What is εr?
εr is the relative permittivity of the material to be sensed, also known as the dielectric constant. When speaking of relative permittivity or dielectrics, we are speaking of materials that do not readily conduct electricity, materials called insulators. The dielectric constant (K) is a ratio of a substance compared to the dielectric constant of a vacuum, where K=1. With capacitive sensors, we typically use air as the starting point, with K=1.00059, which is close enough for our purposes. Capacitive sensors trigger output when an object with a higher K than air is sensed in the electrostatic field. But first, we must interact with the target material, which is where the “K” becomes important.
Relative permittivity is a measure of how easy/difficult it is to polarize a substance (as a ratio to a vacuum which equals 1). Polarizing is accomplished by placing the matter in an electrostatic field, which causes the molecules of the matter to rotate, lining up with the field. The easier the matter lines up, the higher the K value.
So, a capacitive sensor works by polarizing the target material, which in turn creates a higher capacitance in the sensor’s circuitry. Internal to the sensor is an oscillator or generator (to create the electrostatic field), comparators, op-amps, etc. These components determine if the internal capacitance of the circuitry has changed enough to trigger an output.
Why is water so easy to polarize? Because it’s already a “polar” molecule.
Due to the hydrogen bond, each water molecule is already a tiny magnet, with a slight positive on one end and a slight negative on the other. When placing water in an electrostatic field, the water molecules easily align with the sensor’s plates, with the plus side of the water molecule pointing towards the negative plate of the sensor, and the minus side of the molecule pointing to the positive plate.
In the end, the density explanation doesn’t hold water, since glass is much denser than water, but it is water, due to how easily it can be polarized, which is easier for a capacitive sensor to recognize. Not to say that a capacitive sensor cannot sense glass, because they can sense just about any material, but with such a difference in dielectric constants between water and glass, the sensor gain (trimpot or teach wire) can be adjusted to reduce the sensitivity of the sensor, to ignore the glass/plastic container, and only sense the water-based media inside. Make sense?
Capacitive sensors work by:
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- Polarizing the target media as it enters the sensor’s electrostatic field
- Measuring the internal increase in capacitance due to the polarized media
- Creating an output once the set threshold of internal capacitance is exceeded
So next time you’re looking to sense an object or liquid, take a look at a table of dielectrics, and consider a capacitive sensor to do the job.