How to Read Vacuum-Tube G-Curves

 

Manufacturers' tube data sheets provide essential information, but they do not always present all the parameters required for practical circuit design. The Conductance Curves, or G-Curves, developed by Keats A. Pullen, provide a more complete graphical method for analysing vacuum tubes.

Using these curves, the designer can determine plate current, transconductance, plate conductance, screen current, gain, distortion, and electrode dissipation at a selected operating point.

The method is useful for designing and evaluating RC-coupled amplifiers, cathode followers, switching circuits, and other vacuum-tube applications.

What Are G-Curves?

A conventional characteristic curve usually shows the relationship between plate voltage and plate current for several grid-bias voltages. G-Curves add further information to the same graph by including contours for small-signal parameters.

For triodes, a typical G-Curve includes:                                      


●        Grid-bias contours.

●        Transconductance (gm) contours.

●        Plate-conductance (gp) contours.

●        Plate-current information.

For pentodes, the curves are arranged differently because plate current depends mainly on control-grid voltage and screen-grid voltage. The graphs normally include:

●        Screen voltage (Ec2).

●        Nominal plate current (Ip).

●        Control-grid bias (ec1).

●        Nominal transconductance (Gm1).

●        Correction factors for different plate-to-screen voltage ratios.

The purpose is to obtain the parameters required for circuit calculations directly from the graph.

Reading a Triode G-Curve

To analyse a triode, first locate the desired operating point on the graph using the plate voltage and grid-bias voltage.

For example, consider a 6J5 operating at eb = 100 V and ec = −2 V.

The procedure is:

1.                   Locate the intersection of the 100 V plate-voltage line and the −2 V grid-bias curve.

2.                   Identify the nearby transconductance (gm) contours.

3.                   Identify the nearby plate-conductance (gp) contours.

4.                   Read the corresponding plate current.

5.                   Interpolate between contours when the operating point falls between two marked values.

In the example given in Pullen's manual, the approximate results are:

gm ≈ 3200 μmhos

gp ≈ 153 μmhos

The result should not be reported with excessive precision. Real tubes vary between individual units and manufacturers, so approximate interpolation is normally appropriate for design work.

Reading a Pentode G-Curve

Pentodes require a slightly different procedure. Begin by selecting plate voltage (eb), screen voltage (Ec2), and control-grid bias (ec1).

The standard pentode curves in the manual are based on the reference condition eb / Ec2 = 2. If the actual circuit uses a different voltage ratio, correction factors must be applied.

The procedure is:

1.                   Locate the selected screen voltage and control-grid bias on the graph.

2.                   Read the nominal plate current (Ip).

3.                   Read the nominal transconductance (Gm1).

4.                   Calculate the actual plate-to-screen voltage ratio.

5.                   Read the plate correction factor (Xp).

6.                   Read the screen correction factor (Xc2).

7.                   Calculate the corrected plate and screen currents.

8.                   Calculate the corrected transconductance values.

The relevant equations are:

ib = Xp × Ip

gm1 = Xp × Gm1

ic2 = Xc2 × Ip

gm12 = Xc2 × Gm1

Here, ib is the actual plate current and ic2 is the actual screen current.

Example: 6AH6 Pentode

Consider a 6AH6 operating with:

●        Plate voltage: 100 V.

●        Screen voltage: 100 V.

●        Control-grid bias: −1 V.

Suppose the G-Curve provides the following nominal values:

Ip = 8.7 mA

Gm1 = 9500 μmhos

The correction curves provide approximately:

Xp = 0.97

Xc2 = 0.23

The corrected plate current is:

ib = 0.97 × 8.7 ≈ 8.4 mA

The corrected control-grid transconductance is:

gm1 = 0.97 × 9500 ≈ 9200 μmhos

The screen current is:

ic2 = 0.23 × 8.7 ≈ 2.0 mA

The control-grid-to-screen transconductance is:

gm12 = 0.23 × 9500 ≈ 2200 μmhos

These corrected values can then be used in the next stage of the circuit design.

Calculating Amplifier Gain

Once the small-signal parameters have been obtained, they can be used to calculate amplifier gain.

For a simple triode RC-coupled amplifier:

K = −(gm × RL) / (1 + gp × RL)

where K is the voltage gain, RL is the load resistance, gm is the transconductance, and gp is the plate conductance.

For a pentode, the plate conductance is often sufficiently small to be neglected. The approximate gain is then:

K ≈ −gm1 × RL

These equations give the small-signal gain, meaning the gain at a particular operating point and for a relatively small input signal.

When the signal amplitude increases, the operating point moves across the characteristic curves. Since transconductance changes with bias, the gain also changes, producing distortion.

Estimating Distortion

Pullen's manual gives a simple method for estimating second-harmonic distortion:

D = 25 × (Kp − Kn) / (Kp + Kn)

where Kp is the gain at the most positive signal excursion, Kn is the gain at the most negative signal excursion, and D is the approximate distortion in percent.

The procedure is:

1.                   Select the static bias point.

2.                   Define the peak-to-peak input signal.

3.                   Determine the positive and negative signal limits.

4.                   Read or calculate the gain at both limits.

5.                   Apply the equation.

If the gains at the two extremes are very different, the stage will produce more distortion. Reducing the input signal generally reduces distortion because the valve operates over a smaller and more linear portion of its characteristics.

Checking Electrode Dissipation

Gain and distortion are not the only design considerations. The dissipation of every electrode must also be checked.

For the plate:

Pp = eb × ib

For a pentode screen:

Pc2 = Ec2 × ic2

These values must remain below the maximum ratings specified for the valve. For improved reliability, the circuit should normally be designed with a safety margin rather than operated continuously at the maximum permissible dissipation.

This is especially important in vintage equipment, where the actual power-supply voltage may be higher than the original design value and old resistors may have drifted significantly from their marked values.

Choosing a Different Valve

The G-Curve method also helps determine whether the selected valve is suitable.

A redesign may be necessary when:

●        The required output voltage cannot be obtained.

●        Distortion is excessive.

●        Plate or screen dissipation is too high.

●        The circuit operates too close to a limiting characteristic.

●        The available gain is much greater or lower than required.

A valve with a higher nominal conductance may provide more output or the same output at lower electrode voltages. Conversely, a lower-conductance valve may be more appropriate when the original design is unnecessarily conservative.

Practical Limitations

G-Curves are valuable design tools, but they should not be treated as exact descriptions of every individual valve.

Differences may result from:

●        Manufacturing tolerances.

●        Variations between manufacturers.

●        Changes in construction during production.

●        Valve ageing and loss of emission.

●        Measurement and interpolation errors.

For this reason, the completed circuit should always be checked with suitable test equipment. Measure the actual plate, screen, and cathode voltages, and calculate the corresponding currents before applying a large signal.

In vintage amplifiers, also check for leaky coupling capacitors, altered resistors, excessive power-supply voltage, and faulty cathode bypass capacitors. These faults can move the valve away from the operating point predicted by the original design.

Conclusion

The G-Curve method provides a practical way to move from a valve data sheet to a working circuit design.

The general procedure is:

1.                   Select the operating voltages and bias.

2.                   Locate the operating point on the appropriate curve.

3.                   Read the current and small-signal parameters.

4.                   Apply the pentode correction factors when necessary.

5.                   Calculate gain and signal excursion.

6.                   Estimate distortion.

7.                   Check plate and screen dissipation.

8.                   Confirm the final values by measurement.

In simple terms, G-Curves combine static and dynamic valve data in a form that makes circuit design more predictable. They are particularly useful when designing or modifying valve amplifiers and when comparing different valves for a particular application.

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