Force-sensing capacitor

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 $\backslash varepsilon\; A\; /d$, where $\backslash varepsilon$ 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:

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

This can be rearranged to:

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

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

:C $\backslash simeq(\backslash varepsilon\; Ad\_\{nominal\}\; +\; \backslash varepsilon\; AF/k)/(d\_\{nominal\}^2)$

It follows that:

:C $\backslash simeq\; C\_\{nominal\}\; +\; \backslash varepsilon\; AF/kd\_\{nominal\}^2$

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

We can express the change in capacitance $\backslash Delta\; C$ as:

:$\backslash Delta\; C\; =\; BF$

[http://www.singletact.com SingleTact] makes force-sensitive capacitors using moulded silicon between two layers of polyimide to construct a 0.35{{nbsp}}mm thick sensor, with force ranges from 1{{nbsp}}N to 450{{nbsp}}N.{{Cite web|url=https://www.singletact.com/SingleTact_Datasheet.pdf|title=SingleTact Datasheet|website=SingleTact}} The 8mm SingleTact has a nominal capacitance of 75{{nbsp}}pF, which increases by 2.2{{nbsp}}pF when the rated force is applied. It can be [https://www.singletact.com/how-to-mount-a-flexible-force-sensor/ mounted on many surfaces] for direct force measurement.

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{{cite patent|country=US|number=US10961981|title=High resolution solid state pressure sensor|status=Grant|pubdate=2015-07-14|gdate=|invent1=Pakrs|inventor1-first=Thomas|assign1=Sierra Scientific Instruments Inc}}{{Cite news|url=https://www.mdtmag.com/article/2016/03/using-capacitive-force-sensors-next-gen-medical-products|title=Using Capacitive Force Sensors in Next-Gen Medical Products|date=2016-03-01|work=Medical Design Technology|access-date=2018-06-21|language=en}} and to image breast{{Cite journal|last1=Egorov|first1=V.|last2=Sarvazyan|first2=A.P.|date=2008-09-01|title=Mechanical Imaging of the Breast|journal=IEEE Transactions on Medical Imaging|language=en-US|volume=27|issue=9|pages=1275–1287|doi=10.1109/tmi.2008.922192|issn=0278-0062|pmc=2581459|pmid=18753043}}{{Cite web|url=http://suretouch.us/|title=SureTouch|website=SureTouch|language=en-US|access-date=2018-06-21}} and prostate cancer.{{Cite web|url=http://www.artannlabs.com/|title=Artann Labs|website=www.artannlabs.com|language=en-US|access-date=2018-06-21}}

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Category:Capacitors

Category:Sensors