## Ideal Potentiometer and its symbol

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A potentiometer is a resistive device with a linear or rotary sliding cont...

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 given by

where x is the distance traveled from the top terminal and is the corres ponding 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 *1. *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 R0, the inductance may be significant, particularly in models with wound resistive elements. For high values of R11, 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 temperature but also by self-heating due to the finite power that the potentiometer dissipates. The rms value of the voltage *V *must be

*V2PR *(2.2)

where *P *is the power.

If the measurement 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 reason ant 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.

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