Gibson Les Paul volume and tone

The knobs

Volume

Turning it down puts the top part of the track in series with the pickup. That damps the resonant peak, so the 2 to 4 kHz presence goes before the level drops much. With the treble bleed or the 1950s wiring, more of that presence stays.

Tone

Turned up, the tone cap hangs off the circuit through the whole pot and does little. Turned down, the cap sits across the pickup and the resonant peak drops to a few hundred hertz, for the dark, vocal sound.

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

Humbucker screw

The humbucker pickup’s screw coil voltage, from the string moving in the magnet’s field under the strings. 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).

Humbucker slug

The humbucker pickup’s slug coil voltage, from the string moving in the magnet’s field under the strings. 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 humbucker pickup’s turns, across its output. A typical figure, not a measurement. It stays the same whichever coils are on.

Volume

500 kΩ, Volume, 500 kΩ audio taper. Even at full it loads the pickup with its whole track.

Tone

500 kΩ, Tone, 500 kΩ audio taper, used as a variable resistor in series with the tone cap. Its resistance goes up as you turn it up.

Tone cap

22 nF, Tone cap. With the tone pot down, it shunts the pickup’s treble to ground, and together with the coil’s inductance it pulls the resonance down.

Bleed cap

1 nF, Treble bleed cap across the top half of the volume pot. 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

Source: the pickup’s own voltage, from the string moving in the magnet’s field. The humbucker is modeled as its two coils. Each has its own measured resistance and inductance and carries half the pickup’s voltage, and the two are coupled magnetically (k comes from the measurements). Use the coil buttons to put them in series (as built), in parallel, or split to either coil with the other shorted. The winding capacitance is part of the network. Load: about 15 feet of cable (450 pF) into a 1 MΩ amp input. With the 1950s wiring option on, the tone network hangs off the volume pot’s wiper instead of its input lug, so turning the volume down cuts less treble.