August 1967 Electronics World
Table
of Contents
Wax nostalgic about and learn from the history of early electronics. See articles
from
Electronics World, published May 1959
 December 1971. All copyrights hereby acknowledged.

Here is yet another example
of where the basics in electronics never changes. There are always new people entering
into the realm, so even if the subject has been covered countless times already,
there is always a need to print it again. Remember that at one time you were a newbie
and appreciated seeing beginners' concepts explained. The oldtimers of the day
probably complained about being tired of seeing the simple stuff rehashed over
and over. Most standard potentiometers (pots) are linear in operation, that is,
the resistance between the moveable wiper contact and the overall resistance between
the two ends is directly proportional to the percentage of travel along the length
of the resistive element (printed or wirewound). One of more popular specialty pots
is the logarithmically tapered type that is used in audio circuits in order to effect
an audible linear sound volume change relative to the percentage of travel of the
wiper arm. Analog stereo systems are major users of tapered potentiometers. The
more things change, the more they remain the same.
Calculation of Potentiometer Linearity and Power Dissipation
By David L. Heiserman
The linearity of a potentiometer can be completely changed by the position
of the wiper arm and the resistance of the load.
Fig. 1. These curves show how the pot linearity varies with
the load.
Most potentiometers used in communications and industrial electronic equipment
are specified according to three characteristics: total resistance of the resistive
material, maximum power dissipation, and the linearity of resistance as a function
of shaft position. Both engineering technicians who must modify existing circuits
and experimenters who are designing their own circuits face the problem of choosing
the right potentiometer for the job at hand. As will be shown, this choice is not
as simple as just selecting a likely looking pot from a catalogue.
Selecting the appropriate pot is somewhat more complex than many people might
be led to believe. The discussion that follows points out the problems involved
in selecting potentiometers for loaded voltagedivider circuits and describes how
to solve the problems using a few equations and the manufacturer's specifications.
The circuit in Fig. 1 shows the conventional method of controlling the voltage
across a load impedance R_{L}. With this particular voltagedivider arrangement,
a clockwise rotation of the shaft decreases the voltage applied to the load. If
a linear voltage response is desired, the natural tendency is to choose a pot that
has a resistive element specified as linear. The fact that the winding is linear,
however, is no guarantee that it will produce a linear response under load. The
curves in Fig. 1 show how the linearity of the output voltage changes with
the ratio of load impedance to specified potentiometer resistance.
When the load resistance is infinite (no load), the response of a linear pot
is truly linear. As the load impedance decreases, however, the response becomes
more nonlinear.
In theory, it is impossible to obtain a linear response from a linear taper pot
that is loaded with any impedance. In practice, though, an R_{L}/R ratio
of 10 or more gives a response that is fairly linear.
Likewise, a log taper pot will produce a truly log response only if the load
impedance is infinite. As the R_{L}/R ratio becomes smaller, the deviation
from the specified log response becomes greater. When loaded, "voltagedivider"
pots with certain nonlinear characteristics will compensate for this undesirable
loading effect and produce a nearly linear output. A discussion of nonlinear pots,
however, is beyond the scope of this article. Because of the unwanted effects of
pot loading, the potentiometer resistance should be kept as low as possible with
respect to the load impedance.
However, a good linear response is bought at a high price  the smaller the specified
pot resistance, the greater the current through its contacts and resistive elements.
Power Dissipation
The potentiometer power dissipation specified by the manufacturer is actually
a reflection of the maximum current that can pass safely through any of the pot's
three connectors or any portion of its resistive element. The following equation
enables the user to calculate this maximum current rating: I_{max} = √(P/R) where
I_{max} is the maximum amount of current that can pass safely through any
part of the pot, P is the specified power rating of the pot, and R is the specified
resistance of the pot.
For example, a 10,000ohm, 1watt potentiometer can safely pass √[1/(1 x 10^{4})]
amperes, or 10 milliamperes.
The current through a voltagedivider circuit such as the one in Fig. 1
is at a maximum when the wiper arm is in the position that makes the circuit strictly
parallel (α
= 0).
The maximum current through any part of a loaded pot may then be determined by
using the equation I_{max} = E [( R + R_{L}) /RR_{L}] where
I_{max} is the maximum current through any part of the pot (at
α = 0), E
is the d.c. or r.m.s. value of applied voltage, and R_{L} is the load impedance.
Substituting I_{max} from this latter equation for I in the first equation,
we find the relationship P_{req} = E^{2} [(R + R_{L}) /RR_{L}]
where P_{req} is the maximum power dissipation of the pot.
Example
Suppose the d.c. or r.m.s, value of applied voltage (E) is 10 volts and the load
impedance (R_{L}) is 10,000 ohms. If a good linear response is desired,
what are the necessary potentiometer specifications?
Consider the linearity problem. The resistance of the pot should be no greater
than 0.1 times R_{L}, so we can select a 1000ohm potentiometer. The maximum
power dissipation of this pot in this circuit can be found by applying the second
equation. In this case, P_{req} = 10^{2} [( 10 x 10^{3}
+ 1 x 10^{3}) / (10 x 10^{3}) (1 x 10^{3})] or 0.1 watt.
The specifications for this particular pot should be 1000 ohms, 1 watt, and a
linear taper.
Posted January 16, 2020(original 9/9/2011)
