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 but traditionally required more complicated electronics.

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:

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

This can be rearranged to:

:$C = (\varepsilon Ad_ + \varepsilon AF/k)/(d_^2-F^2/k^2)$

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

:C $\simeq(\varepsilon Ad_ + \varepsilon AF/k)/(d_^2)$

It follows that:

:C $\simeq C_ + \varepsilon AF/kd_^2$
:C $\simeq C_ + BF$ 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. The 8mm SingleTact has a nominal capacitance of 75pF, which increases by 2.2pF when the rated force is applied. It can b
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 and to image breast and prostate cancer.

References

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Capacitors
Sensors