SynthMaker How a diode clipper works
A diode clipper is a resistor into two diodes facing opposite ways. Silicon diodes pass almost nothing below about 0.3 V and conduct hard past 0.6 V, so a loud wave's tops are flattened into distortion: in this circuit, a 6 V peak is held to 0.63 V at the diodes.
circuit Pedal setting input: 6 V, from 0.5 V to 40 V setting output: 0.65 V, from 0.1 V to 2 V setting tone: 15k, from 1.5k to 150k R1 in a 2.2k C1 a gnd 10n D1 a gnd 1N4148 D2 gnd a 1N4148 R2 a out tone C2 out gnd 10nendPress Play to see the wave inside the circuit, at a.
What you're hearing
A diode is a knee, not a switch. Its current grows exponentially with the voltage across it: I = Is (e^(V / n·Vt) − 1). For the 1N4148 here (Is = 2.52 nA, n = 1.752, Vt = 25.9 mV), every extra 0.1 V lets about nine times more current through (e^(0.1 / 0.0453) ≈ 9.1). At 0.3 V a diode passes about 2 µA. At 0.6 V it passes about 1.4 mA, about 750 times more.
The resistor turns that knee into a ceiling. Whatever voltage the diodes don't hold drops across R1, the 2.2 kΩ resistor. A full-scale sound reaches the circuit at the input setting's voltage, 6 V peak as set. At the peak, about 2.4 mA flows through R1 and one diode, and the diode holds 0.63 V. The other 5.37 V drops across R1. The peak comes out at about a tenth of what went in.
More drive changes the shape, not the level. Here are the peaks at the diodes for the input setting's range:
| input (peak) | at the diodes (peak) |
|---|---|
| 0.5 V | 0.43 V |
| 1 V | 0.52 V |
| 6 V | 0.63 V |
| 40 V | 0.72 V |
Going from 6 V to 40 V is 16.5 dB more in, but only 1.3 dB more out. What grows instead is how much of each cycle sits flattened against the ceiling. Even the lowest setting bends the peaks a little: at 0.5 V, they lose 14%.
Flattened tops are new harmonics. A flattened wave is closer to a square wave, and a square wave is a note plus its harmonics. Both diodes are the same, so both halves of the wave are clipped alike. That makes only odd harmonics: 3, 5 and 7 times the note's frequency, and so on. A 110 Hz note gains 330 Hz, 550 Hz and 770 Hz. Harder drive makes it squarer and the harmonics stronger. That buzz is what we hear as distortion. Measured here: at 6 V in, a 110 Hz note comes out with its third harmonic 11 dB below the note, its fifth 16 dB below and its seventh 20 dB below. At 0.5 V in they're 26, 40 and 53 dB below. Even harmonics are absent, because both diodes clip alike.
The small capacitor takes the edge off. Between the peaks, while the diodes barely conduct, R1 and C1 make a low-pass filter: f = 1/(2πRC) = 1/(2π × 2.2 kΩ × 10 nF) ≈ 7.2 kHz. It softens the highest, fizziest harmonics. At the peaks the conducting diode is only about 19 Ω (n·Vt ÷ 2.4 mA), so there the diodes set the shape, not C1.
The tone control is a second low-pass. R2 (the tone knob) and C2 (10 nF) roll off the top: 1/(2π × 8.2 kΩ × 10 nF) ≈ 1.9 kHz as set. The knob runs from 1.5 kΩ (about 10.6 kHz, bright) to 150 kΩ (about 106 Hz, dark). Between the peaks, when the diodes barely conduct, R1 adds to the tone resistor: at 8.2 kΩ the corner is about 1.4 kHz rather than 1.9, and at the bright end about 3 kHz rather than 10.6. The output setting, 0.65 V, is the voltage at the output that plays at full scale. For a 110 Hz note at 6 V in, the output after the tone control peaks at 0.626 V, the same as at the diodes, because the tone corner is far above the note. The tone control trims the harmonics instead.
Try this
- Turn input up from 0.5 V to 40 V and watch the Scope. The tops flatten more and more, but the peaks only rise from 0.43 V to 0.72 V. You hear more buzz, not much more volume.
- Turn tone down towards 150 kΩ. The corner falls towards 106 Hz, the fizz goes, and the sound turns dark and woolly. Turn it up towards 1.5 kΩ for a bright, raspy edge.
- Open it in SynthMaker to change the parts. Type
#at the start of C1's line to take it out, and listen: the clipped edges get fizzier. Delete the#to bring C1 back.
The parts list
circuit Pedal setting input: 6 V, from 0.5 V to 40 V setting output: 0.65 V, from 0.1 V to 2 V setting tone: 15k, from 1.5k to 150k R1 in a 2.2k C1 a gnd 10n D1 a gnd 1N4148 D2 gnd a 1N4148 R2 a out tone C2 out gnd 10nendThis is Circuits 1's starter as written. The playable sound sets tone to 8.2 kΩ (Pedal(input: 6 V, tone: 8.2k)), and the parts list's own default is 15 kΩ, about 1.1 kHz.
How we checked it
Checked against ngspice, a standard circuit simulator: the whole circuit, tone control included, as this page plays it (6 V in, tone 8.2 kΩ, the 2× rate it runs at), driven by a 1 kHz sine, is within 0.14% of ngspice across the audible band (up to 20 kHz). Its fundamental is within 0.001 dB and its third harmonic within 0.03 dB.
Build it step by step
- The lesson: A distortion pedal from six parts (opens in a new tab). Ned builds this circuit part by part, then swaps the diodes and makes a germanium bass.
- The video: This distortion pedal is six lines of text: a real circuit, simulated. It loads only when tapped.
Further reading
- D. T. Yeh, J. S. Abel and J. O. Smith, "Simulation of the diode limiter in guitar distortion circuits by numerical solution of ordinary differential equations", DAFx 2007. PDF
- D. T. Yeh, "Digital Implementation of Musical Distortion Circuits by Analysis and Simulation", PhD thesis, Stanford University, 2009 (the DK method). PDF
- M. Holters and U. Zölzer, "A Generalized Method for the Derivation of Non-Linear State-Space Models from Circuit Schematics", EUSIPCO 2015. PDF
- The diode model (Shockley's equation, as SPICE uses it): ngspice documentation; background in Wikipedia: Shockley diode equation.