Chapter 1:
Fundamentals of electrostatics
and capacitance &
an introduction to capacitive touch sensors
1.1 Basics of electrostatics, current and conductors
Electric current, Conductivity & Resistivity
Thanks to Benjamin Franklin’s pioneering experiments, that took place almost three centuries ago, almost everyone knows today that electric charges can travel through materials causing flow of electric current.
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.
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.
Key takeaways from this section:
Considering its ability to allow electric current flow, almost every material can be classified as a conductor or dielectric.
Basics of electrostatics, conductors &
electric field
As we mentioned above, conductors allow the flow of electric current, so a considerable amount of electric charge can be accumulated on their surfaces. Assuming a system consisting of two conductors with an electric potential (voltage) difference applied between them, electric charge appears at the surfaces of both conductors. In such a system, electric charge of opposite polarity is accumulated on each conductor, and higher charge density is observed on the conductor surfaces that are closer to each other.
These effects are also depicted through the properties of electric field. Actually, electric field lines start from positive and end to negative charges, whereas they are more dense where the charge density is higher.
Picture 2. Electric charge of two conductive plates (Source)
Picture 3. Electric field lines of two conductive plates (Source)
Key takeaways from this section:
When there is a voltage difference applied between two conductors, electric charge of opposite polarity appears on their surfaces.
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