Capacitive Sensors—Displacement

Capacitive sensors are extensively used in industrial and scientific applications. They are based on changes in capacitance in response to physical variations. These sensors find many diverse applications — from humidity and moisture measurements to displacement sensing. In some cases, the basic operational and sensing principles are common in dissimilar applications; and in other cases, different principles can be used for the same applications. For example, capacitive microphones are based on variations of spacing between plates in response to acoustical pressure, thus turning audio signals to variations in capacitance. On the other hand, a capacitive level indicator makes use of the changes in the relative permittivity between the plates. However, capacitive sensors are best known to be associated with displacement measurements for rotational or translational motions, as will be described next. Other applications of capacitance sensors such as humidity and moisture will be discussed.

Capacitive Displacement Sensors

The measurement of distances or displacements is an important aspect of many industrial, scientific, and engineering systems. The displacement is basically the vector representing a change in position of a body or point with respect to a reference point. Capacitive displacement sensors satisfy the requirements of applications where high linearity and wide ranges (from a few centimetres to a couple of nanometres) are needed.

The basic sensing element of a typical displacement sensor consists of two simple electrodes with capacitance C. The capacitance is a function of the distance d (cm) between the electrodes of a structure, the surface area A (cm2 ) of the electrodes, and the permittivity ε (8.85 × 10–12 F m–1 for air) of the dielectric between the electrodes; therefore:

There are three basic methods for realizing a capacitive displacement sensor: by varying d, A, or ε, as discussed below.

Variable Distance Displacement Sensors

A capacitor displacement sensor, made from two flat coplanar plates with a variable distance x apart, is illustrated in Figure 6.23. Ignoring fringe effects, the capacitance of this arrangement can be expressed by:

The capacitance of this transducer is nonlinear with respect to distance x, having a hyperbolic transfer function characteristic. The sensitivity of capacitance to changes in plate separation is

Variable Area Displacement Sensors

Alternatively, the displacements may be sensed by varying the surface area of the electrodes of a flat plate capacitor, as illustrated in Figure 6.24. In this case, the capacitance would be:

Then, the transducer output is linear with displacement x. This type of sensor is normally implemented as a rotating capacitor for measuring angular displacement. The rotating capacitor structures are also used as an output transducer for measuring electric voltages as capacitive voltmeters.