Gibson Les Paul volume and tone

The knobs

Neck volume

Works in the neck and both positions. With both pickups on, it also sets how hard the neck side loads the bridge pickup, and at zero it mutes the guitar.

Bridge volume

The same for the bridge side.

Neck tone

Turned down, the neck cap sits across the neck pickup and the peak moves down.

Bridge tone

The same for the bridge pickup.

Switch positions

Neck

The neck pickup with its volume and tone. The bridge side is disconnected.

Both

Both volume wipers tie together at the switch. Now each volume pot loads the other pickup too, and turning either volume to zero mutes both.

Bridge

The bridge pickup with its volume and tone.

Coil modes

Series

Both coils in series, the way the pickup is normally wired.

Parallel

Both coils in parallel, in phase. The pickup’s inductance and resistance drop to about a quarter, so its resonant peak moves up and its output drops.

Screw coil

The screw coil alone, with the slug coil shorted, as a coil-split switch does it. The shorted coil still sits next to the live one and pulls a little current through their coupling.

Slug coil

The slug coil alone, with the screw coil shorted. Which coil stays live in a split depends on how the pickup and the switch are wired.

Parts

Neck screw

The neck pickup’s screw coil voltage, from the string moving in the magnet’s field near the neck. It’s half the pickup’s voltage, since the two coils are assumed to have equal turns.

Screw R

4.5 kΩ, The screw coil’s resistance, measured alone on a PAF-style humbucker (screw coil 4.5 kΩ, slug coil 4.2 kΩ).

Screw L

2.67 H, The screw coil’s inductance, measured alone at 1 kHz (screw coil 2.675 H, slug coil 2.56 H).

Neck slug

The neck pickup’s slug coil voltage, from the string moving in the magnet’s field near the neck. It’s half the pickup’s voltage, since the two coils are assumed to have equal turns.

Slug R

4.2 kΩ, The slug coil’s resistance, measured alone on a PAF-style humbucker (screw coil 4.5 kΩ, slug coil 4.2 kΩ).

Slug L

2.56 H, The slug coil’s inductance, measured alone at 1 kHz (screw coil 2.675 H, slug coil 2.56 H).

Coupling

k 0.127, How strongly the two coils share their magnetic field, entered as k (0 is none, 1 is complete). Measured alone, the two coils add up to 5.235 H, and the pickup in series reads 5.9 H. So each coil adds M = 0.33 H to the other, and k = M / √(L1 L2) = 0.127.

Winding C

140 pF, The capacitance between the neck pickup’s turns, across its output. A typical figure, not a measurement. It stays the same whichever coils are on.

Bridge screw

The bridge pickup’s screw coil voltage, from the string moving in the magnet’s field near the bridge. It’s half the pickup’s voltage, since the two coils are assumed to have equal turns.

Screw R

4.5 kΩ, The screw coil’s resistance, measured alone on a PAF-style humbucker (screw coil 4.5 kΩ, slug coil 4.2 kΩ).

Screw L

2.67 H, The screw coil’s inductance, measured alone at 1 kHz (screw coil 2.675 H, slug coil 2.56 H).

Bridge slug

The bridge pickup’s slug coil voltage, from the string moving in the magnet’s field near the bridge. It’s half the pickup’s voltage, since the two coils are assumed to have equal turns.

Slug R

4.2 kΩ, The slug coil’s resistance, measured alone on a PAF-style humbucker (screw coil 4.5 kΩ, slug coil 4.2 kΩ).

Slug L

2.56 H, The slug coil’s inductance, measured alone at 1 kHz (screw coil 2.675 H, slug coil 2.56 H).

Coupling

k 0.127, How strongly the two coils share their magnetic field, entered as k (0 is none, 1 is complete). Measured alone, the two coils add up to 5.235 H, and the pickup in series reads 5.9 H. So each coil adds M = 0.33 H to the other, and k = M / √(L1 L2) = 0.127.

Winding C

140 pF, The capacitance between the bridge pickup’s turns, across its output. A typical figure, not a measurement. It stays the same whichever coils are on.

Neck vol

500 kΩ, Neck volume, 500 kΩ audio taper. Its wiper goes to the switch, so with both pickups on, turning it to zero grounds the output and mutes both.

Neck tone

500 kΩ, Neck tone, 500 kΩ audio taper, used as a variable resistor in series with its cap.

Tone cap

22 nF, The neck tone cap.

Bleed cap

1 nF, Treble bleed cap across the neck volume pot’s top half. It keeps the treble as the volume comes down.

Bleed R

150 kΩ, Sits in parallel with the bleed cap so the treble lift doesn’t get too big at low volume settings.

Bridge vol

500 kΩ, Bridge volume, 500 kΩ audio taper. Its wiper goes to the switch, so with both pickups on, turning it to zero grounds the output and mutes both.

Bridge tone

500 kΩ, Bridge tone, 500 kΩ audio taper, used as a variable resistor in series with its cap.

Tone cap

22 nF, The bridge tone cap.

Bleed cap

1 nF, Treble bleed cap across the bridge volume pot’s top half. It keeps the treble as the volume comes down.

Bleed R

150 kΩ, Sits in parallel with the bleed cap so the treble lift doesn’t get too big at low volume settings.

Pickups and load

Each humbucker is two coupled coils, each with its own measured resistance and inductance and half the pickup’s voltage. Both pickups use the same values. The coil buttons switch between series (as built), parallel, or one coil by itself. With 1950s wiring on, each tone control hangs off its volume’s wiper, so turning a volume down cuts less treble. With two pickups on, each one loads the other through its coil. Without the string model, the graph adds them as if their voltages were equal and in phase. On a real string each harmonic reaches the two pickups at a different strength and sign, and that’s what makes the in-between positions sound the way they do. The string model uses a 24.56 in scale, with the pole rows measured from the bridge saddle at about neck 5.51 and 6.2 in, bridge 1.3 and 1.99 in (measured by Swell Amplification to the visible pole row of each covered humbucker, approximate, with the other row 17.5 mm away). Harmonic n reaches a pickup x from the saddle scaled by sin(nπx/L), with L the string length, so a pickup near a node barely picks that harmonic up, and two pickups can cancel it. Each humbucker counts as its two pole rows, half its voltage each, which cancels the harmonics whose wavelength on the string is twice the row spacing. The string is ideal and each pole row is a point under it (a real pickup’s wider window softens the top harmonics). Saddle intonation is left out. The treble bleed option puts 1 nF in parallel with 150 kΩ across the top half of each volume pot. Other values are common too, and you can change both. The cable is about 15 feet (450 pF) into a 1 MΩ amp input.