▼ Menu

    
Extras ▼

How Undistorted Output is Computed.

In the bald form in which they are presented in the valve maker's catalogue, valve curves are rather dull and unenlightening, and they seem at first sight to have but little connection with the practical behaviour of the valve as it is used in the set.

The main reason why valve curves, considered by themselves, do not give much direct information is that they represent the response of the valve to the application of various steady voltages to grid and anode, and it is always assumed in taking them that no resistance or impedance of any kind is connected between anode, or grid, and the battery supplying it with voltage. In a set the voltages with which we are chiefly concerned are not steady, but alternating, while every valve has to have a component in its anode circuit to enable it to provide useful amplification. The official valve curves are therefore only the raw material from which the performance that the valve will give in the set can be deduced.

In practice, the voltage and current changes caused by the reception of a signal do not interest us very greatly except in the case of the output valve, from which we nearly always need to obtain the maximum volume that can be had before overloading and consequent distortion begin to be manifest. We will therefore restrict our scope to the examination and analysis of the curves of output valves, which will serve as well as any others as an example of the relationship between conventional and operating curves, while at the same time we shall see how the correct loud speaker load for any valve is found, and how the volume of available sound can be estimated for each case. Incidentally, we shall derive a very clear understanding of the rather complicated voltage and current changes taking place at the anode of a valve during the process of amplifying.

Curves for Measurements

Fig. 1. - Anode volts-anode current curves of typical two-volt power valve. Each curve refers to the grid voltage indicated against it.

In Fig. 1 are reproduced a series of curves connecting the anode voltage Ea of an output valve with its anode current I_a. These curves are obtained from a series of measurements made with a circuit like that of Fig. 2, in which the three meters read anode and grid voltages, and anode current.

Fig. 2. - Measuring circuit for plotting curves of Fig. 1. For each value of Eg, Ea is varied over a wide range and the corresponding values of Ia. are noted.

For any one curve the grid bias, as indicated on the meter E_g, is held constant; the anode voltage read on the meter E_a is raised from zero in a series of small steps, the anode current shown by the meter I_a being noted for each voltage. The resulting figures, when plotted on squared paper, give one the curves of Fig. 1, while the whole process has to be repeated, each time with a different value of grid bias E_g, for each of the curves shown on the diagram.

The completed family of curves gives fairly full information as to the anode current resulting from any combination of grid and anode voltages that may be chosen. All values of anode current that can be obtained with a bias of -6 Volts, for example, appear on the third curve, each value being indicated by the point at which the curve crosses the vertical line representing the value of anode voltage chosen. For this grid voltage the anode current is 7 mA. at Ea:-80, 14½ mA at Ea=100, and 24½ mA at Ea=120. Keeping the anode voltage at this last value and changing the bias to -9 Volts shifts us to the next curve, which shows an anode current of 15½ milliamps.

We will suppose that our high-tension battery gives 150 Volts; the grid bias recommended by the makers of this particular valve at this anode voltage is -14 Volts. Point A on Fig. 1, at which the curve for E_g 1-4 cuts the vertical line indicating E_a =150, will therefore represent the condition of the valve as it is used in the set. The anode current, as the diagram shows, will set itself at 15½ milliamps.

Fig. 3. - Output valve without anode-circuit load. The application of the signal swings anode current only, along the load line AB of Fig. 1.

To begin with, we will suppose that there is no loud speaker or other component connected between the anode of the valve and the battery, so that the circuit will be that of Fig. 3. The steady state of the valve is already defined by the point A of Fig. 1, but we still have to trace the course of events when a signal is applied to the grid. The voltage of the latter will begin to swing up and down on either side of the fixed bias value, the magnitude of the swing depending upon the amplitude of the signal. What will the anode current do? Since the anode voltage is fixed at 150 by a direct and presumably resistance-less connection to the battery, the anode cannot depart from that portion of Fig. 1 which gives its possible currents for that voltage. All these values are to be found on the vertical line BC running upwards from 150 on the anode voltage scale; as the signal swings the grid through various momentary voltages the corresponding currents will be shown by the intersection of the appropriate curves with BC. If, for example, the signal has a maximum value of 5 Volts, the grid will swing up and down between -9 and - 19 Volts; the anode current, as the curves show, will swing in sympathy between the values represented by points D and E. A weaker signal, of amplitude only three Volts, will swing the grid from -11 to -17 Volts, and the anode current will now vary less widely, swinging as before between the points where the curves for these two bias values, if drawn, would cut the vertical line BC.

Having seen the uses of the curves of Fig. 1 by considering this very simple case, we will progress a stage farther and imagine that a resistance is connected in the anode circuit of the valve in place of the loud speaker that would normally be used. The justification for the choice of a resistance is found in the fact that it offers the same impedance to direct as to alternating currents, and so allows us to trace out at our leisure from a DC diagram effects which, in reality, are taking place by virtue of the impedance of the speaker to rapidly changing voltages.

Fig. 4. - Output valve with 4,500 Ω load R, and battery voltage adjusted to correspond. The application of the signal swings both anode current and anode voltage along the load line PQ of Fig. 5.

At the operating voltages taken, the correct load for the particular valve whose curves are shown will be assumed to be 4,500 Ω. This, then, must be the value of the resistance inserted as in Fig. 4 in the anode circuit. If we insert this resistance there will be a voltage drop across it, the magnitude of the drop depending, as Ohm's law describes, upon that of the steady anode current; to maintain the correct operating conditions for the valve we shall have to increase the battery voltage to compensate for this drop. At 15½ mA. the voltage drop in R will be 4.5 × 15.5, or 70 Volts; adding this to the 150 Volts that we require at the anode of the valve shows that the battery must now be one of 220 Volts, as indicated in Fig, 4.

Fig. 5. - The line PQ, drawn across the valve curves repeated from Fig. 1, gives the combinations of anode-voltage and anode-current possible with a load of 4,500 Ω with A as the operating point.

The main difference between this new arrangement and the last is that now any change in anode current will be accompanied by a corresponding variation in the voltage drop across R, and hence by a variation of the voltage on the anode itself. If the anode current drops the anode voltage will rise, approaching a maximum of 220 (the battery voltage) as the current approaches zero. Zero current at 220 Volts is shown by point P of Fig. 5, on which the valve curves are repeated from Fig. 1.

Starting from this point, we can find the voltage on the anode of the valve at various anode currents. At 10 mA., for example, 45 Volts will be dropped in R, leaving 175 Volts out of the total of 220 for the valve itself. At 20 mA. 90 Volts will be lost in R, so that the anode will have a voltage of 130. Similarly, the anode voltage will drop to 85 Volts at 30 mA. Plotting on Fig. 5 the points corresponding to these calculated voltages and currents, We find that they mark out the straight line PQ, and from the way in which the points were worked out we know that with the battery voltage held at 220, and the value of R fixed at 4,500 Ω the valve can only take up voltage current combinations shown by points on this line.

The Load Line

The fact that PQ, which is called the load line, passes through the operating point A is not an accident, but is an inevitable result of so choosing the battery voltage that the voltage at the anode of the valve should be 150 while passing its normal current of 15½ milliamps.

With the load line drawn across the valve curves, we are in a position to follow the course of events when the grid voltage of the valve in the circuit of Fig. 4. is altered. If we set it at -9 Volts the voltage current condition must necessarily lie on some point of the curve representing a 9 Volt bias. But equally it must lie, as we have seen, somewhere along the load line PQ. The only possible values for which both conditions can be simultaneously fulfilled are those given by the point where the curve cuts PQ at R, where the current is 20 milliamps, and there are 130 Volts on the anode.

We can now extend this argument to see what happens if a signal, the peak voltage of which we will take as 14, is applied to the grid, Such a signal will swing the grid backwards and forwards over the voltage range 0 to -28, and the anode current and anode voltage will swing in sympathy along the line PQ between the points where the curves for these limiting voltages cut the load line; that is, between S and T.

In the simpler case already discussed in connection with Fig. 3, we saw that the anode current swung through the series of values marked out by the vertical line AB of Fig. 1, the anode voltage remaining constant. In the more complex case of Fig. 4 anode voltage and anode current swing together through the series of values marked out by the load line PQ. In both cases the extent of the swing is controlled by the amplitude of the signal applied to the grid, and extends along AB or PQ as far as the points where the curves for the extreme limits of the grid voltage swing cut the line in question.

Slope of the Load Line

Comparison of the two cases brings another point into prominence. A vertical load line, such as AB, indicates a zero load, while a diagonal line like PQ represents a load of a fair number of Ohms. Clearly a lower load than 4,500 Ω would produce a load line more nearly vertical, and a higher load one more nearly horizontal than PQ. The slope of the load line, expressed in voltage change for each change of one milliampere of current, gives the resistance, in thousands of Ohms, of the load it represents. The choice of the correct numerical value of load for any particular output valve is necessary to enable the greatest amount of undistorted power to be extracted from the valve.

Reverting to the case of Fig. 5, we see from the diagram that the total swing of anode current is from 28.7 to 4.2 milliamps (at S and T respectively), this making a total variation of 24½ mA. Similarly, the voltages taken up by the anode lie between 201 and 90, a range of 111 Volts.

Fig. 6.- (a) Showing relationship between total voltage swing, peak voltage and RMS voltage. (b) The same relationships for current. With a resistance load, power is product of RMS voltage by RMS current.

There is therefore present at the anode an alternating signal voltage of total sweep 111 Volts, and hence of peak value 55½ Volts (see Fig. 6), and this drives through the resistance an alternating current of maximum sweep 24½ mA., and of peak value ¼ mA. On this information the power dissipated in the resistance can be computed; it is half the product of peak current by peak voltage. In the present case this is 0.5 (12.25 × 55.5) = 340 mW. This power, of course, is that due to the signals; the power used up in R by the passage of the steady current has not been taken into consideration. The 340 milliwatts are, in fact, available for operating the loud speaker for which R is standing, and causing it to deliver audible signals.

Undistorted Output

The question of distortion has not been entered into at all in this discussion, but it is not difficult to see that if each separate Volt of the total swing applied to the grid evokes the same change in anode current as every other, there will be no distortion. In terms of Fig. 5, this implies that if curves were drawn for each Volt of grid bias, they should divide PQ into a number of exactly equal lengths. It is evident from an inspection of the figure that this is not the case, for the curves are more closely crowded together at the bottom right hand corner of the diagram, where the grid voltages are higher.

Since distortion cannot be eliminated altogether, it becomes necessary to fix some allowable limit on the basis of which to compare the output available from different valves. For the case of the triode output valve which we have been considering quite a simple convention is usually adopted. It is laid down that distortion due to the distance AS, taken as a whole, being greater than AT shall be limited, no attention being paid to the equal spacing of points lying between A and S or A and T. Experience shows that a discrepancy in these two lengths just barely begins to make itself manifest by slightly impaired quality of reproduction when AS exceeds AT in the ratio of 11 to 9. This ratio is therefore taken as that to be satisfied when specifying the load to be connected in the output circuit, and when quoting the undistorted output of a valve.

Fig. 7. - Although the output transformer T may have negligible DC resistance, the anode voltage will swing, at signal frequency, far above and below the 150 Volts of the battery.

When working out the correct load and the undistorted output from any valve it is almost always assumed that the load will be a pure resistance, and that the voltage of the anode current supply will be augmented sufficiently to keep the anode of the valve at its normal working potential in spite of the introduction of this resistance. In practice, however, this is never done; the anode supply voltage is not raised above the normal value, and a loud speaker or output transformer of negligible DC resistance is connected in the anode circuit as in Fig. 7. It would seem at first sight that the anode voltage can now never rise above the normal working value, since there are no extra battery Volts.

It is true that if in Fig. 7 the grid-bias battery is augmented from 14 to 28 Volts, the anode voltage will not rise, any more than it did in the almost equivalent circuit of Fig. 3. The cases, indeed, are exactly parallel in that neither anode circuit contains any resistance to speak of to direct current. But there is a distinction, and a very big one, when rapidly alternating grid voltages, such as those due to the signal, are applied. Towards the rapidly changing anode currents called forth by the signal the transformer primary offers a very appreciable impedance; the natural result of this is that as the alternating currents flow through it a voltage is set up across it. Since the zero point round which this voltage is built up is the steady anode voltage of the valve, there are instants when the voltage at the anode is considerably in excess of that of the battery.

If we consider that to the grid of the valve of Fig. 7 there is applied an alternating voltage, at first very slow, but gradually increasing in its rate of alteration, rather a curious point comes to light. For the slowest alternations the transformer has no appreciable impedance, so that the load line corresponding to it is vertical. As the rate of alternation increases the load begins to be effective, and the load line swings over to the left and takes up a position similar to that of PQ. There is thus the possibility that for full description of the behaviour of the output valve it might be necessary to draw a separate load line for every frequency, each line passing through the operating point of the valve, and having an angle expressing the impedance of the speaker to the particular frequency.

In practice no one ever bothers with such a family of load lines, but instead one assumes that the impedance of the speaker is roughly constant. The value that it should have, as an average over the audible scale, is found by examination of the curves of the valve it is to follow.

In finding the best load for a newly developed valve the maker of it will lay a rule on the working point A and try, by swinging the rule round about that point, to find a load line such that the 11 to 9 ratio already mentioned is exactly satisfied when the maximum permissible grid swing is applied. From this can be worked out in the manner already detailed the power available with this working point, for which the load has already been adjusted to be that giving greatest output at the predetermined level of distortion. Then a new working point is tried, taking it a little higher or lower than A on the vertical line AB of Fig. 1; keeping, that is to say, the anode voltage at its full rated value but trying different values of bias. For each of these the output available at the maximum distortion permitted is found as for the first point. Comparing the outputs for each of these tentative working points, the one for which the output is greatest can be found. The value of bias which gives it and the load that fits it best are then included in the instruction leaflet.

A typical output valve (PX4) with the data supplied by the makers. From this sheet of details the load line is derived.