How it works - electric part

Math 

How Capacitance Relates to Distance

1. Size of the plates: As the plate size increases so does the capacitance.
2. Gap Size: capacitance decreases as the gap increases
3. Material between the plates (the dielectric): Dielectric material will cause the capacitance to increase or decrease depending on the material.

Capacitance is determined by dielectric (the material in the gap) Area, and Gap. Capacitance increases when Dielectric or Area increase. Capacitance decreases when the Gap increases.

Calculate total sensor capacitance (CX)

When finger is present the total sensor capacitance (CX) is defined by equation 

 where CF is finger's capacitance and CP is the sum of the distributed capacitance on the sensor. This is how sensor can calculate if the finger is on the sensor as seen in figure 1 . This capacitive is then converted into digital values called Raw Counts which was explained on Position sensor page. 

Figure 1

Capacitance sensor activation

There are several integrated capacitance-to-digital converters (CDCs) that can interface with external capacitance sensors. They can implement functions such as capacitive buttons, scroll bars or wheels. Two of these are the AD7142 and the AD7143.

When the sensor is not active the AD714x sensors measures the capacitance value as ambient value as seen from figure 2. As previously explained in Position sensor page, the capacitive increases when the finger is touching screen or a button and it decrease when finger is moving away of the screen or button.

Figure 2

Figure 2 shows a situation, where the ambient capacitance value does not change. The ambient capacitance changes constantly and is unpredictably due to changes in humidity and temperature. If the ambient capacitance value changes sufficiently, it can affect the sensor activation.

Terms:

dielectric= An electrically insulating or nonconducting material considered for its electric susceptibility, i.e. its property of polarization when exposed to an external electric field.

capacitance= The property of an electric circuit or its element that permits it to store charge, defined as the ratio of stored charge to potential over that element or circuit (Q/V); SI unit: farad (F).

Sources

1. http://www.analog.com/library/analogdialogue/archives/40-10/cap_sensors.html
2. http://www.capacitive-sensing.com/capacitive-sensor-theory.html