Error Sources: Probe/Target Angle

Capacitive Sensor TechNote LT03-0010
Copyright © 2007 Lion Precision.


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:


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r = radius [meters] of probe sensor area
d = probe/target gap, directly under the probe center axis [meters]
Θ = 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.