Transistor and op-amp stages
One transistor or op-amp gain stage, the kind every pedal is built from. Set the supply and the resistors, and see where the part sits, how far the output can swing each way before it clips, and the gain. Then drive it with a sine and watch the output.
Swipe sideways for the whole drawing. Tap a part to jump to its value. The red numbers are DC voltages to ground.
Transfer curve and self-bias line
Output at the load, one cycle
Harmonics
evenodd dB below the fundamental, 2nd to 10th
All values
Reading the chart
Each grey curve is the collector current at one base current as the collector voltage changes. The curves are nearly flat: the base current sets the collector current, times the transistor’s gain (its hFE), almost whatever the collector voltage. They bend down near 0 V, where the transistor saturates.
The collector and emitter resistors allow only the currents on the DC load line, from the full supply at zero current up to the current with the transistor as a short. The bias resistors set the base current, and so where on that line the transistor sits: the operating point. For audio, the output cap puts the load in parallel with the collector resistor, so the signal moves along the steeper AC load line. An emitter resistor that isn’t bypassed adds to its resistance and sets the gain, close to the collector load over the emitter resistance.
Swinging down, the collector runs into saturation, about 0.2 V. Swinging up, the current falls to zero and the transistor cuts off. Whichever comes first sets the clean headroom. A stage biased with its collector near half the supply has about the same room both ways.
PNP. A PNP transistor is an NPN with every polarity turned round. Its emitter goes to the positive side, so a PNP pedal runs on a negative supply: positive ground, with the battery’s plus to ground, as in the germanium fuzzes and treble boosters. Every voltage on the drawing reads negative. The chart shows its curves the same way as an NPN, against the voltage from emitter to collector.
Leakage. Germanium transistors pass some collector current with no base current at all. When that shows, the lowest curve is the one at no base current, sitting above zero. Leakage grows quickly with temperature, so germanium stages drift as they warm up.
Collector feedback. With a resistor from the collector to the base, the bias steadies itself: if the current rises, the collector falls and feeds the base less current. That makes the bias less fussy about the transistor’s gain, and the same resistor feeds back some signal, which lowers the input impedance.
Each grey curve is the drain current at one gate voltage, from 0 V down toward cutoff. Past the knee, at a few volts, the curves are flat: the gate voltage sets the current. Below the knee the JFET acts like a resistor. The top curve, the gate at 0 V, is the most current the JFET can pass, its IDSS.
The source resistor biases the stage by itself. The current through it lifts the source above the grounded gate, so the gate sits negative to the source. The self-bias line is where the gate is at minus the current times that resistor, and the JFET sits where it crosses the curves: the operating point. The small chart under the curves shows the same thing as the transfer curve, current against gate voltage, crossed by the straight self-bias line.
The DC and AC load lines work as on a BJT. Swinging down, the drain runs into the knee. Swinging up, the current falls to zero. JFETs vary a lot from one to the next, so the same resistors put two of the same part at different points. That’s why many JFET pedals have a trimmer on the drain or source.
The chart is the stage’s response: its gain against frequency, from the bench’s engine. The grey line is the op-amp’s own open-loop gain, which falls 6 dB per octave above a low corner. The stage’s gain can’t be more than that, so it rolls off where the two meet. That’s near the gain-bandwidth product over the noise gain (1 + Rf / Rg, or 1 + Rf / Ri when inverting).
On a single supply the op-amp needs a reference halfway up, so the output can swing both ways. The output stops short of each rail by an amount that depends on the op-amp, about 1.5 V on a TL072 or a 4558 and a few tens of millivolts on a rail-to-rail part. The waveform shows the output pin with both limits.
Slew rate limits how fast the output can move. A full swing at a high frequency turns into a triangle once it needs more than the op-amp can deliver. The full-power bandwidth is the highest frequency a full clean swing can reach.
Warnings. Red flags a transistor saturated or cut off at rest, a JFET in its ohmic region or with its gate forward-biased, an op-amp output near a rail at rest, or the solver not settling.
How this tool works. The curves come from the transistor laws the circuit bench uses, a transport Ebers-Moll model with Early effect for a BJT and a square law for a JFET, with each preset’s typical values. They aren’t measurements of a particular part. We solve the stage with the bench’s engine: the operating point, the small-signal gain at the sine’s frequency and the sine itself, every part in place. The op-amp is the bench’s macromodel: gain, gain-bandwidth, slew rate, and an output that stops short of each rail. The coupling caps are 10 µF and the bypass caps 100 µF, large enough to be shorts at these frequencies. For the corner a smaller coupling cap makes, try the corner calculator. The sine runs 40 ms (at least 12 cycles) so the caps settle, then the last four cycles are kept. For tube stages, try the triode load line and gain stage tools.
Spot an error, or want a circuit added? Email info@swellamps.com. A schematic or a clear photo of one helps. Anything you send may be used to improve these models and our desktop app.
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