Triode Load Line
Plot plate curves, find the operating point, gain and headroom.
Operating Conditions
Grid-leak of the following stage (AC load)
How it works
A load line is the set of all voltage/current pairs the plate can visit given the external circuit. For a resistor-loaded stage, Ohm's law forces every operating point onto a straight line running from B+ (zero current) to B+/(Ra+Rk) (zero volts across the valve).
The valve itself is modelled with Norman Koren's triode equations, which reproduce the plate-curve family (green) from five parameters (µ, Ex, Kg1, Kp, Kvb). The quiescent point Q is found where the valve's own curve, evaluated at the self-bias grid voltage Vgk = −Ip·Rk, meets the load line, solved numerically by bisection.
At Q, the small-signal parameters are found by tiny numerical derivatives: gm = ∂Ip/∂Vg, rp = ∂Va/∂Ip, and µ = gm·rp. The gain then follows from the classic common-cathode equations:
The dashed AC load line is steeper when a following grid-leak RL shunts Ra (RL' = Ra ∥ RL). The violet dots mark how far the plate swings when the grid is driven from 0 V to 2·Vgk: unequal upper and lower excursions reveal second-harmonic distortion, estimated as D₂ ≈ (ΔV₊ − ΔV₋) / 2(ΔV₊ + ΔV₋).
In Transformer mode the DC load line is almost vertical (only the winding's small DC resistance, assumed zero here) while the AC line has slope −1/Raa (the reflected primary impedance), which is how single-ended 300B and 2A3 amplifiers are designed.
Model parameters are approximate; real valves vary ±20% from sample to sample.