How this gain stage works

This is the workhorse booster of the pedal world: one J201 wired common-source. The signal comes in through R1 and C1 into the gate, with R2 tying the gate to ground. Together they set two things: the pedal's input impedance (mostly R2) and a high-pass corner at 1/(2π·C1·(R1+R2)). At the stock values that corner sits under 2 Hz, but shrink C1 and you can thin the bass on purpose.

Bias is the part that trips people up. R3 sets the drain current: the current through R3 pulls the source above the gate, which turns the JFET partly off until it settles at an operating point. R4 then has to drop the supply so the drain idles near half voltage (4.5 V on a 9 V battery), or a little above, so the signal has room to swing both ways. In this calculator R4 recomputes automatically as 4.5 V divided by the bias current, so every R3 you pick is biased properly. On the bench it is not that clean: real J201s vary enormously from part to part, so treat the R4 shown here as a starting point and tune it (or use a trimmer) until your drain actually measures half supply.

Gain comes from the ratio of the drain load to what is in the source leg: A ≈ g_m·(R4 ∥ R5) / (1 + g_m·Z_s). With C2 removed, R3 stays in the signal path and tames the gain (and cleans it up). Switch C2 in and it shorts R3 out for AC, unlocking the full gain of the stage. The size of C2 decides how far down that boost reaches: a big cap bypasses everything and lifts the whole band, a small one only bypasses treble, which is a classic way to build a bright boost. The fz and fp markers on the graph show where the bypass starts working and where it levels off.

The math here uses a typical square-law J201 model (I_dss ≈ 0.47 mA, V_gs(off) ≈ −0.61 V) with the drain pinned at half supply. C3 couples the output, R5 gives it a load reference to ground, and R6 isolates the stage from whatever comes next. The dashed curve is the nearest-E12 build, including the E12 value of the auto-computed R4.