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Capacitive Sensors


There are a few intrinsic advantages of capacitive sensing:

  1. A capacitive measurement system can be very fast, and is therefore suitable for measuring vibrations, motion and distance
  2. The resolution is very high: up to nanometers can be measured, the maximum range is up to $500\mu m$ for the smaller micromachined sensors, but with larger plates distances up to centimeters are no problem
  3. Capacitive sensing is contactless and normally does not affect the object that is being measured
  4. Absolute positions can be measured
  5. The mechanical integration in a system is also not difficult, the only thing you should add to your system is a ground plane, this ground plane acts as the second, grounded plate, of the capacitor. The upper plate, in fact the sensor, should be connected in a smart way to your system (so that it doesn’t influence the performance of your total system). The ultimate integration is done in Micro-ElectroMechanical Systems (MEMS) where silicon micromachining allows the integration of electronic circuitry and capacitive sensors. Typical examples are MEMS accelerometers and DLP arrays for video projectors.

There are varous applications:

  • Semiconductor industry: a wafer, exposed to a light beam, should be within very narrow tolerances, perpendicular to the exposed light beam, in order to control this accurate position capacitive sensors, on each edge of the wafer stage, will be used.
  • Automotive industry: can be applied in acceleration sensors
  • Metrology & precision machining: measuring various kinds of distances with a very high accuracy.

A capacitive sensor is a sensor, mounted on a moving object, which transfers a displacement of the object (on which is it mounted) into a change of it’s capacitor value. The change is capacitor value is measured.

In an ideal measurement set-up the change in capacitance is transformed, in a linear way, to a change in voltage. The block diagram represents this transformation. Speed op operation: we aim for a system which can measure mechanical vibrations, this means that besides the measurement of static distances we also want to measurement fast movements of mechanical structures.

Fig. 1: Transduction chain of a capacitive displacement sensor

A common sensitivity setting is $100 \mu m$ displacement results in an DC output of $1V$. This means that for every $100 \mu m$ change in distance, the output voltage changes exactly $1.0V$.

Capacity, displacement and permittivity

Before explaining the principle of a capacitive sensors let’s explain why an AC voltage is used to bias the capacitive sensor.

When a DC voltage is applied to a capacitor the plates of the capacitor will be charged and that’s it. When an AC voltage is applied to a capacitor the current which flow’s ‘through’ this capacitor depends on the value of the capacitor.

The larger the distance between the plates, the smaller the current will be (assuming a constant AC voltage applied to this capacitor), this according to the capacitor impedance equation $Z=1/j \omega C$ with $\omega$ the frequency [in radians] of the AC voltage applied to the capacitor, and C the value of the capacitor.

As shown in the following slides, any change in the capacitor can be used to sense something with a capacitive set-up:

  • In-plane displacements make the effective capactor plate size larger or smaller
  • Any perpendicular displacement makes the air gap larger or smalle
  • A change in the material inside the air gap will change the capacitor value.

Fig. 2: Dia06 Fig. 3: Dia07 Fig. 4: Dia08

Basic configurations

When using the (approximated) expression an error is made due to stray fields (fringes) at the edges of the plates. The practical implication of this error is a non-linear relationship between displacement and capacitance.

Generally, electric fields are better manageable than magnetic fields: by (active) guarding it is easy to create electric fields that are homogeneous over a wide area. This is the major reason why displacement sensors based on capacitive principles have excellent linearity

The effect of stray fields can be reduced by the application of guarding. One electrode is grounded; the other, active electrode of the capacitor is completely surrounded by an additional conducting electrode in the same plane, and isolated from the active electrode. The potential of the guard electrode is made equal to that of the active electrode (active guarding). The result is that the electric field is homogeneous over the total area of the active electrode, assuming infinite guard electrodes and a zero gap width between the two electrodes. However, since the guard electrode has finite dimensions and the gap width is not zero, a residual error occurs. This error depends on the dimensions of the guard electrode and the gap. As a rule of thumb, for x/d and d/s equal to 5, these errors are less than 1 ppm.

Fig. 5: Dia09 Fig. 6: Dia10 Fig. 7: Dia11 Fig. 8: Dia12 Fig. 9: Dia13 Fig. 10: Dia14 Fig. 11: Dia15

Some interface circuits

There are four commonly used basic methods to read-out a capacitive sensor:

  1. (Differential) Impedance measurement in a bridge
  2. Current-voltage measurement with C in the feedback loop of an OpAmp
  3. Frequency measurement with C as the frequency-determining element in an LC oscillator
  4. Time measurement by charging and discharging a capacitor at constant current

Fig. 12: (Differential) Impedance measurement in a bridge Fig. 13: Current-voltage measurement with C in the feedback loop of an OpAmp

Fig. 14: Frequency measurement with C as the frequency-determining element in an LC oscillator Fig. 15: Time measurement by charging and discharging a capacitor at constant current


  • Capacitive sensors are contactless and have a high impedance
  • They can be used for micro-precision measurements of conductive and non-conductive elements
  • Read-out circuits are always AC
  • Problems are stray-fields and parasitic capacitors

Sensor Technology TOC

These are the chapters for the Sensor Technology course:

theory/sensor_technology/st17_capacitive_sensors.txt · Last modified: 2018/10/10 02:48 by