How a fuzz pedal works: two germanium transistors

What you're hearing

Two transistors multiply their gains. These are PNP transistors, so everything runs below ground, from a −9 V supply. The first is a common-emitter stage: a small voltage at its base makes a large one at its collector, 34 times larger here. That collector drives the second transistor's base directly. With the fuzz full up, the 20 µF capacitor ties the second emitter to ground for audio, so the second stage multiplies by another 112. From the first base to the second collector, that's 34 × 112 ≈ 3,800, or 72 dB. From the pickup's voltage it's about 1,000, as the guitar loses three quarters of its signal on the way in (more on that below).

It squares the wave because the second transistor runs out of room. At rest the second collector sits at −4.3 V. It can swing up to about −0.6 V, where the transistor is fully on, and down to −8.9 V, where it's off. So the output stays clean only while the pickup gives under about 4 mV: that's 1 mV at the fuzz's own input. A 0.1 V note is 25 times more, 28 dB. The collector then sits at one limit or the other 97% of the time: a square wave. Its 3rd harmonic is 9.7 dB under the note and its 5th 14.4 dB under, close to a perfect square's 9.5 and 14.0 dB. The output is taken off the 470 Ω end of the collector's 8.67 kΩ, about an eighteenth of the swing, so the square leaves at about ±0.27 V.

The fuzz knob sets the feedback. A 100 kΩ resistor runs from the second emitter back to the first base. For the bias, that loop always works: if the second transistor draws too much current, its emitter pulls the first base down, the first transistor turns further on, and that turns the second back down. For the signal, it depends on the fuzz knob. At 100%, the 20 µF grounds the emitter, so no signal goes back: full gain. At 0%, the emitter swings with the signal through the whole 1 kΩ. The second stage's gain falls to 8 (8.67 kΩ / 1 kΩ, near enough), and the 100 kΩ now feeds the signal back against itself, which pulls the input down to 0.67 kΩ. From the pickup the gain falls from about 1,000 to 90, 21 dB less. It still squashes from about 41 mV, so a 0.1 V note is 60% squashed: gritty, never clean.

A low input is why the guitar's volume knob cleans it up. A guitar amp's input is about 1 MΩ. This fuzz takes only 2.3 kΩ at 220 Hz (2.7 kΩ at 1 kHz), because its first transistor's base draws real current. Even at full volume, the pickup's own 6.8 kΩ against that 2.3 kΩ lets only a quarter of the signal in. Turn the guitar's 250 kΩ volume pot down to 90% and it puts about 60 kΩ between the pickup and the fuzz: the signal going in falls by 21 dB. At 50% it's 29 dB down, so the note has to reach 111 mV before the fuzz squares it, and a 0.1 V note comes through only 5% squashed. Its 3rd harmonic drops from 9.7 to 35 dB under the note. The output is just 3.2 dB quieter, because the fuzz still amplifies 36 times. So the knob changes the sound, from square back towards the clean note, more than the level.

The bias puts the second collector near half the supply. The bias knob is the first transistor's collector resistor, and through the loop it sets where the second collector rests. At 20 kΩ it's −4.3 V, near the middle of the supply, so the square's two halves are close to even: its 2nd harmonic is 25 dB under the note. At 47 kΩ the collector rests at −8.2 V, close to off, and the square goes lopsided, with its 2nd harmonic only 8 dB under. At 10 kΩ it rests at −1.1 V, nearly fully on, and the 2nd is 5.5 dB under. With this pair of transistors, 33 kΩ, the value many schematics show, puts the collector at −7.5 V. No two germanium transistors are alike, so builders set the bias for each pair, usually aiming at about half the supply.

Germanium is leaky, low-voltage and touchy about heat. In SynthMaker's AC128 model, measured from old transistors, each base sits under 0.1 V from its emitter (86 mV here), where a silicon 2N3906 needs 0.68 V. Germanium also leaks: switched off, the second transistor still passes 9 µA, so its collector stops at −8.9 V instead of −9 V. Swap in two 2N3906s with the same parts and the second collector rests at −1.5 V, far from the middle. The loop holds the second emitter one silicon base voltage below ground, so the bias resistor hardly moves it. The silicon button also changes the 8.2 kΩ to 4.7 kΩ, which brings the collector back to −4.5 V. Then it has 1.8 times the gain, squares from 2.3 mV, and its square is less even (2nd harmonic 14 dB under, against 25). Many players describe germanium as smoother and silicon as harsher. What the model leaves out is temperature: SynthMaker's transistors stay at 27 °C, with no noise. A real germanium transistor's leakage rises steeply with heat, so its bias drifts as it warms up.

Try this

• Turn fuzz from 100% down to 0%. The square softens into grit, but it never comes clean. Most of the change is in the top half: from the pickup, the gain is about 1,000 at 100%, 165 at 50% and 90 at 0%.
• Press "Guitar volume at 50%: it cleans up", then turn guitar slowly back up. The note is nearly clean at 50% and grows gritty by 90%, where the pot still puts 60 kΩ in front of the fuzz's 2.3 kΩ. The last tenth of the knob lets 21 dB more signal in, and the full square comes back.
• Open it in SynthMaker to change the parts. Turn bias from 20 kΩ to 47 kΩ and the square goes lopsided as the second transistor nears off. Or press "Silicon", then change R3 c2 o 4.7k back to 8.2k: the collector rests at −1.5 V, nearly fully on, and the square goes lopsided.

The parts list

circuit Fuzz  setting input: 0.083 V, from 0.01 V to 1 V  setting output: 0.5 V, from 0.05 V to 5 V  setting fuzz: 100%  setting guitar: 100%  setting volume: 100%  setting bias: 20k, from 10k to 47k  V1 gnd vcc 9V  Rp in p 6.8k  P1 p g gnd 250k guitar audio  C1 g b1 2.2u  Q1 c1 b1 gnd AC128  R1 vcc c1 bias  Q2 c2 c1 e2 AC128  R4 e2 b1 100k  P2 e2 f gnd 1k fuzz  C2 f gnd 20u  R3 c2 o 8.2k  R2 o vcc 470  C3 o v 10n  P3 v out gnd 500k volume audioend

in is the pickup's voltage, and Rp is the pickup's resistance. The silicon button writes 2N3906 in place of AC128 in Q1 and Q2, changes R3 to 4.7k and sets output to 0.8 V, so its peaks match the germanium version's.

How we checked it

Checked against ngspice, a standard circuit simulator: the whole circuit, guitar in front, at full fuzz and at 0%, driven by a 250 Hz sine, is within 0.06% of ngspice across the audible band at the 2× rate it runs at.

Build it step by step

• The manual: Circuit demos. A two-transistor germanium fuzz is among the example sounds, with bias and a supply you can run down like a battery.
• The circuit format: Start a circuit, for writing transistors and pots in a parts list.

Next and previous

All circuits

Further reading

• B. Holmes, M. Holters and M. van Walstijn, "Comparison of germanium bipolar junction transistor models for real-time circuit simulation", DAFx-17, Edinburgh, 2017: the measured AC128 and OC44 models this page plays. PDF
• Those models as SPICE files: Germanium BJT SPICE models.
• The single-transistor stage each half is built from: Wikipedia: Common emitter.
• Setting a transistor's resting point, and why feedback steadies it: Wikipedia: Bipolar transistor biasing.
• How feedback trades gain for a lower input impedance: Wikipedia: Negative-feedback amplifier.
• Why a square wave is the odd harmonics: Wikipedia: Square wave.
• 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