Volume pot taper: linear vs log, and why loading matters

What you're hearing

A pot is a voltage divider you can turn. Its track is one resistor, 250 kΩ here, from the input to ground. The wiper splits it into two: the part above the wiper and the part below. The output is the input times the bottom part's share of the track, exactly as in a voltage divider. At 100% the wiper sits at the input, so you get everything. At 0% it sits at ground, so you get nothing.

The taper is how the share follows the turn. In a linear pot, the share is the rotation: half way round, half the track is below the wiper. In an audio pot, the share starts slowly and speeds up. SynthMaker's audio taper puts (81^p − 1)/80 of the track below the wiper at rotation p. Half way, that's (9 − 1)/80 = 10%.

Ears hear ratios, so they need the log. A 10 dB drop sounds roughly half as loud, wherever you start. So a volume knob feels even when each part of the turn takes off about the same number of decibels. The audio taper nearly does this: about 10 dB per quarter turn. The linear pot loses only 6 dB in the whole top half, then plunges from −20 dB to silence in the last 10%.

Loading bends the curve. Whatever the wiper drives is a resistor to ground in parallel with the bottom part of the track. A 25 kΩ load is ten times smaller than the pot, and it pulls the output down most where the bottom part is large. At 75% the audio pot drops from −9.8 dB to −19.8 dB. The last quarter of the turn then has to make up 20 dB, so the knob does little for most of its travel and then rushes. The rule of thumb this shows: whatever follows a pot should be much larger than the pot, or a buffer.

A cable's capacitance takes the treble. Seen from the output, the pot is a resistor: the top part and the bottom part in parallel. With 1 nF to ground, that resistor and the capacitor make a low-pass filter. At 100% the resistor is almost nothing, so nothing is lost. At 75% it's about 55 kΩ, and the corner falls to about 2.9 kHz. The worst point is about 85%, where the resistor is 62.5 kΩ and the corner is about 2.5 kHz. That's why turning a guitar down a little can sound duller as well as quieter. Here the input is an ideal source; a real guitar pickup has resistance and inductance of its own, so it loses some treble into the cable even at full volume.

The model's limits. SynthMaker's pots have no wiper resistance or tolerance. Its audio taper is one smooth curve, where real audio pots are usually made of two straight pieces, so a real pot's numbers will differ a little.

Try this

• Turn volume from 100% down to 0% with each taper. With the audio taper, the level falls evenly all the way. With linear, almost nothing happens until near the bottom, then it drops away.
• Press "Audio, 25k load" and turn volume again. The top quarter now does most of the work, and the rest of the knob feels dead.
• Press "Audio, 1 nF cable" and set volume to about 85%. The sound goes duller as well as quieter. Turn back up to 100% and the treble returns. To change the pot, the load or the capacitor, open it in SynthMaker.

The parts list

circuit Volume  setting volume: 50%  P1 in out gnd 250k volume audio  # Rload out gnd 25k  # Ccable out gnd 1nend

The two commented lines are the load and the cable. Remove the # to put one in. Write linear in place of audio for a linear pot.

How we checked it

Checked against ngspice, a standard circuit simulator: the rotation table matches it to 0.01 dB, and the cable and load versions are within 0.15 dB of ngspice up to 4 kHz.

Build it step by step

• The manual: OTAs and pots, its "A pot" section: writing a pot, its position and its taper.
• The example sounds: one of the circuit demos in the manual ends with a volume pot on an audio taper, after a tone control with a pot of its own.

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Further reading

• Pots, tapers and how they're made: Wikipedia: Potentiometer.
• Pots in audio, tapers and loading: Elliott Sound Products: Potentiometers (Beginners' Guide to Pots).
• Why 10 dB sounds about twice as loud: Wikipedia: Sone.