Potentiometer as a Voltage Divider, With Taper and Loading

Potentiometer Voltage Divider and Taper

Everything about a pot follows from one constraint that an ordinary divider does not have: the two resistances are not independent. Move the wiper and one grows exactly as much as the other shrinks. That single fact explains the output resistance, the loading behaviour and why volume controls behave the way they do.

The two halves always add to the track

A pot is one resistive track with a contact sliding along it. The wiper divides the track into two parts, and however it moves:

Feed the two ends from a supply and the wiper is the output of a divider. Substituting that constraint into the divider formula collapses it to something simpler than the two-resistor case:

So with nothing connected the output is simply the supply times the track fraction, and the pot’s value does not appear at all. A 1 kΩ pot and a 1 MΩ pot at the same setting give the same voltage — the value only decides the standing current and how much a load matters.

Taper: rotation is not resistance

For a linear pot the track fraction equals the rotation, and the two words can be used interchangeably. For every other kind they cannot, and that is the entire point of a taper. A logarithmic pot puts far less resistance below the wiper at mid-rotation than a linear one — typically 10 to 20 % rather than 50 %.

Real log pots are approximated from two or three linear segments and every manufacturer’s curve differs, so any formula is a model rather than a fact about the part in your drawer. The model used here is fitted to the one specification pots are actually sold on — the fraction at mid-rotation:

The curve passes exactly through (0, 0), (0.5, m) and (1, 1) and rises smoothly between them. A reverse-log or "C" taper is the same curve rotated through 180 degrees: fast at the start and slow at the end.

Why bother? Because hearing is roughly logarithmic. A linear pot used as a volume control spends most of its travel in a range where the change is barely audible and does all its useful work in the last fifth — a log taper redistributes the travel so that equal rotation gives roughly equal perceived change.

Output resistance, and why the middle is worst

The Thevenin resistance at the wiper is the two halves in parallel, and because they sum to a constant this has a shape rather than a value:

At either end stop one of the two is zero, so the output resistance is zero — the wiper is connected straight to a rail. At the centre both are half the track, giving the maximum:

Why loading bends the curve instead of shifting it

From the voltage divider theory, a load costs an output −R_out/(R_out + R_L) of its unloaded value. For an ordinary divider R_out is fixed, so a load is an offset. For a pot R_out varies with position — zero, zero at the ends and a maximum in the middle — so the same load causes no error at either extreme and its largest error somewhere near the centre.

That is a distortion of the shape, not a scaling of it. The audible consequence on a volume control is that the top of the travel flattens: the last third barely changes, because the wiper is close enough to the supply end that the load has little effect while the region below it has been pulled down. Combine that with a log taper, which already concentrates the action at the low end, and a loaded control ends up doing almost all of its work in the first third of its rotation.

Worked example

A 20 % error from a load equal to the pot value, and this is the worst point on the travel — at 10 % or 90 % of rotation the same load costs far less. Check it against the Thevenin form: R_out at mid-rotation is 10 kΩ/4 = 2.5 kΩ, and −2.5/(2.5 + 10) is exactly −20 %. The two routes agree, which they must.

Choosing a Potentiometer Value

The value does not affect the unloaded output at all, so it is chosen entirely on the two things it does affect.

Too low: it loads the source and wastes current

The track draws Vin/R_total continuously, whatever the setting. A 1 kΩ pot on a 9 V rail is 9 mA and 81 mW — significant on a battery, and enough to load a weak source so that the input voltage you assumed is no longer there.

Too high: noise and loading by the next stage

A 1 MΩ pot has a 250 kΩ output resistance at mid-travel, which picks up hum and coupled noise readily and is disturbed by almost anything you connect. High-value pots also tend to be noisier mechanically — the wiper contact resistance is a larger fraction of the track.

The usual range

For audio, 10 kΩ to 100 kΩ covers nearly everything: 10 kΩ for a low-impedance source driving a following stage of a few hundred kilohms, 100 kΩ where the source is weak. For setting a bias or a reference where nothing much is connected, higher is fine. The test is always the same — is the pot’s maximum output resistance, R_total/4, at least ten times below whatever it drives?

Taper Codes and What They Actually Mean

The letter codes are not standardised across regions, which is a genuine trap when ordering.

• A — logarithmic (audio) in European and Asian marking, the standard volume-control taper. In older American marking, A meant audio too, so this one is usually safe.
• B — linear in European and Asian marking. In older American marking B could mean reverse-log, which is the collision to watch for.
• C — reverse logarithmic, sometimes called anti-log. Used where the useful adjustment is at the anticlockwise end.
• W, S, and others — manufacturer-specific curves, including S-shaped laws used for balance and panning controls.

The reliable approach is to read the datasheet curve rather than the letter, and to check the specified fraction at mid-rotation. If you have the pot in hand, measuring wiper-to-end resistance at half travel settles it in seconds: about half the total means linear, about a tenth means log.

Faking a log taper from a linear pot

Since loading pulls the middle of the curve down, a resistor deliberately connected from the wiper to the ground end makes a linear pot approximate a log law. A resistor of roughly a fifth of the track value gives a passable approximation. It is a genuine technique, and it also explains the reverse: a log pot that is loaded is no longer following the curve you chose it for.

Pots, Rheostats and Trimmers

Three terminals or two

Using all three terminals makes a divider, and the output is a voltage that does not depend on the pot’s value. Using only the wiper and one end makes a rheostat — a variable resistor — and the value is then everything. The two uses have almost nothing in common, and a great deal of confusion comes from calling both a "potentiometer".

Always tie the unused terminal

When using a pot as a rheostat, connect the unused end terminal to the wiper. It costs nothing and it means that if the wiper contact goes intermittent — which is what worn pots do — the resistance rises to the track value rather than going open circuit. In a circuit where an open circuit means full volume or full current, that difference matters.

Trimmers are for setting once

Trimmer potentiometers are rated for a few hundred adjustments, not continuous use, and they drift with temperature, humidity and vibration. Where a value can be fixed in production or corrected in firmware, that is almost always better.

Digital potentiometers

A digital pot is a resistor ladder with analogue switches, and it behaves like the model here with two caveats: the wiper has a real series resistance, often 50 to 200 Ω, and the taper is whatever the register map says — usually linear, with log done in software. The step count sets the resolution, so a 256-tap pot cannot be set finer than 0.4 % of travel.

What This Calculator Assumes

• An ideal track with zero wiper resistance. Real wipers add tens to hundreds of ohms, which matters most at the extremes where the calculated output resistance is zero.
• The log model above rather than your specific pot. It is exact at 0, 50 and 100 % of travel by construction, and an approximation in between — real pots are piecewise linear.
• A purely resistive load. A capacitive load on the wiper forms a filter whose corner frequency moves with the setting, since the output resistance does.
• DC or audio frequencies. Track inductance and capacitance are negligible there and not at radio frequencies.
• A supply stiff enough to drive the track. A pot across a weak source loads it, and the input voltage assumed here is then wrong.

Common mistakes

• Expecting the pot’s value to change the output voltage. Unloaded it does not — the output is the supply times the track fraction, whatever the value.
• Assuming a log pot is at 50 % of its resistance at 50 % of rotation. It is typically at 10 to 20 %, which is the whole point of the taper.
• Loading a pot and expecting the error to be a constant offset. Output resistance varies with position, so a load bends the curve — no error at the ends, worst in the middle.
• Using a linear pot as a volume control. Most of the travel produces barely audible change and the last fifth does all the work.
• Leaving the unused end terminal floating when using a pot as a rheostat. Tie it to the wiper so a worn contact means full resistance rather than an open circuit.
• Trusting the taper letter code. A and B mean different things in different markets — read the curve, or measure the wiper resistance at half travel.

Frequently asked questions

How does a potentiometer work as a voltage divider?

The wiper splits the track into two resistances that always add to the pot’s value, so connecting the two ends across a supply makes the wiper the output of a divider. Unloaded, the output is the supply times the fraction of the track below the wiper.

What is the difference between a linear and a logarithmic pot?

On a linear pot the resistance below the wiper is proportional to rotation. On a log pot it rises slowly at first and steeply at the end — typically only 10 to 20 % of the track at half rotation. Log tapers are used for volume because hearing is roughly logarithmic.

What is the output impedance of a potentiometer?

The two halves in parallel, R_upper × R_lower / R_total. It is zero at both end stops and a maximum of R_total/4 at mid-rotation — so a 10 kΩ pot has a 2.5 kΩ output resistance at its worst point.

Why does my volume control go flat at the top?

Because the following stage is loading the pot. The loading error is largest near mid-travel and vanishes at the ends, which pulls the middle of the curve down and leaves the top compressed. Use a lower pot value or buffer the wiper.

What value potentiometer should I use?

10 kΩ to 100 kΩ suits most audio and biasing uses. The test is whether the maximum output resistance — a quarter of the pot value — is at least ten times below whatever is connected to the wiper. Lower values waste standing current; higher values pick up noise and are more easily loaded.

Can I make a linear pot behave like a log pot?

Approximately, by connecting a resistor from the wiper to the ground end — about a fifth of the track value gives a reasonable log-like curve. It works because loading bends the middle of the curve down, which is the same effect that spoils a log pot when it is loaded unintentionally.

What does the A, B or C code on a potentiometer mean?

Usually A for logarithmic, B for linear and C for reverse logarithmic — but the lettering differs between European, Asian and older American marking, and B has meant reverse-log in some. Check the datasheet curve, or measure wiper-to-end resistance at half travel.