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Practical guide

The load line explorer

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.

Tube

Supply
Anode load
Bias

A resistor shared by both output tubes is entered here at twice its marked value — it carries both tubes' current, so each bottle develops its bias across an effective 2R.

Chart
Plate characteristic chart
The chart as a table
Grid biasPlate current at the operating voltagePlate dissipation there

Start from a circuit in the archive

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.

5C1 6V6GT · 324 V · cathode bias 5D3 6V6GT ×2 · 360 V · cathode bias 5E1 6V6GT · 305 V · cathode bias 5E3 6V6GT ×2 · 370 V · cathode bias 5E4-A 6V6GT ×2 · 390 V · fixed bias 5E5-A 5881 ×2 · 390 V · fixed bias 5E6-A 5881 ×2 · 420 V · fixed bias 5F1 6V6GT · 340 V · cathode bias 5F10 6V6GT ×2 · 305 V · fixed bias 5F2-A 6V6GT · 360 V · cathode bias 5F4 5881 ×2 · 415 V · fixed bias 5F6 5881 ×2 · 432 V · fixed bias 5F6-A 5881 ×2 · 432 V · fixed bias 6161 6973 ×2 · 369 V · cathode bias 6G2 6V6GT ×2 · 315 V · fixed bias 6G3 6V6GT ×2 · 375 V · fixed bias 6G4 6L6GC ×2 · 456 V · fixed bias 6G5 6L6GC ×2 · 456 V · fixed bias 6G6-B 5881 ×2 · 428 V · fixed bias AA1164 6V6GT ×2 · 420 V · fixed bias AA764 6V6GT · 360 V · cathode bias AA764 (Vibro Champ-style) 6V6GT · 355 V · cathode bias AA864 (Bassman-style) 6L6GC ×2 · 422 V · fixed bias AA964 6V6GT ×2 · 420 V · fixed bias AB165 6L6GC ×2 · 425 V · fixed bias AB763 6V6GT ×2 · 415 V · fixed bias AB763 (Super Reverb-style) 6L6GC ×2 · 460 V · fixed bias AB763 (Twin Reverb-style) 6L6GC ×4 · 460 V · fixed bias AC15 EL84 ×2 · 315 V · cathode bias AC30 EL84 ×4 · 320 V · cathode bias B15N 6L6GC ×2 · 450 V · fixed bias DR103 EL34 ×4 · 480 V · fixed bias GA40 6V6GT ×2 · 310 V · cathode bias JTM100 KT66 ×4 · 560 V · fixed bias JTM45 KT66 ×2 · 450 V · fixed bias M1959 EL34 ×4 · 453 V · fixed bias M1987 EL34 ×2 · 490 V · fixed bias M2204 EL34 ×2 · 470 V · fixed bias S1484 6L6GC ×2 · 475 V · fixed bias

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.

How to read a load line

The curves are what the tube can do

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 load line is what the circuit allows

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.

Where they cross is the answer

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 curve you must not cross

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.

The things a load line will not tell you

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.

Where these numbers come from

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.

TubeFormFitted toMax 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.

Checked against the simulator

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.