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von ROBERT M. MITCHELL
(Über die Leistung von Endstufenröhren und deren Auswahl)

The right approach in making any selection of anything is to have all the information about it. Then, if you weight the information correctly, you will come out with the correct decision. The author tells you how to go about the weighing.

Every audio designer has been faced at one time or another with the problem of choosing tube types for a design. Since the design of an audio amplifier normally commences with the power stage, the audio output tubes are usually the first to be investigated. If the designer had available a method which helped him to select invariably the best tubes, it would reward him in both performance and pride, not to mention time and effort. How such selection may be readily done is described below.

The usual procedure of choosing a tube is to consult the manuals, and compare data by glancing back and forth among the specification sheets, perhaps making an occasional note. The information thus gleaned is combined with the designer's personal knowledge of how some of these tubes have behaved in certain equipment. On the basis of this information a choice is made. In many cases the choice thus made is a good one. In other instances, however, events prove that the second-best tube has been chosen.

In such cases the wrong tube was chosen, not because the data sheet of a better one was unavailable, but because the data on the available tubes was not properly evaluated. It is therefore of considerable interest to the designer to have available a method of systematically evaluating the characteristics of various tubes, so that an intelligent choice can be made.


The method discussed here consists of grouping the various tube characteristics so that substitution of proper values gives a result which can be compared numerically with that of any other tube. Such an expression is called a Figure of Merit, since it indicates the relative value of the tube for a given application. The phrase italicized is an important qualification. A tube "which may have a fine Figure of Merit for audio output service, may have a very poor one for class C oscillator service, for example.

All tubes in Class AB, with 400 volts or less on plates

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*B = BEAM POWER - P = PENTODE - T = TRIODE
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A Figure of Merit must adequately reflect the variations of its make-up factors so that significant differences can be seen. In order to achieve this, it may sometimes be necessary to "weight" some of the factors - that is, to assign them arbitrarily a multiplying factor which increases their relative value. This point will be discussed later in greater detail.

Specifically, a Figure of Merit for audio output tubes should be so arranged that it indicates relative worth not only when tubes operate under "tube manual" conditions, but also under other practical and likely conditions. For example, if we put tubes in parallel, or apply feedback around the tubes, our Figure of Merit formula should still be valid. We may then determine the relative value of different tubes in parallel, or the relative value of different tubes with the same amount of feedback around each. We may also, of course, compare two tubes of type A without feedback with two tubes of type B with feedback, and so forth.

In deriving any Figure of Merit it must be understood that the cost of the
tube is a parameter of primary interest, even to the quality-minded purist. This is so because almost any Figure of Merit will include the power sensitivity (watts out per volt in) as one term, and it is obvious that the power sensitivity can be increased ad infinitum merely by putting more tubes in parallel with the initial set. However, since this cost factor can be evaluated only by the user we will not explicitly consider it. We will find, though, that it tends to enter indirectly in some of the other terms of the expression.

To formulate our Figure of Merit we first take inventory of the various factors which we wish to consider. Among these may be power output, driving voltage, distortion at rated output, damping factor (ratio of load impedance to source impedance), efficiency, maximum grid circuit resistance, cost, size, and so on. These may then be sorted quite arbitrarily into two groups: desirable and undesirable. The figure will be designed so that a large desirable term makes a better figure and a large undesirable one makes the figure poorer. This will mean our figure is a fraction with the desirable factors in the numerator and the undesirable ones in the denominator. See Table I.

In looking over this inventory of factors we may find terms which actually affect the merit-figure of the driver tube more than the output tube. Driving voltage and maximum grid circuit resistance are two such terms. Low driving voltage is desirable because it means lower distortion in the driver stage, or possibly lower voltage for a given distortion. A high permissible grid circuit resistance is desirable because it means that awkward coupling methods, such as transformers, are not necessary, or that the loading on the preceding tube can be made less, or that the size of a coupling capacitor can be made smaller for the same low-frequency time constant.

The terms of the figure might be grouped, if we desire, in terms of quality and terms of quantity. The distinction however, is not clear-cut and there is overlapping of the groups. It is this overlapping that the element of cost invariably creeps into, whether we want it or not. If this cost element is neglected to the greatest possible extent we can make up a simple figure which is predominantly a quality figure and therefore very suitable for home constructors or experimenters.

A basic Figure of Merit is the following :

Figure of Merit = F =  PD/EH

where P = power output - a "quantity" factor

D = Damping factor (load Z/Source Z), - a "quality" factor
E = Input voltage required to produce P - a "quantity" factor
H = Harmonic distortion at power P - a "quality" factor
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Damping factor is a quality factor for three reasons. Not only does it indicate a measure of the transient response of the loudspeaker system, but it also indicates frequency response, since a low source impedance relative to the reflected load means a wider response from a given output transformer or (to let the factor of cost creep in) a cheaper output transformer for the same frequency response. Low source impedance also means less distortion due to the transformer itself.

The other terms are relatively self-evident. Power is wanted, but we want to get it at no expense to the preceding stage, that is, with as little driving voltage as possible. Our quantity terms are therefore:

power out / driving voltage = power sensitivity

The distortion term needs no explanation. If, because of the magnitudes of the various terms, our figure ends up as a decimal, we may multiply the result by some arbitrary number. In this case final results have been multiplied by 1000.
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Let's see how feedback affects this figure. If enough voltage feedback (6db) is applied (around the output tubes only) to increase the required driving voltage by a factor of two, our quantity term in the expression is reduced by two, making the figure only one-half as good as before. Our quality term has been increased by more than two, however. The distortion has been cut in half (for the same power output, of course), and this alone has brought the total figure back to its original value.

The change in the clamping factor, however, is considerably more than two to one, typical values for a triode being about two, and for a beam power tube about 10. This is because the plate resistance variation due to voltage feedback is dependent on the amplification factor, [i, of the tube and not just on the stage gain. Whether we agree that the merit of our system has gone up by a factor of two (or ten) is a question of how much weight we give the damping factor term. The problem of what weights should be assigned to any of the terms is one which the designer must decide on in advance.

With this basic Figure of Merit at hand, let us see how some of the well-known power tubes fare.
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Table II lists not only the final Figure of Merit but also the component terms which go to make up that figure. The ratio of the first factors is also given separately as the power sensitivity (column headed P/E), a sort of sub-figure-of-merit.

Type 2A3, an obsolescent filamentary type triode, has been deliberately included in Table I since it helps demonstrate a particular point. The point is that the value of a Figure of Merit depends on how important the designer feels the individual factors are. The 2A3 has the highest Figure of Merit according to Table II. There are many designers who would not agree at all with this rating. They would point out that the 2A3 achieved top rating almost solely on the basis of its damping factor, and that conversely the 2A3 is by far the hardest tube of the group to drive.

A glance at the columns for Power Sensitivity P/E and Damping Factor will show that, in these two respects, they are right. It takes 88 volts rms or 125 volts peak to drive a pair of 2A3's in fixed bias. This is quite a large voltage to achieve without distortion. It is therefore quite possible that the distortion in the driver stage will exceed the distortion in the output stage. There is no disputing the fact that the 2A3 has a high damping factor. Is the damping factor, however as important as we have made it appear?

Let us compare the 6Y6 tabulation for a moment. The 6V6 gives about the same power output as the 2A3 at almost the same d.c. supply voltage. It is therefore a tube that may be fairly compared with the 2A3. Let us suppose that we have available a driver tube that can supply 88 volts rms with low distortion, say one per cent. Are we justified in using 2A3's in the output, or could we do better with 6V6's and how?

The 6Y6 requires 26 volts drive. Let us apply negative voltage feedback around the 6Y6 until it requires 88 volts drive. Its power sensitivity will then be equal to that of the 2A3. This requires a feedback of 3.4 or 10.6 db. This application of feedback will reduce the distortion from 3.5 percent to 1.0 percent. It will also increase the damping factor from 0.072 to 2.65. The new Figure of Merit for the 6Y6 is 450. This figure implies that the 6V6 with 10.6 db of feedback is 3.5 times better than the 2A3 without feedback. Note, however, that the relative values of the Figures of Merit again depend very much on the damping factor and the importance which we assign to it.

The foregoing shows how we may recompute our basic Figure of Merit for a tube with feedback (around output stage only). Our Figure may also be used to determine the result of placing tubes in parallel to achieve more desirable performance.

For example, if we want an output stage capable of 35 watts, we may wish to determine whether a pair of tubes in push-pull is best, or whether two pairs of a different type in push-pull-parallel will be still better. For a single pair we could use the FL34 which has a Figure of 15.7 in fixed bias. A smaller tube which could deliver adequate output in push-pull parallel is the EL84. It has a Figure of 23.4. In paralleling tubes we double the power output, but the voltage input remains the same. The power sensitivity is therefore doubled. The distortion at full output remains the same for each tube. The damping factor remains the same since both the tube plate resistance and the load resistance have been halved, keeping their ratio constant. The basic Figure of Merit is therefore doubled by putting tubes in parallel.

As a result of the above discussion we see that we may obtain 35 watts from a pair of EL34 tubes with a Figure of Merit of 15.7, or that we may achieve it with four EL84 tubes and a Figure of 46.8 (See Table III). This is quite a substantial increase over 15.7, and leads us to winder whether a high Figure of Merit is not to be obtained merely by paralleling enough tubes.

The answer is yes, if we confine ourselves only to the basic Figure of Merit, and choose to disregard other factors, among them the cost. Even the most devoted purist, however, would pause to think before putting twenty or thirty small tubes in parallel in order to achieve what just two large tubes can do.

Aside from the cost, there is another danger in putting too many tubes in parallel. This is the effect which paralleling has on the driver tube. Each time a tube is added in parallel, the input impedance goes down. As the number of tubes in parallel grows large, the input capacitance may easily become large enough to affect the high-frequency response of the driver stage, particularly
if the output tubes are triodes. There is the matter of grid-circuit resistance, however, which may be of considerable importance when adding only one additional pair in parallel.

The data on every output tube always includes a characteristic called Maximum Permissible Grid-Xo. 1 Circuit Resistance. This characteristic, as its name implies, shows the highest value of resistance which may be placed in the grid circuit. The value varies over a range of as much as five to one for a given tube, depending on whether fixed or cathode bias is used. Fixed bias always requires a lower value of resistor.

If a tube has a relatively low value of permissible grid-circuit resistance, than severe limitations are placed on the driver stage. The a.c. load resistance seen by the driver cannot be large. This will limit the gain or increase the distortion of the driver and often does both. Paralleling tubes always makes this problem worse, since as tubes are paralleled the permissible grid-circuit resistance is greatly reduced. (Halved for twTo pairs, divided by three for three pairs, and so on.) It may be greatly to our advantage then to include the maximum permissible grid circuit resistance as a factor in our Figure of Merit. In addition there are several other characteristics which we may w7ish to use.

The efficiency of the tube type is important. A good tube is one which converts a large percentage of the d.e. supply power into a.c. power. It would certainly be poor design if we added more cost and complexity to the power supply than we saved on the output stage. Let us then include plate-circuit efficiency as one of our factors.

The power required by the filament circuit may influence our opinion of a tube considerably. Tube A may appear to have a much higher efficiency than tube B, until we see that A's heater power more than makes up the difference in plate circuit efficiency. This is admittedly of minor interest to the home constructor, but as before he may omit this factor from his Figure of Merit if he so desires.

The final factor is that of cost. This may be taken care of easily by giving the cost of the lowest priced tube (6V6) the arbitrary value of 1, and then expressing the cost of any other tube as its ratio to the 6V6 cost.

A new table taking these factors into consideration is Table III. Table III has two Figure of Merit columns. The column headed F2 does not include cost while F3 does. Each of the new Figures includes the factors that went into making up the first Figure of Merit (Fj).

The following are the formulas used:

F2 = Eff x Rgmax x F1
F3 = F2 x Cf

where Eff = Efficiency
Rgmax = Maximum grid-circuit resistance
Cf = Cost factor

Table IV lists the additional characteristics used to make Table III from Table II.

With these tables at hand the designer is now able to make a logical and systematic choice of output tubes. And if he chooses to omit certain factors it will not be from ignorance, but because he chose to give that factor an arbitrary value of 1. (Note that multiplying (or dividing) any Figure of Merit by one will not change its value.)

As new tubes are brought out they can be appraised by this method, and if new factors are considered important they can be added conveniently to the framework already established.
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