5.3 Power supply for the fixed grid bias of a vacuum tube amplifier

The grid of a vacuum tube needs to be negative with respect to the cathode. When fixed bias is used, as explained in Section 3.6.1, the cathode is connected to ground and a separate power supply is needed to produce the needed negative grid bias voltage.

Figure 45 reports a basic schema to produce the negative grid voltage bias. Required voltage is generally lower than 100V. Therefore, a step-down transformer is used to reduce the mains voltage to a voltage closer to the needed one. In this discussion, we use a bridge rectifier. However, the other rectifier options, discussed in Section 5.1.1, can be used as well. In particular, note that a very limited current flows in a well-designed grid bias circuit. Consequently, in some cases, also a half wave rectifier is sufficient to have a very limited ripple, further simplifying the overall schema.

Negative voltage is obtained by connecting the positive end of the rectifier to ground. In this way, the other end of the rectifier has a voltage negative with respect to ground (and to the cathode) and can be used to provide the negative bias voltage. As usual, a reservoir capacitor and a smoothing filter follow the rectifier to produce a stable DC voltage. The voltage divider, composed of resistors R1 and R2, brings the voltage, exiting from the smoothing filter, to the needed grid bias voltage –Vg. The bias voltage goes to the grid, of the two vacuum tubes of the push-pull stage, through the two grid leak resistors Rl.

Note however that, the same negative grid bias circuit is generally used to provide bias voltage to all the vacuum tubes of all the push-pull stages. Using this schema in a stereo amplifier, the residual input signal seen at the grid of a channel can go to the grid of the other channel, through the grid leak resistors, and produce some unwanted cross-talk among the different channels. In order to eliminate this problem, the residual signal seen at the end of the grid leak resistors, should be shorted to ground. This task, as discussed in Section 3.6.1, is accomplished by the decoupling capacitors Cd.

Since, in normal operation, no current goes through the grid and the grid leak resistors, current mainly flows through the voltage divider, used to set the correct grid bias voltage. The voltage divider can be designed using appropriate large values of the resistors, to minimize the current and simplifying the job of the step-down transformer, the rectifier, the reservoir capacitor, and the smoothing filter. However, remember that, as we discussed in Section 4.1.1, vacuum tube datasheets specify a maximum value for the resistance between the grid and the cathode, to avoid the thermal runaway problem. With fixed grid bias, given that the cathode is at ground level, the resistance between grid and cathode is the sum of the grid stopper, grid leak, and resistor R2 of the grid bias voltage divider. Therefore, there is a limitation on the value of the resistors that can be used in this voltage divider.

Figure 45: Power supply for grid bias
Negative voltage with respect to ground is obtained by connecting the positive terminal of the rectifier to ground. In this way, the other terminal is negative with respect to ground. As usual, a reservoir capacitor and a smoothing filter follow the rectifier, to reduce the ripple voltage. The wanted grid bias voltage –Vg is obtained with the voltage divider composed of resistors R1 and R2. Grid bias voltage is fed to the grids of the two push-pull vacuum tubes through their grid leak resistors Rl. In order to avoid cross-talk among vacuum tubes biased by the same circuit, any residual AC signal traversing the grid leak resistors has to be shorted to ground. This is accomplished by the decoupling capacitors Cd connected between the grid leaks and the ground.
Example 25: Power supply design for fixed grid bias

Suppose we use a step-down transformer that provides 100V output, has a primary resistance of 4 Ohm, and has a secondary resistance of 20 Ohm. Suppose also we use a filter resistor Rflt=32K Ohm and the total resistance wanted in the voltage divider is 35K Ohm, so that the total load seen by the rectifier is 67K Ohm. If we chose a reservoir capacitor CR=1 μF, and a capacitor filter Cflt=1μF, according to what we discussed in Sections 5.1.5, 5.1.6, and 5.1.8, we can conclude that the output of the rectifier is -135.7V and that the output of the smoothing filter is -70V. The ripple voltage at the rectifier output is around 5V and the ripple voltage at the smoothing filter output is around 0.25V.

Suppose now we want to set the grid bias voltage to -40V. Using the voltage divider equation, we obtain that we can set the resistors of the voltage divider to R1=15K Ohm and R2=20K Ohm. The value of R2 has to be added to the grid leak and to the grid stopper to check that the maximum grid to cathode resistance is not exceeded. Elsewhere smaller values of R1 and R2 have to be chosen.

Note also that, we take the grid bias at the voltage divider. Therefore, the ripple voltage arriving at the grid will be reduced as well by the voltage divider, and will be around 0.14V. Suppose we are using EL34 vacuum tubes, since the grid voltage peak of an EL34 vacuum tube is around 35V, which is much larger than 0.14V, we can safely accept this ripple voltage at the grids, in a push-pull configuration.

Figure 46: Improved schema for supplying the grid bias voltage
The basic voltage divider used in Figure 45, to obtain –Vg, is refined here to allow fine-tuning of the grid bias voltage for each vacuum tube. Potentiometer P2 allows increasing or reducing the grid bias voltage of both vacuum tubes, to choose the wanted operating point. Potentiometer P1, with the help of the two resistors R1, allows fine balancing the grid bias in the two vacuum tubes of a push-pull amplifier, to have exactly the same operating point in both tubes.

5.3.1    Fine tuning the grid bias

The voltage divider, in the dashed box in Figure 45, provides the same grid bias voltage –Vg to all vacuum tubes connected to it. However, pairs of vacuum tubes, even matched pairs, have some small differences and react differently under the same conditions. For instance, even if two vacuum tubes have the same anode voltage, and the same grid bias, they can conduct slightly differently and can stay on different operating points. Two not perfectly paired vacuum tubes can compromise the benefits of the push-pull configuration. In addition, suppose we also want to be able to vary the grid bias voltage in order to choose different operating points, to obtain the best sonic performance, or even to choose our preferred amplifier class (A, AB, or B). In all these cases, we require the capability to fine-tune the bias voltage, to provide each different vacuum tube with its needed bias voltage.

Figure 46 shows a modified schema of the basic voltage divider. At the bottom of the figure we can see that there is a potentiometer P2between R2 and ground. The wiper terminal of P2 is connected directly to one of the other two terminals. The position of the potentiometer modifies the resistance between its two ends. Higher resistance produces a more negative voltage, and vice versa. In this way, it is possible to increase or reduce the bias voltage of both vacuum tubes, to choose the wanted operating point. Note that if, for some reasons, the wiper fails to be in contact with the carbon track of the potentiometer, the potentiometer gives its full resistance, pushing the bias at the more negative possible voltage. In this way, in case of failure of the potentiometer, the vacuum tubes are simply cut-off, without damaging them. Other designs, in case of failure of the potentiometer, can leave the grids floating or, even worse, to ground level, by damaging the vacuum tubes.

Example 26: Setting the grid bias voltage

In Example 25 we chose a reference grid bias voltage of -40V. Suppose we want to be able to fine-tune the grid bias in a range of approximately +/- 50% of the reference. This can be obtained by choosing R2=6K Ohm and P2=100K. In this way, we can vary the grid bias roughly in a range from -20V to -60V.

The new schema in Figure 46 also uses the potentiometer P1, along with the two resistors R1, connected at the two terminal ends of the potentiometer P1 itself. This schema allows balancing the bias between the two vacuum tubes of a push-pull amplifier, to set the same operating point, in case they react slightly differently at the same grid bias voltage. The two resistors, along with the potentiometer, act as two parallel variable voltage dividers. For instance, when the potentiometer shaft is positioned more on the left, the voltage divider on the left has the resistance between the terminal and the wiper reduced. Therefore, the grid bias voltage on the left will be less negative (closer to zero), while the one on the right will be more negative. Also in this case, if the potentiometer fails, for instance if the wiper fails to be in contact with the carbon track, the two grids are put at a more negative voltage, so cutting the vacuum tubes off and avoiding to damage them.

Example 27: Balancing the grid bias voltage of two vacuum tubes in push-pull.

Suppose we want to be able to set exactly the same operating point, for two vacuum tubes in a push-pull amplifier. Suppose that, in order to do that, we want to fine-tune their grid bias voltage in a range of approximately +/- 10% of the reference grid bias chosen in Example 25. This can be obtained by setting the two resistors R1=33K Ohm and the potentiometer P1=10k. In this way, for instance, if P2 is set to provide us with a grid bias voltage of -40V, we can use P1 to balance the grid bias of the two vacuum tubes, approximatively, in a range from -36V to -44V.

Note that if the circuit for grid bias fine tuning is used to in a stereo amplifier, the voltage divider, composed of the two parallel resistors R1and the potentiometer P1, should be duplicated. Both voltage dividers should be connected to R2 through their potentiometer P1. In addition, the values of R1 and P1 should be doubled as well, since they work in parallel.

5.3.2    Probing the grid bias current

It is easy to tune the bias voltage for each vacuum tube of the push-pull stage, using the circuit shown in Figure 46. However, in order to set the correct operating point we need to know the bias current flowing through the vacuum tubes. The bias current can be easily measured by connecting the cathodes of the vacuum tubes to ground through two resistors, indicated as Rp1 and Rp2 in Figure 47. The resistance of the two resistors should be very small, in order not to introduce practically any cathode voltage elevation, and local negative feedback. For instance, values of 1 Ohm or at most 10 Ohm are generally used. Some probe pins, possibly accessible without opening the amplifier chassis, are connected to the terminals of the resistors, as depicted by the pins A, B, and C, in the figure.

Figure 47: Probing the grid bias current
In order to be able to measure the bias current, when operating on the potentiometers of the improved grid bias circuit, the cathodes of the vacuum tubes are connected to ground through two very small resistors Rp1 and Rp2. The bias current can be computed by measuring the voltage between pin A, connected to ground, and the other two pins A or B, and then using the Ohm law.

The bias current can be obtained by measuring the voltage between pin A, connected to ground, and pin B or pin C, and by using the Ohm law to calculate the current.

Example 28: Measuring the bias current

Suppose Rp1 Rp2 = 10 Ohm. If we measure 0.4V between A and B, and 0,35V between A and C, then the bias current of one vacuum tube is 0.4/10=40 mA, and the bias current of the other is 0.35/10=35 mA.

Fine-tuning starts by connecting a voltmeter to either A and B, or A and C and then turning the potentiometer P2 until the wanted bias current is measured. After this, the voltmeter must be connected to B and C, and the potentiometer P1 turned until the measured voltage is zero, that is B and C are at the same potential. Then, the voltmeter is connected again to either A and B, or A and C and the two steps are repeated until both tubes have the wanted identical bias current.

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