The permittivity term ε is made up of two parts – εr and ε0, where εr is the relative static permittivity (sometimes called the dielectric constant) of the material between the plates and ε0 is the electric constant (ε0 ≈ 8.854×10-12 F/m).
The capacitance effect is used in lots of sensors, notably in the touch sensors of devices such as mobile phones and tablet computers. These capacitive sensors detect the absence or presence of a person’s finger, acting as an alternative to a push button switch. The presence of a person’s finger – or rather the water in it – is to change the relative static permittivity causing a shift in capacitance.
Another type of capacitive sensor is the capacitive displacement sensor, which works by measuring change in capacitance from the change in dimensions of the capacitor. As can be seen by the mathematical formula in Fig 1, capacitance varies in proportion to the distance between the plates (d) as well as their overlap (A). Displacement can be measured axially (variation in d) or in the planar direction of plate overlap (variation in A). Advantageously, capacitor plates can be generated using printed circuit boards.
In order to store any significant amount of charge, the separation dimension d must be small compared to the area of the plates. Dimension d is usually <<1mm. Hence, such a technique is well-suited to load or strain measurement which might cause relatively large changes in this small dimension. Similarly, capacitive linear or rotary sensors can be arranged so that displacement causes a variation in A, the effective overlap of the plates. In other words one set of plates is on the moving element of the sensor while the other set is on the stationary element. As the two elements displace relative to each other, A varies.
Unfortunately, capacitance is also sensitive to factors other than displacement. If the capacitor’s plates are surrounded by air then its permittivity will also vary with temperature and humidity, because water has a different dielectric constant to air. A nearby object which varies the permittivity of the surrounding area will also vary the capacitance. With a touch sensor, it is the water in the finger that causes a change in local permittivity, changing the capacitance and thus triggering a switch. This is why the operation of unresponsive touch sensors can be improved by wetting the end of the operator’s finger.
Unless the surrounding environment can be sealed or tightly controlled, capacitive sensors are not suited to harsh environments where there is the possibility of ingress of foreign matter or large temperature swings. Unsurprisingly, capacitive sensors are not suitable for environments where condensation may occur at lower temperatures.
Given the inherent physics, the distance between the sensor’s plates must be kept small relative to the size of the capacitor plates and set within tight limits. This can require extremely precise mechanical installation of the sensor and this may not be practical or economical, as differential thermal expansion, vibration or mechanical tolerances of the host system will cause the separation distance to vary and hence distort measurement.
Inductive Position Sensors – Operating Principles
In 1831, Michael Faraday, discovered that an alternating current flowing in one conductor could ‘induce’ a current to flow in an opposite direction in a second conductor. Since then, inductive principles have been widely used as a basis for position and speed measurement in devices such as resolvers, synchros and linearly variable differential transformers (LVDTs). The basic theory can be explained by considering two coils – a transmit coil (Tx), with an alternating current applied to it, and a receive (Rx) coil, in which a current will be induced: