3.6.2    Cathode bias or self-bias for vacuum tubes

Negative voltage between grid and cathode can also be obtained by connecting the grid to ground voltage and by elevating the cathode voltage. This technique is generally referred as cathode bias or self-bias. The cathode voltage is elevated by connecting it to ground through the resistor R_k, generally called the cathode resistor, as shown in Figure 12. Given that, generally, there is an anode current also at the quiescent state, the resistor R_k produces a voltage drop from the cathode to ground so that the cathode voltage is above ground. The grid, being at ground voltage, is negative with respect to the cathode.

Note that, also in this case, the grid is not directly connected to ground. Rather, a grid leak resistor R_l is used to provide the input signal with a high impedance path to ground, as we already discussed for the fixed bias. Since there is no current flowing through the grid, it is at ground voltage.

The value of R_k can be computed using the Ohm law by knowing the bias current, that is the cathode current at the operating point (quiescent state), as shown in next Example.

Example 4: Determining the cathode resistor for self-bias Suppose we use a 12AX7 vacuum tube and we want to set the operating point at the red spot in Figure 8, using the green loadline. This corresponds to a bias current of 0.75 mA. Using the average anode characteristics graphs, we see that a grid voltage of -1.5V, with respect to the cathode, is needed to obtain a current of 0,75 mA. Using the Ohm law, we find that the resistance needed to elevate the cathode at 1.5V, when the current is 0.75 mA, is: .

It is important to mention that the cathode resistor introduces a form of local negative feedback. In fact, when the current increases, the cathode voltage increases as well. In this case, the grid becomes more negative, with respect to the cathode, and tends to reduce the vacuum tube conduction. When current decrease, we have the opposite effect and the grid becomes less negative, increasing vacuum tube conduction. In other words, the cathode resistor tends to oppose the amplification of the signal and reduces the gain of the vacuum tube. In order to mitigate and almost eliminate this effect, a bypass or decoupling capacitor C_k, is generally introduced in the circuit, as shown in Figure 12. The bypass capacitor compensates the cathode voltage variation trying to maintain it as stable as possible, when amplifying a signal. In this way, local negative feedback is significantly reduced and gain significantly increased, as discussed in next Section.