Engineering:Force-sensing capacitor

Short description: Material whose capacitance changes when a force is applied

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

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

This can be rearranged to:

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

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

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

It follows that:

C [math]\displaystyle{ \simeq C_{nominal} + \varepsilon AF/kd_{nominal}^2 }[/math]

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

We can express the change in capacitance [math]\displaystyle{ \Delta C }[/math] as:

[math]\displaystyle{ \Delta C = BF }[/math]

Production

SingleTact makes force-sensitive capacitors using moulded silicon between two layers of polyimide to construct a 0.35 mm thick sensor, with force ranges from 1 N to 450 N. The 8mm SingleTact has a nominal capacitance of 75 pF, which increases by 2.2 pF 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 and to image breast and prostate cancer.