# Inductive Versus Capacitive Position Sensors

## Introduction

Design engineers find the differences between some inductive and capacitive position sensors confusing as they look quite similar. Both adopt a non-contact approach to measure position, and both can be constructed by using printed circuit boards.

However, the fundamental physics behind each kind of sensor is different. In other words, each type is suited to specific applications. This article explains the physics behind each technology, and makes a comparison of the consequent advantages and weaknesses of each approach.

## Operating Principles – Capacitive Sensors

In 1745, scientist Ewald Georg von Kleist suddenly learnt that it was possible to store a big electrical charge when he was electrocuted by his laboratory apparatus. He had inadvertently built the world’s first capacitorl, or a condenser as it used to be called.

A capacitor stores electrical charge and usually consists of two conductive plates separated by non-conductive material, or dielectric. The dielectric can be air, plastic or ceramic. Figure 1 shows a simple mathematical model of a capacitor.

Figure 1. A simple capacitor

The permittivity term ε is made up of two parts: εr and ε0, where εr is the relative static permittivity (also known as the dielectric constant) of the material between the plates and ε0 is the electric constant (ε0 ≈ 8.854 x 10-12 F/m).

Touch sensors of devices such as mobile phones and tablet computers, employ the capacitance effect. Instead of a push button switch, these capacitive sensors detect the presence or absence of a person’s finger. The presence of a person’s finger - or rather the water in it - changes the relative static permittivity and cause a shift in capacitance.

A capacitive displacement sensor is another type of capacitive sensor, which works by measuring the change in capacitance resulting from the change in dimensions of the capacitor. Capacitance varies proportionately to the distance between the plates (d) as well as their overlap (A), as shown by the mathematical formula in Figure 1.

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.

The separation dimension d must be small in comparison to the area of the plates, to store any significant amount of charge. Dimension d is usually << 1 mm. Hence, this technique is ideal to measure load or strain measurement, which which might cause relatively large changes in this small dimension.

Similarly, capacitive rotary or linear sensors can be arranged so that displacement causes a variation in A, which is the effective overlap of the plates. In other words, one set of plates is on the stationary element of the sensor while the other set is on the moving element. A varies when the two elements displace relative to each other.

Other than displacement, capacitance is also sensitive to other factors. The permittivity of air can vary with temperature and humidity when the capacitor’s plates are surrounded by air, since water has a different dielectric constant to air.

Capacitance can also change when a nearby object varies the permittivity of the surrounding area. In a touch sensor, water present in the finger causes a change in local permittivity, changing the capacitance and triggering a switch. Therefore, wetting the end of an operator’s finger can improve the operation of unresponsive touch sensors.

Capacitive sensors are not suited to harsh environments where there is a possibility of ingress of foreign matter or large temperature changes, unless the surrounding environment can be sealed or tightly controlled. Not surprisingly, capacitive sensors are ill-suited for environments where condensation can occur at lower temperatures.

Considering the inherent physics, the separating distance between the sensor’s plates needs to be kept small in relation to the size of the capacitor plates and set within tight limits. This requires exceptionally precise mechanical installation of the sensor which may not be economical or practical, as differential thermal expansion, vibration or mechanical tolerances of the host system, can cause changes in the separation distance and distort measurement.

## Operating Principles – Inductive Sensors

In 1831, Michael Faraday made a discovery that an alternating current (AC) flowing in a conductor could ‘induce’ current flow in the opposite direction in a secondconductor. Since that discovery, inductive principles have formed the basis for speed and position measurement in devices such as synchros, resolvers, and linearly variable differential transformers (LVDTs).

The basic principle can be explained by looking at two coils: a transmit coil (Tx), with an AC current applied to it, and a receive (Rx) coil, where a current will be induced.

Figure 2. Faraday’s Induction Law

The voltage signal in the Rx coil is in proportion to the relative areas, geometry, and displacement of both the coils. However, as seen in capacitive techniques, other factors can also influence the behavior of the coils. One of them is temperature, but its effect can be neutralized using several Rx coils and calculating position from the ratio of the received signals (similar to a differential transformer).

Therefore, if there is a change in temperature, the effect is canceled out because the ratio of the signals is not changed for a given position.

In contrast to capacitive techniques, inductive methods are less influenced by foreign matter such as dirt or water. The coils can be set at a relatively large distance apart, precision of the installation is not a major issue, and the principal components of the sensors can be mounted with relatively relaxed tolerances.

This helps to reduce costs of sensor and host equipment, and enables encapsulation of the components, ensuring that the sensors can bear environmental effects such as extreme shock, vibration, long-term immersion, or the effects of explosive gaseous or dust-laden environments.

Inductive sensors provide a reliable, robust, and stable approach to position sensing, and are the popular choice in applications where harsh conditions exist, such as aerospace, defense, industrial, and the oil and gas sectors.

Despite their reliability and robustness, conventional inductive sensors have some drawbacks that prevent their uptake from becoming popular. A series of wound conductors or spools are used in their construction, and they need to be wound accurately to obtain accurate position measurement.

To obtain strong electrical signals, a substantial number of coils will have to be wound. This wound spool construction makes traditional inductive position sensors heavy, bulky, and expensive.

Engineers considering inductive position sensors, often cite electromagnetic noise susceptibility as a concern. This concern is misplaced as resolvers have been used in harsh electromagnetic environments of motor enclosures for speed control and commutation, for many years.

As with temperature stability, using a differential approach where the electromagnetic energy entering different parts of the sensor is effectively self-cancelling, robustness in harsh electromagnetic environments can be achieved. This is why inductive sensors such as LVDTs and resolvers have been the popular choice for many years in safety conscious sectors such as civil aerospace applications.

## A Different Approach to Inductive Sensing

An alternative approach to inductive sensors uses the same physics principles, but instead of wire wound spools, employs laminar, printed constructions. Zettlex follows this approach. Here, windings are produced from etched copper or by printing on various substrates such as paper, polyester film, epoxy laminates, or even ceramics.

Such printed constructions are more accurate than windings, which means that better measurement performance is achievable at a lower cost, with less weight, and bulk, but still maintaining the robustness and inherent stability of the inductive technique.

Figure 3. Example of a dirty but fully functioning inductive sensor with printed laminar construction

Zettlex IncOders are non-contact devices used to make precision angle measurements. IncOders have two main components, a stator and a rotor, and both of them are in the shape of a flat ring. The large bore enables easy accommodation of through-shafts, optical-fibers, slip-rings, cables, and pipes.

IncOder inductive angle encoders do not warrant precise mechanical mounting; the stator and the rotor can be easily screwed to the host product. Zettlex angle encoders are usually not affected by foreign matter, making them well-suited to harsh environments in which capacitive devices may not be reliable.

There are 100 million product variants of Zettlex’s IncOder range of inductive angle encoders. The variants include mini IncOders at 37 mm diameter with up to 17 bit resolution, midi IncOders at 58 mm diameter with up to 19 bit resolution, and maxi InCoders from 75 up to 300 mm diameter with up to 22 bit resolution.

## Summary

The table below summarizes the benefits of each of the three approaches. Out of the three, the greatest number of advantages is provided by Zettlex’s non-conventional inductive approach using printed laminar coils.

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

This information has been sourced, reviewed and adapted from materials provided by Zettlex UK Ltd.

For more information on this source, please visit Zettlex UK Ltd.

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