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April 1966 Radio-Electronics
 [Table of Contents]
Wax nostalgic about and learn from the history of early electronics.
See articles from Radio-Electronics,
published 1930-1988. All copyrights hereby acknowledged.
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This article on applications
for the most basic of adjustable electronic components - the potentiometer (aka
"pot") - will probably surprise a lot of readers with the wide variety of configurations
in which it can be used to perform much more than a boring light bulb dimmer or
motor speed control. In this 1966 issue of Radio-Electronics magazine, Mr. F.H.
Franz educates us on how to add components around the pot to perform specialized linear and nonlinear responses, and even some wild curves when a battery is inserted.
Stereo systems have used logarithmic responses in speaker circuits for more than
a century using some of these tricks (audio taper potentiometer). Your time will not be wasted reading through
this piece.
Potentiometer Facts & Trickery
Fig. 1 - How loading affects a potentiometer. Fig. 1a
is usually wishful thinking; in most applications, pot arm is loaded by external
circuit resistance - R3 in Fig. 1b .
If R1 and R2 (Fig. 1c) are equal,
loading on source Ein is double that in an ideal situation.
In Fig. 1d, actual transfer function is quite different from the expected
one. Power dissipation holds some surprises, too!
You can do some interesting things by connecting potentiometers to generate special
voltage-vs-rotation curves- even find square roots or take tangents.
By F. H. Frantz*
The simple potentiometer is frequently taken for granted, because it's relatively
simple and straightforward. Yet potentiometers are the heart of many electronic
sensing, computing, instrumentation and control devices. In advanced applications,
they are much more important as sensing elements (motion or position to voltage
converters) and computing elements (position to special voltage function converters)
than they are as mere voltage dividers. Several frequently neglected facets of potentiometers
and the trickery possible with them should prove useful to anyone in electronics.
In Fig. 1-a, output voltage Eout is the input voltage Ein
times R2/R1, where R1 is the total potentiometer resistance and R2 is the resistance
between the common terminal and the slider arm. R2/R1 is the transfer function of
the potentiometer. The slider-arm position determines the resistance of R2, of course.
This circuit arrangement is commonly called a voltage divider because Ein
is divided by R1/R2 to produce an output voltage Eout less than Ein.
Actually, the assumption that Eout equals Ein times R2/R1
isn't true in the strictest sense when the potentiometer is used in a circuit.
Why?
Because any attempt to use the output involves parallel-connecting an-other resistance
R3 across the section we labeled R2 (Fig. 1-b). This loading invalidates the ideal
no-load condition. If R3 is much (100 or more times) greater than R1, the error
in assuming Eout equals R2/R1 times Ein is small - negligible
in practical applications. If R3 is about 10 to 50 times R1, the loading is still
relatively small, but must be considered in many applications. The importance of
taking loading into account increases with precision requirements. And, of course,
loading effect becomes more serious as R3 becomes smaller with respect to R1.
For Instance?
Loading considerations can become important in relatively simple circuit applications.
In Fig. 1-c the potentiometer is set full up (Eout equals Ein).
Assume, for example, that R1 is 100 ohms and R3 is 100 ohms. If Ein is
10 volts, there is a current of 10/100 or 0.1 ampere through R1 and a current of
0.1 ampere through R3. That's a total of 0.2 ampere, or twice the current from the
source Ein that would be required if R3 were infinite. Obviously, if
load R3 had been neglected, the circuit would not perform to the design requirements.
Fig. 2a - Common use of a potentiometer: measuring liquid levels
(auto gas gages work this way).
Fig. 2b - Pot shaft driven by changes in gas
pressure can show pressure remotely on dc meter.
Fig. 3a - Loading a potentiometer to get a "drooped" curve.
You can approximate a logarithmic function.
Fig. 3b - A "bulged" curve.
Fig. 4a - Sticking in an extra battery makes these kinds
of curves.
Fig. 4b - Series resistor acts as electrical "stop", limiting maximum
Eout. Slope is altered. c - Resistor in "bottom" leg
limits minimum Eout, also alters slope of curves.
Fig. 5a - This circuit approximates a square-root relationship
- 1.79 times the ratio of Eout to Ein (each
of which can be measured) is the square root of the resistance value of R2 (which
could be marked off on a dial).
Fig. 5b - Values of tangents of angles between
+50° and -50° come out of this circuit. Angle θ and angle of pot rotation
are not necessarily same thing. Angle θ refers to electrical rotation.
Fig. 5c - A secant circuit.
Now, let's take a look at the effect of loading on Eout relative to
Ein, neglecting the effect that loading might have on Ein
itself. We'll assume again that Ein is 10 volts and that R1 and R3 are
100 ohms. But we'll assume the potentiometer is set so that R2 is 70 ohms (Fig.
1-d). The parallel combination of 70 and 100 ohms has an equivalent resistance of
about 41 ohms. Then Eout is Ein times 41/(41 + 30) or in this
case 10 X 41/71. Therefore Eout is about 5.6 volts instead of 7, as predicted
by the assumption of no loading. The circuit transfer function for this particular
circuit is 0.56 instead of 0.7!
So What?
The effect of loading on the potentiometer transfer function is unimportant for
most simple circuit applications.
But, the effect of loading is important if the output voltage Eout
is to be related to shaft position as in:
1. Potentiometers with calibrated dials where the operator sets shaft position
to obtain a given output. Typically, many instrumentation and control schemes, including
even some simple signal generator attenuation schemes, fall into this category.
So do applications in analog computers and calculators.
2. Potentiometers used to translate shaft position from another instrument into
a voltage proportional to position. The shaft position may be a function of another
quantity such as pressure, valve displacement, liquid level or distance. See Fig.
2.
If potentiometer loading is severe but neglected in these applications, the precision
of control or measurement is degraded.
But potentiometer loading has its blessings. Loading may be used to arrive at
a pocketful of fancy transfer functions that might otherwise require a large batch
of electronics (or mechanics).
A little understanding of potentiometers and potentiometer loading principles
will go a long way toward saving time and dollars in designing or modifying your
equipment. And they'll go a long way toward helping an industrial electronics technician
get the "wizard" award from his customers.
Before we get into this trickery, let's review some often neglected potentiometer
facts. Unless we're together on those, it's futile to attempt potentiometer trickery
expecting happy results.
Potentiometer Facts
Total resistance is the commonest electrical characteristic in that it is basic
to the electronic or electrical circuit. Total resistance is R1 in Fig. 1. The total
resistance accuracy is not too important if the voltage source Ein is
independent of loading or if the load on the potentiometer (R3 in Fig. 1) is negligible.
If loading design is to be intelligent, the tolerance of the total resistance must
be considered. If you're building one instrument only, you can measure total potentiometer
resistance with a bridge and base your design on the measurement. If you are designing
for production, you'll have to specify the tolerance of total resistance. The total
resistance tolerance for most inexpensive commercial wirewound potentiometers is
5% to 10%. Precision potentiometers with 1% or smaller tolerances are available
at considerably higher prices.
Taper is an important potentiometer characteristic that relates the voltage transfer
function to shaft position. The linear taper potentiometer (output voltage directly
proportional to shaft position) is most commonly used in applications of the type
discussed in this article. The trickery of loading is to change the taper from linear
to some other form.
Independent linearity is the accuracy of the taper or transfer function without
regard to the total potentiometer resistance tolerance. Inexpensive commercial potentiometers
which have independent linearity tolerances of about 1% to 3% are easy to obtain.
The Clarostat 58C1 series has an independent linearity of 1%. The Clarostat 58 series
has an independent linearity of about 2%.
Dissipation rating is another characteristic. A potentiometer should be operated
below its power rating. Bear in mind that loading increases potentiometer dissipation
and must be considered.
Resolution of a potentiometer refers to the smallest percentage increment of
change that can be obtained by shaft movement. Resolution is obviously a function
of the number of turns on a wirewound pot and the number of turns the wiper arm
covers at one fixed position.
Mechanical rotation refers to the number of degrees the shaft can be rotated
from one end stop to the other.
Electrical rotation refers to the number of degrees from the point where the
arm leaves zero resistance to the point where the arm first reaches maximum resistance.
Electrical and mechanical rotation are rarely the same because part of the mechanical
rotation is over the relatively broad metal contact connection ends of the pot.
The Clarostat 58 series has 280° of electrical rotation and 300° of mechanical rotation.
Obviously, if you're going to calibrate a dial scale, it should cover a span of
only 280°.
Potentiometer Trickery
Fig. 3-a shows the effect of heavy loading in a conventional loading circuit
. The ratio R2/R1 is proportional to percentage of electrical rotation and can be
readily transferred to a dial scale . Thus if 280° represents full electrical
rotation (= 1), 0.1 corresponds to 28°. Note that when R3 is one-tenth of R1
(R1/R3 = 10), the potentiometer-load taper differs considerably from a linear taper.
A particularly interesting relationship exists for the case where R3 is half
of R1. If Eout/Ein is multiplied by 10, this quantity approximates
the anti-logarithm of R2/R1 for values of R2/R1 from 0.15 to 1.0 to a reasonable
degree of accuracy. The dotted curve in Fig. 3-a is the antilogarithm plot. This
arrangement might be used in an instrumentation or computer application where a
shaft rotation represented a logarithm and a voltage proportional to the antilog
is desired. Obviously the general basic loading principle may be used to obtain
unusual transfer functions where a "droop" in the curve is desired.
If you want to get "bulge" in the transfer curve, simply load the opposite side
at the pot, as shown in Fig. 3-b.
In Fig. 4-a we've added to the trickery by putting a bias battery (EB)
in the circuit. Note the effect of changing the battery voltage ratios and polarities.
This set of curves is for the condition R1/R3 = 10. By varying this ratio, you can
generate still other functions.
Another basic potentiometer trickery scheme is to employ fixed resistance in
series with one of the potentiometer end legs. Note that the connection arrangement
of Fig. 4-b changes the slope and maximum output voltage. The arrangement of Fig.
4-c changes the minimum voltage and the slope of the transfer function curve. In
each case the curve is a straight line.
The basic methods of Fig. 3 and 4 can be combined to derive an almost limitless
number of variations. I'll leave the number to the enthusiastic reader. But I'll
throw in a few special tricks as a wind-up gesture. In Fig. 5-a I've shown the circuit
for a square-rooter. The pot scale should be divided into 100 equal units. The relationships
are shown in the figure. A tangent solver good over a range of -50° to +50° is shown
in Fig. 5-b. A secant solver is shown in Fig. 5-c.
* Project engineer, Vought Electronics, Arlington, Tex.
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