Capacitive Sensor Operation Part 2: System Optimization

Last month we discussed the basics of capacitive sensing, both how the sensor works and explanations of the important terminology. Now it's time to apply this knowledge and explain how to optimize the performance of capacitive sensors.

Effects of Target Size
The target size is a primary consideration when selecting a probe for a specific application. When the sensing electric field is focused by guarding, it creates a slightly conical field that is a projection of the sensing area. The minimum target diameter is usually 130% of the diameter of the sensing area. The further the probe is from the target, the larger the minimum target size.

Range of Measurement
The range in which a probe is useful is a function of the size of the sensing area. The greater the area, the larger the range. Because the driver electronics are designed for a certain amount of capacitance at the probe, a smaller probe must be considerably closer to the target to achieve the desired amount of capacitance. In general, the maximum gap at which a probe is useful is approximately 40% of the sensing area diameter. Typical calibrations usually keep the gap to a value considerably less than this. Although the electronics are adjustable during calibration, there is a limit to the range of adjustment.

Multiple Channel Sensing
Frequently, a target is measured simultaneously by multiple probes. Because the system measures a changing electric field, the excitation voltage

Figure 10. Nonconductors can be measured by passing the electric field through them to a stationary conductive target behind
for each probe must be synchronized or the probes will interfere with each other. If they were not synchronized, one probe would be trying to increase the electric field while another was trying to decrease it; the result would be a false reading. Driver electronics can be configured as masters or slaves; the master sets the synchronization for the slaves in multichannel systems.

Effects of Target Material
The sensing electric field is seeking a conductive surface. Provided that the target is a conductor, capacitive sensors are not affected by the specific target material; they will measure all conductors—brass, steel, aluminum, or salt water—as the same. Because the sensing electric field stops at the surface of the conductor, target thickness does not affect the measurement.

Measuring Nonconductors
Capacitive sensors are most often used to measure the change in position of a conductive target. But capacitive sensors can be very effective in

Figure 11. Without a conductive target behind, a fringe field can form through a nearby nonconductor allowing the nonconductor to be sensed
measuring presence, density, thickness, and location of nonconductors as well. Nonconductive materials such as plastic have a different dielectric constant than air. The dielectric constant determines how a nonconductive material affects the capacitance between two conductors. When a nonconductor is inserted between the probe and a stationary reference target, the sensing field passes through the material to the grounded target (Figure 10). The presence of the nonconductive material changes the dielectric and therefore changes the capacitance. Capacitance will change in relationship to the thickness or density of the material.

It is not always feasible to have a reference target in front of the probe. Often, measurements can still be made by a technique called fringing (Figure 11). If there is no conductive reference directly in front of the probe, the sensing electric field will wrap back to the body of the probe itself. This is called a fringe field. If a nonconductive material is brought in proximity to the probe, its dielectric will change the fringe field; this can be used to sense the nonconductive material. The sensitivity of the sensor to the nonconductive target is directly proportional to the dielectric constant of the material. Figure 12 lists some common dielectric constants.


Figure 12. Dielectric constants of common nonconductive materials
MaterialDielectric Constant
Relative (ξr)


Figure 13. An undersized target causes the sensing field to extend to the sides of the target, introducing error
Maximizing Accuracy
Accuracy requires that the measurements be made under the same conditions in which the sensor was calibrated. Whether it's a sensor calibrated at the factory, or one that is calibrated during use, repeatable results come from repeatable conditions. If we only want distance to affect the measurement, then all the other variables must be constant. The following sections discuss common error sources and how to minimize them.

Target Size. Unless otherwise specified, factory calibrations are done with a flat conductive target that is considerably larger than the sensing area. A sensor calibrated in this way will give accurate results when measuring a flat target >30% larger than the sensing area. If the target area is too small, the electric field will begin to wrap around the sides of the target, meaning that the electric field extends farther than it did in calibration and will measure the target as farther away (Figure 13). In this case, the probe must be closer to the target for the same zero point. Because this distance differs from the original calibration, error will be introduced. Error is also created


Figure 14. A curved target will require that the probe be closer and the sensitivity will be affected
because the probe is no longer measuring a flat surface.

If the distance between the probe and the target is considered the Z axis, then an additional problem with an undersized target is that the sensor becomes sensitive to the X and Y location of the probe. Without changing the gap, the output will change significantly if the probe is moved in either the X or Y axis because less of the electric field is going to the center of the target and more is going around to the sides.

Target Shape. Shape is also a consideration. Because the probes are calibrated to a flat target, measuring a target with a curved surface will cause errors (Figure 14). Because the probe will measure the average distance to the curved target, the gap at 0.0 V will be different from the gap at 0.0 V when the system was calibrated. Errors will also be introduced because of the different behavior of the electric field with the curved surface. In cases where a nonflat target must be measured, the system can be factory calibrated to the final target shape. Alternatively, when flat calibrations are used with curved surfaces, multipliers can be determined to correct the measurement value.

Figure 15. Rough surfaces will tend to average but can give different results at different locations on the target, especially with very small probes
Surface Finish. When the target surface is not perfectly smooth, the system will average over the area covered by the spot size of the sensor (Figure 15). The measurement value can change as the probe is moved across the surface due to a change in the average location of the surface. The magnitude of this error depends on the nature and symmetry of the surface irregularities and on the probe's sensing area size; larger probes average over a larger area and are less susceptible to small surface irregularities.

Parallelism. During calibration the surface of the sensor is parallel to the target surface. If the probe or target is tilted any significant amount, the shape of the spot where the field hits the target elongates and changes the interaction of the field with the target (Figure 16). Because of the different behavior of the electric field, measurement errors will be introduced. At very high resolutions, even a few degrees of tilt can introduce error. Parallelism must be considered when designing a fixture for the measurement.

Figure 16. Lack of parallelism will introduce errors
Environment. All capacitive sensors exhibit some temperature sensitivity, but they are usually well-designed and temperature-compensated, resulting in very small changes with temperature over a limited range. A more troublesome problem is that virtually all target and fixture materials exhibit a significant expansion and contraction with temperature. When this happens, the changes in the measurement are not gauge error; they are real changes in the gap between the target and the probe. Careful fixture design goes a long way toward maximizing accuracy. The dielectric constant of air is affected by humidity; as humidity increases, the dielectric constant increases. Humidity can also interact with the materials from which the probe is constructed. Humidity changes from 50%–80% RH can cause errors up to 0.5% F.S.

While probe materials are selected to minimize these environmental errors, in applications requiring utmost precision, control of temperature and humidity is standard practice. International standards specify that measurements shall be performed at 20°C or corrected to "true length" at 20°C.

Capacitive sensors provide stable, high-resolution measurements that can solve a myriad of measurement problems. Understanding their operation, terminology, and susceptibilities will make it easier for you to choose the right sensor and to use it successfully in your application.

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