Understanding Loadlines
The graphical key to amplifier design. Select a tube, set your supply voltage and load, and watch the loadline, operating point, and gain update in real time.
What Is a Loadline?
The most powerful tool in tube amplifier design
Every tube has a family of plate characteristic curves — plots of plate current (Ia) vs plate voltage (Va) at different grid voltages (Vg). These curves are the tube. They contain everything you need to know about its behavior.
A loadline is a straight line drawn on these curves that represents your circuit constraints. Given a supply voltage B+ and a load resistance RL, the loadline shows every possible combination of plate voltage and plate current the tube can operate at.
Y-intercept (max current)
X-intercept (max voltage)
The operating point (Q-point) is where the loadline crosses the bias curve — the steady-state condition around which the signal swings. The signal swings the grid above and below bias, and you read the output swing directly from the loadline.
Live Loadline Calculator
Adjust B+, load resistance, and bias — the plot updates instantly
Reading the Loadline
How to extract every design parameter from the graph
Once you have the Q-point, the loadline reveals everything about your amplifier stage:
The grid signal swings above and below bias. Follow the loadline up and down from Q to read the peak-to-peak output voltage swing.
If the tube clips harder on one side, 2nd harmonic dominates (triode). Symmetric clipping produces odd harmonics (push-pull behavior).
Av = μ × RL / (rp + RL)
Gain depends on where you are on the curves — it varies with the operating point.
Pout = (Vswing × Iswing) / 8
Maximum undistorted power for Class A operation.
Choosing the Q-Point
The bias point determines everything
| Bias | Effect | Trade-off |
|---|---|---|
| Hot (high Ia) | More power, more gain | More heat, shorter tube life, thermal runaway risk |
| Center | Max symmetric swing | Optimal Class A — lowest distortion |
| Cold (low Ia) | Less power, cooler | Crossover distortion, thin sound, asymmetric clipping |
Safe starting point — headroom for signal peaks
Use the interactive plotter above to experiment: drag the Vg slider and watch how the Q-point moves along the loadline. Notice how gain, plate current, and dissipation all change together.
The Power Hyperbola
The curve you must never cross
Every tube has a maximum plate dissipation rating: Pd = Va × Ia. On the plate characteristics, this defines a hyperbola — a curve that the operating point must stay below at all times. The region above the hyperbola is the danger zone: operating there risks overheating the plate structure, outgassing, and destroying the tube.
When designing, your Q-point must sit below this curve, and the signal swing must not push instantaneous dissipation above the limit for extended periods. In Class A, the idle point is the maximum dissipation point (signal actually reduces average dissipation).
DC vs AC Loadline
Why the signal sees a different load than the DC bias
With a capacitor-coupled or transformer-coupled load, the AC load differs from the DC load. The plate resistor sets the DC operating point, but the signal sees the plate resistor in parallel with the next stage's input impedance (or the transformer's reflected impedance).
Sets the Q-point
Sets the signal swing
The AC loadline pivots around the Q-point with a steeper slope (lower impedance). Enable the “Show AC loadline” checkbox in the plotter above to see this in action — the blue dashed line shows the AC load while the orange solid line shows the DC load.
This matters enormously for power stage design: the transformer reflects the speaker impedance back to the plate, creating an AC load that's typically much lower than the DC load through the output transformer primary winding.
Key Equations
Everything you need for loadline analysis
The Koren SPICE model used in the interactive plotter calculates plate current from grid and plate voltage using the equation: Ia = (E1Ex) / Kg1 where E1 is a function of Vp, Vg, μ, Kp, and Kvb. This gives accurate plate curves for circuit simulation without lookup tables.
Test Your Knowledge
Review the key concepts of loadline analysis for tube amplifier design.
What two things define a DC loadline on the plate characteristics?