Dear Son:

You remember the audion characteristics which I used in Figs. 55, 56 and 57 of Letter 14 to show you how an incoming signal will affect the current in the plate circuit. Look again at these figures and you will see that these characteristics all had the same general shape but that they differed in their positions with reference to the “main streets” of “zero volts” on the grid and “zero mil-amperes” in the plate circuit. Changing the voltage of the B-battery in the plate circuit changed the position of the characteristic. We might say that changing the B-battery shifted the curve with reference to the axis of zero volts on the grid.

You see that what we have done is to arrange the point on the audion characteristic about which the tube is to work by properly choosing the value of the grid voltage E_C.

There is an important method of using an audion for a detector where we arrange to have the grid voltage change steadily, getting more and more negative all the time the signal is coming in. Before I tell how it is done I want to show you what will happen.

Suppose we start with an audion detector, for which the characteristic is that of Fig. 56, but arranged as in Fig. 86 to give the grid any potential which we wish. The batteries and slide wire resistance which are connected in the grid circuit are already familiar to you.

Every time the incoming signal makes one complete cycle of changes we shift the slider a little further and make the grid permanently more negative. You can see what happens. As the grid becomes more negative the current in the plate circuit decreases on the average. Finally, of course, the grid will become so negative that the current in the plate circuit will be reduced to zero. Under these conditions an incoming signal finally makes a large change in the plate current and hence in the current through the telephone.

The method of shifting a slider along, every time the incoming signal makes a complete cycle, is impossible to accomplish by hand if the frequency of the signal is high. It can be done automatically, however, no matter how high the frequency if we use a condenser in the grid circuit as shown in Fig. 88.

When the incoming signal starts a stream of electrons through the coil L of Fig. 88 and draws them away from plate 1 of the condenser C it is also drawing electrons away from the 1 plate of the condenser C_G which is in series with the grid. As electrons leave plate 1 of this condenser others rush away from the grid and enter plate 2. This means that the grid doesn’t have its ordinary number of electrons and so is positive.

If the grid is positive it will be pleased to get electrons; and it can do so at once, for there are lots of electrons streaming past it on their way to the plate. While the grid is positive, therefore, there is a stream of electrons to it from the filament. Fig. 89 shows this current.

All this takes place during the first half-cycle of the incoming signal. During the next half-cycle electrons are sent into plate 1 of the condenser C and also into plate 1 of the grid condenser C_G. As electrons are forced into plate 1 of the grid condenser those in plate 2 of that condenser have to leave and go back to the grid where they came from. That is all right, but while they were away the grid got some electrons from the filament to take their places. The result is that the grid has now too many electrons, that is, it is negatively charged.

An instant later the signal e. m. f. reverses and calls electrons away from plate 1 of the grid condenser. Again electrons from the grid rush into plate 2 and again the grid is left without its proper number and so is positive. Again it receives electrons from the filament. The result is still more electrons in the part of the grid circuit which is formed by the grid, the plate 2 of the grid condenser and the connecting wire. These electrons can’t get across the gap of the condenser C_G and they can’t go back to the filament any other way. So there they are, trapped. Finally there are so many of these trapped electrons that the grid is so negative all the time as almost entirely to oppose the efforts of the plate to draw electrons away from the filament.

That’s the way to arrange an audion so that the incoming signal makes the largest possible change in plate current. We can tell if there is an incoming signal because it will “block” the tube, as we say. The plate-circuit current will be changed from its ordinary value to almost zero in the short time it takes for a few cycles of the incoming signal.

We can detect one signal that way, but only one because the first signal makes the grid permanently negative and blocks the tube so that there isn’t any current in the plate circuit and can’t be any. If we want to put the tube in condition to receive another signal we must allow these electrons, which originally came from the filament, to get out of their trapped position and go back to the filament.

One way of making a high resistance like this is to draw a heavy pencil line on a piece of paper, or better a line with India ink, that is ink made of fine ground particles of carbon. The leak should have a very high resistance, usually one or two million ohms if the condenser is about 0.002 microfarad. If it has a million ohms we say it has a “megohm” of resistance.

This method of detecting with a leaky grid-condenser and an audion is very efficient so far as telling the listener whether or not a signal is coming into his set. It is widely used in receiving radio-telephone signals although it is best adapted to receiving the telegraph signals from a spark set.

In Fig. 91 I have drawn a sketch to show the e. m. f. which the signals from a spark set impress on the grid of a detector and to show how the plate current varies if there is a condenser and leak in the grid circuit. I have only shown three signals in succession. If the operator sends at the rate of about twenty words a minute a dot is formed by about sixty of these signals in succession.

The frequency of the alternations in one of the little signals will depend upon the wave length which the sending operator is using. If he uses the wave length of 600 meters, as ship stations do, he will send with a radio frequency of 500,000 cycles a second. Since the signals are at the rate of a thousand a second each one is made up of 500 complete cycles of the current in the antenna. It would be impracticable therefore to show you a complete picture of the signal from a spark set. I have, however, lettered the figure quite completely to cover what I have just told you.

You can see that there is always a little favoritism on the part of the grid-condenser detector. It doesn’t exactly reproduce the variations in intensity of the radio signal which were made at the sending station. It distorts a little. As amateurs we usually forgive it that distortion because it is so efficient. It makes so large a change in the current through the telephone when it receives a signal that we can use it to receive much weaker signals, that is, signals from smaller or more distant sending stations, than we can receive with the arrangement described in Letter 14.

My Dear Receiver:

There is one way of making an audion even more efficient as a detector than the method described in the last letter. And that is to make it talk to itself.

Suppose we arrange a receiving circuit as in Fig. 92. It is exactly like that of Fig. 90 of the previous letter except for the fact that the current in the plate circuit passes through a little coil, L_T, which is placed near the coil L and so can induce in it an e. m. f. which will correspond in intensity and wave form to the current in the plate circuit.

If we should take out the grid condenser and its leak this circuit would be like that of Fig. 54 in Letter 13 which we used for a generator of high-frequency alternating currents. You remember how that circuit operates. A small effect in the grid circuit produces a large effect in the plate circuit. Because the plate circuit is coupled to the grid circuit the grid is again affected and so there is a still larger effect in the plate circuit. And so on, until the current in the plate circuit is swinging from zero to its maximum possible value.

Start with the coils at right angles to each other and turn L_T so as to bring its windings more and more parallel to those of L. If we want L_T to have a large effect on L its windings should be parallel and also in the same direction just as they were in Fig. 54 of Letter 13 to which we just referred. As we approach nearer to that position the current in L_T induces more and more e. m. f. in coil L. For some position of the two coils, and the actual position depends on the tube we are using, there will be enough effect from the plate circuit upon the grid circuit so that there will be continuous oscillations.

We want to stop just short of this position. There will then be no continuous oscillations; but if any changes do take place in the plate current they will affect the grid. And these changes in the grid voltage will result in still larger changes in the plate current.

You see now why I said the tube talked to itself. It repeats to itself whatever it receives. It has a greater strength of signal to detect than if it didn’t repeat. Of course, it detects also just as I told you in the preceding letter.

In adjusting the coupling of the two coils of Fig. 92 we stopped short of allowing the tube circuit to oscillate and to generate a high frequency. If we had gone on increasing the coupling we should have reached a position where steady oscillations would begin. Usually this is marked by a little click in the receiver. The reason is that when the tube oscillates the average current in the plate circuit is not the same as the steady current which ordinarily flows between filament and plate. There is a sudden change, therefore, in the average current in the plate circuit when the tube starts to oscillate. You remember that what affects the receiver is the average current in the plate circuit. So the receiver diaphragm suddenly changes position as the tube starts to oscillate and a listener hears a little click.

There will be impressed on the grid of the tube two alternating e. m. f.’s, one due to the tube’s own oscillations and the other incoming from the distant transmitting station. The two e. m. f. ’s are both active at once so that at each instant the e. m. f. of the grid is really the sum of these two e. m. f.’s. Suppose at some instant both e. m. f.’s are acting to make the grid positive. A little later one of them will be trying to make the grid negative while the other is still trying to make it positive. And later still when the first e. m. f. is ready again to make the grid positive the second will be trying to make it negative.

It’s like two men walking along together but with different lengths of step. Even if they start together with their left feet they are soon so completely out of step that one is putting down his right foot while the other is putting down his left. A little later, but just for an instant, they are in step again. And so it goes. They are in step for a moment and then completely out of step. Suppose one of them makes ten steps in the time that the other makes nine. In that time they will be once in step and once completely out of step. If one makes ten steps while the other does eight this will happen twice.

This circuit of Fig. 92 will let us detect signals which are not varying in intensity. And consequently this is the method which we use to detect the telegraph signals which are sent out by such a “continuous wave transmitter” as I showed you at the end of Letter 13.

When the key of a C-W transmitter is depressed there is set up in the distant receiving-antenna an alternating current. This current doesn’t vary in strength. It is there as long as the sender has his key down. Because, however, of the effect which I described above there will be an audible note from the telephone receiver if the detector tube is oscillating at a frequency within two or three thousand cycles of that of the transmitting station.

This method of receiving continuous wave signals is called the “heterodyne” method. The name comes from two Greek words, “dyne” meaning “force” and the other part meaning “different.” We receive by combining two different electron-moving-forces, one produced by the distant sending-station and the other produced locally at the receiving station. Neither by itself will produce any sound, except a click when it starts. Both together produce a musical sound in the telephone receiver; and the frequency of that note is the difference of the two frequencies.

It is not necessary to use a grid condenser in a feed-back circuit but it is perhaps the usual method of detecting where the regenerative circuit is used. The whole value of the regenerative circuit so far as receiving is concerned is in the high efficiency which it permits. One tube can do the work of two.

It means that two volts in the grid circuit have the same effect on the plate current as ten volts in the plate circuit. If we apply a volt to the grid circuit we get five times as large an effect in the plate circuit as we would if the volt were applied there. We get a greater effect, the effect of more volts, by applying our voltage to the grid. We say that the tube acts as an “amplifier of voltage” because we can get a larger effect than the number of volts which we apply would ordinarily entitle us to.

We have replaced the telephone receiver by a “transformer.” A transformer is two coils, or windings, coupled together. An alternating current in one will give rise to an alternating current in the other. You are already familiar with the idea but this is our first use of the word. Usually we call the first coil, that is the one through which the alternating current flows, the “primary” and the second coil, in which a current is induced, the “secondary.”

The secondary of this transformer is connected to the grid circuit of another vacuum tube, to the plate circuit of which is connected another transformer and the telephone receiver. The result is a detector and “one stage of amplification.”

The primary of the first transformer, so we shall suppose, has in it the same current as would have been in the telephone. This alternating current induces in the secondary an e. m. f. which has the same variations as this current. This e. m. f. acts on the grid of the second tube, that is on the amplifier. Because the audion amplifies, the e. m. f. acting on the telephone receiver is larger than it would have been without the use of this audion. And hence there is a greater response on the part of its diaphragm and a louder sound.

In the circuit which I have just described an audion is used to amplify the current which comes from the detector before it reaches the telephone receiver. Sometimes we use an audion to amplify the e. m. f. of the signal before impressing it upon the grid of the detector. Fig. 95 shows a circuit for doing that. In the case of Fig. 94 we are amplifying the audio-frequency current. In that of Fig. 95 it is the radio-frequency effect which is amplified. The feed-back or regenerative circuit of Fig. 92 is a one-tube circuit for doing the same thing as is done with two tubes in Fig 95.

Dear Son:

In our use of the audion we form three circuits. The first or A-circuit includes the filament. The B-circuit includes the part of the tube between filament and plate. The C-circuit includes the part between filament and grid. We sometimes speak of the C-circuit as the “input” circuit and the B-circuit as the “output” circuit of the tube. This is because we can put into the grid-filament terminals an e. m. f. and obtain from the plate-filament circuit an effect in the form of a change of current.

Suppose we had concealed in a box the audion and circuit of Fig. 96 and that only the terminals which are shown came through the box. We are given a battery and an ammeter and asked to find out all we can as to what is between the terminals F and G. We connect the battery and ammeter in series with these terminals. No current flows through the circuit. We reverse the battery but no current flows in the opposite direction. Then we reason that there is an open-circuit between F and G.

Now suppose we take several cells of battery and try in the same way to find what is hidden between the terminals P and F. We start with one battery and the ammeter as before and find that if this battery is connected so as to make P positive with respect to F, there is a feeble current. We increase the battery and find that the current is increased. Two cells, however, do not give exactly twice the current that one cell does, nor do three give three times as much. The current does not increase proportionately to the applied voltage. Therefore we reason that whatever is between P and F acts like a resistance but not like a wire resistance.

Then, we try another experiment with this hidden audion. We connect a battery to G and F, and note what effect it has on the current which our other battery is sending through the box between P and F. There is a change of current in this circuit, just as if our act of connecting a battery to G-F had resulted in connecting a battery in series with the P-F circuit. The effect is exactly as if there is inside the box a battery which is connected into the hidden part of the circuit P-F. This concealed battery, which now starts to act, appears to be several times stronger than the battery which is connected to G-F.

All this, of course, is merely a review statement of what we already know. These experiments are interesting, however, because they follow somewhat those which were performed in studying the audion and finding out how to make it do all the wonderful things which it now can.

As far as we have carried our series of experiments the box might contain two separate circuits. One between G and F appears to be an open circuit. The other appears to have in it a resistance and a battery (or else an alternator). The e. m. f. of the battery, or alternator, as the case may be, depends on what source of e. m. f. is connected to G-F. Whatever that e. m. f. is, there is a corresponding kind of e. m. f. inside the box but one several times larger.

The men who first performed such experiments wanted some convenient way of saying that if an alternator, which has an e. m. f. of V volts, is connected to F and G, the effect is the same as if a much stronger alternator is connected between F and P. How much stronger this imaginary alternator is depends upon the design of the audion. For some audions it might be five times as strong, for other designs 6.5 or almost any other number, although usually a number of times less than 40. They used a little Greek letter called “mu” to stand for this number which depends on the design of the tube. Then they said that the hidden alternator in the output circuit was mu times as strong as the actual alternator which was applied between the grid and the filament. Of course, instead of writing the sound and name of the letter they used the letter μ itself. And that is what I have done in the sketch of Fig. 97.

As to the circuit F-P, we can treat it as a resistance in series with which there is a generator μ times as strong as that which is connected to F and G. The next problem is how to get the most out of this hidden generator. We call the resistance which the tube offers to the passage of electrons between P and F the “internal resistance” of the plate circuit of the tube. How large it is depends upon the design of tube. In some tubes it may be five or six thousand ohms, and in others several times as high. In the large tubes used in high-powered transmitting sets it is much less. Since it will be different in different cases we shall use a symbol for it and say that it is R_P ohms.

Then one rule for using an audion as an amplifier is this: To get the most out of an audion see that the telephone, or whatever circuit or piece of apparatus is connected to the output terminals, shall have a resistance of R_P ohms. When the resistance of the circuit, which an audion is supplying with current, is the same as the internal resistance of the output side of the tube, then the audion gives its greatest output. That is the condition for the greatest “amount of energy each second,” or the “greatest power” as we say.

This leads to the next rule: If the telephone receiver, or the circuit, which we wish to connect to the output of an audion, does not have quite nearly a resistance of R_P ohms we use a properly designed transformer as we have already done in Figs. 94 and 95.

A transformer is two separate coils coupled together so that an alternating current in the primary will induce an alternating current in the secondary. Of course, if the secondary is open-circuited then no current can flow but there will be induced in it an e. m. f. which is ready to act if the circuit is closed. Transformers have an interesting ability to make a large resistance look small or vice versa. To show you why, I shall have to develop some rules for transformers.

If we want a high-voltage alternating e. m. f. all we have to do is to send an alternating current through the primary of a transformer which has in the secondary, many times more turns of wire than it has in the primary. From the secondary we obtain a higher voltage than we impress on the primary.

You can see one application of this rule at once. When we use an audion as an amplifier of an alternating current we send the current which is to be amplified through the primary of a transformer, as in Fig. 94. We use a transformer with many times more turns on the secondary than on the primary so as to apply a large e. m. f. to the grid of the amplifying tube. That will mean a large effect in the plate circuit of the amplifier.

You remember that the grid circuit of an audion with a proper value of negative C-battery is really open-circuited and no current will flow in it. For that case we get a real gain by using a “step-up” transformer, that is, one with more turns in the secondary than in the primary.

Suppose we have a transformer with twice as many turns on the secondary as on the primary. To the primary we apply an alternating e. m. f. of a certain number of volts. In the secondary there will be twice as many volts because it has twice as many turns. The current in the secondary, however, will be only half as large as is the current in the primary. We have twice the force in the secondary but only half the electron stream.

It is something like this: You are out coasting and two youngsters ask you to pull them and their sleds up hill. You pull one of them all the way and do a certain amount of work. On the other hand suppose you pull them both at once but only half way up. You pull twice as hard but only half as far and you do the same amount of work as before.

We can’t get more work out of the secondary of a transformer than we do in the primary. If we design the transformer so that there is a greater pull (e. m. f.) in the secondary the electron stream in the secondary will be correspondingly smaller.

Before we return to the question of using a transformer in an audion circuit let us turn this transformer around as in Fig. 99 and send the current through the side with the larger number of windings. Let’s talk of “primary” and “secondary” just as before but, of course, remember that now the primary has twice the turns of the secondary. On the secondary side we shall have only half the current, but there will be twice the e. m. f. The resistance of the secondary then is four times that of the primary.

In the first place the primary of the transformer has a number of ohms just equal to the internal resistance of the tube. The tube, therefore, will give its best to that transformer. In the second place the secondary of the transformer has a resistance just equal to the telephone receivers so it can give its best to them. The effect of the transformer is to make the telephones act as if they had four times as much resistance and so were exactly suited to be connected to the audion.

This whole matter of the proper use of transformers is quite simple but very important in setting up vacuum-tube circuits. To overlook it in building or buying your radio set will mean poor efficiency. Whenever you have two parts of a vacuum-tube circuit to connect together be sure and buy only a transformer which is designed to work between the two impedances (or resistances) which you wish to connect together.

There is one more precaution in connection with the purchase of transformers. They should do the same thing for all the important frequencies which they are to transmit. If they do not, the speech or signals will be distorted and may be unintelligible.