A tube on its own does nothing. Give it a supply voltage, something to drive, and a way to set its bias, and it settles at exactly one operating point — one plate voltage, one plate current. The load line is the drawing that finds that point, and it is the single most useful picture in amplifier design. This one is live: pick a tube, set the circuit around it, and watch the point move.
| Grid bias | Plate current at the operating voltage | Plate dissipation there |
|---|
Every documented amplifier's output stage, with the supply voltages, cathode resistor and transformer primary its own netlist and parts list record. Each link loads that stage into the explorer above.
Supply voltages here are simulated from each circuit's redrawn netlist, not measured on a chassis. Where a drawing prints no transformer primary impedance, the parts list says so and the field is left for you to fill — see each circuit's own page for what the drawing does and does not state.
The fan of curves behind the chart is the tube's plate characteristic. Each curve answers one question: if I hold the grid this far below the cathode, how much plate current flows at each plate voltage? The top curve is zero bias — grid and cathode at the same potential, the tube passing as much current as it can. Each curve below it is a step more negative on the grid, and each passes less current. Far enough down and the tube stops conducting altogether: cut-off.
Notice the shape. On a triode the curves rise steadily with plate voltage — plate voltage and grid voltage both have a say in how much current flows. On a pentode or beam power tube they flatten out almost immediately: past the knee, the screen grid has taken over, and plate voltage barely matters. That single difference is why triodes and pentodes sound and behave so differently in an amplifier.
The tube does not get to choose its own operating point, because it is not alone. Current drawn through the plate load drops voltage across it, so the more current the tube passes, the less voltage is left across the tube itself. Draw that relationship on the same axes and you get a straight line, sloping down from the supply voltage on the right to the short-circuit current on the left. Its steepness is the load: a small plate resistor gives a steep line, a large one a shallow one.
An output transformer behaves differently at DC than it does at signal frequencies, which is why two lines are drawn. Its primary winding is close to a short circuit for direct current, so the DC load line stands almost upright: the plate sits near the full supply voltage no matter how much current it draws. To the audio signal, though, the transformer reflects the speaker back as several thousand ohms, so the AC load line tilts across the operating point at that much shallower slope. The amplifier idles on the first line and swings along the second.
Only one point satisfies both the tube and the circuit at once: the point where the load line crosses the grid curve the bias is actually holding. That is the operating point, marked here with a ring.
With a fixed-bias stage the grid voltage is set by a supply and you can read the answer straight off. With cathode bias it is circular — the bias comes from the cathode resistor, and the voltage across that resistor depends on the very current you are trying to find. There is no closed-form answer, so this page does what the circuit does: guesses a cathode voltage, works out the current it would allow, compares that against the voltage the resistor would actually develop, and closes the gap until the two agree. That is the same convergence the amplifier performs in the first few milliseconds after the tube warms up.
The sweeping line falling away to the right is the maximum plate dissipation, taken from the tube's own datasheet. Everything the plate passes that does not become signal becomes heat, and the heat is simply plate voltage times plate current — so the limit is a hyperbola, not a straight line. An operating point on that curve is at the rated limit with the amplifier idling and no signal at all. Sitting above it is how plates go red.
Load the 5F1 preset and watch where it lands: around eleven and a half watts against a twelve-watt plate rating, with the operating point sitting almost on the limit curve. That is not a mistake in the drawing — the small tweed circuits idle their output tubes hard, and it is part of why they compress the way they do. Several circuits in this archive compute higher still, past the printed rating.
Read those figures as what the model says, not as a measurement. The tube models here are fitted to a datasheet point at 250 V and extrapolated to whatever rail a circuit runs; on the highest-voltage circuits that extrapolation is known to run rich, which is one reason some of them are published as drafts rather than verified. Each circuit's own page records where its simulation and its published chart part company.
This is a DC picture. It shows where a stage idles and how far it can swing before it runs out of voltage or current, and that is genuinely most of what matters when choosing a plate load or a bias resistor. It says nothing about frequency response, nothing about what negative feedback does around the stage, and nothing about how the circuit behaves once the grid is driven positive and starts drawing current — the models here carry no grid-current term. Treat the swing figures as the graphical estimate they are.
The curves are not traced from a datasheet plot. They are computed, in your browser, from the Koren plate-current equations using the parameters in this archive's own tube models — the same CC0 files fitted to published datasheet anchor points and handed to ngspice when a circuit's operating point is verified. Each model's anchor is listed below.
| Tube | Form | Fitted to | Max plate dissipation |
|---|---|---|---|
| 6L6GC | pentode | Va=250 V, Vg2=250 V, Vg1=−14 V → Ia=72 mA, Ig2=5 mA, gm=6000 µmho | 30 W |
| 6SJ7 | pentode | Va=250 V, Vg2=100 V, Vg3=0 V, Vg1=-3 V → Ia=3.0 mA, Ig2=0.8 mA, gm=1650 µmho | 2.5 W |
| 6V6GT | pentode | Va=250 V, Vg2=250 V, Vg1=-12.5 V → Ia=45 mA, Ig2=4.5 mA, gm=4100 µmho | 12 W |
| 5879 | pentode | Va=250 V, Vg2=100 V, Vg3=0 V, Vg1=-3 V → Ia=1.8 mA, Ig2=0.4 mA, gm=1000 µmho | 1.25 W |
| 5881 | pentode | Va=250 V, Vg2=250 V, Vg1=-14 V → Ia=72 mA, Ig2=5 mA, gm=6000 µmho | 23 W |
| 6973 | pentode | Va=250 V, Vg2=250 V, Vg1=-15 V → Ia=46 mA, Ig2=3.5 mA, gm=4800 µmho | 12 W |
| 7591 | pentode | Va=300 V, Vg2=300 V, Vg1=-10 V → Ia=60 mA, Ig2=8 mA, gm=10200 µmho | 19 W |
| EF86 | pentode | Va=250 V, Vg2=140 V, Vg3=0 V, Vg1=-2.2 V → Ia=3.0 mA, Ig2=0.6 mA, gm=2200 µmho | 1 W |
| EL34 | pentode | Va=250 V, Vg2=250 V, Vg1=-13.5 V → Ia=100 mA, Ig2=14.9 mA, gm=12500 µmho | 25 W |
| EL84 | pentode | Va=250 V, Vg2=250 V, Vg1=-7.3 V → Ia=48 mA, Ig2=5.5 mA, gm=11300 µmho | 12 W |
| KT66 | pentode | Va=250 V, Vg2=250 V, Vg1=-15 V → Ia=85 mA, gm=7000 µmho (gm test point) | 25 W |
| 6AT6 | triode | Va=250 V, Vg=-3 V → Ia=1.0 mA, gm=1200 µmho, µ=70 | 0.5 W |
| 6CG7 | triode | Va=250 V, Vg=−8 V → Ia=9 mA, gm=2600 µmho, rp=7700 Ω, µ=20 | 4 W |
| 6SL7GT | triode | Va=250 V, Vg=-2 V → Ia=2.3 mA, gm=1600 µmho, µ=70 | 1 W |
| 12AT7 | triode | Va=250 V, Vg=-2.0 V (200 Ω cathode bias) → Ia=10 mA, gm=5500 µmho, µ=60 | 2.5 W |
| 12AU7 | triode | Va=250 V, Vg=-8.5 V → Ia=10.5 mA, gm=2200 µmho, µ=17 | 2.75 W |
| 12AX7 | triode | Va=250 V, Vg=-2 V → Ia=1.2 mA, gm=1600 µmho, µ=100 | 1 W |
| 12AY7 | triode | Va=250 V, Vg=-4 V → Ia=3.0 mA, gm=1750 µmho, µ=44 | 1.5 W |
Maximum ratings are the limiting values printed on each tube's own datasheet, with the sheet, its date and its rating system cited on that tube's page. 11 of the 18 are design-centre figures, which already carry an allowance for manufacturing spread; the 6L6GC, 5879, 6973, 7591, KT66, 6CG7 and 12AU7 sheets quote design-maximum values instead — the stricter line an individual valve may never cross. Judge a tube against its own sheet, not against another tube's. All of the modelled amplifying tubes carry a rated plate dissipation, so the limit curve is available on every one. Rectifier diodes have no grid and no load line, and are not listed.
The same equations solved here are solved by ngspice when each circuit's operating point is gated, so the two have to agree — and the archive checks that they do rather than assuming it. Load a preset and the panel prints both answers side by side: this page's solution for the output tube, and the value the simulator settles on inside the whole amplifier. Across all 39 documented output stages the two agree to better than a hundredth of one percent.
A preset holds the screen at the voltage the simulator settled on rather than re-solving the dropper network and the preamp behind it. Fixing an already-converged voltage does not move the rest of the solution, which is why the residual is numerical rather than physical.