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Self Bias

Author: N.H. Crowhurst

Assume that the cathode resistor is 2000 ohms. If the plate current is 1 milliampere, the grid bias will be 2 volts, and so on. We can now find the operating point of this value of cathode resistor by plotting a curve on the tube characteristics. We mark the points where the 2-volt bias curve crosses 1 milliampere, where the 4-volt bias curve crosses 2 milliamperes, and so on. The operating point of the tube is the point at which this curve crosses the load line for the chosen value of the plate resistor.

Finding the operating point using a cathode-bias resistor. The operating point is at the intersection of the load line and the automatic bias line.

Fluctuations of the plate voltage affect a self-biased circuit

An advantage of this method of biasing is that the bias automatically adjusts to any variations in the circuit. Suppose, for example, that the plate potential drops from 250 volts to 200 volts. If the bias voltage were fixed, this might well over-bias the tube. Using this bias system, however, the shift in load line corresponding with the drop in plate supply voltage produces a new operating point, which will still be optimum. For this reason, this method of biasing is called automatic or self bias.

The cathode resistor is not quite all that is needed for providing bias in some instances. Suppose that the plate load resistor is 50,000 ohms and that, with this value of load line, the tube gives a gain of 50. A 1-volt audio signal between grid and cathode will produce 50 volts audio at the plate. The same audio current fluctuation passes through both the plate and the cathode resistors; consequently there will be a proportionate audio voltage at the cathode.

Because the plate resistor is 50,000 ohms and the cathode resistor is 2000 ohms, a 50-volt fluctuation at the plate will be accompanied by a 2-volt fluctuation at the cathode. This fluctuation effectively takes the grid positive from its bias point, increasing plate current, which makes the plate swing negative and the cathode swing positive. Thus a positive fluctuation from grid to cathode will be accompanied by a positive fluctuation from cathode to ground. The total input voltage from grid to ground must be the total of these fluctuations: 1 volt from grid to cathode and 2 volts from cathode to ground, or 3 volts from grid to ground. Thus a 3-volt input is required to produce a 50-volt output and instead of the tube giving a gain of 50, the gain is only about 17. The cathode resistor is providing negative feedback.

To get the full gain of the tube we must avoid this feedback effect. This is accomplished by shunting the cathode resistor by a large-value low-voltage electrolytic capacitor that bypasses the audio voltages. A 50-microfarad capacitor has a reactance of only 63 ohms at 50 cycles and much lower reactances at higher frequencies. With a 1-volt audio input from grid to cathode (at 50 cycles), there will be 50 volts audio output at the plate and about 60 millivolts at the cathode, which is not sufficient to make an appreciable difference in the gain of the stage.

Left: the cathode resistor provides negative feedback.
Right: negative feedback is avoided through the use of a bypass capacitor which bypasses the audio current. Only the steady d-c current flows through Rk.

Last Update: 2010-11-03