4.1.3 Reactive load and reactive loadline computation

A transformer is a reactive load that offers an impedance just when an AC signal goes through its primary. The transformer primary, practically, does not offer impedance when just DC is applied to it. When no signal is applied to the grid, the vacuum tube is in a quiescent state and no AC signal is produced at its anode. In this case, only the DC current goes through the transformer primary and no impedance is seen by the anode. In addition, no signal is transferred from the primary to the secondary of the transformer.

Since there is not impedance and there is no voltage drop, the anode receives the full V+ voltage, at the quiescent reactive operating point. Accordingly, the quiescent current is the one associated with V+ along the plot corresponding to the chosen grid bias voltage.

When the anode produces an AC signal, then the transformer offers a resistance and the anode voltage and current start oscillating around the operating point along the reactive loadline. The reactive loadline is parallel to the resistive loadline, which can be computed as described in Section 3.2, and shifted so that it goes through the reactive operating point. Figure 19 shows the resistive loadline (green line) and the reactive loadline (red line) in correspondence of a load of 3.8K Ohm, a voltage V+=400V, and a bias current of 40 mA. The red line is parallel to the green line and shifted higher so that it passes through the reactive operating point (red spot).

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Figure 19: Reactive loadline.
In case of a resistive load, with an anode voltage of 400V, the loadline would be along the green line, and the operating point with a bias current of 40mA would be at the green spot. However, an output transformer has a reactive behaviour. In this case, there is a resistance just when an AC signal goes through it. There is no resistance when the vacuum tube is quiescent, so the quiescent voltage remains 400V independently of the bias current. In case of a bias current of 40mA the operating point is depicted by the red spot. When the vacuum tube amplifies an AC signal, an AC current goes from anode to cathode and trough the transformer, which now offers a resistance. The loadline, in this case, as depicted by the red line, is parallel to the resistive loadline, and shifted so that it passes through the reactive operating point. Note that the voltage reached by the anode, in case of a reactive load, might be higher than the voltage V+ applied to the transformer primary. This is due to the transformer reacting to current variations, virtually accumulating and releasing energy accordingly.

Example 8 below clarifies this. Also try the loadline calculator for vacuum tubes and experiment with various settings.

Example 8: Determining the reactive loadline

If we had a resistive load, we could have computed the loadline as we described in Section 3.2. For instance, suppose we had a load of 3.8K Ohm and a voltage V+ of 400V. At no conduction, the anode voltage would have been 400V. At full conduction, the anode voltage would have been 0 and the current 400V/3.8K Ohm=105mA. In this case, the resistive loadline would have been represented by the green line in Figure 19. A bias current of 40mA would have set the quiescent operating point at the green spot in the figure.

However, in our case the load is an output transformer, which has a reactive load. The transformer offers resistance just to AC signals that go through it. There is almost no resistance to DC. More specifically, when the vacuum tube is in a quiescent state, just DC goes from the anode to the cathode, corresponding to the bias current. In this case, the transformer does not offer resistance. This means that the voltage applied to the anode is the same than the V+ voltage applied to the transformer primary, 400V in our example. Therefore, a bias current of 40mA sets the reactive operating point as depicted by the red spot in Figure 19. When an AC signal goes through the vacuum tube, the transformer offers its 3.8K Ohm of impedance, so the anode voltage and current start oscillating along the reactive loadline represented by the red line in the figure. Note that reactive loadline is parallel to the resistive loadline and shifted higher so that it goes through the reactive operating point. It might seem strange that the anode voltage can now reach values higher than the 400V applied to the transformer primary. However, this is due to the transformer reacting to current variations, virtually accumulating and releasing energy in accordance to these variations.

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