12AX7 Load Lines

Explore a cathode-biased 12AX7/ECC83 voltage amplifier on plate-characteristic curves digitised from an RCA 12AX7-A chart. Change the resistors or B+ to move the real-data-based DC operating point, then examine an idealised AC load line and estimated loaded gain.

B+ at plate resistor (V) Plate resistor (kOhms) Cathode resistor (kOhms) Cathode bypass capacitor (uF) Use 0 for an unbypassed cathode. Output coupling capacitor (nF) Following stage input load (kOhms)

Try a plate resistor:

Try a cathode resistor:

Estimated operating point and gain

Plate-to-cathode voltage

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Plate voltage to ground

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Plate current

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Cathode voltage / bias magnitude

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Estimated 1 kHz gain (RC model)

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Estimated plate dissipation

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RCA 12AX7-A characteristic curves and load lines

RCA grid-voltage curves DC load line Approximate resistive AC load line, when applicable ● Estimated Q point

The grey curves are traced from the supplied RCA chart (grid-to-cathode voltage in 0.5 V increments). The DC load line includes both plate and cathode resistors.

RC-only gain response: 40 Hz to 10 kHz

This is not a complete frequency-response prediction. The plot includes the standard guitar's low E (82.4 Hz) and extends to 10 kHz, with reference points at 1 kHz, 5 kHz and 10 kHz. It shows the effects of the cathode bypass capacitor, output coupling capacitor and following-stage load. It does not include Miller capacitance, the preceding stage's source impedance, grid-stopper effects or stray capacitance. In particular, the upper-frequency curve is an RC-only estimate and cannot predict actual treble roll-off.

What is changing?

Bias and plate resistor

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Cathode bypass capacitor

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Following-stage load

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Coupling capacitor and bass response

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Gain comparison at guitar frequencies

Frequency	Loaded gain	Gain (dB)	Relative to 1 kHz

How this version calculates the operating point

The curves are digitised samples of the supplied RCA 12AX7-A plate chart: anode current versus plate-to-cathode voltage at grid voltages from 0 to -5 V. Values between plotted samples and the 0.5 V grid curves are interpolated; they are not generated from the synthetic valve model used in the earlier version.

The DC load line is V(plate-to-cathode) = B+ - plate current multiplied by (plate resistor + cathode resistor). Self-bias requires V(grid-to-cathode) = -plate current multiplied by cathode resistance. The displayed Q point satisfies both relationships as closely as the chart data allow.

Small-signal plate resistance and amplification factor are estimated locally around the Q point from the digitised curves. AC voltage gain then uses the actual resistor values and complex capacitor impedances. A real valve's operating point will vary with manufacturing, age, component tolerances and actual supply voltage.

The dashed AC load line appears only when the 1 kHz circuit is close to a resistive load: either no cathode bypass capacitor, or a cathode effectively bypassed at that frequency, with negligible coupling capacitor reactance. For intermediate capacitor values there is no single straight AC line, so the calculator hides it while continuing to calculate the low-frequency complex-impedance response.

If a value falls beyond the plotted RCA data, the calculator reports that it cannot estimate a reliable operating point. This is intentional: it does not invent characteristic curves outside the source chart.

Important: This is an educational estimate based on one published characteristic chart. Any displayed AC load line is a resistive midband approximation, not a full transient distortion simulation. Valve amplifiers contain potentially lethal voltages.