Introduction
Rapid developments in the fields of control engineering and in microprocessor and semiconductor technology have resulted in the widespread use of electronically controlled systems in every branch of industry today. This has created a need for sensors that are inexpensive but, at the same time, sufficiently robust, both electrically and mechanically, to withstand a wide range of temperatures (e.g. from 40 to +160 degrees centigrade), particularly in applications involving large quantities, such as the automobile industry. Fig. 1 provides a summary of the various types of sensors for angular and linear motion that are in use today. Such potentiometers essentially comprise the following components:
1. The resistance element (support material + a resistance track of conductive plastic)
2. A wiper (precious metal alloy)
3. A drive shaft or acutating rod
4. Bearings (ball bearing or plain bearing)
5. Housing
Terminology / Terms and Definitions
Linearity/Conformity
Whereby m characterizes the gradient, the offset voltage of the potentiometer and the linear or angular travel. Where there is a linear relationship, deviation is referred to as linearity. Where the relationship is nonlinear.
U = f (x) + a + b
the deviation is referred to as conformity.
Absolute linearity
Fig. 9
Absolute conformity
As already indicated already, conformity is a more general concept than linearity. The definition of absolute conformity is similar to that of absolute linearity. It is essential for an index point to be defined. The functional relationship can either be determined mathematically to be defined. The functional relationship can either be determined mathematically or by plotting a number of points to establish a curve with the aid of suitable interpolation. It is also possible with a potentiometer to achieve steadily increasing or steadily decreasing functions such as logarithmic, exponential, sinusoidal or cosinal functions.
Contact resistance
Contact resistance is the resistance between the wiper terminal and the wiper's immediate point of contact on the potentiometer's resistive track. As will be subsequently explained, this contact resistance affects all the important quality features of a potentiometer. Contact or transition resistance can be broken down into three components. The first component, describes the integral voltage drop between the currentcarrying track and the contact surface. This component is largely dependent on technology factors and amounts to several hundred Ohm. The second component, the external component, is far more difficult to master than the first. This external transition resistance has much in common with the contact resistances occurring in switches and plug and socketconnectors. It is caused by the transition between the wiper and the potentiometer track not being ideal from an electrical viewpoint. Metal oxides, chlorides and sulphides, mixed with various organic substances, can result in the formation of thin nonconductive facings at the interface. If not kept within bounds, this external transition resistance can, under unfavourable conditions, lead to complete failure to keep within a tolerance range. It is absolutely essential that the materials used in potentiometer manufacutre be subjected to stringent quality control and be matched one with another. The third component, the dynamic component, is related to dynamic drive forces acting on the wiper at high speeds of actuation. With the aid of damped wipers, actuation speeds of up to 10 m/sec can be achieved without any appreciable increase in the dynamic component of contact resistance.
Linearity errors due to electrical circuitry
From here onwards, we are only concerned with the linear characteristics (linearity). Relationships must be suitably adapted for applications with nonlinear characteristics (conformity) but there are no essential differences. As already mentioned, the required linearity values can only be utilized so long as the signal output by the sensor "potentiometer" carries no current. We have now to consider the effect of wiper current on linearity. Fig. 10a illustrates the functional relationship between wiper current, contact resistance and linearity error. As is shown by the example in Fig. 10b, with a wiper current of 10 µA and a contact resistance of 10 kOhm, a potentiometer which has a resistance of 2 kOhm already has linearity error of 1.1 %. A similar situation arises with an ohmic load. This clearly shows how important are the roles played by both wiper current and contact resistance.
Fig. 10b
Linearity errors resulting from mechanical coupling
If there is axial misalignment (eccentricity) between the drive shaft and the shaft of a potentiometer used to sense angular, motion, this will cause a linearity error that increases as the coupling radius decreases in relation to the degree of eccentricity. The following equation determines the maximum relative error
Fmax = E/Pi · rk
where E = Eccentricity
und rk = the coupling radius.
It is only possible to take full advantage of the linearity or conformity of any rotationary sensor system, if coupling alignment errors (offset and angular misalignment) are avoided or at least reduced to a mimimum. This means that with highly accurate measurement systems, due allowance must be made for any coupling misalingment in accordance with the above equation.
Smoothness
Smoothness is a measure of the deviations from perfect regularity that appear in the output voltage of a potentiometer. This irregularity is measured over a specified travel increment, for example 1 %, and is expressed as a percentage of the applied voltage. For the measurement of smoothness, the VRCI definition calls for a bandpass filter to be used as a means of suppressing any linearity error and for the potentiometer to be operated with a load resistance (e.g. 100 . Rp). This method has certain disadvantages:
b) The load applied to the potentiometer also contributes to error by causing variation in the contact resistance which is greatest with the wiper at the voltage application end and lowest at the grounded end of the potentiometer track.
d) The sometimes arbitrary selection of a filter type, load resistance and travel increment results insmoothness values not being directly comparable.
Microlinearity
Microlinearity, which is defined as the maximum linearity variation within a travel or angular increment that amounts  as with smoothness measurement  to 1 % of the electrical range if nothing to the contrary is defined. Microlinearity is indicated as a percentage of the absolute voltage that is applied. Fig. 11 illustrates the characteristic obtained for a potentiometer with a microlinearity error. This was evaluated by a computersupported system while making linearity measurements. The travel increments are superimposed on the linearity curve and have an overlap of at least 50 %. Contrary to a smoothness measurement, the error here is pureley a linearity error that describes the maximum error within a defined increment. Microlinearity does not, however, make it possible to determine whether a potentiometer will be suitable for a particular applications because any variations in gradient (sensitivity) can only be determined with considerable difficult.
Relative gradient variation (RGV)
If, in a highly sensitive control system, the amplification should, for example, be so arranged that the control circuit will be stable with the mean slope (gradient) of the sensor, then it is important to be aware of any variations there may be in that slope (Fig. 12a, Fig. 12b). If, at any point, the gradient is appreciably steeper than the mean gradient, then there will be a higher closedloop gain in this position and this could lead to feedback oscillation. If, on the other hand, the gradient is less steep at some point than the mean gradient, then repeatability would be reduced and there would be less control accuracy. If we relate this type of local gradient variation gl to the mean gradient go of the potentiometer, then this criterion is independent of the potentiometer length and can be used for the direct comparison of various potentiometers.
RGV 
local gradient 
g_{l} 

= 
————————— 
= 
— 

mean gradient 
g_{o} 
(Fig. 13)
The RGV is indicated as a ± deviation in percentage terms from L (standardized mean gradient).
Interpretation of RGV
Measurements have shown that with conductiveplastic potentiometers, gradient fluctuations are statistically distributed to travel increments of less than 1 µm, i.e. there is no periodicity or regularity. Fig. 14a shows the RGV curve and Fig. 14b the RGV values with step widths of 0.1, 0.2 and 0.3°. The form of these distributions more or less in conformity with the normal distribution to be expected in view of the central limit value principle. The mean distribution value is around 1 (mean gradient), the variance (STDEV) decreases as the step width increases. Since each individual RGV value represents a mean value, it is to be expected that the variance of such mean values will decrease with a root function in proportion to the increase in step size, since each such increase amounts to an increase in the size of the random sample.
RGV(X) 
√ 
Y 

———— 
= 
— 
applies for STDEV 

RGV(Y) 
X 
In Fig. 15 this variance has been plotted as a function of the step width. RGV variance can thus be considered as a characteristic quality feature of a potentiometer. The functional relationsship also serves to indicate the maximum resolution of a potentiometer which is not infinite, as many potentiometer manufacturers would imply. Maximum RGV values have also been plotted in Fig. 15. This curve, like the mimimum value curve, does not of course, obey statistical laws but arises from the inclusion of defective positions and faults in the system "potentiometer" as a whole. These values are vital criteria for assessing the stability and repeatability to be expected of a control system.
Resolution
When measuring RGV values of potentiometers up to synchro size 20 from series production, with step widths of 0.1° RGV values of ± 10 % are obtained. If we specify the RGV value of ± 100 % as the resolution limit, from the equation in 7.4 we obtain with 10 % a resolution of 1/1000°. The degree of resolution is primarily determined by the homogeneity and grainsize distribution in the conductive plastic layer, by the wiper contact surface running parallel to the equipotential lines (Fig. 16a, 16b) and by the wiper current.
Hysteresis
The hysteresis value specifies the signal differential resulting if a prescribed position is approached from one side, the point is travelled over and the same position approached from the other side. Hysteresis is mainly affected by mechanical factors such as the bearings, th stiffness of the wiper system and the coefficient of friction between the conductive layer and the wiper. For this reason, attention must be paid to ensure a backlashfree, rigid mechanical coupling. This can be achieved using, for example, a springborne concial pin or lever. Fig. 18 shows the recorded hysteresis of a standard potentiometer. The measuements were taken with clockwise and counterclockwise rotation being repeated three times. While the curves recorded in one direction almost coincide (indicating goog resolution), in the opposite direction they indicate an hysteresis of around four thousands of a degree. The fact that the curves in one direction almost coincide and that there is an constant hystersis in the opposite direction indicates a stable displacement of the wiper contact line which means there is no stickslip effect.
Fig. 18
Reproducibility
This term is taken to mean any optional approach movement towards a prescribed position from various directions. It represents the sum of 2 x resolution + hyteresis.
Temperature and humidity coefficients
In many data sheets issued by potentiometer manufacturers, reference is frequently made to the temperature coefficient (Tk) and humidity coefficient (Fk) of the nominal resistance. Where potentiometers are used as voltage dividers (Fig. 2), these values are irrelevant. For this application, it is the Tk and Fk applicable to the voltage divider behaviour which are of significance. It often also happens that the humidity is not kept constant while making Tk measurements, with a result that a mixture of Tk and Fk is often given as a temperature coefficient. Detailed measurements have show that the Tk and Fk of the nominal resistance in conductiveplastic potentiometers (without housing) are of an order of magnitude somewhat less than 200 ppm/°C and 500 ppm/% RH respectively. The Tk and Fk of the voltagedividing behaviour are some two orders of magnitdue lower which means that here changes within a range of less than 5 ppm/°C and 5 ppm/% RH can be expected, ensuring constancy over a wide temperature and humidity range. However, this advantage can only be utilized given a suitably designed housing and if, for example, no trimming resistances are used in the potentiometer circuit.
Service life
The magnitude of the contact resistance and the wear to which the resistance track is subjected and the resulting change in electrical characteristics dertermine the number of operations to which a potentiometer can be subjected and thus also its service life. Although of considerable importance for industrial applications, no standard has so far been issued that specifies a servicelife definition or a particular method of testing. It is, of course, most difficult to specify a value for wear or for an increase in contact resistance for a given number of actuation cycles since such values are markedly influenced by such external factors as temperature and humidity, and by mechanical and chemical influences. Such values need to be established for each particular application. This applies to a lesser extent for the method of testing, and here the establishment of standard method would facilitate comparing the service life of various potentiometers. The first is a practical test in which extremely small wiper movements are simulated such as frequently occur in feedback control systems. Typical values are: Wiper travel 2° Test frequency 100 Hz. This dither test permits a relatively rapid result to be obtained concerning contact reliability and any change in gradient within a micro range since, at such a high frequency, some 8.6 million cycles can be effected daily. The second test, the halfstroke test, gives information concerning linearity changes, zeropoint shift and wiper wear. This test is performed at a frequency of 10 Hz (0.86 million cycles per day) over 50 % of the track length. As is shown in Fig. 19, this results in a maximum linearity change. A criterion for rejection here might be a doubling of linearity in relation to the state when new and a maximum contact resistance value.
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