How a treble booster works

What you're hearing

One transistor multiplies the signal by about 75. The OC44 is a germanium PNP transistor, so it runs below ground, from a −9 V supply. It's a common-emitter stage: a small voltage at its base makes a large one at its collector. The 3.9 kΩ emitter resistor sets its current: the emitter sits at −0.94 V, so 0.24 mA flows. The 47 µF capacitor across that resistor ties the emitter to ground for audio, so nothing holds the gain back: about 75, or 37.5 dB, from the base to the output.

The small input capacitor makes it a high-pass filter. The capacitor sits in series with everything behind it: the transistor's own input, about 15 kΩ with its bias resistors, plus the guitar's 6.8 kΩ. Together they make a high-pass filter like the one on the RC filter page, with its corner at f = 1/(2πRC) = 1/(2π × 21.8 kΩ × 4.7 nF) ≈ 1.6 kHz. Above the corner the booster gives its full gain. Below it, the gain falls 6 dB for every octave down. So from the pickup, 5 kHz is multiplied by 49 (34 dB), 1 kHz by 27 (29 dB) and 100 Hz by only 3.2 (10 dB). The highs and upper mids come out 24 dB louder than the bass. A bigger capacitor moves the corner down and lets the body of the note through too:

The bias leaves more room one way than the other. The 470 kΩ and 68 kΩ resistors hold the base at −1.06 V. In SynthMaker's OC44 model, measured from old transistors, the base sits only 0.12 V from the emitter. The collector rests at −6.6 V. That leaves it 2.4 V of room towards the −9 V supply, where the transistor turns off, and about 5.6 V the other way, where it's fully on. So a loud treble note clips first on one side, and gently: at 1 kHz that half of the wave is 10% squashed at 50 mV from the pickup, and at 5 kHz from about 24 mV. A 0.1 V note at 1 kHz comes out with one half 26% squashed and the other only 3%. Clipping only one half adds even harmonics: here the 2nd is 16 dB under the note. That's the booster's own grit.

Into an amp that's already breaking up, the treble hits hardest. The last two buttons add a stand-in for an amp turned up until it just starts to break up: a gain of 5, then the two diodes to ground from the diode clipper. With the guitar straight in, a 0.1 V note comes out only 12% squashed. Put the booster in front and every note goes in harder, but not evenly: at 100 Hz 10 dB harder, so it's 65% squashed, and at 1 kHz 29 dB harder, so it's 95% squashed. The amp's clipping is now driven by the upper mids and treble, where a guitar's bite is, while the low notes stay less crushed. That's the classic use: an amp already turned up, with the booster pushing it in the frequencies that cut through. With range at 47 nF, the full-range setting, 100 Hz is 95% squashed too, so the low notes crush as hard as the high ones.

The guitar's volume knob moves the corner. At 1 kHz the booster's input is 37 kΩ, and at 5 kHz 16.5 kΩ, far more than the 2.3 kΩ of the two-transistor fuzz. So at full volume the pickup's 6.8 kΩ loses little: 3 dB at 5 kHz. But the guitar's volume pot adds its own resistance to the R in the corner's formula. At 70% on its knob, the pot puts 48 kΩ in front, and the corner drops to about 1/(2π × 63 kΩ × 4.7 nF) ≈ 530 Hz, while the level falls 21 dB. So turning the guitar down makes the booster quieter and less trebly at once: the boost reaches down into the mids, and the grit goes, since the note no longer comes out big enough to clip.

What the model covers, and what it leaves out. The OC44 model is a measured germanium transistor, with its low base voltage and its leakage. It has no temperature, noise or internal capacitances: a real germanium booster drifts as it warms up. The pickup here is just its 6.8 kΩ. A real pickup is also a coil, whose impedance rises in the treble, exactly where this circuit works, so with a real guitar the treble and the corner shift. And the amp is a stand-in that shows the direction, not any real amp's sound.

Try this

• Turn range from 1 nF to 47 nF. The sound goes from thin and cutting to full: the corner moves from 7.3 kHz down to about 170 Hz. At 1 nF, 100 Hz comes out 3 dB quieter than it went in.
• Press "Guitar straight into a driven amp", then "Treble booster into the driven amp". The first just breaks up. The second bites, mostly in the highs. Then turn range up to 47 nF, and the low notes crush too.
• Press "Range 4.7 nF: treble" and turn guitar from 100% to 70%. The note gets quieter and fuller, as the corner falls from 1.6 kHz to about 530 Hz. Open it in SynthMaker to change the parts: change Re from 3.9 kΩ to 2.2 kΩ and the current rises to 0.39 mA. The collector then rests at −5.1 V, nearer the middle, with room both ways, and the treble gain rises by 1.7 dB.

The parts list

circuit Booster  setting input: 0.083 V, from 0.01 V to 1 V  setting output: 8 V, from 0.5 V to 10 V  setting range: 4.7n, from 1n to 47n  setting guitar: 100%  V1 gnd vcc 9V  Rp in p 6.8k  P1 p g gnd 250k guitar audio  C1 g b range  R1 vcc b 470k  R2 b gnd 68k  Q1 c b e OC44  Re e gnd 3.9k  Ce e gnd 47u  Rc vcc c 10k  C2 c out 10n  Rl out gnd 1M  # The amp stand-in, for the last two buttons:  # U1 a m o opamp  # Rg m gnd 10k  # Rf o m 40k  # Ro o out 2.2k  # D1 out gnd 1N4148  # D2 gnd out 1N4148end

in is the pickup's voltage, and Rp is the pickup's resistance. The amp buttons take the # off the last six parts and send C2 and Rl to the amp's input, a. "Guitar straight into a driven amp" also connects C2 to the guitar, g, instead of the collector, and moves C1's input end to ground, so the booster sits idle. Both amp buttons set output to 1 V.

How we checked it

Checked against ngspice, a standard circuit simulator: the booster with the guitar in front, driven by a 1 kHz sine, is within 0.02% of ngspice across the audible band at the 2× rate it runs at, also where it starts to clip.

Build it step by step

• The manual: Circuit demos. A one-transistor germanium treble booster is among the example sounds, with its range knob.
• 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 OC44 model this page plays. PDF
• That model as a SPICE file: Germanium BJT SPICE models.
• The stage itself: Wikipedia: Common emitter.
• The corner formula and the 6 dB per octave slope: Wikipedia: High-pass filter.
• Setting the resting point with two resistors: Wikipedia: Bipolar transistor biasing.
• 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