#### August 1967 Electronics World
[Table
of Contents] People old and young enjoy waxing nostalgic about
and learning some of the history of early electronics. Electronics World
was published from May 1959 through December 1971. All copyrights are hereby acknowledged.
See all
*Electronics World* articles. |

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 old-timers of the day probably complained
about being tired of seeing the simple stuff re-hashed over
and over. The more things change, the more they stay 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.

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
voltage-divider 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 voltage-divider 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
non-linear.

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, "voltage-divider" pots
with certain non-linear characteristics will compensate for
this undesirable loading effect and produce a nearly linear
output. A discussion of non-linear pots, however, is beyond
the scope of this article.

Fig. 1. These curves show how the pot linearity varies with
the load.

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 10,000-ohm, 1-watt potentiometer
can safely pass √[1/(1 x 10

^{4})] amperes, or 10 milliamperes.

The current through a voltage-divider 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 1000-ohm 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 9/9/2011