Resistive sensors potentiometers
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Sensors based on the variation of the electric resistance of an element are probably the most common. That is because there are many physical quantities able to affect the electric resistance of a material. Thus resistive sensors are used to solve...
Sensors based on the variation of the electric resistance of an element are probably the most common. That is because there are many physical quantities able to affect the electric resistance of a material. Thus resistive sensors are used to solve many measurement problems. In the case of temperature dependent resistors, they also offer a means for thermal compensation that can be applied to systems measuring other quantities.
In this chapter we describe the more common sensors based on a variation in resistance. we will describe their fundamentals, technology, equivalent electric circuits and applications. We will use sensors, models, and definitions given in Chapter I when dealing with some of the applications.
chapter 3 will describe the circuits to obtain a useful electric signal. The different resistive sensors will be classified by the physical quantity being measured as mechanical, thermal, magnetic, optical, and chemical variables.
A potentiometer is a resistive device with a linear or rotary sliding contact (Figure 2.1). The resistance between that contact and the bottom terminal is
where x is the distance traveled from the top terminal and a is the corresponding length fraction. From a dynamic point of view, it is in principle a zero-order system, although it can be itself a component of a nonzero-order sensor, for example, a mass-spring system.
The behavior described by (2.1), means that the resistance is proportional to the travel of the wiper. This implies the acceptance of several simplifications that are worth explaining because they can not always be taken for granted.
First, we assume that the resistance is uniform along the length /. But the resistance is not perfectly uniform, which limits the linearity of the potentiometer. Second, we assume that the sliding contact gives a smooth resistance variation, not a stepped one, and therefore that the resolution is infinite. But that is not true for all resistive elements.
For the model described by (2.1) to be valid, if the potentiometer is supplied by an alternating voltage, its inductance and capacitance should be insignificant. For low values of R., the inductance may be significant, particularly in models with wound resistive elements. For high values of Rn, the
parasitic capacitance may be important.
Another factor to be taken into account is that resistors drift with temperature. Therefore the model is valid only if the temperature does not change.
Temperature changes can be produced not only by fluctuations in ambient temperatirre but also by self-heating due to the finite power that the potenti ometer dissipates. The rms value of the voltage V must be
where P is the power
If the measr."-"n, circuit has a low input impedance, it will load the potentiometer, and may cause excessive heating in part of the potentiometer
(see Problem 2.1).
Another factor limiting the validity of the model is the friction and inertia of the wiper. These should be insignificant but at the same time ensure a good contact. As a compromise the force required to displace the wiper is from 4 to 15 g. For variable movements the starting torque is approximately twice the dynamic torque, and this is reduced by lubrication. For rapid movements there is a risk of losing contact during vibrations. Thus some units have two wipers of different arm lengths, and therefore different resonant frequencies.
Finally, if the desired resolution is high, then the noise associated with the contact resistance must be considered. Its value can increase because of dust, humidity, oxidation, and wear. When contact resistance changes with movements from one position to another, current circulating through it produces changes in the output voltage. These fluctuations may be significant for the attached measuring device.
Most of these limitations are outweighed by the advantages of this device. It is simple and robust and yields a high accuracy relative to its cost. Models available accept linear and rotary movements (one or more turns in helical units). In some models the output is deliberately nonlinear with respect to the displacement . In other models the output is a sinusoidal function of the angle turned by the sliding contact. If, for example, a wire is wound or a conductor is deposited on a triangular mandrel (Figure 2.2), the resistance between the sliding contact and the left end is
where / is the length of the mandrel, r is the distance to the right end, A is the wire's cross section, D its diameter, and p its resistivity. A nonlinear relationship can also be obtained by using a nonuniform spacing for the wire or by varying its size along its length. When the measuring circuit loads the potentiometer a nonlinear characteristic is also obtained (Section 3.2.1). A computation method to generate a resistor geometry with a prescribed potential drop along the wiper path is described in .
To obtain a useful device, a single wire is not used. Even if the wire were very thin (while retaining enough strength), it would be impossible to obtain
a high enough resistance value. The usual configuration has beqr a wire around a (ceramic) insulating form. Some of the materials used are nickel-chrome, nickel-copper, and precious metal alloys. But then the inductance is high and the resolution low. Advantages are a low temperature coefflcient
and a high power dissipation capability.
High resolution and long life at a moderate cost are obtained with potentiometers based on a carbon film, sometimes mixed with plastic and deposited
on a form. Their temperature coefficient is high. For high power dissipation and high resolution, there are models in which the resistive element is based
on particles of precious metals fused in a ceramic base. Table 2.1 gives some specifications of commercially available models. The Thevenin equivaldnt circuit for a potentiometer shows that its output impedance depends on the wiper position. If a direct voltage is supplied, the output resistance Ro is the parallel combination of R.(1 - a) and Rna,
Potentiometers find application in the measurement of linear or rotary displacements exceeding full-scale values of I cm or 10o. Displacements of
this magnitude can be found in position feedback systems and also in some sensors-for example, in pressure sensors based on Bourdon tubes, bellows, or capsules (Section 1.7.3), Figure 2.3, and in float-based level sensors.
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