Gain

A gain stage takes a voltage signal and outputs a larger copy. A guitar pickup delivers somewhere between 50 and 200 mV. For the circuit below, the size of the copy is set — to a first approximation — by two resistors:

Two things to notice. The formula does not contain the transistor: the gain is set by parts costing a rappen each. That is almost true, and the error will be visible in the simulation below. Second, the minus sign — the output is inverted. For a single stage this is inaudible; the ear does not register absolute polarity. It starts to matter when stages are chained, which is a later article.

Decibels, since they come up constantly here: . A gain of 25 is about 28 dB.

The circuit

Component values are from traced vintage units [3], [4]; the current reissue matches [5].

Code

import schemdraw
import schemdraw.elements as elm

with schemdraw.Drawing() as d:
    d.config(unit=2.2, fontsize=11)
    Q = elm.BjtNpn(circle=True).anchor('base').label('Q1', 'right', ofst=.8)

    # input side: a short lead first, so the divider tap sits
    # clearly left of the transistor
    elm.Line().at(Q.base).left(d.unit*0.75)
    tap = d.here
    elm.Capacitor().left().label('C1\n100n', 'top').reverse()
    elm.Dot(open=True).label('in', 'left')

    # bias divider, now on its own vertical line
    elm.Line().at(tap).up(d.unit*0.5)
    elm.Resistor().up().label('R1\n430k', 'bottom')
    elm.Vdd().label('+9 V')
    elm.Resistor().at(tap).down(d.unit*2.2).label('R2\n43k', 'bottom')
    elm.Ground()

    # collector side: rise first, then branch — R3 continues up,
    # C2 taps the junction and exits right, clear of the transistor
    elm.Line().at(Q.collector).up(d.unit*0.5)
    junc = d.here
    elm.Resistor().up().label('R3\n10k', 'bottom')
    elm.Vdd().label('+9 V')
    elm.Line().at(junc).right(d.unit*0.6)
    elm.Capacitor().right().label('C2\n100n', 'top')
    elm.Dot(open=True).label('out', 'right')

    # emitter side unchanged
    elm.Resistor().at(Q.emitter).down().label('R4\n390', 'bottom')
    elm.Ground()

Signal path, left to right. C1 passes the signal and blocks DC — the base must sit at a fixed resting voltage, and the guitar is not invited to disturb it. R1 and R2 divide the 9 V supply down to about 0.82 V at the base, which sets roughly 0.5 mA of collector current, which drops the collector to about 4.1 V — near half the supply, leaving close to maximum room to swing in both directions. Wiggle the base and the collector current follows; R3 converts that current wiggle back into a voltage, larger than the input by the resistor ratio:

C2 passes the amplified signal out and keeps the 4.1 V to itself.

Simulation

Claims require receipts. The netlist sits next to this article as spice/lpb1.cir; run it yourself with ngspice -b. Input: a 100 mV, 1 kHz sine — guitar-scale.

import subprocess, tempfile, pathlib
import pandas as pd

NETLIST = pathlib.Path("spice/lpb1.cir").read_text()

def run_stage(amplitude_v=0.1):
    """Run the LPB-1 deck with a given input amplitude; return a DataFrame."""
    deck = NETLIST.replace("SIN(0 0.1 1k)", f"SIN(0 {amplitude_v} 1k)")
    with tempfile.TemporaryDirectory() as tmp:
        deckfile = pathlib.Path(tmp) / "deck.cir"
        deckfile.write_text(deck)
        subprocess.run(["ngspice", "-b", deckfile.name], cwd=tmp,
                       check=True, capture_output=True)
        df = pd.read_csv(pathlib.Path(tmp) / "waves.dat",
                         sep=r"\s+", names=["t", "vin", "t2", "vout"])
    return df[["t", "vin", "vout"]]

Code

import matplotlib.pyplot as plt

df = run_stage(0.1)
fig, ax = plt.subplots(figsize=(8, 3.5))
ax.plot(df.t * 1e3, df.vin, color="grey", lw=1, label="input")
ax.plot(df.t * 1e3, df.vout, color="black", lw=1.2, label="output")
ax.set_xlabel("time (ms)"); ax.set_ylabel("volts")
ax.legend(frameon=False); ax.grid(alpha=.3)
plt.tight_layout()

In: 100 mV. Out: 2.2 V, upside down. Gain of 22.

The formula said 26. The missing part is the transistor’s internal emitter resistance — about 50 Ω at this operating point — which adds to R4. SPICE includes it; the napkin does not [7, Ch. 2]. That term, and why it makes gain drift with bias and temperature, is a future article.

Clipping

The collector can swing between the supply rail and slightly above ground: about 8.5 V of room. Feed the stage 1 V and it would need 22 V of output. It does this instead:

Code

df = run_stage(1.0)
fig, ax = plt.subplots(figsize=(8, 3.5))
ax.plot(df.t * 1e3, df.vin, color="grey", lw=1, label="input")
ax.plot(df.t * 1e3, df.vout, color="black", lw=1.2, label="output")
ax.set_xlabel("time (ms)"); ax.set_ylabel("volts")
ax.legend(frameon=False); ax.grid(alpha=.3)
plt.tight_layout()

The tops and bottoms are cut off, and unevenly — the stage runs out of room downward before upward. A flattened waveform contains harmonics that were not in the string’s motion; that is what “breakup” is. The asymmetry decides which harmonics, and a good share of pedal design consists of shaping exactly that.

Distortion is a gain stage pushed past politeness. Most circuits this site will ever analyze are variations on the two plots above: where the ceiling sits, how hard the signal hits it, and what shape the clipping takes.

Skipped, deliberately

Bias stability. What C1 and C2 do to the low end. Input and output impedance, and why the pickup cares about them. The internal resistance behind the 22-versus-26 gap. Each gets its own article; this one only needed the atom.

Netlist, schematic code, and page source are in the site repository. Run the deck, bend the values, argue with the results.

The realization

A pedal is not a secret. It is a circuit in a folded steel box, and circuits can be read. The King of Tone in particular has been traced, discussed, and documented by the DIY community for years. The parts cost very little. What stood between wanting one and having one was not seven years — it was a soldering iron and the willingness to be wrong a few times.

So I built one.

The king gets a king

A circuit with this reputation deserved better than a bare enclosure. My build got artwork: a crowned king, silver-bearded, the crown grown through with coral branches and jewels in violet, turquoise and amber. Designing that image took longer than populating the board, and it was worth it — it set the rule every pedal from this bench still follows: if the circuit is iconic, the box has to be too.

The first batch

The King of Tone build did not stay alone. Next to it came a Kingtone Duelist — the other transparent dual overdrive with a serious reputation — with its own artwork in the same spirit. Two circuits, two painted boxes, into the hands of musicians around here.

What came back was not applause. It was conversation: which channel, which clipping mode, which order in the chain, what to change. That conversation has not stopped since, and it is the actual product of that first batch — the workshop exists because of it, and this site documents what it keeps producing.

For the record

The King of Tone is Analog Man’s design and trademark; the Duelist belongs to King Tone. Those first builds were exactly that — builds, for my own board and for learning. What is sold from this bench under the Sense Pedals name are its own designs. But the debt is real, and this post is the receipt.