Force-sensing capacitor explained

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,

C , equals \varepsilon A /d , where \varepsilon is permeability, A is the area of the sensor and 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 F , is x = F/k , where k is the spring constant. Combining these equations gives the capacitance after an applied force as:C = \varepsilon A /(d _{nominal} - F/k) , where d _{nominal} is the separation between parallel plates when no force is applied.

This can be rearranged to:

C = (\varepsilon Ad _{nominal} + \varepsilon AF/k)/(d ^{2- F} _{nominal} ^{2/k} ^{2)}

Assuming that

d ^{2} _{nominal} >> F ^{2/k} ^{2} , which is true for small deformations where d _{nominal} >> x , we can simplify this to:

C

\simeq(\varepsilon Ad _{nominal} + \varepsilon AF/k)/(d ^{2 )} _{nominal}

It follows that:

C

\simeq C _{nominal} + \varepsilon AF/kd ^{2} _{nominal}

C

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

We can express the change in capacitance

\Delta C as:\Delta C = BF

Production

SingleTact makes force-sensitive capacitors using moulded silicon between two layers of polyimide to construct a 0.35mm thick sensor, with force ranges from 1N to 450N.^[3] The 8mm SingleTact has a nominal capacitance of 75pF, which increases by 2.2pF when the rated force is applied. It can be mounted on many surfaces for direct force measurement.

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]

Notes and 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. 10.1097/01.blo.0000218730.59838.6a. 16672899. 28558376. 0009-921X.
2. Book: Principles of measurement systems. Bentley, John P.. 1995. Longman Scientific & Technical. 0470234458. 3rd. Harlow [England]. 30781109.
3. Web site: SingleTact Datasheet. SingleTact.
4. US. US10961981. High resolution solid state pressure sensor. Grant. 2015-07-14. Pakrs. Thomas. Sierra Scientific Instruments Inc.
5. News: Using Capacitive Force Sensors in Next-Gen Medical Products. 2016-03-01. Medical Design Technology. 2018-06-21. en.
6. Egorov. V.. Sarvazyan. A.P.. 2008-09-01. Mechanical Imaging of the Breast. IEEE Transactions on Medical Imaging. en-US. 27. 9. 1275–1287. 10.1109/tmi.2008.922192. 0278-0062. 2581459. 18753043.
7. Web site: SureTouch. SureTouch. en-US. 2018-06-21.
8. Web site: Artann Labs. www.artannlabs.com. en-US. 2018-06-21.