permeability, ${\displaystyle A}$ is the area of the sensor and ${\displaystyle d}$ is the distance between parallel plates. If the material is linearly elastic (so follows Hooks Law), then the displacement, due to an applied force ${\displaystyle F}$, is ${\displaystyle x=F/k}$, where ${\displaystyle k}$ is the spring constant. Combining these equations gives the capacitance after an applied force as:

${\displaystyle C=\varepsilon A/(d_{nominal}-F/k)}$, where ${\displaystyle d_{nominal}}$ is the separation between parallel plates when no force is applied.

This can be rearranged to:

${\displaystyle C=(\varepsilon Ad_{nominal}+\varepsilon AF/k)/(d_{nominal}^{2}-F^{2}/k^{2})}$

Assuming that ${\displaystyle d_{nominal}^{2}>>F^{2}/k^{2}}$, which is true for small deformations where ${\displaystyle d_{nominal}>>x}$, we can simplify this to:

C ${\displaystyle \simeq (\varepsilon Ad_{nominal}+\varepsilon AF/k)/(d_{nominal}^{2})}$

It follows that:

C ${\displaystyle \simeq C_{nominal}+\varepsilon AF/kd_{nominal}^{2}}$

C ${\displaystyle \simeq C_{nominal}+BF}$ where ${\displaystyle B=\epsilon A/kd^{2}}$, which is constant for a given sensor.

We can express the change in capacitance ${\displaystyle \Delta C}$ as:

${\displaystyle \Delta C=BF}$

Production

SingleTact makes force-sensitive capacitors using moulded silicon between two layers of polymide to construct a 0.35 mm thick sensor, with force ranges from 1 N to 450 N.[3] The 8mm SingleTact has a nominal capacitance of 75 pF, which increases by 2.2 pF when the rated force is applied.[3]

Uses

Force-sensing capacitors can be used to create low-profile force-sensitive buttons. They have been used in medical imaging to map pressures in the esophagus[4][5]and to image breast[6][7] and prostate cancer.[8]

References

1. Martinelli, L; Hurschler, C; Rosenbaum, D (2006-06-01). "Comparison of Capacitive versus Resistive Joint Contact Stress Sensors". Clinical Orthopaedics and Related Research. 447: 214–220. doi:10.1097/01.blo.0000218730.59838.6a. ISSN 0009-921X. PMID 16672899.
2. 1943-, Bentley, John P. (1995). Principles of measurement systems (3rd ed.). Harlow [England]: Longman Scientific & Technical. ISBN 0470234458. OCLC 30781109.CS1 maint: numeric names: authors list (link)
3. "SingleTact Datasheet" (PDF). SingleTact.
4. US Grant US10961981, Pakrs, Thomas, "High resolution solid state pressure sensor", published 2015-07-14, assigned to Sierra Scientific Instruments Inc
5. "Using Capacitive Force Sensors in Next-Gen Medical Products". Medical Design Technology. 2016-03-01. Retrieved 2018-06-21.
6. Egorov, V.; Sarvazyan, A.P. (2008-09-01). "Mechanical Imaging of the Breast". IEEE Transactions on Medical Imaging. 27 (9): 1275–1287. doi:10.1109/tmi.2008.922192. ISSN 0278-0062. PMC 2581459. PMID 18753043.
7. "SureTouch". SureTouch. Retrieved 2018-06-21.
8. "Artann Labs". www.artannlabs.com. Retrieved 2018-06-21.