Capacitive Sensors – Part II

Written by: Bjoern Schaefer

In a previous post we saw the myriad of different applications capacitive technology is involved in. We will discuss today the underlying physical principles of these sensors.

Figure 1 shows a normal plate capacitor, in which two conductive plates of equal size (A) oppose each other in distance (d). Once a voltage is applied to both plates, an electric field will exist between them. Depending on the so called dielectric in between, the electric field will hold a certain amount of electrons captured within. Capacitance refers therefore to the capacity to store and hold this electric charge.

Figure 1: Plate capacitor
Figure 1: Plate capacitor

Figure 2 shows a typical electrode design of a capacitive proximity sensor. The formerly opposing plates have now circular shapes and lie within small proximity on one layer.

Figure 2: Capacitive Sensor Electrodes
Figure 2: Capacitive Sensor Electrodes

The capacitance can be measured by determining the amount charge necessary to reverse the polarity of the conductive plates. The more energy the system needs, the higher the underlying capacitance value.

The following formula reveals the relationship between the plate distance, size and dielectric material properties on the capacitance value.

Formula 1: Formula of a plate capacitor
Formula 1: Formula of a plate capacitor

C is the capacitance, in farads;
A is the area of overlap of the two plates, in square meters;
εr is the relative static permittivity (sometimes called the dielectric constant) of the material between the plates (for a vacuum, εr = 1);
ε0 is the electric constant (ε0 ≈ 8.854×10−12 F m–1); and
d is the separation between the plates, in meters.

In the next part we will discuss implications of the formula and the ways capacitive sensors can detect physical changes.


Jack Moermond has more than 41 years of experience in the manufacturing and automation industry. His roles have included controls engineer, systems specialist, systems department manager, and product manager. His product experience covers sensors, PLCs and drives, steel and paper industries, packaging, food and beverage industries, semicon and life sciences. In addition to his roles at various automation suppliers, Jack has taught PLC programming and various other training classes on automation devices.

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