Error Sources: Probe/Target Angle

Capacitive Sensor TechNote LT03-0010

Summary

This TechNote describes the extent and nature of measurement errors as a result of a capacitive probe’s sensing surface not being parallel to the target surface.

Error Sources: Capacitive Probe/Target Angle

Nature of the Error:

Systems are calibrated with the probe perpendicular to the target surface. As that angle changes, the output will show a DC (offset) shift relative to the actual gap from the probe’s center axis to the target.

Probe angle introduces a positive DC (offset) shift in the output causing the target to appear closer.
Gain (scaling) error due to probe angle is insignificant in comparison to DC (offset) shift.

Extent of the Error:

In addition to the Probe/Target angle, the magnitude of the error is dependent on:Sensor Radius,Probe/Target Gap,Sensor Geometry.
Error [m] is described by this function:

Where:
r = radius [meters] of probe sensor area
d = probe/target gap, directly under the probe center axis [meters]
= probe/target angle [radians]
k = experimentally determined constant to account for field fringing errors
Typical k values are around 5.
Example 1: 0.5mm sensor radius, at 0.25mm gap, with a 0.0002 radian angle produces an error of approximately 0.05nm.
Example 2: 3mm sensor radius, at 0.75mm gap, with a 0.03 radian angle produces an error of approximately 13µm.