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 {\displaystyle C}, equals ε A / d {\displaystyle \varepsilon A/d}, where ε {\displaystyle \varepsilon } is permeability, A {\displaystyle A} is the area of the sensor and d {\displaystyle 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 {\displaystyle F}, is x = F / k {\displaystyle x=F/k}, where k {\displaystyle k} is the spring constant. Combining these equations gives the capacitance after an applied force as:

C = ε A / ( d n o m i n a l − F / k ) {\displaystyle C=\varepsilon A/(d_{nominal}-F/k)}, where d n o m i n a l {\displaystyle d_{nominal}} is the separation between parallel plates when no force is applied.

This can be rearranged to:

C = ( ε A d n o m i n a l + ε A F / k ) / ( d n o m i n a l 2 − F 2 / k 2 ) {\displaystyle C=(\varepsilon Ad_{nominal}+\varepsilon AF/k)/(d_{nominal}^{2}-F^{2}/k^{2})}

Assuming that d n o m i n a l 2 >> F 2 / k 2 {\displaystyle d_{nominal}^{2}>>F^{2}/k^{2}}, which is true for small deformations where d n o m i n a l >> x {\displaystyle d_{nominal}>>x}, we can simplify this to:

C ≃ ( ε A d n o m i n a l + ε A F / k ) / ( d n o m i n a l 2 ) {\displaystyle \simeq (\varepsilon Ad_{nominal}+\varepsilon AF/k)/(d_{nominal}^{2})}

It follows that:

C ≃ C n o m i n a l + ε A F / k d n o m i n a l 2 {\displaystyle \simeq C_{nominal}+\varepsilon AF/kd_{nominal}^{2}}

C ≃ C n o m i n a l + B F {\displaystyle \simeq C_{nominal}+BF} where B = ϵ A / k d 2 {\displaystyle B=\epsilon A/kd^{2}}, which is constant for a given sensor.

We can express the change in capacitance Δ C {\displaystyle \Delta C} as:

Δ C = B F {\displaystyle \Delta C=BF}

Production

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 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.