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RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The Internet was still largely an unknown entity at the time and not much was available in the form of WYSIWYG ...

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July 1944 QST Article

July 1944 QST These articles are scanned and OCRed from old editions of the ARRL's QST magazine. Here is a list of the QST articles I have already posted. All copyrights are hereby acknowledged. |

Practical Applications of Simple Math

BY EDWARD M. NOLL.* EX-W3FQJ

Fig. 1 - Triode resistance-coupled amplifier circuit. |

The characteristic curves for the type 6J5 tube are shown in Fig. 2. The E

When a load is applied, such as the plate resistor of a resistance-coupled amplifier, an additional line called the load line must be drawn to represent the dynamic variations in tube potentials and currents. It is apparent that the .plate-current variations through the load resistance cause a varying voltage drop across the plate resistance, which is actually a change in plate voltage. Thus, a change in grid potential with the applied signal does not change the plate current without changing the plate voltage. In fact, the resultant change in plate voltage, caused by the variations of plate current through the load resistance, represents the useful output of the amplifier. Therefore, a load line representing the plate load resistance (total resistance between plate and cathode) is drawn on the characteristic curves to show the actual dynamic changes in tube operation.

Many excellent articles have been written on the theory of characteristic curves and load lines. Since this article is aimed at illustrating the practical application of the curves, theoretical considerations will be brought into the discussion only when necessary.

In constructing the load line on the characteristic curves, the actual resistance of the load depends upon the circumstances under which the amplifier is to be operated. Each set of conditions may require a slightly different value of load resistance for optimum performance. Optimum values may be chosen, for instance, for maximum possible undistorted voltage output with a given value of input signal, or for maximum possible undistorted voltage output with a definite amount of plate supply voltage. Each of these requirements may necessitate the use of different values.

As an illustration of the method used in arriving at the first of these objectives, let us assume that the maximum peak-to-peak signal delivered to the grid of the amplifier of Fig. 1 from the preceding stage is 8 volts. It is necessary to place the load line on the curves in such a position as to permit the signal to swing over the linear portion of the characteristic curves. Therefore the signal must not swing into the curved portions at low plate-current values, nor must it swing into the positive grid distortion region. In the case of the 6J5 triode curves the least value of bias that can be employed with an 8-volt signal is -4 volts, permitting the signal to swing between 0 and -8 volts. Bias in excess of -4 volts should not be used because it would result in an undesirable reduction in gain. As a result, the load line must be drawn to permit the grid signal to swing over the linear region, between the 0- and -8-volt bias curves.

The actual load line might be drawn at any one of a number of different slopes and in each case the plate voltage swing each side of the mean value would be equal and therefore distortionless. However, we are interested in obtaining a maximum plate-voltage swing with a low value of average plate current and a minimum variation in plate current. From this consideration, it is evident that the load line should appear practically horizontal and well down on the characteristic curves. Since a load line which approaches a horizontal position represents a high value of resistance (large change in plate voltage with a small change in plate current) the resistance-coupled voltage amplifier has a high value of plate resistance in comparison to a power amplifier, where we are interested in a large plate-current variation to develop power. Thus we find our 6J5 load line for an 8-volt signal well down on the curve; in fact, point B on the-8-volt curve was chosen as far down as possible without moving into the region of distortion as indicated by excessive curvature.

Using the point on the -8-volt curve as one point of the load line, a straightedge is moved about this point as a pivot until an equal plate voltage is set off by the swing of the signal on each side of the average bias value set on the -4-volt curve. When this position is found, a line is drawn along the straightedge which represents the value of plate resistance which permits maximum nondistorted voltage output. The value of this resistance is readily calculated by extending the load line until it crosses the plate-voltage and plate-current coordinates, as shown in Fig. 2. The slope of the load line, or the resistance represented by the load line, is equal to the change in plate voltage divided by the change in plate current.

We are now ready to consider Some typical problems.

1) What should the total plate load resistance, R

From Fig. 2 we find that the slope of the load line is

2) Find the plate power-supply voltage, E

Since the maximum plate voltage is applied to the plate only when no plate current flows through the load, the plate voltage indicated at zero plate current is the power-supply voltage. The position at which the load line crosses the zero plate-current axis is point C, representing 270 volts. Therefore, E

3) Calculate the required value of the cathode resistor, R

Examination of the curve shows that the average plate current at our operating bias, point O, is equal to 2.1 ma. Therefore, the resistance required to develop this amount of bias across the cathode resistor is

4) Calculate the required value of the plate load resistor, R

Since the total plate resistance includes the cathode-biasing resistance, the actual value required for the plate resistor is the total plate resistance minus the value of the cathode resistor, or

R

5)

The value of the grid resistor should be at least four times greater than the plate load resistor of the previous stage, but should not exceed the maximum value set by the tube manufacturer for safe operation of the tube. In the case of the 6J5, the maximum value set by the manufacturers when using cathode bias is 1 megohm. In most cases the value used is in the vicinity of 500,000 ohms.

6) Determine the value of the cathode bypass condenser, C

The capacity of the cathode bypass condenser is set at a value which will pass the lowest frequency to be amplified with a gain equal to 70.7 percent of the gain over the middle range of frequencies. (The calculation of capacity values will be elaborated upon in the next installment. However, it is a basic rule that, if the reactance of the condenser at the lowest frequency is equal to the resistor value, the amplifier response will be down 70.7 per cent at this frequency.) Since R

7) Determine the value of the coupling condenser, C

The coupling condenser, which also causes a loss of low frequencies because of its reactance, is calculated in like manner with respect to the grid resistor, or

Fig. 2 - Family of plate-voltage vs. plate-current characteristic curves for the Type 6J5 triode tube. |

By dropping perpendicular lines to the coordinates from the points A, O, and B in Fig. 2, which represent the average bias and the extremities of grid-signal swing, the peak-to-peak plate voltage and current can be determined by simple subtraction.

Peak-to-peak plate voltage = 175 - 40 = 135 Peak-to-peak plate current = 3 - 1.25 = 1.75 ma.

9) Determine the peak-to-peak voltage output of the tube.

Since the plate-voltage swing represents the variations in potential between plate and cathode, the portion of the variation across the cathode resistor is lost. The actual voltage output, E

E

10) Determine the voltage gain of the amplifier stage.

Voltage gain is equal to the output voltage divided by the input voltage.

Let us consider now the case where it is desired to obtain maximum possible undistorted output for a selected plate-supply voltage. As an example, in the circuit of Fig. 3 a supply voltage of 200 (E

Fig. 3 - Pentode resistance-coupled amplifier circuit. |

From the information available we may now proceed to calculate suitable circuit values and some of the operating conditions:

1) Find the total plate resistance represented by the load line, AC.

2) Find the proper value for the cathode resistor R

Since the bias point, midway between points D and E which represent the extremities of permissible grid swing without distortion, is at -4 1/2 volts, the average plate-current flow is 1 ma. and our average plate voltage is 80 volts. The screen current is approximately 25 percent of the average plate current and, therefore, the total current passing through R

3) What should be the value of the plate resistor, R

R

4) Determine the value of the cathode condenser, C

5) What should be the value of the coupling condenser, C

Fig. 4 - Plate-voltage vs. plate-current characteristic curves for the Type 65J7 pentode tube. |

7) In order to bypass the screen-dropping resistor adequately, the reactance of the bypass condenser, C

8) If the resistance-coupled amplifier is employed in an audio system which has three or more stages, it may be necessary to employ a decoupling network, R

R

9) The condenser C

10) The new supply voltage would, of necessity, be 200 volts plus the voltage drop across R

E = 200 + (I

11) The total plate-voltage swing as determined by the perpendiculars of Fig. 4 is 130-30 = 150 volts. From the ratio,

If a different screen voltage were selected the curves would change somewhat, calling for alterations in the values.

In the next installment, covering the design of a two-stage audio amplifier, an approximate method will be outlined to convert the curves to a lower screen potential.

Posted 6/11/2013