Tone-stack lab

The vertical axis is level in decibels, referred to the open-circuit signal of the stage driving the network — what that stage would deliver into no load at all, before its own output resistance is charged for. That is the useful reference, because the loss the driving stage's output resistance suffers into the stack is part of what the stack costs: on a plate-fed circuit it is more than a decibel of the reading, on a follower-fed one a rounding error. Nothing here is an amplifier: a passive tone stack has no gain of its own, so every curve on this page sits at or below the 0 dB line. What the controls choose is which frequencies get thrown away and how much of them — the stage after the stack then makes the level back up.

The scoop is the point. Set a three-knob preset to five all round and the curve sags in the middle, a broad dip several hundred hertz wide with the bass climbing away below it and the treble climbing away above. That dip is what people mean by a scooped midrange, and it is not a side-effect: it is what happens when a bass path and a treble path are recombined with nothing filling the gap between them. Pull the Middle control down and the dip deepens into a proper notch; push it up and the notch fills, but never quite to flat.

Everything on 10 is not flat. Turn all three controls fully up and the curve does not become a straight line — the dip is still there, only shallower, and the whole response stays below 0 dB across the midrange. The controls set where the network's three paths hand over to each other; they cannot remove the hand-over. That is the reference curve drawn faintly behind every setting, and it is the single most useful thing to know about these circuits: the stack has a voice of its own that no knob position turns off.

Insertion loss is real, and it is large. Look at where the midrange sits on a three-knob preset — nine to fifteen decibels down at five all round, and deeper as the Middle comes down. The circuit pays for the tone controls in level, which is exactly why these stacks are fed from a cathode follower and followed by another gain stage. A designer who wanted a milder tone control could have one; what these amps wanted was range, and range costs signal.

The controls interact — and the wiring sets what happens at the stops. Set Bass and Middle both to zero on any of the three-knob presets and the curve stops around thirty decibels down rather than falling off the chart: in the ladder wiring every one of these drawings prints, the middle pot's full 25 kΩ track always stands between the network's foot and ground, and it props the output up at every knob setting. The textbook redrawing of the same parts — output node joined to both wipers, rheostat mid leg — would instead tie the output to ground through the remains of the network and go nearly silent; the solver holds that form too, but no preset uses it, because no published sheet the archive has read draws it.

Ignore the knobs for a moment and follow the signal. It arrives at one node and leaves from another, and between them it can take three routes to the output.

The treble route starts at a very small capacitor — 250 pF on the tweed circuits, 270 pF and 500 pF on the British ones. A capacitor that small is close to an open circuit at bass frequencies and close to a wire at treble, so this path carries only the top end. It lands on the treble pot; the wiper decides how much of that top end reaches the output and how much is bled away into the rest of the network.

The bass and mid routes both start behind the slope resistor — the resistor between the input and the network's lower half, 33 kΩ to 100 kΩ depending on the circuit. From there two much larger capacitors, in the tens of nanofarads, feed the bass pot and the mid leg. Large capacitors pass low frequencies happily, so this half of the network carries the body of the sound. The slope resistor's job is to hold this whole lower half back relative to the treble route: it sets the tilt of the curve, which is why changing it, as Marshall did in going from 56 kΩ to 33 kΩ, changes the amp's whole character without moving a single knob.

The output is the treble pot's wiper, alone. That is the ladder wiring, and it is the form every published drawing behind these presets prints — the Fender 5F6, 5F6-A, AA964, AB763 and AA1164 sheets and the Marshall JTM45, 1987 and 1959 drawings alike: the bass pot is a rheostat in series down the network's lower half, and the Bass control works by varying how hard that lower half loads the treble pot. The joined wiring — the textbook redrawing of the same parts, with the treble and bass wipers meeting at a single output node — is kept in the solver as the reference form, but no preset uses it: none of the sheets the archive has read draws it. Either way the controls cannot be separated; the wirings differ in where the collision happens, and, as the sections below show, in what happens at the stops.

The mid leg is the network's foot. Below the bass pot the network runs to ground through whatever the circuit puts there. A three-knob stack puts a small pot there — 25 kΩ, tiny beside the 1 MΩ bass pot — and that pot is the Middle control: the pot's full track always stands in the leg, the mid capacitor lands on its wiper, and the control slides the capacitor's injection point along a fixed resistance. Fender's two-knob blackface circuits replace the pot with a fixed resistor — 6.8 kΩ on the Deluxe Reverb and both Princetons, 15 kΩ on the blackface Champ — but keep the capacitor that feeds the leg. The tweed Super's two knobs are no member of this family at all: its sheet draws a different network — treble and bass on two separate branches, recombined at the output — and its preset below is solved as that network. One solver holds all of these forms; each preset is solved with the wiring its own circuit's schematic draws.

Switch between the presets and the difference in the curve is larger than one missing control, and it is not the missing control that does it. What carves the notch is the second low-end path: a capacitor on the mid leg as well as on the bass leg, two routes down from the slope resistor arriving at the output node from different places. Every three-knob circuit here has it, and so does the blackface two-knob stack — which is why a blackface amp is scooped with both knobs at five even though it has no Middle control to blame. The tweed Super's preset is the odd one out because its circuit is: with treble and bass on separate branches and no shared cap ladder, five-and-five leaves only a shallow saddle — about 7 dB at its deepest, near 190 Hz — though pushing both controls to ten deepens the crossover valley between the two branches to around 18 dB at 1 kHz.

The foot of the network is worth trying at the extremes, because the families end differently. On the three-knob presets — the 5F6, the 5F6-A and all three Marshalls — Bass and Middle both at zero bottoms out around 30 dB down: the 25 kΩ middle track stands permanently in the ground leg, and the stack never collapses. The blackface two-knob presets hold up for the same reason in fixed form: the 6.8 kΩ leg keeps them around 29 dB down rather than silent. The split-network 5F4 behaves differently again — Bass at zero grounds its bass branch's injection point, and the low end falls some fifty decibels while the treble branch keeps playing, only about 13 dB down at 5 kHz: one branch can go quiet while the other carries on. The resistance that sets a circuit's floor is also the reason it never goes entirely quiet.

The Middle control's authority is worth a moment too. On the 5F6 preset with Treble and Bass at five, moving Middle from 0 to 10 lifts the bottom of the notch from about 23 dB down to about 10 dB down and walks it from roughly 860 Hz to 640 Hz. It is a real control — but it fills the dip rather than removing it, which is why a three-knob amp still sounds like a three-knob amp with the Middle buried.

The curve is not sampled from a table or traced from a published plot. At each of 361 frequencies across the sweep the network is solved from scratch by nodal analysis: one Kirchhoff current-law equation per node, capacitors entered as an admittance of jωC and resistors as 1/R, the driving stage entered as an ideal source behind its own output resistance, and the resulting complex system solved for the voltage at the output node. The wiper positions enter as two resistances per pot — the track above the wiper and the track below it — which is why a control at either stop behaves so differently from the same control near the middle.

Five assumptions are worth naming, because they are the difference between this curve and a measurement at the back of a real amplifier:

• The driving stage is a resistance. A cathode follower is entered at roughly 1/g_m of the driving triode; a plate is entered at its plate resistance in parallel with its plate-load resistor. Both figures come from the driving tube's published small-signal data and the circuit's own parts list — for a 12AX7 that is about 625 Ω from a follower and 38 kΩ from a plate. The difference matters: a stack fed from a plate is loaded by its own source in a way a follower-fed stack is not.
• The output is loaded by one resistor — the grid leak or volume pot the stack actually drives, again read from the parts list. The following stage's input capacitance, and the Miller capacitance of the tube behind it, are not modelled; both push the very top of the treble down a little further than the plot shows.
• The slider is track, not dial. A control at 5 here means half of the pot's resistance is in circuit. On a real amp with an audio-taper pot, half the track arrives at around 7 on the printed dial — see the guide to potentiometer taper, which classifies every pot in the corpus from its own parts list.
• The parts are their marked values. Carbon-composition resistors of the era were ±10% or ±20% parts, and the paper and mica capacitors were no better; two amps off the same production line did not share this curve exactly. Read the shape, not the third decimal place.
• This is the network alone. The speaker, the output transformer, and every coupling capacitor elsewhere in the amp shape the sound at least as much as the tone stack does, and none of them is in this plot.

The solver behind the page was checked against independent ngspice AC sweeps of the same element lists — the joined reference form, the ladder network in both its mid-leg forms (the three-knob 5F6 and 5F6-A, the fixed-leg AA964 and AB763), and the 5F4's split network, using the same simulator the archive uses to verify every operating point — and agrees with each to within 5 × 10⁻⁵ dB across the sweep. For what a decibel is, see units and notation.

The small tweed amps carry a single Tone knob, and it is not a cut-down version of the stacks above — it is a different circuit doing a different job. The pot is wired as a rheostat, two terminals instead of three, in series with one small capacitor from the signal line straight to ground. That branch is a variable drain: at one end of the shaft the capacitor is bled to ground through the whole million ohms of the track and almost nothing escapes; at the other the capacitor sits directly across the signal and takes the treble with it.

Load the 5F2-A preset and sweep the knob, and the network's real character shows up immediately: almost the entire audible change is crowded into the bottom of the travel. Above about 2 on the slider the bleed branch is a much higher impedance than the stage driving it, so it does essentially nothing; below that it takes over quickly. This is a genuine property of a 1 MΩ pot working against a 0.005 µF capacitor and a plate of a few tens of kilohms, not a quirk of the plot — and it is why a tweed tone control is so often described as doing nothing until it is nearly off.

It is also why the driving impedance is not a detail here. The three-knob stacks are fed from a follower stiff enough that the network barely loads it; this one is fed from a plate, and the bleed works against that plate resistance. Take the source impedance away and the control would do nothing at all.

Where each circuit sits on that ladder — no tone control, one knob, two, three — is gathered on the topology pages.