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:


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

This can be rearranged to:


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

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

It follows that:


 * C $$ \simeq C_{nominal} + \varepsilon AF/kd_{nominal}^2 $$
 * 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. 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 and to image breast  and prostate cancer.