Capacitive displacement sensor: Difference between revisions

Revision as of 05:17, 31 October 2024

Revision as of 14:53, 31 October 2024

Line 5:

==Basic capacitive theory==

Two identical parallel conductive plates of area <math>A</math> separated by a gap of distance <math>d</math> will have a [[capacitance]] <math>C</math> of:

:<math> C = \dfrac{\varepsilon_0 K\varepsilon_r A}{d} </math> <ref name="Physics">{{cite book|isbn=0-87901-135-1|title=Physics Second Edition|author=Paul Allen Tipler|pages=653–660|publisher=Worth Publishers|year=1982}}</ref>

where <math>\varepsilon_0</math> is the [[permittivity of free space]] constant and ''<math>K\varepsilon_r</math>'' is the [[dielectricrelative constantpermittivity]] (also called the dielectric constant) of the material in the gap.

There are two general types of capacitive displacement sensing systems. One type is used to measure thicknesses of conductive materials. The other type measures thicknesses of non conductive materials or the level of a fluid.

Line 12:

A capacitive sensing system for conductive materials uses a model similar to the one described above, but in place of one of the conductive plates, is the [[sensor]], and in place of the other, is the conductive target to be measured. Since the area of the probe and target remain constant, and the [[dielectric]] of the material in the gap (usually air) also remains constant, "any change in capacitance is a result of a change in the distance between the probe and the target."<ref name="LionCapTheory">[http://www.lionprecision.com/tech-library/technotes/cap-0020-sensor-theory.html Capacitive Sensor Operation and Optimization How Capacitive Sensors Work and How to Use Them Effectively] {{Webarchive|url=https://web.archive.org/web/20151202093819/http://www.lionprecision.com/tech-library/technotes/cap-0020-sensor-theory.html |date=2015-12-02 }}, An in depth discussion of capacitive sensor theory from Lion Precision.</ref> Therefore, the equation above can be simplified to:

:<math>C \propto \dfrac{1}{d} </math>

where α indicates a proportional relationship. Due to this proportional relationship, a capacitive sensing system is able to measure changes in capacitance and translate these changes in distance measurements.

Where α indicates a proportional relationship.

Due to this proportional relationship, a capacitive sensing system is able to measure changes in capacitance and translate these changes in distance measurements.

The operation of the sensor for measuring thickness of non-conductive materials can be thought of as two capacitors in series, with each having a different dielectric (and dielectric constant). The sum of the thicknesses of the two dielectric materials remains constant but the thickness of each can vary. The thickness of the material to be measured displaces the other dielectric. The gap is often an air gap, (dielectric constant ≈ 1''<math>\varepsilon_r</math>''≈1) and the material has a higher dielectric. As the material gets thicker, the capacitance increases and is sensed by the system.

A sensor for measuring fluid levels works as two capacitors in parallel with constant total area. Again the difference in the dielectric constant of the fluid and the dielectric constant of air results in detectable changes in the capacitance between the conductive probes or plates.