Letters of a Radio-Engineer to His Son
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Every time the diaphragm moves it affects the air in the immediate neighborhood of itself and that air in turn affects the air farther away and so the ear of the listener. Therefore if there are changes in the intensity or strength of the incoming signal there are going to be corresponding motions of the receiver diaphragm. And something to listen, too, if these changes are frequent enough but not so frequent that the receiver diaphragm has difficulty in following them.

There are many ways of affecting the strength of the incoming signal. Suppose, for example, that we arrange to decrease the current in the antenna of the transmitting station. That will mean a weaker signal and a smaller increase in current through the winding of the telephone receiver at the other station. On the other hand if the signal strength is increased there is more current in this winding.

Suppose we connect a fine wire in the antenna circuit as in Fig. 64 and have a sliding contact as shown. Suppose that when we depress the switch in the oscillator circuit and so start the oscillations that the sliding contact is at o as shown. Corresponding to that strength of signal there is a certain value of current through the receiver winding at the other station. Now let us move the slider, first to a and then back to b and so on, back and forth. You see what will happen. We alternately make the current in the antenna larger and smaller than it originally was. When the slider is at b there is more of the fine wire in series with the antenna, hence more resistance to the oscillations of the electrons, and hence a smaller oscillating stream of electrons. That means a weaker outgoing signal. When the slider is at a there is less resistance in the antenna circuit and a larger alternating current.

A picture of what happens would be like that of Fig. 65. The signal varies in intensity, therefore, becoming larger and smaller alternately. That means the voltage impressed on the grid of the detector is alternately larger and smaller. And hence the stream of electrons through the winding of the telephone receiver is alternately larger and smaller. And that means that the diaphragm moves back and forth in just the time it takes to move the slider back and forth.

Instead of the slider we might use a little cup almost full of grains of carbon. The carbon grains lie between two flat discs of carbon. One of these discs is held fixed. The other is connected to the center of a thin diaphragm of steel and moves back and forth as this diaphragm is moved. The whole thing makes a telephone transmitter such as you have often talked to.

Wires connect to the carbon discs as shown in Fig. 66. A stream of electrons can flow through the wires and from grain to grain through the "carbon button," as we call it. The electrons have less difficulty if the grains are compressed, that is the button then offers less resistance to the flow of current. If the diaphragm moves back, allowing the grains to have more room, the electron stream is smaller and we say the button is offering more resistance to the current.

You can see what happens. Suppose some one talks into the transmitter and makes its diaphragm go back and forth as shown in Fig. 67a. Then the current in the antenna varies, being greater or less, depending upon whether the button offers less or more resistance. The corresponding variations in the antenna current are shown in Fig. 67b.

In the antenna at the receiving station there are corresponding variations in the strength of the signal and hence corresponding variations in the strength of the current through the telephone receiver. I shall show graphically what happens in Fig. 68. You see that the telephone receiver diaphragm does just the same motions as does the transmitter diaphragm. That means that the molecules of air near the receiver diaphragm are going through just the same kind of motions as are those near the transmitter diaphragm. When these air molecules affect your eardrum you hear just what you would have heard if you had been right there beside the transmitter.

That's one way of making a radio-telephone. It is not a very efficient method but it has been used in the past. Before we look at any of the more recent methods we can draw some general ideas from this method and learn some words that are used almost always in speaking of radio-telephones.

In any system of radio-telephony you will always find that there is produced at the transmitting station a high-frequency alternating current and that this current flows in a tuned circuit one part of which is the condenser formed by the antenna and the ground (or something which acts like a ground). This high-frequency current, or radio-current, as we usually say, is varied in its strength. It is varied in conformity with the human voice. If the human voice speaking into the transmitter is low pitched there are slow variations in the intensity of the radio current. If the voice is high pitched there are more rapid variations in the strength of the radio-frequency current. That is why we say the radio-current is "modulated" by the human voice.

The signal which radiates out from the transmitting antenna carries all the little variations in pitch and loudness of the human voice. When this signal reaches the distant antenna it establishes in that antenna circuit a current of high frequency which has just the same variations as did the current in the antenna at the sending station. The human voice isn't there. It is not transmitted. It did its work at the sending station by modulating the radio-signal, "modulating the carrier current," as we sometimes say. But there is speech significance hidden in the variations in strength of the received signal.

If a telephone-receiver diaphragm can be made to vibrate in accordance with the variations in signal intensity then the air adjacent to that diaphragm will be set into vibration and these vibrations will be just like those which the human voice set up in the air molecules near the mouth of the speaker. All the different systems of receiving radio-telephone signals are merely different methods of getting a current which will affect the telephone receiver in conformity with the variations in signal strength. Getting such a current is called "detecting." There are many different kinds of detectors but the vacuum tube is much to be preferred.

The cheapest detector, but not the most sensitive, is the crystal. If you understand how the audion works as a detector you will have no difficulty in understanding the crystal detector.

The crystal detector consists of some mineral crystal and a fine-wire point, usually platinum. Crystals are peculiar things. Like everything else they are made of molecules and these molecules of atoms. The atoms are made of electrons grouped around nuclei which, in turn, are formed by close groupings of protons and electrons. The great difference between crystals and substances which are not crystalline, that is, substances which don't have a special natural shape, is this: In crystals the molecules and atoms are all arranged in some orderly manner. In other substances, substances without special form, amorphous substances, as we call them, the molecules are just grouped together in a haphazard way.

For some crystals we know very closely indeed how their molecules or rather their individual atoms are arranged. Sometime you may wish to read how this was found out by the use of X-rays.[6] Take the crystal of common salt for example. That is well known. Each molecule of salt is formed by an atom of sodium and one of chlorine. In a crystal of salt the molecules are grouped together so that a sodium atom always has chlorine atoms on every side of it, and the other way around, of course.

Suppose you took a lot of wood dumb-bells and painted one of the balls of each dumb-bell black to stand for a sodium atom, leaving the other unpainted to stand for a chlorine atom. Now try to pile them up so that above and below each black ball, to the right and left of it, and also in front and behind it, there shall be a white ball. The pile which you would probably get would look like that of Fig. 69. I have omitted the gripping part of each dumbell because I don't believe it is there. In my picture each circle represents the nucleus of an atom. I haven't attempted to show the planetary electrons. Other crystals have more complex arrangements for piling up their molecules.

Now suppose we put two different kinds of substances close together, that is, make contact between them. How their electrons will behave will depend entirely upon what the atoms are and how they are piled up. Some very curious effects can be obtained.

The one which interests us at present is that across the contact points of some combinations of substances it is easier to get a stream of electrons to flow one way than the other. The contact doesn't have the same resistance in the two directions. Usually also the resistance depends upon what voltage we are applying to force the electron stream across the point of contact.

The one way to find out is to take the voltage-current characteristic of the combination. To do so we use the same general method as we did for the audion. And when we get through we plot another curve and call it, for example, a "platinum-galena characteristic." Fig. 70 shows the set-up for making the measurements. There is a group of batteries arranged so that we can vary the e. m. f. applied across the contact point of the crystal and platinum. A voltmeter shows the value of this e. m. f. and an ammeter tells the strength of the electron stream. Each time we move the slider we get a new pair of values for volts and amperes. As a matter of fact we don't get amperes or even mil-amperes; we get millionths of an ampere or "microamperes," as we say. We can plot the pairs of values which we measure and make a curve like that of Fig. 71.

When the voltage across the contact is reversed, of course, the current reverses. Part of the curve looks something like the lower part of an audion characteristic.

Now connect this crystal in a receiving circuit as in Fig. 72. We use an antenna just as we did for the audion and we tune the antenna circuit to the frequency of the incoming signal. The receiving circuit is coupled to the antenna circuit and is tuned to the same frequency. Whatever voltage there may be across the condenser of this circuit is applied to the crystal detector. We haven't put the telephone receiver in the circuit yet. I want to wait until you have seen what the crystal does when an alternating voltage is applied to it.

We can draw a familiar form of sketch as in Fig. 73 to show how the current in the crystal varies. You see that there flows through the crystal a current very much like that of Fig. 62a. And you know that such a current is really equivalent to two electron streams, one steady and the other alternating. The crystal detector gives us much the same sort of a current as does the vacuum tube detector of Fig. 54. The current isn't anywhere near as large, however, for it is microamperes instead of mil-amperes.

Our crystal detector produces the same results so far as giving us a steady component of current to send through a telephone receiver. So we can connect a receiver in series with the crystal as shown in Fig. 74. Because the receiver would offer a large impedance to the high-frequency current, that is, seriously impede and so reduce the high-frequency current, we connect a condenser around the receiver.

There is a simple crystal detector circuit. If the signal intensity varies then the current which passes through the receiver will vary. If these variations are caused by a human voice at the sending station the crystal will permit one to hear from the telephone receiver what the speaker is saying. That is just what the audion detector does very many times better.

In the letter on how to experiment you'll find details as to the construction of a crystal-detector set. Excellent instructions for an inexpensive set are contained in Bull. No. 120 of the Bureau of Standards. A copy can be obtained by sending ten cents to the Commissioner of Public Documents, Washington, D. C.

[Footnote 6: Cf. "Within the Atom," Chapter X.]

LETTER 16

THE HUMAN VOICE

DEAR SIR:

The radio-telephone does not transmit the human voice. It reproduces near the ears of the listener similar motions of the air molecules and hence causes in the ears of the listener the same sensations of sound as if he were listening directly to the speaker. This reproduction takes place almost instantaneously so great is the speed with which the electrical effects travel outward from the sending antenna. If you wish to understand radio-telephony you must know something of the mechanism by which the voice is produced and something of the peculiar or characteristic properties of voice sounds.

The human voice is produced by a sort of organ pipe. Imagine a long pipe connected at one end to a pair of fire-bellows, and closed at the other end by two stretched sheets of rubber. Fig. 75 is a sketch of what I mean. Corresponding to the bellows there is the human diaphragm, the muscular membrane separating the thorax and abdomen, which expands or contracts as one breathes. Corresponding to the pipe is the windpipe. Corresponding to the two stretched pieces of rubber are the vocal cords, L and R, shown in cross section in Fig. 77. They are part of the larynx and do not show in Fig. 76 (Pl. viii) which shows the wind pipe and an outside view of the larynx.

When the sides of the bellows are squeezed together the air molecules within are crowded closer together and the air is compressed. The greater the compression the greater, of course, is the pressure with which the enclosed air seeks to escape. That it can do only by lifting up, that is by blowing out, the two elastic strips which close the end of the pipe.

The air pressure, therefore, rises until it is sufficient to push aside the elastic membranes or vocal cords and thus to permit some of the air to escape. It doesn't force the membranes far apart, just enough to let some air out. But the moment some air has escaped there isn't so much inside and the pressure is reduced just as in the case of an automobile tire from which you let the air escape. What is the result? The membranes fly back again and close the opening of the pipe. What got out, then, was just a little puff of air.

The bellows are working all the while, however, and so the space available for the remaining air soon again becomes so crowded with air molecules that the pressure is again sufficient to open the membranes. Another puff of air escapes.

This happens over and over again while one is speaking or singing. Hundreds of times a second the vocal cords vibrate back and forth. The frequency with which they do so determines the note or pitch of the speaker's voice.

What determines the significance of the sounds which he utters? This is a most interesting question and one deserving of much more time than I propose to devote to it. To give you enough of an answer for your study of radio-telephony I am going to tell you first about vibrating strings for they are easier to picture than membranes like the vocal cords.

Suppose you have a stretched string, a piece of rubber band or a wire will do. You pluck it, that is pull it to one side. When you let go it flies back. Because it has inertia[7] it doesn't stop when it gets to its old position but goes on through until it bows out almost as far on the other side.

It took some work to pluck this string, not much perhaps; but all the work which you did in deforming it, goes to the string and becomes its energy, its ability to do work. This work it does in pushing the air molecules ahead of it as it vibrates. In this way it uses up its energy and so finally comes again to rest. Its vibrations "damp out," as we say, that is die down. Each swing carries it a smaller distance away from its original position. We say that the "amplitude," meaning the size, of its vibration decreases. The frequency does not. It takes just as long for a small-sized vibration as for the larger. Of course, for the vibration of large amplitude the string must move faster but it has to move farther so that the time required for a vibration is not changed.

First the string crowds against each other the air molecules which are in its way and so leads to crowding further away, just as fast as these molecules can pass along the shove they are receiving. That takes place at the rate of about 1100 feet a second. When the string swings back it pushes away the molecules which are behind it and so lets those that were being crowded follow it. You know that they will. Air molecules will always go where there is the least crowding. Following the shove, therefore, there is a chance for the molecules to move back and even to occupy more room than they had originally.

The news of this travels out from the string just as fast as did the news of the crowding. As fast as molecules are able they move back and so make more room for their neighbors who are farther away; and these in turn move back.

Do you want a picture of it? Imagine a great crowd of people and at the center some one with authority. The crowd is the molecules of air and the one with authority is one of the molecules of the string which has energy. Whatever this molecule of the string says is repeated by each member of the crowd to his neighbor next farther away. First the string says: "Go back" and each molecule acts as soon as he gets the word. And then the string says: "Come on" and each molecule of air obeys as soon as the command reaches him. Over and over this happens, as many times a second as the string makes complete vibrations.

If we should make a picture of the various positions of one of these air molecules much as we pictured "Brownie" in Letter 9 it would appear as in Fig. 78a where the central line represents the ordinary position of the molecule.

That's exactly the picture also of the successive positions of an electron in a circuit which is "carrying an alternating current." First it moves in one direction along the wire and then back in the opposite direction. The electron next to it does the same thing almost immediately for it does not take anywhere near as long for such an effect to pass through a crowd of electrons. If we make the string vibrate twice as fast, that is, have twice the frequency, the story of an adjacent particle of air will be as in Fig. 78b. Unless we tighten the string, however, we can't make it vibrate as a whole and do it twice as fast. We can make it vibrate in two parts or even in more parts, as shown in Fig. 79 of Pl. VII. When it vibrates as a whole, its frequency is the lowest possible, the fundamental frequency as we say. When it vibrates in two parts each part of the string makes twice as many vibrations each second. So do the adjacent molecules of air and so does the eardrum of a listener.

The result is that the listener hears a note of twice the frequency that he did when the string was vibrating as a whole. He says he hears the "octave" of the note he heard first. If the string vibrates in three parts and gives a note of three times the frequency the listener hears a note two octaves above the "fundamental note" of which the string is capable.

It is entirely possible, however, for a string to vibrate simultaneously in a number of ways and so to give not only its fundamental note but several others at the same time. The photographs[8] of Fig. 80 of Pl. VII illustrate this possibility.

What happens then to the molecules of air which are adjacent to the vibrating string? They must perform quite complex vibrations for they are called upon to move back and forth just as if there were several strings all trying to push them with different frequencies of vibration. Look again at the pictures, of Fig. 80 and see that each might just as well be the picture of several strings placed close together, each vibrating in a different way. Each of the strings has a different frequency of vibration and a different maximum amplitude, that is, greatest size of swing away from its straight position.

Suppose instead of a single string acting upon the adjacent molecules we had three strings. Suppose the first would make a nearby molecule move as in Fig. 81A, the second as in Fig. 81B, and the third as in Fig. 81C. It is quite evident that the molecule can satisfy all three if it will vibrate as in Fig. 81D.

Now take it the other way around. Suppose we had a picture of the motion of a molecule and that it was not simple like those shown in Fig. 78 but was complex like that of Fig. 81D. We could say that this complex motion was made up of three parts, that is, had three component simple motions, each represented by one of the three other graphs of Fig. 81. That means we can resolve any complex vibratory motion into component motions which are simple.

It means more than that. It means that the vibrating string which makes the neighboring molecules of air behave as shown in Fig. 81D is really acting like three strings and is producing simultaneously three pure musical notes.

Now suppose we had two different strings, say a piano string in the piano and a violin string on its proper mounting. Suppose we played both instruments and some musician told us they were in tune. What would he mean? He would mean that both strings vibrated with the same fundamental frequency.

They differ, however, in the other notes which they produce at the same time that they produce their fundamental notes. That is, they differ in the frequencies and amplitudes of these other component vibrations or "overtones" which are going on at the same time as their fundamental vibrations. It is this difference which lets us tell at once which instrument is being played.

That brings us to the main idea about musical sounds and about human speech. The pitch of any complex sound is the pitch of its fundamental or lowest sound; but the character of the complex sound depends upon all the overtones or "harmonics" which are being produced and upon their relative frequencies and amplitudes.

The organ pipe which ends in the larynx produces a very complex sound. I can't show you how complex but I'll show you in Fig. 82 the complicated motion of an air molecule which is vibrating as the result of being near an organ pipe. (Organ pipes differ—this is only one case.) You can see that there are a large number of pure notes of various intensities, that is, strengths, which go to make up the sound which a listener to this organ pipe would hear. The note from the human pipe is much more complex.

When one speaks there are little puffs of air escaping from his larynx. The vocal cords vibrate as I explained. And the molecules of air near the larynx are set into very complex vibrations. These transmit their vibrations to other molecules until those in the mouth are reached. In the mouth, however, something very important happens.

Did you ever sing or howl down a rain barrel or into a long pipe or hallway and hear the sound? It sounds just about the same no matter who does it. The reason is that the long column of air in the pipe or barrel is set into vibration and vibrates according to its own ideas of how fast to do it. It has a "natural frequency" of its own. If in your voice there is a note of just that frequency it will respond beautifully. In fact it "resonates," or sings back, when it hears this note.

The net result is that it emphasizes this note so much that you don't hear any of the other component notes of your voice—all you hear is the rain barrel. We say it reinforces one of the component notes of your voice and makes it louder.

That same thing happens in the mouth cavity of a speaker. The size and shape of the column of air in the mouth can be varied by the tongue and lip positions and so there are many different possibilities of resonance. Depending on lip and tongue, different frequencies of the complex sound which comes from the larynx are reinforced. You can see that for yourself from Fig. 83 which shows the tongue positions for three different vowel sounds. You can see also from Fig. 84, which shows the mouth positions for the different vowels, how the size and shape of the mouth cavity is changed to give different sounds. These figures are in Pl. VIII.

The pitch of the note need not change as every singer knows. You can try that also for yourself by singing the vowel sound of "ahh" and then changing the shape of your mouth so as to give the sound "ah—aw—ow—ou." The pitch of the note will not change because the fundamental stays the same. The speech significance of the sound, however, changes completely because the mouth cavity resonates to different ones of the higher notes which come from the larynx along with the fundamental note.

Now you can see what is necessary for telephonic transmission. Each and every component note which enters into human speech must be transmitted and accurately reproduced by the receiver. More than that, all the proportions must be kept just the same as in the original spoken sound. We usually say that there must be reproduced in the air at the receiver exactly the same "wave form" as is present in the air at the transmitter. If that isn't done the speech won't be natural and one cannot recognize voices although he may understand pretty well. If there is too much "distortion" of the wave form, that is if the relative intensities of the component notes of the voice are too much altered, then there may even be a loss of intelligibility so that the listener cannot understand what is being said.

What particular notes are in the human voice depends partly on the person who is speaking. You know that the fundamental of a bass voice is lower than that of a soprano. Besides the fundamental, however, there are a lot of higher notes always present. This is particularly true when the spoken sound is a consonant, like "s" or "f" or "v." The particular notes, which are present and are important, depend upon what sound one is saying.

Usually, however, we find that if we can transmit and reproduce exactly all the notes which lie between a frequency of about 200 cycles a second and one of about 2000 cycles a second the reproduced speech will be quite natural and very intelligible. For singing and for transmitting instrumental music it is necessary to transmit and reproduce still higher notes.

What you will have to look out for, therefore, in a receiving set is that it does not cut out some of the high notes which are necessary to give the sound its naturalness. You will also have to make sure that your apparatus does not distort, that is, does not receive and reproduce some notes or "voice frequencies" more efficiently than it does some others which are equally necessary. For that reason when you buy a transformer or a telephone receiver it is well to ask for a characteristic curve of the apparatus which will show how the action varies as the frequency of the current is varied. The action or response should, of course, be practically the same at all the frequencies within the necessary part of the voice range.

[Footnote 7: Cf. Chap. VI of "The Realities of Modern Science."]

[Footnote 8: My thanks are due to Professor D. C. Miller and to the Macmillan Company for permission to reproduce Figs. 79 to 83 inclusive from that interesting book, "The Science of Musical Sounds."]

LETTER 17

GRID BATTERIES AND GRID CONDENSERS FOR DETECTORS

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.

In the case of the three characteristics which we are discussing the shift was made by changing the B-battery. Increasing B-voltage shifts characteristic to the left. It is possible, however, to produce such a shift by using a C-battery, that is, a battery in the grid circuit, which makes the grid permanently negative (or positive, depending upon how it is connected). This battery either helps or hinders the plate battery, and because of the strategic position of the grid right near the filament one volt applied to the grid produces as large an effect as would several volts in the plate battery. Usually, therefore, we arrange to shift the characteristic by using a C-battery.

Suppose for example that we had an audion in the receiving circuit of Fig. 63 and that its characteristic under these conditions is given by Fig. 56. I've redrawn the figures to save your turning back. The audion will not act as a detector because an incoming signal will not change the average value of the current in the plate circuit. If, however, we connect a C-battery so as to make the grid negative, we can shift this characteristic so that the incoming signal will be detected. We have only to make the grid sufficiently negative to reduce the plate current to the value shown by the line oa in Fig. 85. Then the signal will be detected because, while it makes the plate current alternately larger and smaller than this value oa, it will result, on the average, in a higher value of the plate current.

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.

When the slider is set as shown in Fig. 86 the grid is at zero potential and we are at the point 1 of the characteristic shown in Fig. 87. Now imagine an incoming signal, as shown in that same figure, but suppose that as soon as the signal has stopped making the grid positive we shift the slider a little so that the C-battery makes the grid slightly negative. We have shifted the point on the characteristic about which the tube is being worked by the incoming signal from point 1 to point 2.

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.

Then the plate current is reduced practically to zero.

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.

To do so we connect a very fine wire between plates 1 and 2 of the grid condenser. We call that wire a "grid-condenser leak" because it lets the electrons slip around past the gap. By using a very high resistance, we can make it so hard for the electrons to get around the gap that not many will do so while the signal is coming in. In that case we can leave the leak permanently across the condenser as shown in Fig. 90. Of course, the leak must offer so easy a path for the electrons that all the trapped electrons can get home between one incoming signal and the next.

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.

I don't propose to stop to tell you how a spark-set transmitter works. It is sufficient to say that when the key is depressed the set sends out radio signals at the rate usually of 1000 signals a second. Every time a signal reaches the receiving station the current in the telephone receiver is sudden reduced; and in the time between signals the leak across the grid condenser brings the tube back to a condition where it can receive the next signal. While the sending key is depressed the current in the receiver is decreasing and increasing once for every signal which is being transmitted. For each decrease and increase in current the diaphragm of the telephone receiver makes one vibration. What the listener then hears is a musical note with a frequency corresponding to that number of vibrations a second, that is, a note with a frequency of one thousand cycles per second. He hears a note of frequency about that of two octaves above middle C on the piano. There are usually other notes present at the same time and the sound is not like that of any musical instrument.

If the key is held down a long time for a dash the listener hears this note for a corresponding time. If it is depressed only about a third of that time so as to send a dot, the listener hears the note for a shorter time and interprets it to mean a dot.

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.

If the grid-condenser and its leak are so chosen as to work well for signals from a 500-cycle spark set they will also work well for the notes in human speech which are about 1000 cycles a second in frequency. The detecting circuit will not, however, work so well for the other notes which are in the human voice and are necessary to speech. For example, if notes of about 2000 cycles a second are involved in the speech which is being transmitted, the leak across the condenser will not work fast enough. On the other hand, for the very lowest notes in the voice the leak will work too fast and such variations in the signal current will not be detected as efficiently as are those of 1000 cycles a second.

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.

LETTER 18

AMPLIFIERS AND THE REGENERATIVE CIRCUIT

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.

What happens depends upon how closely the coils _L_ and _L_{t}_ are coupled, that is, upon how much the changing current in one can affect the other. If they are turned at right angles to each other, so that there is no possible mutual effect we say there is "zero coupling."

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.

Now suppose that there is coming into the detector circuit of Fig. 92 a radio signal with, speech significance. The current in the plate circuit varies accordingly. So does the current in coil _L_{t}_ which is in the plate circuit. But this current induces an e. m. f. in coil _L_ and this adds to the e. m. f. of the incoming signal so as to make a greater variation in the plate current. This goes on as long as there is an incoming signal. Because the plate circuit is coupled to the grid circuit the result is a larger e. m. f. in the grid circuit than the incoming signal could set up all by itself.

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.

The frequency of the alternating current which the tube produces depends upon the tuned circuit formed by L and C. Suppose that this frequency is not the same as that to which the receiving antenna is tuned. What will happen?

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.

The same thing happens in the audion detector circuit when two e. m. f.'s which differ slightly in frequency are simultaneously impressed on the grid. If one e. m. f. passes through ten complete cycles while the other is making eight cycles, then during that time they will twice be exactly in step, that is, "in phase" as we say. Twice in that time they will be exactly out of step, that is, exactly "opposite in phase." Twice in that time the two e. m. f.'s will aid each other in their effects on the grid and twice they will exactly oppose. Unless they are equal in amplitude there will still be a net e. m. f. even when they are exactly opposed. The result of all this is that the average current in the plate circuit of the detector will alternately increase and decrease twice during this time.

The listener will then hear a note of a frequency equal to the difference between the frequencies of the two e. m. f.'s which are being simultaneously impressed on the grid of the detector. Suppose the incoming signal has a frequency of 100,000 cycles a second but that the detector tube is oscillating in its own circuit at the rate of 99,000 cycles per second, then the listener will hear a note of 1000 cycles per second. One thousand times each second the two e. m. f.'s will be exactly in phase and one thousand times each second they will be exactly opposite in phase. The voltage applied to the grid will be a maximum one thousand times a second and alternately a minimum. We can think of it, then, as if there were impressed on the grid of the detector a high-frequency signal which varied in intensity one thousand times a second. This we know will produce a corresponding variation in the current through the telephone receiver and thus give rise to a musical note of about two octaves above middle C on the piano.

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.

There are a number of words used to describe this circuit with some of which you should be familiar. It is sometimes called a "feed-back" circuit because part of the output of the audion is fed back into its input side. More generally it is known as the "regenerative circuit" because the tube keeps on generating an alternating current. The little coil which is used to feed back into the grid circuit some of the effects from the plate circuit is sometimes called a "tickler" coil.

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.

We can get just as loud signals by using another tube instead of making one do all the work. In the regenerative circuit the tube is performing two jobs at once. It is detecting but it is also amplifying.[9] By "amplifying" we mean making an e. m. f. larger than it is without changing the shape of its picture, that is without changing its "wave form."

To show just what we mean by amplifying we must look again at the audion and see how it acts. You know that a change in the grid potential makes a change in the plate current. Let us arrange an audion in a circuit which will tell us a little more of what happens. Fig. 93 shows the circuit.

This circuit is the same as we used to find the audion characteristic except that there is a clip for varying the number of batteries in the plate circuit and a voltmeter for measuring their e. m. f. We start with the grid at zero potential and the usual number of batteries in the plate circuit. The voltmeter tells us the e. m. f. We read the ammeter in the plate circuit and note what that current is. Then we shift the slider in the grid circuit so as to give the grid a small potential. The current in the plate circuit changes. We can now move the clip on the B-batteries so as to bring the current in this circuit back to its original value. Of course, if we make the grid positive we move the clip so as to use fewer cells of the B-battery. On the other hand if we make the grid negative we shall need more e. m. f. in the plate circuit. In either case we shall find that we need to make a very much larger change in the voltage of the plate circuit than we have made in the voltage of the grid circuit.

Usually we perform the experiment a little differently so as to get more accurate results. We read the voltmeter in the plate circuit and the ammeter in that circuit. Then we change the number of batteries which we are using in the plate circuit. That changes the plate current. The next step is to shift the slider in the grid circuit until we have again the original value of current in the plate circuit. Suppose that the tube is ordinarily run with a plate voltage of 40 volts and we start with that e. m. f. on the plate. Suppose that we now make it 50 volts and then vary the position of the slider in the grid circuit until the ammeter reads as it did at the start. Next we read the voltage impressed on the grid by reading the voltmeter in the grid circuit. Suppose it reads 2 volts. What does that mean?

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.

Now let's take a simple case of the use of an audion as an amplifier. Suppose we have a receiving circuit with which we find that the signals are not easily understood because they are too weak. Let this be the receiving circuit of Fig. 88 which I am reproducing here as part of Fig. 94.

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 setting up such a circuit as this there are several things to watch. For some of these you will have to rely on the dealer from whom you buy your supplies and for the others upon yourself. But it will take another letter to tell you of the proper precautions in using an audion as an amplifier.

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.

[Footnote 9: There is always some amplification taking place in an audion detector but the regenerative circuit amplifies over and over again until the signal is as large as the tube can detect.]

LETTER 19

THE AUDION AMPLIFIER AND ITS CONNECTIONS

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.

As long as we do not use a higher voltage than that of the C-battery which is in the box no current can flow. Even if we do use a higher voltage than the "negative C-battery" of the hidden grid-circuit there will be a current only when the external battery is connected so as to make the grid positive with respect to the filament.

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.

Sometimes this hidden battery helps the B-battery which is on the outside; and sometimes it seems to oppose, for the current in the P-F circuit either increases or decreases, depending upon how we connect the battery to G and F. The hidden battery is always larger than our battery connected to G and F. If we arrange rapidly to reverse the battery connected to G-F it appears as if there is inside the box in the P-F circuit an alternator, that is, something which can produce an alternating e. m. 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.

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 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.

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.

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.

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.

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.

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 illustrates 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.

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.

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.

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.

Now, I don't say that there are any atoms at all like the ones I have pictured. There is still a great deal to be learned about how electrons act inside different kinds of atoms. We do know, however, that the atoms of iron act just as if they were tiny loops with electron streams.

Suppose we had several loops and that they were lined up like the three loops in Fig. 105. You can see that they would all attract the other loop, on the right in the figure. On the other hand if they were grouped in the triangle of Fig. 106 they would barely affect the loop because they would be pulling at cross purposes. If a lot of the tiny loops of the iron atoms are lined up so as to act together and attract other loops, as in the first figure, we say the iron is magnetized and is a magnet. In an ordinary piece of iron, however, the atoms are so grouped that they don't pull together but like the loops of our second figure pull in different directions and neutralize each other's efforts so that there is no net effect.

And like the loops of Fig. 106 the atoms in an unmagnetized piece of iron are pretty well satisfied to stay as they are without all lining up to pull together. To magnetize the iron we must force some of these atomic loops to turn part way around. That can be done by bringing near them a strong magnet or a coil of wire which is carrying a current. Then the atoms are forced to turn and if enough turn so that there is an appreciable effect then the iron is magnetized. The more that are properly turned the stronger is the magnet. One end or "pole" we call north-seeking and the other south-seeking, because a magnetized bar of iron acts like a compass needle.

A coil of wire, carrying a current, acts just like a magnet because its larger loops are all ready to pull together. I have marked the coil of Fig. 107 with N and S for north and south. If the electron stream in it is reversed the "polarity" is reversed. There is a simple rule for this. Partially close your left hand so that the fingers form loops. Let the thumb stick out at right angles to these loops. If the electron streams are flowing around the loops of a coil in the same direction as your fingers point then your thumb is the N pole and the coil will repel the north poles of other loops or magnets in the direction in which your thumb points. If you know the polarity already there is a simple rule for the repulsion or attraction. Like poles repel, unlike poles attract.

From what has been said about magnetism you can now understand why in a telephone receiver the current in the winding can make the magnet stronger. It does so because it makes more of the atomic loops of the iron turn around and help pull. On the other hand if the current in the winding is reversed it will turn some of the loops which are already helping into other positions where they don't help and may hinder. If the current in the coil is to help, the electron stream in it must be so directed that the north pole of the coil is at the same end as the north pole of the magnet.

This idea of the attraction or repulsion of electron streams, whether in coils of wire or in atoms of iron and other magnetizable substances, is the fundamental idea of most forms of telephone receivers, of electric motors, and of a lot of other devices which we call "electromagnetic."

The ammeters and voltmeters which we use for the measurement of audion characteristics and the like are usually electromagnetic instruments. Ammeters and voltmeters are alike in their design. Both are sensitive current-measuring instruments. In the case of the voltmeter, as you know, we have a large resistance in series with the current-measuring part for the reason of which I told in Letter 8. In the case of ammeters we sometimes let all the current go through the current-measuring part but generally we let only a certain fraction of it do so. To pass the rest of the current we connect a small resistance in parallel with the measuring part. In both types of instruments the resistances are sometimes hidden away under the cover. Both instruments must, of course, be calibrated as I have explained before.

In the electromagnetic instruments there are several ways of making the current-measuring part. The simplest is to let the current, or part of it, flow through a coil which is pivoted between the N and S poles of a strong permanent magnet. A spring keeps the coil in its zero position and if the current makes the coil turn it must do so against this spring. The stronger the current in the coil the greater the interaction of the loops of the coil and those of the iron atoms and hence the further the coil will turn. A pointer attached to the coil indicates how far; and the number of volts or amperes is read off from the calibrated scale.

Such instruments measure direct-currents, that is, steady streams of electrons in one direction. To measure an alternating current or voltage we can use a hot-wire instrument or one of several different types of electromagnetic instruments. Perhaps the simplest of these is the so-called "plunger type." The alternating current flows in a coil; and a piece of soft iron is so pivoted that it can be attracted and moved into the coil. Soft iron does not make a good permanent magnet. If you put a piece of it inside a coil which is carrying a steady current it becomes a magnet but about as soon as you interrupt the current the atomic loops of the iron stop pulling together. Almost immediately they turn into all sorts of positions and form little self-satisfied groups which don't take any interest in the outside world. (That isn't true of steel, where the atomic loops are harder to turn and to line up, but are much more likely to stay in their new positions.)

Because the plunger in an alternating-current ammeter is soft iron its loops line up with those of the coil no matter which way the electron stream happens to be going in the coil. The atomic magnets in the iron turn around each time the current reverses and they are always, therefore, lined up so that the plunger is attracted. If the plunger has much inertia or if the oscillations of the current are reasonably frequent the plunger will not move back and forth with each reversal of the current but will take an average position. The stronger the a-c (alternating current) the farther inside the coil will be this position of the plunger. The position of the plunger becomes then a measure of the strength of the alternating current.

Instruments for measuring alternating e. m. f.'s and currents, read in volts and in amperes. So far I haven't stopped to tell what we mean by one ampere of alternating current. You know from Letter 7 what we mean by an ampere of d-c (direct current). It wasn't necessary to explain before because I told you only of hot-wire instruments and they will read the same for either d-c or a-c.

When there is an alternating current in a wire the electrons start, rush ahead, stop, rush back, stop, and do it all over again and again. That heats the wire in which it happens. If an alternating stream of electrons, which are doing this sort of thing, heats a wire just exactly as much as would a d-c of one ampere, then we say that the a-c has an "effective value" of one ampere. Of course part of the time of each cycle the stream is larger than an ampere but for part it is less. If the average heating effect is the same the a-c is said to be one ampere.

In the same way, if a steady e. m. f. (a d-c e. m. f.) of one volt will heat a wire to which it is applied a certain amount and if an alternating e. m. f. will have the same heating effect in the same time, then the a-c e. m. f. is said to be one volt.

Another electromagnetic instrument which we have discussed but of which more should be said is the iron-cored transformer. We consider first what happens in one of the coils of the transformer.

The inductance of a coil is very much higher if it has an iron core. The reason is that then the coil acts as if it had an enormously larger number of turns. All the atomic loops of the core add their effects to the loops of the coil. When the current starts it must line up a lot of these atomic loops. When the current stops and these loops turn back into some of their old self-satisfied groupings, they affect the electrons in the coil. Where first they opposed the motion of these electrons, now they insist on its being continued for a moment longer. I'll prove that by describing two simple experiments; and then we'll have the basis for understanding the effect of an iron core in a transformer.

Look again at Fig. 33 of Letter 9 which I am reproducing for convenience. We considered only what would happen in coil cd if a current was started in coil ab. Suppose instead of placing the coils as shown in that figure they are placed as in Fig. 108. Because they are at right angles there will be no effect in cd when the current is started in ab. Let the current flow steadily through ab and then suddenly turn the coils so that they are again parallel as shown by the dotted positions. We get the same temporary current in cd as we would if we should place the coils parallel and then start the current in ab.

The other experiment is this: Starting with the coils lined up as in the dotted position of Fig. 108 and the current steadily flowing in ab, we suddenly turn them into positions at right angles to each other. There is the same momentary current in cd as if we had left them lined up and had opened the switch in the circuit of ab.

Now we know that the atomic loops of iron behave in the same general way as do loops of wire which are carrying currents. Let us replace the coil ab by a magnet as shown in Fig. 109. First we start with the magnet at right angles to the coil cd. Suddenly we turn it into the dotted position of that figure. There is the same momentary current in cd as if we were still using the coil ab instead of a magnet. If now we turn the magnet back to a position at right angles to cd, we observe the opposite direction of current in cd. These effects are more noticeable the more rapidly we turn the magnet. The same is true of turning the coil.

The experiment of turning the magnet illustrates just what happens in the case of a transformer with, an iron core except that instead of turning the entire magnet the little atomic loops do the turning inside the core. In the secondary of an iron-cored transformer the induced current is the sum of two currents both in the same direction at each instant. One current is caused by the starting or stopping of the current in the primary. The other current is due to the turning of the atomic loops of the iron atoms so that more of them line up with the turns of the primary. These atomic loops, of course, are turned by the current in the primary. There are so many of them, however, that the current due to their turning is usually the more important part of the total current.

In all transformers the effect is greater the more rapidly the current changes direction and the atomic loops turn around. For the same size of electron stream in the primary, therefore, there is induced in the secondary a greater e. m. f. the greater is the frequency with which the primary current alternates.

Where high frequencies are dealt with it isn't necessary to have iron cores because the effect is large enough without the help of the atomic loops. And even if we wanted their help it wouldn't be easy to obtain, for they dislike to turn so fast and it takes a lot of power to make them do so. We know that fact because we know that an iron core increases the inductance and so chokes the current. For low frequencies, however, that is those frequencies in the audio range, it is usually necessary to have iron cores so as to get enough effect without too many turns of wire.

The fact that iron decreases the inductance and so seriously impedes alternating currents leads us to use iron-core coils where we want high inductance. Such coils are usually called "choke coils" or "retard coils." Of their use we shall see more in a later letter where we study radio-telephone transmitters.

LETTER 21

YOUR RECEIVING SET AND HOW TO EXPERIMENT

MY DEAR STUDENT:

In this letter I want to tell you how to experiment with radio apparatus. The first rule is this: Start with a simple circuit, never add anything to it until you know just why you are doing so, and do not box it up in a cabinet until you know how it is working and why.

Your antenna at the start had better be a single wire about 25 feet high and about 75 feet long. This antenna will have capacity of about 0.0001 m. f. If you want an antenna of two wires spaced about three feet apart I would make it about 75 feet long. Bring down a lead from each wire, twisting them into a pigtail to act like one wire except near the horizontal part of the antenna.

Your ground connection can go to a water pipe. To protect the house and your apparatus from lightning insert a fuse and a little carbon block lightning arrester such as are used by the telephone company in their installations of house phones. You can also use a so-called "vacuum lightning arrester." In either case the connections will be as shown in Fig. 111. If you use a loop antenna, of course, no arrester is needed.

At first I would plan to receive signals between 150 meters and 360 meters. This will include the amateurs who work between 160 and 200 m., the special amateurs who send C-W telegraph at 275 m., and the broadcasting stations which operate at 360 m. This range will give you plenty to listen to while you are experimenting. In addition you will get some ship signals at 300 m.

To tune the antenna to any of the wave lengths in this range you can use a coil of 75 turns wound on a cardboard tube of three and a half inches in diameter. You can wind this coil of bare wire if you are careful, winding a thread along with the wire so as to keep the successive turns separated. In that case you will need to construct a sliding contact for it. That is the simplest form of tuner.

On the other hand you can wind with single silk covered wire and bring out taps at the 0, 2, 4, 6, 8, 10, 14, 20, 28, 36, 44, 56, 66, and 75th turns. To make a tap drill a small hole through the tube, bend the wire into a loop about a foot long and pull this loop through the hole as shown in Fig. 110. Then give the wire a twist, as shown, so that it can't pull out, and proceed with your winding.

Use 26 s. s. c. wire. You will need about 80 feet and might buy 200 to have enough for the secondary coil. Make contacts to the taps by two rotary switches as shown in Fig. 112. You can buy switch arms and contacts studs or a complete switch mounted on a small panel of some insulating compound. Let switch s{1} make the contacts for taps between 14 and 75 turns, and let switch s{2} make the other contacts.

For the secondary coil use the same size of wire and of core. Wind 60 turns, bringing out a tap at the middle. To tune the secondary circuit you will need a variable condenser. You can buy one of the small ones with a maximum capacity of about 0.0003 mf., one of the larger ones with a maximum capacity of 0.0005 mf., or even the larger size which has a maximum capacity of 0.001 mf. I should prefer the one of 0.0005 mf.

You will need a crystal detector—I should try galena first—and a so-called "cat's whisker" with which to make contact with the galena. For these parts and for the switch mentioned above you can shop around to advantage. For telephone receivers I would buy a really good pair with a resistance of about 2500 ohms. Buy also a small mica condenser of 0.002 mf. for a blocking condenser. Your entire outfit will then look as in Fig. 112. The switch S is a small knife switch.

To operate, leave the switch S open, place the primary and secondary coils near together as in the figure and listen. The tuning is varied, while you listen, by moving the slider of the slide-wire tuner or by moving the switches if you have connected your coil for that method. Make large changes in the tuning by varying the switch s{1} and then turn slowly through all positions of s{2}, listening at each position.

When a signal is heard adjust to the position of _s_{1}_ and _s_{2}_ which gives the loudest signal and then closing _S_ start to tune the secondary circuit. To do this, vary the capacity of the condenser in the secondary circuit. Don't change the primary tuning until you have tuned the secondary and can get the signal with good volume, that is loud. You will want to vary the position of the primary and secondary coils, that is, vary their coupling, for you will get sharper tuning as they are drawn farther apart. Sharper tuning means less interference from other stations which are sending on wave lengths near that which you wish to receive. Reduce the coupling, therefore, and then readjust the tuning. It will usually be necessary to make a slight change in both circuits, in one case with switch _s_{1}_ and in the other with the variable condenser.

As soon as you can identify any station which you hear sending make a note of the position of the switches s{1} and s{2}, and of the setting of the condenser in the secondary circuit. In that way you will acquire information as to the proper adjustments to receive certain wave-lengths. This is calibrating your set by the known wave-lengths of distant stations.

After learning to receive with this simple set I should recommend buying a good audion tube. Ask the seller to supply you with a blue print of the characteristic[11] of the tube taken under the conditions of filament current and plate voltage which he recommends for its use. Buy a storage battery and a small slide-wire rheostat, that is variable resistance, to use in the filament circuit. Buy also a bank of dry batteries of the proper voltage for the plate circuit of the tube. At the same time you should buy the proper design of transformer to go between the plate circuit of your tube and the pair of receivers which you have. It will usually be advisable to ask the dealer to show you a characteristic curve for the transformer, which will indicate how well the transformer operates at the different frequencies in the audio range. It should operate very nearly the same for all frequencies between 200 and 2500 cycles.

The next step is to learn to use the tube as a detector. Connect it into your secondary circuit instead of the crystal detector. Use the proper value of C-battery as determined from your study of the characteristic of the tube. One or two small dry cells, which have binding-post terminals are convenient C-batteries. If you think you will need a voltage much different from that obtained with a whole number of batteries you can arrange to supply the grid as we did in Fig. 86 of Letter 18. In that case you can use a few feet of 30 German-silver wire and make connections to it with a suspender clip. Learn to receive with the tube and be particularly careful not to let the filament have too much current and burn out.

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