SynthMaker How a tone stack works: passive bass, middle and treble
A tone stack is three pots, three capacitors and a resistor that share out an amp's signal by frequency. Being passive, it only cuts: with every knob at noon it scoops the mids, 12.9 dB down at about 770 Hz, against about 6 dB at 100 Hz and 5 kHz.
circuit ToneStack setting output: 1.4 V setting bass: 50% setting middle: 50% setting treble: 50% Rs in a 1k C1 a t1 250p P1 t1 out t3 250k treble R4 a s 56k C2 s t3 20n C3 s m 20n P2 t3 t3 m 1M bass audio P3 m m gnd 25k middle Rl out gnd 1MendPress Play to see the wave after the circuit, at out.
What you're hearing
A passive stack can only cut. It's made of resistors, capacitors and pots, and none of them can add energy. So the output is always a share of the input, never more. At every setting tried here, the loudest the output gets is 0.2 dB under the input, with everything on full. Turning a knob "up" really means cutting that band less. Amps usually follow the stack with a gain stage to win the level back.
Highs and lows take different roads. The highs reach the output through the 250 pF capacitor into the treble pot. A capacitor passes high frequencies more easily: 250 pF is 637 kΩ at 1 kHz but 64 kΩ at 10 kHz, so this road carries mostly the top end. The lows go through the 56 kΩ resistor and the two 20 nF capacitors into the bass and middle pots, which hang under the treble pot. The treble knob slides the output between the two roads.
The middle falls between the roads, and that's the scoop. The mids are too low for the 250 pF road. On the other road, the second 20 nF capacitor (8.0 kΩ at 1 kHz) and the middle pot pull the mids towards ground. With every knob at noon, the response at 100 Hz is −6.9 dB, at 5 kHz −6.1 dB, and in between it dips to −12.9 dB at about 770 Hz: a scoop about 6 dB deep. The middle knob sets how hard that pull is. At 0 it grounds the bottom of the bass pot, and the dip falls to −21.2 dB. At full it's −9.8 dB, still a scoop.
What each knob does, with the other two at noon:
| setting | 100 Hz | 1 kHz | 5 kHz | deepest point |
|---|---|---|---|---|
| all at noon | −6.9 dB | −12.5 dB | −6.1 dB | −12.9 dB at about 770 Hz |
| bass 0 | −16.6 dB | −11.8 dB | −6.0 dB | none: the lows fall away |
| bass full | −4.0 dB | −12.9 dB | −6.1 dB | −13.7 dB at about 710 Hz |
| middle 0 | −7.9 dB | −20.4 dB | −8.1 dB | −21.2 dB at about 860 Hz |
| middle full | −6.1 dB | −9.5 dB | −4.9 dB | −9.8 dB at about 710 Hz |
| treble 0 | −6.0 dB | −12.6 dB | −13.7 dB | none: flat from about 3.4 kHz up |
| treble full | −7.7 dB | −10.7 dB | −1.6 dB | −13.1 dB at about 580 Hz |
| all on full | −5.1 dB | −8.9 dB | −1.4 dB | −11.1 dB at about 490 Hz |
Each knob moves its own band by 11 to 13 dB: bass at 100 Hz, middle at 1 kHz, treble at 5 kHz.
The knobs interact, because they share the same nodes. The treble pot's bottom end sits on the bass pot, and the bass pot sits on the middle pot, so turning one changes what the others are dividing against. In the table, turning treble from 0 to full cuts the bass by 1.7 dB (100 Hz from −6.0 to −7.7 dB) and moves the dip down from about 770 Hz to 580 Hz. Turning middle from 0 to full lifts 100 Hz by 1.8 dB and 5 kHz by 3.2 dB, so it's partly a level knob. Turn all three to 0 and the output is joined almost straight to ground: about 80 dB down, silence.
It can't go flat without losing level. Its flattest setting is bass 0, middle full, treble 0: −11.3 dB at 100 Hz, −10.2 dB at 1 kHz and −9.5 dB at 5 kHz, within 2 dB across that range but about 10 dB down. With everything on full it's louder, but the dip is still there, 11.1 dB down at about 490 Hz. So an amp with this stack sounds a little scooped at most settings.
The bass pot is an audio-taper pot (at noon it's 10% of its track, 100 kΩ; see volume pot taper); treble and middle are linear.
Try this
- Press "Middle off", then "All at noon". The middle of the note drops out, then comes back. That's 7.9 dB at 1 kHz, from the middle knob alone.
- Turn treble from 0 to full and listen to the low end too. The top opens up by 12 dB, and the bass gets slightly thinner as the knobs fight over the same nodes.
- Press "Flat", then "All on full". Flat is even across the range but quieter. Full is louder and brighter, but the scoop is still there. Open it in SynthMaker to change the parts: try 25 kΩ in place of the 56 kΩ slope resistor and hear the bass and middle come up, and the dip move higher.
The parts list
circuit ToneStack setting output: 1.4 V setting bass: 50% setting middle: 50% setting treble: 50% Rs in a 1k C1 a t1 250p P1 t1 out t3 250k treble R4 a s 56k C2 s t3 20n C3 s m 20n P2 t3 t3 m 1M bass audio P3 m m gnd 25k middle Rl out gnd 1MendRs is the stage that drives the stack and Rl the stage after it. Bass and middle are pots with their wiper joined to one end, so each one is a resistor you can turn. setting output: 1.4 V gives the loudest settings a little room.
How we checked it
Checked against ngspice, a standard circuit simulator: at every knob setting we tried, its response matches ngspice's within 0.1 dB from 20 Hz to 15 kHz, at the 1× rate it runs at. Its values are the classic ones published by Yeh and Smith (DAFx 2006).
Build it step by step
- The lesson: A distortion pedal from six parts (opens in a new tab). Its tone control is the simplest passive tone control: one resistor you can turn and a 10 nF capacitor, the RC filter.
- The video: This distortion pedal is six lines of text: a real circuit, simulated. It loads only when tapped.
- The manual: Your first circuit: how a parts list is written, one part per line.
Further reading
- D. T. Yeh and J. O. Smith, DAFx 2006: this tone stack's response worked out exactly from its parts, with its classic values, and checked against SPICE. PDF
- How the bass, middle and treble controls and the slope resistor shape the curve: Rob Robinette: How the TMB tone stack works.
- Where tone stacks are used, passive and active: Wikipedia: Tone stack.
- Linear and audio tapers: Wikipedia: Potentiometer.