Letters of a Radio-Engineer to His Son Part 16

We might, therefore, pay no further attention to what is actually inside the box or how all these effects are brought about. We might treat the entire box as if it was formed by two separate circuits as shown in Fig.

97. If we do so, we are replacing the box by something which is equivalent so far as effects are concerned, that is we are replacing an actual audion by two circuits which together are equivalent to it.

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 [Greek: m] itself. And that is what I have done in the sketch of Fig. 97.

Now we are ready to talk about the audion as an amplifier. The first thing to notice is the fact that we have an open circuit between _F_ and _G_. This is true as long as we don't apply an e. m.

f. large enough to overcome the C-battery of Fig. 96 and thus let the grid become positive and attract electrons from the filament. We need then spend no further time thinking about what will happen in the circuit _G-F_, for there will be no current.

As to the circuit _F-P_, we can treat it as a resistance in series with which there is a generator [Greek: m] 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 pa.s.sage 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.

That rule is why we always select the telephone receivers which we use with an audion and always ask carefully as to their resistance when we buy. Sometimes, however, it is not practicable to use receivers of just the right resistance. Where we connect the output side of an audion to some other circuit, as where we let one audion supply another, it is usually impossible to follow this rule without adding some special apparatus.

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.

Suppose you have an alternating e. m. f. of ten volts applied to the primary of an iron-cored transformer which has ten turns. There is one volt applied to each turn. Now, suppose the secondary has only one turn.

That one turn has induced in it an alternating e. m. f. of one volt. If there are more turns of wire forming the secondary, then each turn has induced in it just one volt. But the e. m. f.'s of all these turns add together. If the secondary has twenty turns, there is induced in it a total of twenty volts. So the first rule is this: In a transformer the number of volts in each turn of wire is just the same in the secondary as in the primary.

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.

It looks at first as if a transformer would always give a gain. _If we mean a gain in energy it will not_ although we may use it, as we shall see in a minute, to permit a vacuum tube to work into an output circuit more efficiently than it could without the transformer. We cannot have any more energy in the secondary circuit of a transformer than we give to 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.

[Ill.u.s.tration: Fig 98]

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.

You remember how we measure resistance. We divide the e. m. f. (number of volts) by the current (number of amperes) to find the resistance (number of ohms). Suppose we do that for the primary and for the secondary of the transformer of Fig. 98 which we are discussing. See what happens in the secondary. There is only half as much voltage but twice as much current. It looks as though the secondary had one-fourth as much resistance as the primary. And so it has, but we usually call it "impedance" instead of resistance because straight wires resist but coils or condensers impede alternating e. m. f.'s.

[Ill.u.s.tration: Fig 99]

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.

Now return to the amplifier of Fig. 94 and see what sort of a transformer should be between the plate circuit of the tube and the telephone receivers. Suppose the internal resistance of the tube is 12,000 ohms and the resistance of the telephones is 3,000 ohms. Suppose also that the resistance (really impedance) of the primary side of the transformer which we just considered is 12,000 ohms. The impedance of its secondary will be a quarter of this or 3,000 ohms. If we connect such a transformer in the circuit, as shown, we shall obtain the greatest output from the tube.

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.

If you take the precautions which I have mentioned your radio receiving set formed by a detector and one amplifier will look like that of Fig.

94. That is only one possible scheme of connections. You can use any detector circuit which you wish,[10] one with a grid condenser and leak, or one arranged for feed-back In either case your amplifier may well be as shown in the figure.

[Ill.u.s.tration: Fig 100]

The circuit I have described uses an audion to amplify the audio-frequency currents which come from the detector and are capable of operating the telephones. In some cases it is desirable to amplify the radio signals before applying them to the detector. This is especially true where a "loop antenna" is being used. Loop antennas are smaller and more convenient than aerials and they also have certain abilities to select the signals which they are to receive because they receive best from stations which lie along a line drawn parallel to their turns.

Unfortunately, however, they are much less efficient and so require the use of amplifiers.

With a small loop made by ten turns of wire separated by about a quarter of an inch and wound on a square mounting, about three feet on a side, you will usually require two amplifiers. One of these might be used to amplify the radio signals before detection and the other to amplify after detection. To tune the loop for broadcasts a condenser of about 0.0005 mf. will be needed. The diagram of Fig. 100 shows the complete circuit of a set with three stages of radio-amplification and none of audio.

[Footnote 10: Except for patented circuits. See p. 224.]

LETTER 20

TELEPHONE RECEIVERS AND OTHER ELECTROMAGNETIC DEVICES

DEAR SON:

In an earlier letter when we first introduced a telephone receiver into a circuit I told you something of how it operates. I want now to tell why and also of some other important devices which operate for the same reason.

You remember that a stream of electrons which is starting or stopping can induce the electrons of a neighboring parallel circuit to start off in parallel paths. We do not know the explanation of this. Nor do we know the explanation of another fact which seems to be related to this fact of induction and is the basis for our explanations of magnetism.

[Ill.u.s.tration: Fig 101]

If two parallel wires are carrying steady electron streams in the same general direction the wires attract each other. If the streams are oppositely directed the wires repel each other. Fig. 101 ill.u.s.trates this fact. If the streams are not at all in the same direction, that is, if they are at right angles, they have no effect on each other.

[Ill.u.s.tration: Fig 102]

These facts, of the attraction of electron streams which are in the same direction and repulsion of streams in opposite directions, are all that one need remember to figure out for himself what will happen under various conditions. For example, if two coils of wire are carrying currents what will happen is easily seen. Fig. 102 shows the two coils and a section through them.

[Ill.u.s.tration: Fig 103]

Looking at this cross section we seem to have four wires, _1_ and _2_ of coil _A_ and _3_ and _4_ of coil _B_. You see at once that if the coils are free to move they will move into the dotted positions shown in Fig 102, because wire _1_ attracts wire _3_ and repels wire _4_, while wire _2_ attracts wire _4_ and repels wire _3_. If necessary, and if they are free to move, the coils will turn completely around to get to this position. I have shown such a case in Fig. 103.

Wires which are not carrying currents do not behave in this way. The action is due, but how we don't yet know, to the motions of the electrons. As far as we can explain it to-day, the attraction of two wires which are carrying currents is due to the attraction of the two streams of electrons. Of course these electrons are part of the wires.

They can't get far away from the stay-at-home electrons and the nuclei of the atoms which form the wires. In fact it is these nuclei which keep the wandering electrons within the wires. The result is that if the streams of electrons are to move toward each other the wires must go along with them.

If the wires are held firmly the electron streams cannot approach one another for they must stay in the wires. Wires, therefore, perform the important service of acting as paths for electrons which are traveling as electric currents. There are other ways in which electrons can be kept in a path, and other means beside batteries for keeping them going.

It doesn't make any difference so far as the attraction or the repulsion is concerned why they are following a certain path or why they stay in it. So far as we know two streams of electrons, following parallel paths, will always, behave just like the two streams of Fig. 101.

[Ill.u.s.tration: Fig 104]

Suppose, for example, there were two atoms which were each formed by a nucleus and a number of electrons swinging around about the nucleus as pictured in Fig. 104. The electrons are going of their own accord and the nucleus keeps them from flying off at a tangent, the way mud flies from the wheel of an automobile. Suppose these two atoms are free to turn but not to move far from their present positions. They will turn so as to make their electron paths parallel just as did the loops of Fig.

102.