Touch Capacitance Model

When designing sensors, a simple approximation of C_t may be derived from the parallel plate capacitor formula.

Note: This approximation loses accuracy where the plate area, A, is less than an order of magnitude greater than the dielectric thickness, d.

Figure 1. Parallel Plate Capacitor

C=∈Ad=∈0∈rAd

Where ‘A’ is the parallel area, ‘ϵ’ is the permittivity of the electrolyte defined by the vacuum permittivity ϵ₀ multiplied by the relative permittivity ϵ_r, 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 ϵ_r = 2
The vacuum permittivity ϵ₀ is given as 8.85 × 10⁻¹² F/m

→ The resulting capacitance is calculated as:

Ct=(8.85×10−12F/m)×2×(8×10−32)×π1×10−3m=0.89⁢pF

Note: 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.