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André Michelle 7a21b78283 fixes mapping changes
2026-03-19 21:12:19 +01:00

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TB-303 Bass Synthesizer — Apparat Emulation

Compiled 2026-03-19 for openDAW Apparat implementation.

Sources

  • Open303 (Robin Schmidt) — full C++ DSP implementation
  • Robin Whittle (Devil Fish) — circuit analysis
  • Tim Stinchcombe — diode ladder filter mathematical model
  • a1k0n/303 — JS/Python resynthesis experiments
  • KVR Audio DSP forums — community measurements
  • Csound diode_ladder documentation

Implementation

Example file: packages/app/studio/src/ui/devices/instruments/examples/tb-303.js

Parameters (Knobs)

Knob Default Range Type Description
waveform 0 0–1 int 0=sawtooth, 1=square
tuning 0 -5–5 linear (st) Pitch offset in semitones
cutoff 500 80–5000 exp (Hz) Base filter cutoff frequency
resonance 0.5 0–1 linear Filter resonance
envmod 0.5 0–1 linear Filter envelope modulation depth
decay 400 200–2000 exp (ms) Filter envelope decay time
accent 0.5 0–1 linear Accent amount
volume 0.7 0–1 linear Output level

Architecture

Monophonic. Overlapping notes trigger slide (portamento). High velocity (>0.78) triggers accent.

1. Oscillator (VCO)

Circuit: Discrete thyristor-based oscillator (Q24, Q25, Q27 as SCR) with integrator capacitor C33. Faster reset time than conventional switched-integrator designs.

Sawtooth

  • NOT mathematically ideal
  • Raw saw passes through ~10 high-pass filters (coupling capacitors), the ladder filter, VCA, and mixer
  • Even harmonics present due to S-curve shaping in the ramp
  • DSP: bandlimited sawtooth via polyBLEP with DC blocking

Square

  • Derived from sawtooth via single-transistor waveshaper (Q8, PNP)
  • Frequency-dependent duty cycle:
    • ~71% at lowest pitches (65 Hz)
    • ~45% at highest pitches (660 Hz)
    • Linear mapping: duty = 0.71 - 0.26 * clamp((freq - 65) / 595, 0, 1)
  • Two capacitors in waveshaper circuit cause this behavior
  • DSP: bandlimited pulse via polyBLEP with pitch-dependent duty cycle

Tuning

  • 3 octaves in pattern mode (C2–C5), 4 in track mode
  • Untransposed low C ≈ 65 Hz (2.0V CV)
  • Tuning control: ±500 cents (±5 semitones)
  • 6-bit R2R DAC: theoretical range ~16.35 Hz to ~659 Hz

2. Filter (VCF) — The Key to the 303 Sound

Architecture: 4-pole DIODE ladder filter (NOT Moog transistor ladder). Transistors with base-collector shorted to function as diodes.

The C18 Mismatch (Critical Characteristic)

  • C18 = 0.18 µF, other three caps = 0.33 µF each
  • First pole sits ~1.83x higher than the other three (≈ one octave)
  • Result: "1+3 pole" filter — three matched poles at nominal cutoff, one pole an octave above
  • Effective slope: ~18 dB/oct near cutoff (not 24 dB/oct)
  • Deeper in stopband: transitions toward 24 dB/oct
  • Prevents true self-oscillation (phase shift never reaches 360°)

Open303 Filter Structure

y1 += 2*b0*(y0 - y1 + y2)   // First stage: 2x coeff (halved cap)
y2 +=   b0*(y1 - 2*y2 + y3) // Stages 2-4: normal coeff
y3 +=   b0*(y2 - 2*y3 + y4)
y4 +=   b0*(y3 - 2*y4)

Cross-coupling terms model the bidirectional coupling between stages through the diodes. Sequential evaluation (each stage uses updated value of previous stage).

Filter Coefficient

For native sample rate (no oversampling):

g = tan(π * cutoff / sampleRate)
b0 = g / (1 + g)

For 2x oversampled inner loop (used in our implementation):

g = tan(π * cutoff / (sampleRate * 2))
b0 = g / (1 + g)

Resonance Feedback

  • Global feedback from y4 back to input
  • High-pass filter in feedback path (~150 Hz cutoff) from coupling capacitors
  • Tim Stinchcombe: ~6 additional poles/zeros from coupling caps
  • Resonant peak around 8–10 Hz (measured on hardware)

Resonance mapping:

resoSkewed = (1 - exp(-3 * resonance)) / (1 - exp(-3))
kFeedback = resoSkewed * 17

Gain Compensation

gNorm = kFeedback / 17
gComp = (gNorm - 1) * resoSkewed + 1
gComp *= (1 + resoSkewed)
output = 2 * gComp * y4

Saturation

  • tanh() nonlinearity at filter input: y0 = tanh(input - feedbackHP)
  • Transistor-diode ladder natural saturation
  • Csound alternative: (1/tanh(k_sat)) * tanh(k_sat * input)

Cutoff Range

Condition Range
Env Mod at minimum ~77 Hz – ~620 Hz
Env Mod at maximum up to ~36 kHz
Practical maximum ~20 kHz

Post-Filter Chain (Open303 reference values)

  • Allpass: 14.008 Hz
  • Highpass: 24.167 Hz
  • Notch: 7.5164 Hz, BW 4.7
  • Pre-filter highpass: 44.486 Hz

3. Envelopes

Two separate envelope generators.

VEG (Volume Envelope) → VCA

Parameter Normal Accented
Attack ~3 ms ~3 ms
Decay 1230 ms 200 ms
Sustain 0 0
Release 0.5 ms 50 ms

RC-filter style:

attack:  out += coeff * (1.3 - out); transition to decay when out >= 1.0
decay:   out *= exp(-1 / (decayTime * sr))
release: out *= exp(-1 / (releaseTime * sr))

MEG (Main Envelope) → Filter Cutoff

  • Attack: near-instantaneous (~3 ms smoothing)
  • Decay: variable, controlled by Decay knob (200 ms – 2000 ms)
  • On accented notes: decay fixed at ~200 ms regardless of knob
megEnv *= exp(-1 / (decayTime * sr))

VCA + MEG Compound

The MEG contributes to the VCA while gate is on:

ampOut = vcaEnv + 0.45 * megEnv + accentGain * 4.0 * megEnv

Retriggering

  • Retriggers on each new note gate
  • During slide: gate stays HIGH → envelope does NOT restart

4. Accent

Accent simultaneously affects multiple parameters. Triggered when velocity > ~0.78 (100/127).

Effect on VCA

  • MEG voltage → Accent pot → VCA control current
  • Through RC: 47k resistor + 0.033 µF capacitor
  • Primary reason accented notes are louder

Accent Sweep Circuit

Adds to filter control current. Components:

Component Value
Diode + resistor in series 47k
Pot (second section of Resonance pot) 100k
Capacitor to ground 1 µF
Mixing resistor to filter 100k

Time constants:

  • Charge: (47k + 100k) × 1 µF = ~147 ms
  • Discharge: 100k × 1 µF = ~100 ms

Accent Stacking (Iconic 303 Behavior)

The 1 µF capacitor does NOT fully discharge between steps. Each successive accented note creates a higher filter peak due to charge accumulation. This "building" effect is one of the most iconic 303 behaviors.

if (accented && gate):
    accentCap += (1 - exp(-1/(0.147*sr))) * (megEnv * accent - accentCap)
else:
    accentCap *= exp(-1/(0.1*sr))
cutoff *= pow(2, accentCap * sweepOctaves)

Accent on Envelopes

  • MEG decay: fixed 200 ms (regardless of Decay knob)
  • VCA decay: 200 ms (vs 1230 ms normal)
  • VCA release: 50 ms (vs 0.5 ms normal)

"Gimmick" Circuit

Three transistors pull cutoff down at end of envelope decay, creating characteristic dip/pluck. Partially modeled by accent sweep discharge behavior.

5. Slide (Portamento)

Characteristics

  • Exponential glide (NOT linear)
  • Equivalent to 6 dB/octave lowpass on pitch CV
  • Constant time regardless of interval size
  • Time constant: ~60 ms (stock TB-303)
  • Devil Fish: 60–360 ms via Slide Time pot

Circuit

RC lowpass on pitch CV. When slide activated, pitch CV charges capacitor through resistor.

Implementation

freqSmoothed += (freqTarget - freqSmoothed) * (1 - exp(-1/(0.012*sr)))

Time constant 12 ms for the RC gives ~60 ms effective glide time.

Behavior

  • Overlapping notes trigger slide (gate stays HIGH)
  • NO envelope retrigger during slide
  • Oscillator phase NOT reset
  • Filter state NOT reset

Sequencer Gate Timing

  • 12 internal clock ticks per 16th note
  • Gate high at tick 0, low halfway through tick 3 (~50% duty)
  • Slide extends gate through current step into next
  • Slide activates on the NEXT note after the slid note
  • Sequencer does NOT anticipate the next note

6. Parameter Ranges Summary

Parameter Range Notes
Cutoff frequency ~77 Hz – ~620 Hz Up to ~36 kHz with full envmod
Resonance 0 – just below self-osc 303 can't truly self-oscillate
Env Mod 0–1 ~4 octaves sweep at maximum
Decay time ~200 ms – ~2000 ms Fixed ~200 ms on accented notes
Tuning ±500 cents ±5 semitones
Oscillator range ~32 Hz – ~660 Hz 3-4 octaves
Slide time ~60 ms Exponential RC lowpass
VCA attack ~3 ms
VCA decay ~1230 ms / ~200 ms Normal / accent
VCA release ~0.5 ms / ~50 ms Normal / accent

7. Circuit Quirks Critical for Authentic Emulation

  1. Mismatched first filter pole — C18=0.18µF vs 0.33µF → first stage 2×b0 coefficient
  2. High-pass in resonance feedback — ~150 Hz HPF from coupling capacitors
  3. Accent stacking — 1µF cap doesn't fully discharge between steps
  4. No true self-oscillation — mismatched poles prevent 360° phase shift
  5. Frequency-dependent square duty cycle — 45% high pitches, 71% low pitches
  6. VCA = ADSR(sustain=0) + MEG — compound envelope, not simple gate
  7. tanh saturation at filter input — transistor-diode ladder natural clipping
  8. Slide prevents envelope retrigger — gate stays high, smooth transitions
  9. Low-frequency resonance peak (~8–10 Hz) — from coupling caps in filter core
  10. BA662 OTA for VCA — introduces subtle saturation and offset

8. Open303 Magic Numbers

Oversampling:           4x
Wavetable length:       2048 samples
Mip-map tables:         12

Square shaping:
  tanhShaperFactor:     dB2amp(36.9) ≈ 69.98
  tanhShaperOffset:     4.37

Filter:
  Feedback HP:          150 Hz (one-pole)
  Cutoff clamp:         200 Hz – 20000 Hz
  Post-filter allpass:  14.008 Hz
  Post-filter HP:       24.167 Hz
  Post-filter notch:    7.5164 Hz, BW 4.7
  Pre-filter HP:        44.486 Hz

Envelopes:
  VCA attack:           3 ms
  VCA decay:            1230 ms (normal), 200 ms (accent)
  VCA release:          0.5 ms (normal), 50 ms (accent)
  MEG RC1 smoothing:    0 ms
  MEG RC2 smoothing:    15 ms

Envelope modulation scaling (from measurement):
  c0   = 3.138152786059267e+002
  c1   = 2.394411986817546e+003
  oF   = 0.048292930943553
  oC   = 0.294391201442418
  sLoF = 3.773996325111173
  sLoC = 0.736965594166206
  sHiF = 4.194548788411135
  sHiC = 0.864344900642434

VCA MEG contribution:
  ampEnvOut += 0.45 * mainEnvOut + accentGain * 4.0 * mainEnvOut

Default level:          -12 dB
Level by velocity:      12 dB
Default cutoff:         1000 Hz
Default envMod:         25%
envUpFraction:          2/3
AmpDeClicker:           Biquad LP 12dB/oct, 200 Hz, Q=sqrt(0.5)
Slide time:             60 ms (tau = 12 ms)
Anti-alias:             Elliptic quarter-band

9. a1k0n/303 JS Reference

VCA:
  attack:     1.0 - 0.94406088 = 0.05593912
  decay:      0.99897516
  amplitude:  0.5
  Update rate: every 64 samples

VCF envelope (measured from x0xb0x):
  vcf_e1 = exp(5.55921003 + 2.17788267*cutoff + 1.99224351*envmod) + 103
  vcf_e0 = exp(5.22617147 + 1.70418937*cutoff - 0.68382928*envmod) + 103

Filter: 5 poles + 1 zero
  Section 1: one-zero + one-pole HP (~100 Hz)
  Section 2: complex conjugate pole pair (biquad)
  Section 3: complex conjugate pole pair (biquad)
  Lookup: 64 resonance × 10 coefficients
  Gain: 2/(1+reso_k) + 0.5*reso, where reso_k = reso * 4.0

10. References

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