Chapter 1: Fundamentals of electrostatics and capacitance & an introduction to capacitive touch sensors

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Capacitive sensing can be overwhelming for a newcomer. The nature of the underlying electromagnetic phenomena is complex. That’s why many newcomers tend to cut corners. They tend to skip the part of understanding the physics involved and jump head-first to projects. Naturally, they soon feel lost and resort to trial and error. This first free chapter contains all the knowledge we wish we had when we first started working on capacitive sensing. It will teach you the basics of electrostatics, conductors, and capacitance tailored to the need of a capacitive touch sensor designer.

 

The tendency of a material to allow the flow of electric current through its body is described by conductivity, σ. On the contrary, the difficulty that a material poses to electric charge conduction can be quantified by resistivity, ρ.

 

conductivity sensitivity relationship

 

We must keep in mind that conductivity, therefore also resistivity, are inherent properties of the material, so they are independent of the size and shape of the sample. Based on its electrical conductivity, almost every material found on earth can be classified as a conductor or insulator. Conductors, like metals, have very high conductivity values (σ > 105 S/m) and consequently very low resistivity (ρ < 10-5 Ohm⋅m). So the electric charges can travel through them very easily, with a high speed and in large amounts. On the other hand, insulators (or dielectrics), like plastics and polymers, have low conductivity values (σ < 10-8 S/m), as they inhibit the motion of electric charges, allowing just a low current flow in the presence of high electric potential. Materials with intermediate conductivity values are called semiconductors, and generally bridge the conductivity gap between conductors and dielectrics.

 

material classification based on conductivity

Picture 1. Range of electrical conductivity and resistivity values of several material types.

 

Considering the materials that are most commonly used in capacitive touch sensors, PET, FR-4 and glass are insulators, whereas silver, copper, and ITO (Indium Tin Oxide), are all metals, that is, conductors, so they have very high conductivity values. This table summarizes typical conductivity values of some of the most popular materials utilized in capacitive sensor industry:

 

Material Resistivity, ρ (Ω∙m)
(at 20 oC, 1 kHz)
Conductivity, σ (Ω/m)
(at 20 oC, 1 kHz)
Copper (Cu) 1.68 x 10-8 5.95x 107
Annealed copper 1.72 x 10-8 5.81x 107
Silver (Ag) 1.59 x 10-8 6.29x 107
Indium Tin Oxide (ITO) 7.2 x 10-8 1.39 x 105

Table 1. Conductivity and resistivity values of typical conductors used in capacitive sensors.

 

Material Resistivity, ρ (Ω∙m)
(at 20 oC, 1 kHz)
Conductivity, σ (Ω/m)
(at 20 oC, 1 kHz)
Air 1.3 x 1016 to 3.3 x 1016 3 x 10-15 to 7.7 x 10-15
Glass 1011 to 1015 10-11 to 10-15
Polyethylene (PE) 1016 10-16
Polyethelene terephtalate (PET) 1021 10-21
Polystyrene (PS) 1018 to 1019 10-18 to 10-19
Polycarbonate (PC) 1016 to 1018 10-16 to 10-18
Poly methyl methacrylate (PMMA) 1019 10-19
FR-4 (fiberglass reinforced epoxy) 1016 10-16

Table 2. Conductivity and resistivity values of typical dielectrics used in capacitive sensors.

 

As shown above, typical conductivity values of conductors and dielectrics used in capacitive sensors are of the order of 107 and in the range of 10-19 to 10-15 Ω∙m, respectively. Concerning ITO, it cannot reach the conductivity levels of copper and silver, whereas PET attains the highest resistivity value among the dielectrics.

 

You can read and learn more about electrostatics and capacitance and download the first chapter HERE for free