Some inductive and capacitive position sensors can look quite similar and so it is no surprise that design engineers can find the differences between them confusing. Both use a non-contact technique to measure position and both can be built using printed circuit boards. Nevertheless, the basic physics, on which each type of sensor relies, is quite different. Ultimately, what this means in practice is that each type is suited to particular applications. This article explains the physics behind each technology and compares the consequent strengths and weaknesses of each approach.

## Capacitive Position Sensors – Operating Principles

When scientist Ewald Georg von Kleist was electrocuted by his laboratory apparatus in 1745, he suddenly learnt that it was possible to store a big electrical charge. Perhaps inadvertently, he had built the world’s first capacitor – or what used to be called, a condenser. A capacitor acts a store of electrical charge and typically comprises two conductive plates separated by non-conductive material, or dielectric. The dielectric is typically air, plastic or ceramic. A simple mathematical model of a capacitor is shown in Figure 1:-

Fig 1 – A simple capacitor

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:

Fig 2 – Faraday’s Induction Law

The voltage signal in the receive coil is proportional to the relative areas, geometry and displacement of the two coils. However, as with capacitive techniques, other factors can also affect the behaviour of the coils. One such factor is temperature but this effect can be negated by the use of multiple receive coils and by calculating position from the ratio of the received signals (as in a differential transformer). Accordingly, if temperature changes, the effect is cancelled out since the ratio of the signals is unaltered for any given position.

Unlike capacitive methods, inductive techniques are much less affected by foreign matter such as water or dirt. Since the coils can be a relatively large distance apart, precision of the installation is less of an issue, and the principal components of inductive position sensors can be installed with relatively relaxed tolerances. This not only helps to minimize costs of both sensor and host equipment, but also enables the components to be encapsulated, allowing the sensors to withstand environmental effects such as long-term immersion, extreme shock, vibration or the effects of explosive gaseous or dust-laden environments.

Inductive sensors provide a robust, reliable and stable approach to position sensing, and are thus the preferred choice in applications where harsh conditions are common, such as defence, aerospace, industrial and the oil & gas sectors.

Despite their robustness and reliability, however, traditional inductive sensors have some downsides which have prevented their uptake from becoming more widespread. Their construction uses a series of wound conductors or spools, which must be wound accurately in order to achieve accurate position measurement. A significant number of coils must be wound in order to achieve strong electrical signals. This wound spool construction makes traditional inductive position sensors bulky, heavy and expensive.

Electromagnetic noise susceptibility is often cited as a concern by engineers considering inductive position sensors. The concern is misplaced given that resolvers have been used for many years within the harsh electromagnetic environments of motor enclosures for commutation and speed control.  As with temperature stability, robustness in harsh electromagnetic environments can be achieved using a differential approach whereby the electromagnetic energy entering different parts of the sensor is effectively self-cancelling. This is why inductive sensors such as resolvers and LVDTs have been the preferred choice in notoriously safety conscious sectors such as civil aerospace applications for many years.

## A Different Approach to Inductive Sensing

Another approach to inductive sensors uses the same physical principles but laminar, printed constructions are used instead of wire wound spools. This is the approach taken by Zettlex. It means that the windings can be produced from etched copper or by printing on a wide variety of substrates such as polyester film, paper, epoxy laminates and even ceramics. Such printed constructions can be made much more accurately than windings. Hence a far greater measurement performance is attainable at less cost, bulk and weight – whilst still maintaining the inherent stability and robustness of the inductive technique.

Fig 3 – Example of a dirty but fully functioning inductive sensors with printed laminar construction

Zettlex IncOders are non-contact devices for precision angle measurement. IncOders have two main parts – a Stator and a Rotor – each shaped like a flat ring. The large bore makes it easy to accommodate through-shafts, slip-rings, optical-fibres, pipes and cables. IncOder inductive angle encoders do not require precise mechanical mounting, rather the Rotor and Stator can simply be screwed to the host product. Zettlex angle encoders are generally unaffected by foreign matter making them ideally suited to harsh environments where capacitive devices may prove unreliable.

Zettlex’s IncOder range of inductive angle encoders has 100million product variants. This includes mini IncOders at 37mm diameter with up to 17bit resolution and midi IncOders at 58mm diameter with up to 19bit resolution.

## Summary

The benefits of each of the three approaches are summarised in the table below. It can be seen that of the three, the non-traditional inductive approach using printed laminar coils, used by Zettlex, provides the greatest number of advantages:

 Capacitive Inductive (Traditional Coils) Inductive (Printed Coils) High Resolution Y Y Y High Repeatability Y Y Y High Accuracy Y Y Y Resilience to Dirt, Water or Condensation Y Y Resilience to electrostatic effects Y Y Robust EMC Operation Y Y Y Low Thermal Drift Y Easy to Install ? Y Compact Y Y Lightweight Y Y Economical ? Y