torvalds-GuitarPedal/Documentation/effects/rat.md

Rat Sketch [RAT]

A model of the ProCo RAT: one op-amp with a great deal of gain, a diode clamp on its output, one pole of treble cut and a buffer. There are no transistors in the signal path, so the whole pedal is a feedback network, two diodes and a filter — which makes it the distortion here with the least in it, and so the one where what is left is the argument.

Five controls. Distortion and Filter and Volume are the pedal's own; Sweep and Mode are the Helios's additions, described below.

Every figure here is drawn by Validation/draw-rat.py from measurements made by Validation/analyse-rat.py, which drives the pedal's own audio core on the host. The numbers behind each one are kept in the source of this page, in comments, and make check-analysis re-measures them and says if the code has moved underneath the drawing — so a figure can be as detailed as it needs to be without the record stopping being text. Comparisons against the hardware and against ngspice carry their date instead, because neither runs on a laptop.

Which RAT this is, and why that is the first question

There is no such thing as "the" RAT, and this matters more here than it would for most pedals, because the two things that vary between versions are the two things this model is mostly about: the op-amp and the diodes.

The reference is an Aion FX Helios Vintage Distortion — a documented kit, built, on the bench, with an OP07CP read off the board. It was chosen because it was to hand and because a kit comes with a schematic, which is the difference between measuring a circuit and guessing at one. Every fitted number in Effects/rat.h came off that unit on 2026-09-06.

The op-amp is a version, not a detail. The original 1978 RAT used an LM308N, externally compensated with the 30 pF cap between pins 1 and 8 that every RAT schematic shows. Pro Co began phasing it out around 1995 and post-1996 RAT 2s carry an OP07, which is internally compensated and needs no such cap. So the Helios's OP07CP is not a deviation from a RAT — it is what a modern one has, and this model is faithful to that generation rather than to the first.

That is the version dependency worth taking seriously, because of what the op-amp turned out to be worth. Giving it a real gain-bandwidth instead of an ideal one moved this model 7.9 dB at 5 kHz with the Distortion at noon and 22.8 dB at the top of the travel, and at full Distortion it was audible in a blind test — level-matched and shuffled, three takes ordered correctly by brightness. An LM308 RAT would want that one number refitted and, on the evidence, very little else: RAT_GBW is fitted at 460 kHz for this OP07, and the whole closed-loop corner falls out of it. What it would not need is a different slew rate, which is the usual folklore about this part — see below.

The diodes are the other version. A stock RAT has one silicon pair to ground and no switch. The Helios adds two common modifications: a Mode switch selecting between three sets of diodes, and a Sweep control that puts up to 1 k in series with the 47 R setting the gain, which takes the treble emphasis away and the gain with it. Fully down, Sweep is the stock pedal.

So Mode = Silicon with Sweep = 0 is a stock post-1996 RAT, and the other positions are the mods. If you are comparing this against a different RAT, that is the setting to compare at.

The gain network, and the loop around it

The feedback leg is two series RC branches in parallel with the Distortion rheostat above them, so the gain is frequency-dependent on purpose: 4.7 µF into 560 R lifts everything above 60 Hz, 2.2 µF into 47 R lifts it again above 1.5 kHz, and the Filter knob then takes the result back off. That shape is the pedal.

The peak moving down as the gain goes up is the gain-bandwidth: the corner sits wherever the gain the network is asking for has fallen to GBW/f, so the knob drags it across most of the audio band — about 2 kHz at noon and down near 560 Hz at the top.

The op-amp's rails are inside that loop, which is where the circuit has them and is not a formality. When it saturates the loop opens, C5 and C6 go on charging from wherever the node was, and when it comes back out is decided by that charge and by which rail it had been against. Two unequal rails and a capacitive feedback leg make a duty cycle, and for a clipped wave the duty cycle is the even harmonics: H2/H1 is |cos(πd)|, which is nothing at all at a half.

220 Hz, −12 dBFS, Distortion full	duty	H2	H3
the Helios	46.83 %	−19.6 dB	−10.1 dB
rat-helios.cir	45.96 %	−14.9 dB	−10.8 dB
this model	45.99 %	−17.9 dB	−11.2 dB
this model, rails outside the loop	49.96 %	−55.2 dB	−9.7 dB

Those are the softest numbers on this page, and it is worth saying by how much. They come from a scope reading of the op-amp's own output, good to something like a tenth of a volt, and a tenth of a volt on the upper rail is worth 0.29 % of duty and 0.65 dB of H2. The remaining disagreement with the pedal is 0.8 % and 1.7 dB — larger than that, but the same order, so the right conclusion is that the mechanism is present and correctly signed rather than that it is calibrated.

That is a table of one number each. The reason to believe it is a picture:

Seventy milliseconds of real playing at full Distortion, at real levels rather than matched. The model's plateaus tilt down at the pedal's rate and its zero crossings are the pedal's; over 150 ms the two correlate at 0.990.

It is also 1.45 dB quieter, and that is drawn rather than normalised away.

It is not a gain constant. At Distortion minimum, where the op-amp is a follower and the input network, the clamp curve, the follower and the output network are the whole signal path, the model matches the pedal to 0.02 dB across the entire level ladder. Nor is it the source the pedal is driven from, whose 1 kΩ output impedance against a 690 kΩ input costs 0.021 dB and is flat across the band.

Driven with the pedal's own recorded stimulus, windowed identically, at full Distortion:

220 Hz burst	rms	crest	plateau droop
the Helios	−8.46 dB	1.69 dB	2.17 dB
this model	−7.66 dB	1.36 dB	1.27 dB

So on a tone the model is 0.8 dB louder, and it has about half the pedal's droop — the tilt away from the rail across each clipped plateau, which is what the waveform above shows. That holds at every drive level tested. A flatter plateau is less peaky for the same energy, and on broadband material, where the level never settles and the tilt is being re-established constantly, it comes out 1.45 dB the other way.

The droop is C7 charging through the diodes, and most of the apparent gap was the bench. A capture reaches the analysis through the pedal's own analog input, whose coupling capacitor into the codec is a single-pole high-pass at 9.28 Hz.¹ Taking it back out — so the numbers are what an ideal capture would have caught — leaves this:

plateau droop	82 Hz	165 Hz	220 Hz	440 Hz
the Helios, corrected	3.80 dB	1.89	1.40	0.71
this model	3.72	1.82	1.33	0.57
rat-helios.cir	2.27	1.53	1.13	0.52

So the model is under 0.15 dB short of the pedal across 2.4 octaves rather than half of it, and the netlist is further short than the model. What remains is small and unattributed.

The op-amp's rails are not the explanation, and they are the obvious place to look: they are measured rather than fitted, a scope on pin 6 reading the output stopping 0.89 V short of the supply and 1.56 V short of ground. That trace settles the larger question too — at full Distortion the plateaus are flat, top and bottom — so whatever tilts this pedal's clipped half cycles, the amplifier does not.

The rest was excluded the same way, all by measurement: C7's value (4.1 µF in circuit), R5's (1 kΩ), the diode saturation current (×30 moves the droop 0.17 dB), its ideality (1.86 to 3.5, another 0.17), C7 leakage (300 µA moves it 0.01 dB) and the Filter branch (0.6 % of the current).

The level is a separate question and the correction does not touch it: +0.8 dB on a tone and −1.45 dB on a chord, pole in or out.

The netlist is not drawn here, and that is worth saying rather than passing over: on this material it correlates with the pedal at 0.574, so the model is the better description of the Helios than rat-helios.cir is. The deck is right about tones — it is what most of the constants on this page were fitted against — and wrong about a chord, by an amount no tone measurement would have found. That is a defect in the netlist rather than in this model, and it is not chased here.

A diode has no clipping level

The clamp is not a limit. A diode's drop is the logarithm of its current, so the node keeps climbing about a hundred millivolts a decade for as long as the drive keeps rising. At Distortion minimum the op-amp is a follower and the input drives the diodes through R5 alone, which is the one place that curve is visible from outside the pedal:

Drawn as compression — output against a straight line — because what matters is how far each bends and that none of them stops bending. Raw, all three are a diagonal with the interesting part squeezed into the last few decibels.

None of the three goes flat, and that is the point rather than a detail of the drawing. Measured on the pedal at 1 dB steps, the last decibel before full scale still moves the output 0.21 dB. A curve that goes flat above a knee cannot do that, and what it costs is visible: the flat top of a clipped note stops tilting as the note decays.

That figure is also the one setting where the Mode switch looks pointless, which it is not. Put some gain in front and the three positions separate by 7.6 dB of output ceiling:

The three positions are not three heights of one mechanism. LED clamps at 1.81 V, which is above the 1.414 V this pedal's input can reach, so at unity gain the LEDs never conduct at all — the green line is the linear chain and nothing else. Silicon at 0.61 V sits far below the op-amp's rails and dominates completely. Stacked is between. The two red LEDs are across the node in all three positions; they contribute nothing to the other two, four decades down where the silicon passes milliamps.

Magnified onto a single clipped edge, at Distortion noon where the clamp and the rails are both in play:

The diode law is fitted to the pedal, not to the netlist:

	this pedal	rat-helios.cir
N	1.859	1.752
Is	2.03 nA	fitted
Rs	31 Ω	absent

Where the 31 Ω lives is not settled. A 1N914's own bulk resistance is single-digit ohms, so most of it is the Mode switch's contacts or the JFET follower sagging at large signal, and those look identical from outside. Only the diode's own share should double in the Stacked position, so it is not doubled — a choice recorded rather than a measurement.

The Filter runs backwards

One pole, and turning it up makes it darker. It is the only tone control and it is after everything, so it removes treble the gain network has already made rather than shaping what the diodes see.

What it gets wrong

The asymmetry turns on more abruptly than the pedal's. Across the Distortion travel both this model and the netlist switch their asymmetry on between 0.25 and 0.30, where the pedal is already part way into it at 0.25:

Point for point at the pedal's own five settings the model is within 0.6 % at four of them and 1.9 % out at 0.25 — rms 0.91 %, against the netlist's 1.12 %. So this is the shape of the onset rather than a different curve, and the first version of this figure said otherwise only because it joined the pedal's five points with straight lines. There is no line through them now: the pedal was measured at five settings and nothing is known about what it does between.

Neither description reproduces the small rise from noon to full either, which is 0.6 %, which is about twice what the same measurement repeats to.

The follower is one number. RAT_KOUT is a flat −1.95 dB, which is a good approximation of a stage the schematic cannot settle anyway: it draws a 2N5457 and the kit shipped a PN4303, which bias half a volt apart. Against the deck with nothing else in the path there is a bow of about +0.4 dB through the midband crossing to −0.78 dB at 16 kHz, and the follower is where to look first.

Everything runs at the sample rate, so the diode clamp aliases. What that costs on this effect has not been measured.

And the slew rate is deliberately absent, which is worth saying because it is the first thing anybody reaches for. The OP07's 0.3 V/µs is never reached here: the closed-loop corner is 2 kHz at noon and 560 Hz at full, so a rail-to-rail swing through it has a maximum slope of 0.07 and 0.02 V/µs. The bandwidth limit wins by four to fifteen times everywhere, and a full swing at 0.3 V/µs would take 0.9 of a sample period in any case — sub-sample, so a per-sample delta clamp would model the sample rate rather than the part.

What it costs

A diode equation solved per sample is a logarithm and four Newton steps, and measured on the pedal that was 59 % of everything this effect costs. The clipping node cannot move while a note is playing, so scripts/rat_clamp.py solves it at every point of a table at build time and the audio core does an index and a lerp instead. What the finished effect costs is 9 % more than the crude sketch that preceded it — the one with a fixed clipping level, a symmetric clamp and the rails outside the loop — so everything on this page arrived for very little.

The table is 1548 bytes of RAM, sized so its interpolation error stays under the 0.62 mV rms residual of the fit it is built from. Ratios rather than percentages of the sample period, because a percentage depends on the clock the firmware happens to be built for and this one does not.

Reproducing this

cd Validation && make bench && ./analyse-rat.py      # every chart above
./compare-spice.py rat                               # against rat-helios.cir
./draw-rat.py                                        # the figures themselves

make check-analysis compares this page against a fresh run and warns when a number has moved. The hardware comparisons need the Helios on the bench and a capture from capture-rat.py; the figures need a guitar recording that is not ours to commit, and draw-rat.py says so on their faces.

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1. 9.28 Hz is measured, not assumed — Validation/test-loop.py fits it and it has held across three board generations, predicted before the third was built. It is 0.008 dB at 220 Hz, so no level, ladder or harmonic measurement here has ever needed to care about it. In the time domain it is not small: τ is 17 ms, so a value held across a 2.27 ms half cycle decays 12 % and a clipped flat top tilts 1.1 dB. loop.uncolour() takes it back out, which is what makes a number describe the pedal rather than the pedal and this bench together. The real fix is hardware and is planned rather than done: DC-coupling the codec inputs removes the pole, and the next-generation board wants that anyway for its headphone amplifier — with a 1 MΩ input and only a DC blocking capacitor in front of it, what is left is too small to correct for. ↩︎