1.2.1 Touch Capacitance Model

When designing sensors, a simple approximation of Ct may be derived from the parallel plate capacitor formula.
: This approximation loses accuracy where the plate area, A, is less than an order of magnitude greater than the dielectric thickness, d.
Equation 1-2. Parallel Plate Capacitor
C = ∈ A d = ∈ 0 ∈ r A d

Where ‘A’ is the parallel area, ‘ϵ’ is the permittivity of the electrolyte defined by the vacuum permittivity ϵ0 multiplied by the relative permittivity ϵr, and d is the thickness of the touch cover.

→ The strongest touch delta is achieved with a large sensor electrode, a thin touch cover, and a high permittivity cover material.

Example:
  • Touch sensor electrode diameter: 12 mm
  • Fingertip area model: 8 mm diameter disc
  • Touch cover: 1 mm plastic with relative permittivity ϵr = 2
  • The vacuum permittivity ϵ0 is given as 8.85 × 10−12 F/m

→ The resulting capacitance is calculated as:

C t = ( 8.85 × 10 − 12 F / m ) × 2 × ( 8 × 10 − 3 2 ) × π 1 × 10 − 3 m = 0.89 ⁢ p F
: Only the 8 mm diameter plate is used in the equation, as this is the area of overlap between the two plates forming the capacitor.