A film layer with electrodes electrically acts as a parallel plate capacitor. The capacitance is proportional to the surface area of the conducting plate and inversely proportional to the distance between the plates.
C = ε . A / t
ε is the dielectric constant, A is the plates and t is the spacing between them
If we want to know the value of the applied stress, the number of charges has to be measured. To do this, two ways can be considered.
Voltage mode measurement: If the signal delivered is measured using an infinite impedance (R) input device, the voltage obtained is :
V = Q / C
This formula can be used as long as the RC time constant is much higher than the stress duration. A charge amplifier can also be used to directly measure the charges.
Current mode measurement: When the signal is measured through an adapted R input impedance device, we get a signal (V) proportional to the current (I) passing through R :
V = R x I
The number of charges delivered by the sensor is then :
Q =
i. dt
The signal measured is proportional to the derivative of stress vs time. This calculation can be made by software after digitizing the signal.