title: Force-sensing capacitor
text: # 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 0.35 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.
  
  