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diff --git a/30688-8.txt b/30688-8.txt new file mode 100644 index 0000000..2a96cc0 --- /dev/null +++ b/30688-8.txt @@ -0,0 +1,7228 @@ +Project Gutenberg's Letters of a Radio-Engineer to His Son, by John Mills + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + +Title: Letters of a Radio-Engineer to His Son + +Author: John Mills + +Release Date: December 16, 2009 [EBook #30688] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK LETTERS--RADIO-ENGINEER TO SON *** + + + + +Produced by Roger Frank, Robert Cicconetti and the Online +Distributed Proofreading Team at https://www.pgdp.net + + + + + +[Transcriber's Note: An underscore character "_" is used around +text to signify italics in the _original_ text, as illustrated. +It also is used to signify a subscript, used frequently in technical +descriptions. For example _E_{C}_ would have been originally typeset +as a capital E followed by a smaller C subscript, and both would +have been in an italic typeface.] + + + + +[Illustration: Pl. I.--One of the Lines of Towers at Radio Central +(Courtesy of Radio Corporation of America).] + + + + +LETTERS OF A RADIO-ENGINEER TO HIS SON + +BY + +JOHN MILLS + +Engineering Department, Western Electric Company, Inc., + +Author of "Radio-Communication," "The Realities of +Modern Science," and "Within the Atom" + +NEW YORK + +HARCOURT, BRACE AND COMPANY + + + + +COPYRIGHT, 1922, BY + +HARCOURT, BRACE AND COMPANY, INC. + +PRINTED IN THE U. S. A. BY + +THE QUINN & BODEN COMPANY + +RAHWAY, N. J. + + + + +TO + +J. M., Jr. + + + + +CONTENTS + + 1 Electricity and Matter 3 + + 2 Why a Copper Wire Will Conduct + Electricity 9 + + 3 How a Battery Works 16 + + 4 The Batteries in Your Radio Set 27 + + 5 Getting Electrons from a Heated Wire 34 + + 6 The Audion 40 + + 7 How to Measure an Electron Stream 48 + + 8 Electron-Moving-Forces 57 + + 9 The Audion-Characteristic 66 + + 10 Condensers and Coils 77 + + 11 A "C-W" Transmitter 86 + + 12 Inductance and Capacity 96 + + 13 Tuning 112 + + 14 Why and How to Use a Detector 124 + + 15 Radio-Telephony 140 + + 16 The Human Voice 152 + + 17 Grid Batteries and Grid Condensers for + Detectors 165 + + 18 Amplifiers and the Regenerative Circuit 176 + + 19 The Audion Amplifier and Its Connections 187 + + 20 Telephone Receivers and Other + Electromagnetic Devices 199 + + 21 Your Receiving Set and How to Experiment 211 + + 22 High-Powered Radio-Telephone + Transmitters 230 + + 23 Amplification at Intermediate + Frequencies 242 + + 24 By Wire and by Radio 251 + + Index 263 + + + + +LIST OF PLATES + + I One of the Lines of Towers at Radio Central + Frontispiece + + II Bird's-Eye View of Radio Central 10 + + III Dry Battery for Use in Audion Circuits, + and also Storage Battery 27 + + IV Radiotron 42 + + V Variometer and Variable Condenser of + the General Radio Company. Voltmeter + and Ammeter of the Weston Instrument + Company 91 + + VI Low-Power Transmitting Tube, U V 202 106 + + VII Photographs of Vibrating Strings 155 + + VIII To Illustrate the Mechanism for the + Production of the Human Voice 170 + + IX Western Electric Loud Speaking + Receiver. Crystal Detector Set of the + General Electric Co. Audibility Meter + of General Radio Co. 203 + + X Audio-Frequency Transformer and + Banked-Wound Coil 218 + + XI Broadcasting Equipment, Developed by + the American Telephone and Telegraph + Company and the Western Electric Company 235 + + XII Broadcasting Station of the American + Telephone and Telegraph Company on the + Roof of the Walker-Lispenard Bldg. in + New York City where the Long-distance + Telephone Lines Terminate 250 + + + + +LETTERS OF A RADIO-ENGINEER TO HIS SON + +LETTER 1 + +ELECTRICITY AND MATTER + + +MY DEAR SON: + +You are interested in radio-telephony and want me to explain it to you. +I'll do so in the shortest and easiest way which I can devise. The +explanation will be the simplest which I can give and still make it +possible for you to build and operate your own set and to understand the +operation of the large commercial sets to which you will listen. + +I'll write you a series of letters which will contain only what is +important in the radio of to-day and those ideas which seem necessary if +you are to follow the rapid advances which radio is making. Some of the +letters you will find to require a second reading and study. In the case +of a few you might postpone a second reading until you have finished +those which interest you most. I'll mark the letters to omit in this +way. + +All the letters will be written just as I would talk to you, for I shall +draw little sketches as I go along. One of them will tell you how to +experiment for yourself. This will be the most interesting of all. You +can find plenty of books to tell you how radio sets operate and what to +do, but very few except some for advanced students tell you how to +experiment for yourself. Not to waste time in your own experiments, +however, you will need to be quite familiar with the ideas of the other +letters. + +What is a radio set? Copper wires, tinfoil, glass plates, sheets of +mica, metal, and wood. Where does it get its ability to work--that is, +where does the "energy" come from which runs the set? From batteries or +from dynamos. That much you know already, but what is the real reason +that we can use copper wires, metal plates, audions, crystals, and +batteries to send messages and to receive them? + +The reason is that all these things are made of little specks, too tiny +ever to see, which we might call specks of electricity. There are only +two kinds of specks and we had better give them their right names at +once to save time. One kind of speck is called "electron" and the other +kind "proton." How do they differ? They probably differ in size but we +don't yet know so very much about their sizes. They differ in laziness a +great deal. One is about 1845 times as lazy as the other. That is, it +has eighteen hundred and forty-five times as much inertia as the other. +It is harder to get it started but it is just as much harder to get it +to stop after it is once started or to change its direction and go a +different direction. The proton has the larger inertia. It is the +electron which is the easier to start or stop. + +How else do they differ? They differ in their actions. Protons don't +like to associate with other protons but take quite keenly to electrons. +And electrons--they go with protons but they won't associate with each +other. An electron always likes to be close to a proton. Two is company +when one is an electron and the other a proton but three is a crowd +always. + +It doesn't make any difference to a proton what electron it is keeping +company with provided only it is an electron and not another proton. All +electrons are alike as far as we can tell and so are all protons. That +means that all the stuff, or matter, of our world is made up of two +kinds of building blocks, and all the blocks of each kind are just +alike. Of course you mustn't think of these blocks as like bricks, for +we don't know their shapes. + +Then there is another reason why you must not think of them as bricks +and that is because when you build a house out of bricks each brick must +rest on another. Between an electron and any other electron or between +two protons or between an electron and a proton there is usually a +relatively enormous distance. There is enough space so that lots of +other electrons or protons could be fitted in between if only they were +willing to get that close together. + +Sometimes they do get very close together. I can tell you how if you +will imagine four small boys playing tag. Suppose Tom and Dick don't +like to play with each other and run away from each other if they can. +Now suppose that Bill and Sam won't play with each other if they can +help it but that either of them will play with Tom or Dick whenever +there is a chance. Now suppose Tom and Bill see each other; they start +running toward each other to get up some sort of a game. But Sam sees +Tom at the same time, so he starts running to join him even though Bill +is going to be there too. Meanwhile Dick sees Bill and Sam running along +and since they are his natural playmates he follows them. In a minute +they are all together, and playing a great game; although some of the +boys don't like to play together. + +Whenever there is a group of protons and electrons playing together we +have what we call an "atom." There are about ninety different games +which electrons and protons can play, that is ninety different kinds of +atoms. These games differ in the number of electrons and protons who +play and in the way they arrange themselves. Larger games can be formed +if a number of atoms join together. Then there is a "molecule." Of +molecules there are as many kinds as there are different substances in +the world. It takes a lot of molecules together to form something big +enough to see, for even the largest molecule, that of starch, is much +too small to be seen by itself with the best possible microscope. + +What sort of a molecule is formed will depend upon how many and what +kinds of atoms group together to play the larger game. Whenever there is +a big game it doesn't mean that the little atomic groups which enter +into it are all changed around. They keep together like a troop of boy +scouts in a grand picnic in which lots of troops are present. At any +rate they keep together enough so that we can still call them a group, +that is an atom, even though they do adapt their game somewhat so as to +fit in with other groups--that is with other atoms. + +What will the kind of atom depend upon? It will depend upon how many +electrons and protons are grouped together in it to play their little +game. How any atom behaves so far as associating with other groups or +atoms will depend upon what sort of a game its own electrons and protons +are playing. + +Now the simplest kind of a game that can be played, and the one with the +smallest number of electrons and protons, is that played by a single +proton and a single electron. I don't know just how it is played but I +should guess that they sort of chase each other around in circles. At +any rate I do know that the atom called "hydrogen" is formed by just one +proton and one electron. Suppose they were magnified until they were as +large as the moon and the earth. Then they would be just about as far +apart but the smaller one would be the proton. + +That hydrogen atom is responsible for lots of interesting things for it +is a great one to join with other atoms. We don't often find it by +itself although we can make it change its partners and go from one +molecule to another very easily. That is what happens every time you +stain anything with acid. A hydrogen atom leaves a molecule of the acid +and then it isn't acid any more. What remains isn't a happy group either +for it has lost some of its playfellows. The hydrogen goes and joins +with the stuff which gets stained. But it doesn't join with the whole +molecule; it picks out part of it to associate with and that leaves the +other part to take the place of the hydrogen in the original molecule of +acid from which it came. Many of the actions which we call chemistry are +merely the result of such changes of atoms from one molecule to another. + +Not only does the hydrogen atom like to associate in a larger game with +other kinds of atoms but it likes to do so with one of its own kind. +When it does we have a molecule of hydrogen gas, the same gas as is used +in balloons. + +We haven't seemed to get very far yet toward radio but you can see how +we shall when I tell you that next time I shall write of more +complicated games such as are played in the atoms of copper which form +the wires of radio sets and of how these wires can do what we call +"carrying an electric current." + + + + +LETTER 2 + +WHY A COPPER WIRE WILL CONDUCT ELECTRICITY + + +MY DEAR YOUNG ATOMIST: + +You have learned that the simplest group which can be formed by protons +and electrons is one proton and one electron chasing each other around +in a fast game. This group is called an atom of hydrogen. A molecule of +hydrogen is two of these groups together. + +All the other possible kinds of groups are more complicated. The next +simplest is that of the atom of helium. Helium is a gas of which small +quantities are obtained from certain oil wells and there isn't very much +of it to be obtained. It is an inert gas, as we call it, because it +won't burn or combine with anything else. It doesn't care to enter into +the larger games of molecular groups. It is satisfied to be as it is, so +that it isn't much use in chemistry because you can't make anything else +out of it. That's the reason why it is so highly recommended for filling +balloons or airships, because it cannot burn or explode. It is not as +light as hydrogen but it serves quite well for making balloons buoyant +in air. + +This helium atom is made up of four electrons and four protons. Right at +the center there is a small closely crowded group which contains all the +protons and two of the electrons. The other two electrons play around +quite a little way from this inner group. It will make our explanations +easier if we learn to call this inner group "the nucleus" of the atom. +It is the center of the atom and the other two electrons play around +about it just as the earth and Mars and the other planets play or +revolve about the sun as a center. That is why we shall call these two +electrons "planetary electrons." + +There are about ninety different kinds of atoms and they all have names. +Some of them are more familiar than hydrogen and helium. For example, +there is the iron atom, the copper atom, the sulphur atom and so on. +Some of these atoms you ought to know and so, before telling you more of +how atoms are formed by protons and electrons, I am going to write down +the names of some of the atoms which we have in the earth and rocks of +our world, in the water of the oceans, and in the air above. + +Start first with air. It is a mixture of several kinds of gases. Each +gas is a different kind of atom. There is just a slight trace of +hydrogen and a very small amount of helium and of some other gases which +I won't bother you with learning. Most of the air, however, is nitrogen, +about 78 percent in fact and almost all the rest is oxygen. About 20.8 +percent is oxygen so that all the gases other than these two make up +only about 1.2 percent of the atmosphere in which we live. + +[Illustration: Pl. II.--Bird's-eye View of Radio Central +(Courtesy of Radio Corporation of America).] + +The earth and rocks also contain a great deal of oxygen; about 47.3 +percent of the atoms which form earth and rocks are oxygen atoms. About +half of the rest of the atoms are of a kind called silicon. Sand is made +up of atoms of silicon and oxygen and you know how much sand there is. +About 27.7 percent of the earth and its rocks is silicon. The next most +important kind of atom in the earth is aluminum and after that iron and +then calcium. Here is the way they run in percentages: Aluminum 7.8 +percent; iron 4.5 percent; calcium 3.5 percent; sodium 2.4 percent; +potassium 2.4 percent; magnesium 2.2 percent. Besides these which are +most important there is about 0.2 percent of hydrogen and the same +amount of carbon. Then there is a little phosphorus, a little sulphur, a +little fluorine, and small amounts of all of the rest of the different +kinds of atoms. + +Sea water is mostly oxygen and hydrogen, about 85.8 percent of oxygen +and 10.7 percent of hydrogen. That is what you would expect for water is +made up of molecules which in turn are formed by two atoms of hydrogen +and one atom of oxygen. The oxygen atom is about sixteen times as heavy +as the hydrogen atom. However, for every oxygen atom there are two +hydrogen atoms so that for every pound of hydrogen in water there are +about eight pounds of oxygen. That is why there is about eight times as +high a percentage of oxygen in sea water as there is of hydrogen. + +Most of sea water, therefore, is just water, that is, pure water. But it +contains some other substances as well and the best known of these is +salt. Salt is a substance the molecules of which contain atoms of sodium +and of chlorine. That is why sea water is about 1.1 percent sodium and +about 2.1 percent chlorine. There are some other kinds of atoms in sea +water, as you would expect, for it gets all the substances which the +waters of the earth dissolve and carry down to it but they are +unimportant in amounts. + +Now we know something about the names of the important kinds of atoms +and can take up again the question of how they are formed by protons and +electrons. No matter what kind of atom we are dealing with we always +have a nucleus or center and some electrons playing around that nucleus +like tiny planets. The only differences between one kind of atom and any +other kind are differences in the nucleus and differences in the number +and arrangement of the planetary electrons which are playing about the +nucleus. + +No matter what kind of atom we are considering there is always in it +just as many electrons as protons. For example, the iron atom is formed +by a nucleus and twenty-six electrons playing around it. The copper atom +has twenty-nine electrons as tiny planets to its nucleus. What does that +mean about its nucleus? That there are twenty-nine more protons in the +nucleus than there are electrons. Silver has even more planetary +electrons, for it has 47. Radium has 88 and the heaviest atom of all, +that of uranium, has 92. + +We might use numbers for the different kinds of atoms instead of names +if we wanted to do so. We could describe any kind of atom by telling how +many planetary electrons there were in it. For example, hydrogen would +be number 1, helium number 2, lithium of which you perhaps never heard, +would be number 3, and so on. Oxygen is 8, sodium is 11, chlorine is 17, +iron 26, and copper 29. For each kind of atom there is a number. Let's +call that number its atomic number. + +Now let's see what the atomic number tells us. Take copper, for example, +which is number 29. In each atom of copper there are 29 electrons +playing around the nucleus. The nucleus itself is a little inner group +of electrons and protons, but there are more protons than electrons in +it; twenty-nine more in fact. In an atom there is always an extra proton +in the nucleus for each planetary electron. That makes the total number +of protons and electrons the same. + +About the nucleus of a copper atom there are playing 29 electrons just +as if the nucleus was a teacher responsible for 29 children who were out +in the play yard. There is one very funny thing about it all, however, +and that is that we must think of the scholars as if they were all just +alike so that the teacher couldn't tell one from the other. Electrons +are all alike, you remember. All the teacher or nucleus cares for is +that there shall be just the right number playing around her. You could +bring a boy in from some other play ground and the teacher couldn't tell +that he was a stranger but she would know that something was the matter +for there would be one too many in her group. She is responsible for +just 29 scholars, and the nucleus of the copper atom is responsible for +just 29 electrons. It doesn't make any difference where these electrons +come from provided there are always just 29 playing around the nucleus. +If there are more or less than 29 something peculiar will happen. + +We shall see later what might happen, but first let's think of an +enormous lot of atoms such as there would be in a copper wire. A small +copper wire will have in it billions of copper atoms, each with its +planetary electrons playing their invisible game about their own +nucleus. There is quite a little distance in any atom between the +nucleus and any of the electrons for which it is responsible. There is +usually a greater distance still between one atomic group and any other. + +On the whole the electrons hold pretty close to their own circles about +their own nuclei. There is always some tendency to run away and play in +some other group. With 29 electrons it's no wonder if sometimes one goes +wandering off and finally gets into the game about some other nucleus. +Of course, an electron from some other atom may come wandering along and +take the place just left vacant, so that nucleus is satisfied. + +We don't know all we might about how the electrons wander around from +atom to atom inside a copper wire but we do know that there are always a +lot of them moving about in the spaces between the atoms. Some of them +are going one way and some another. + +It's these wandering electrons which are affected when a battery is +connected to a copper wire. Every single electron which is away from its +home group, and wandering around, is sent scampering along toward the +end of the wire which is connected to the positive plate or terminal of +the battery and away from the negative plate. That's what the battery +does to them for being away from home; it drives them along the wire. +There's a regular stream or procession of them from the negative end of +the wire toward the positive. When we have a stream of electrons like +this we say we have a current of electricity. + +We'll need to learn more later about a current of electricity but one of +the first things we ought to know is how a battery is made and why it +affects these wandering electrons in the copper wire. That's what I +shall tell you in my next letter.[1] + +[Footnote 1: The reader who wishes the shortest path to the construction +and operation of a radio set should omit the next two letters.] + + + + +LETTER 3 + +HOW A BATTERY WORKS + + +(This letter may be omitted on the first reading.) + +MY DEAR BOY: + +When I was a boy we used to make our own batteries for our experiments. +That was before storage batteries became as widely used as they are +to-day when everybody has one in the starting system of his automobile. +That was also before the day of the small dry battery such as we use in +pocket flash lights. The batteries which we made were like those which +they used on telegraph systems, and were sometimes called "gravity" +batteries. Of course, we tried several kinds and I believe I got quite a +little acid around the house at one time or another. I'll tell you about +only one kind but I shall use the words "electron," "proton," "nucleus," +"atom," and "molecule," about some of which nothing was known when I was +a boy. + +We used a straight-sided glass jar which would hold about a gallon. On +the bottom we set a star shaped arrangement made of sheets of copper +with a long wire soldered to it so as to reach up out of the jar. Then +we poured in a solution of copper sulphate until the jar was about half +full. This solution was made by dissolving in water crystals of "blue +vitriol" which we bought at the drug store. + +Blue vitriol, or copper sulphate as the chemists would call it, is a +substance which forms glassy blue crystals. Its molecules are formed of +copper atoms, sulphur atoms, and oxygen atoms. In each molecule of it +there is one atom of copper, one of sulphur and four of oxygen. + +When it dissolves in water the molecules of the blue vitriol go +wandering out into the spaces between the water molecules. But that +isn't all that happens or the most important thing for one who is +interested in making a battery. + +Each molecule is formed by six atoms, that is by six little groups of +electrons playing about six little nuclei. About each nucleus there is +going on a game but some of the electrons are playing in the game about +their own nucleus and at the same time taking some part in the game +which is going on around one of the other nuclei. That's why the groups +or atoms stay together as a molecule. When the molecules wander out into +the spaces between the water molecules something happens to this +complicated game. + +It will be easiest to see what sort of thing happens if we talk about a +molecule of ordinary table salt, for that has only two atoms in it. One +atom is sodium and one is chlorine. The sodium molecule has eleven +electrons playing around its nucleus. Fairly close to the nucleus there +are two electrons. Then farther away there are eight more and these are +having a perfect game. Then still farther away from the nucleus there is +a single lonely electron. + +The atom of chlorine has seventeen electrons which play about its +nucleus. Close to the nucleus there are two. A little farther away there +are eight just as there are in the sodium atom. Then still farther away +there are seven. + +I am going to draw a picture (Fig. 1) to show what I mean, but you must +remember that these electrons are not all in the same plane as if they +lay on a sheet of paper, but are scattered all around just as they would +be if they were specks on a ball. + +[Illustration: Fig. 1] + +You see that the sodium atom has one lonely electron which hasn't any +play fellows and that the chlorine atom has seven in its outside circle. +It appears that eight would make a much better game. Suppose that extra +electron in the sodium atom goes over and plays with those in the +chlorine atom so as to make eight in the outside group as I have shown +Fig. 2. That will be all right as long as it doesn't get out of sight of +its own nucleus because you remember that the sodium nucleus is +responsible for eleven electrons. The lonely electron of the sodium atom +needn't be lonely any more if it can persuade its nucleus to stay so +close to the chlorine atom that it can play in the outer circle of the +chlorine atom. + +[Illustration: Fig. 2] + +The outer circle of the chlorine atom will then have a better game, for +it will have just the eight that makes a perfect game. This can happen +if the chlorine atom will stay close enough to the sodium atom so that +the outermost electron of the sodium atom can play in the chlorine +circle. You see everything will be satisfactory if an electron can be +shared by the two atoms. That can happen only if the two atoms stay +together; that is, if they form a molecule. That's why there are +molecules and that's what I meant when I spoke of the molecule as a big +game played by the electrons of two or more atoms. + +This molecule which is formed by a sodium atom and a chlorine atom is +called a molecule of sodium chloride by chemists and a molecule of salt +by most every one who eats it. Something strange happens when it +dissolves. It wanders around between the water molecules and for some +reason or other--we don't know exactly why--it decides to split up again +into sodium and chlorine but it can't quite do it. The electron which +joined the game about the chlorine nucleus won't leave it. The result is +that the nucleus of the sodium atom gets away but it leaves this one +electron behind. + +What gets away isn't a sodium atom for it has one too few electrons; and +what remains behind isn't a chlorine atom for it has one too many +electrons. We call these new groups "ions" from a Greek word which means +"to go" for they do go, wandering off into the spaces between the water +molecules. Fig. 3 gives you an idea of what happens. + +You remember that in an atom there are always just as many protons as +electrons. In this sodium ion which is formed when the nucleus of the +sodium atom breaks away but leaves behind one planetary electron, there +is then one more proton than there are electrons. Because it has an +extra proton, which hasn't any electron to associate with, we call it a +plus ion or a "positive ion." Similarly we call the chlorine ion, which +has one less proton than it has electrons, a minus or "negative ion." + +[Illustration: Fig. 3] + +Now, despite the fact that these ions broke away from each other they +aren't really satisfied. Any time that the sodium ion can find an +electron to take the place of the one it lost it will welcome it. That +is, the sodium ion will want to go toward places where there are extra +electrons. In the same way the chlorine ion will go toward places where +electrons are wanted as if it could satisfy its guilty conscience by +giving up the electron which it stole from the sodium atom, or at least +by giving away some other electron, for they are all alike anyway. + +Sometimes a positive sodium ion and a negative chlorine ion meet in +their wanderings in the solution and both get satisfied by forming a +molecule again. Even so they don't stay together long before they split +apart and start wandering again. That's what goes on over and over +again, millions of times, when you dissolve a little salt in a glass of +water. + +Now we can see what happens when copper sulphate dissolves. The copper +atom has twenty-nine electrons about its nucleus and all except two of +these are nicely grouped for playing their games about the nucleus. Two +of the electrons are rather out of the game, and are unsatisfied. They +play with the electrons of the part of the molecule which is called +"sulphate," that is, the part formed by the sulphur atom and the four +oxygen atoms. These five atoms of the sulphate part stay together very +well and so we treat them as a group. + +The sulphate group and the copper atom stay together as long as they are +not in solution but when they are, they act very much like the sodium +and chlorine which I just described. The molecule splits up into two +ions, one positive and one negative. The positive ion is the copper part +except that two of the electrons which really belong to a copper atom +got left behind because the sulphate part wouldn't give them up. The +rest of the molecule is the negative ion. + +The copper ion is a copper atom which has lost two electrons. The +sulphate ion is a combination of one sulphur atom, four oxygen atoms and +two electrons which it stole from the copper atom. Just as the sodium +ion is unsatisfied because in it there is one more proton than there are +electrons, so the copper ion is unsatisfied. As a matter of fact it is +twice as badly unsatisfied. It has two more protons than it has +electrons. We say it has twice the "electrical charge" of the sodium +ion. + +Just like a sodium ion the copper ion will tend to go toward any place +where there are extra electrons which it can get to satisfy its own +needs. In much the same way the sulphate ion will go toward places where +it can give up its two extra electrons. Sometimes, of course, as ions of +these two kinds wander about between the water molecules, they meet and +satisfy each other by forming a molecule of copper sulphate. But if they +do they will split apart later on; that is, they will "dissociate" as we +should say. + +Now let's go on with the kind of batteries I used to make as a boy. You +can see that in the solution of copper sulphate at the bottom of the jar +there was always present a lot of positive copper ions and of negative +sulphate ions. + +On top of this solution of copper sulphate I poured very carefully a +weak solution of sulphuric acid. As I told you, an acid always has +hydrogen in its molecules. Sulphuric acid has molecules formed by two +hydrogen atoms and one of the groups which we decided to call sulphate. +A better name for this acid would be hydrogen sulphate for that would +imply that its molecule is the same as one of copper sulphate, except +that the place of the copper is taken by two atoms of hydrogen. It takes +two atoms of hydrogen because the copper atom has two lonely electrons +while a hydrogen atom only has one. It takes two electrons to fill up +the game which the electrons of the sulphate group are playing. If it +can get these from a single atom, all right; but if it has to get one +from each of two atoms, it will do it that way. + +I remember when I mixed the sulphuric acid with water that I learned to +pour the acid into the water and not the other way around. Spatterings +of sulphuric acid are not good for hands or clothes. With this solution +I filled the jar almost to the top and then hung over the edge a sort of +a crow's foot shape of cast zinc. The zinc reached down into the +sulphuric acid solution. There was a binding post on it to which a wire +could be connected. This wire and the one which came from the plate of +copper at the bottom were the two terminals of the battery. We called +the wire from the copper "positive" and the one from the zinc +"negative." + +Now we shall see why and how the battery worked. The molecules of +sulphuric acid dissociate in solution just as do those of copper +sulphate. When sulphuric acid molecules split, the sulphate part goes +away with two electrons which don't belong to it and each of the +hydrogen atoms goes away by itself but without its electron. We call +each a "hydrogen ion" but you can see that each is a single proton. + +In the two solutions are pieces of zinc and copper. Zinc is like all the +rest of the metals in one way. Atoms of metals always have lonely +electrons for which there doesn't seem to be room in the game which is +going on around their nuclei. Copper as we saw has two lonely electrons +in each atom. Zinc also has two. Some metals have one and some two and +some even more lonely electrons in each atom. + +What happens then is this. The sulphate ions wandering around in the +weak solution of sulphuric acid come along beside the zinc plate and +beckon to its atoms. The sulphate ions had a great deal rather play the +game called "zinc sulphate" than the game called "hydrogen sulphate." So +the zinc atoms leave their places to join with the sulphate ions. But +wait a minute! The sulphate ions have two extra electrons which they +kept from the hydrogen atoms. They don't need the two lonely electrons +which each zinc atom could bring and so the zinc atom leaves behind it +these unnecessary electrons. + +Every time a zinc atom leaves the plate it fails to take all its +electrons with it. What leaves the zinc plate, therefore, to go into +solution is really not a zinc atom but is a zinc ion; that is, it is the +nucleus of a zinc atom and all except two of the planetary electrons. + +Every time a zinc ion leaves the plate there are left behind two +electrons. The plate doesn't want them for all the rest of its atoms +have just the same number of protons as of electrons. Where are they to +go? We shall see in a minute. + +Sometimes the zinc ions which have got into solution meet with sulphate +ions and form zinc sulphate molecules. But if they do these molecules +split up sooner or later into ions again. In the upper part of the +liquid in the jar, therefore, there are sulphate ions which are negative +and two kinds of positive ions, namely, the hydrogen ions and the zinc +ions. + +Before the zinc ions began to crowd in there were just enough hydrogen +ions to go with the sulphate ions. As it is, the entrance of the zinc +ions has increased the number of positive ions and now there are too +many. Some of the positive ions, therefore, and particularly the +hydrogen ions, because the sulphate prefers to associate with the zinc +ions, can't find enough playfellows and so go down in the jar. + +Down in the bottom of the jar the hydrogen ions find more sulphate ions +to play with, but that leaves the copper ions which used to play with +these sulphate ions without any playmates. So the copper ions go still +further down and join with the copper atoms of the copper plate. They +haven't much right to do so, for you remember that they haven't their +proper number of electrons. Each copper ion lacks two electrons of being +a copper atom. Nevertheless they join the copper plate. The result is a +plate of copper which has too few electrons. It needs two electrons for +every copper ion which joins it. + +How about the zinc plate? You remember that it has two electrons more +than it needs for every zinc ion which has left it. If only the extra +electrons on the negative zinc plate could get around to the positive +copper plate. They can if we connect a wire from one plate to the other. +Then the electrons from the zinc stream into the spaces between the +atoms of the wire and push ahead of them the electrons which are +wandering around in these spaces. At the other end an equal number of +electrons leave the wire to satisfy the positive copper plate. So we +have a stream of electrons in the wire, that is, a current of +electricity and our battery is working. + +That's the sort of a battery I used to play with. If you understand it +you can get the general idea of all batteries. Let me express it in +general terms. + +At the negative plate of a battery ions go into solution and electrons +are left behind. At the other end of the battery positive ions are +crowded out of solution and join the plate where they cause a scarcity +of electrons; that is, make the plate positive. If a wire is connected +between the two plates, electrons will stream through it from the +negative plate to the positive; and this stream is a current of +electricity. + +[Illustration: Pl. III.--Dry Battery for Use in Audion Circuits +(Courtesy of National Carbon Co., Inc.). Storage Battery (Courtesy of +the Electric Storage Battery Co.).] + + + + +LETTER 4 + +THE BATTERIES IN YOUR RADIO SET + + +(This letter may be omitted on the first reading.) + +MY DEAR YOUNG MAN: + +You will need several batteries when you come to set up your radio +receiver but you won't use such clumsy affairs as the gravity cell which +I described in my last letter. Some of your batteries will be dry +batteries of the size used in pocket flash lights. + +These are not really dry, for between the plates they are filled with a +moist paste which is then sealed in with wax to keep it from drying out +or from spilling. Instead of zinc and copper these batteries use zinc +and carbon. No glass jar is needed, for the zinc is formed into a jar +shape. In this is placed the paste and in the center of the paste a rod +or bar of carbon. The paste doesn't contain sulphuric acid, but instead +has in it a stuff called sal ammoniac; that is, ammonium chloride. + +The battery, however, acts very much like the one I described in my last +letter. Ions of zinc leave the zinc and wander into the moist paste. +These ions are positive, just as in the case of the gravity battery. The +result is that the electrons which used to associate with a zinc ion to +form a zinc atom are left in the zinc plate. That makes the zinc +negative for it has more electrons than protons. The zinc ions take the +place of the positive ions which are already in the paste. The positive +ions which originally belonged with the paste, therefore, move along to +the carbon rod and there get some electrons. Taking electrons away from +the carbon leaves it with too many protons; that is, leaves it positive. +In the little flash light batteries, therefore, you will always find +that the round carbon rod, which sticks out of the center, is positive +and the zinc casing is negative. + +The trouble with the battery like the one I used to make is that the +zinc plate wastes away. Every time a zinc ion leaves it that means that +the greater part of an atom is gone. Then when the two electrons which +were left behind get a chance to start along a copper wire toward the +positive plate of the battery there goes the rest of the atom. After a +while there is no more zinc plate. It is easy to see what has happened. +All the zinc has gone into solution or been "eaten away" as most people +say. Dry batteries, however, don't stop working because the zinc gets +used up, but because the active stuff in the paste, the ammonium +chloride, is changed into something else. + +There's another kind of battery which you will need to use with your +radio set; that is the storage battery. Storage batteries can be used +over and over again if they are charged between times and will last for +a long time if properly cared for. Then too, they can give a large +current, that is, a big swift-moving stream of electrons. You will need +that when you wish to heat the filament of the audion in your receiving +set. + +The English call our storage batteries by the name "accumulators." I +don't like that name at all, but I don't like our name for them nearly +as well as I do the name "reversible batteries." Nobody uses this last +name because it's too late to change. Nevertheless a storage battery is +reversible, for it will work either way at an instant's notice. + +A storage battery is something like a boy's wagon on a hill side. It +will run down hill but it can be pushed up again for another descent. +You can use it to send a stream of electrons through a wire from its +negative plate to its positive plate. Then if you connect these plates +to some other battery or to a generator, (that is, a dynamo) you can +make a stream of electrons go in the other direction. When you have done +so long enough the battery is charged again and ready to discharge. + +I am not going to tell you very much about the storage battery but you +ought to know a little about it if you are to own and run one with your +radio set. When it is all charged and ready to work, the negative plate +is a lot of soft spongy lead held in place by a frame of harder lead. +The positive plate is a lead frame with small squares which are filled +with lead peroxide, as it is called. This is a substance with molecules +formed of one lead atom and two oxygen atoms. Why the chemists call it +lead peroxide instead of just lead oxide I'll tell you some other time, +but not in these letters. + +Between the two plates is a wood separator to keep pieces of lead from +falling down between and touching both plates. You know what would +happen if a piece of metal touched both plates. There would be a short +circuit, that is, a sort of a short cut across lots by which some of the +electrons from the negative plate could get to the positive plate +without going along the wires which we want them to travel. That's why +there are separators. + +The two plates are in a jar of sulphuric acid solution. The sulphuric +acid has molecules which split up in solution, as you remember, into +hydrogen ions and the ions which we called "sulphate." In my gravity +battery the sulphate ions used to coax the zinc ions away into the +solution. In the storage battery on the other hand the sulphate ions can +get to most of the lead atoms because the lead is so spongy. When they +do, they form lead sulphate right where the lead atoms are. They don't +really need whole lead atoms, because they have two more electrons than +they deserve, so there are two extra electrons for every molecule of +lead sulphate which is formed. That's why the spongy lead plate is +negative. + +The lead sulphate won't dissolve, so it stays there on the plate as a +whitish coating. Now see what that means. What are the hydrogen ions +going to do? As long as there was sulphuric acid in the water there was +plenty of sulphate ions for them to associate with as often as they met; +and they would meet pretty often. But if the sulphate ions get tied up +with the lead of the plate there will be too many hydrogen ions left in +the solution. Now what are the hydrogen ions to do? They are going to +get as far away from each other as they can, for they are nothing but +protons; and protons don't like to associate. They only stayed around in +the first place because there was always plenty of sulphate ions with +whom they liked to play. + +When the hydrogen ions try to get away from each other they go to the +other plate of the battery, and there they will get some electrons, if +they have to steal in their turn. + +I won't try to tell you all that happens at the other plate. The +hydrogen ions get the electrons which they need, but they get something +more. They get some of the oxygen away from the plate and so form +molecules of water. You remember that water molecules are made of two +atoms of hydrogen and one of oxygen. Meanwhile, the lead atoms, which +have lost their oxygen companions, combine with some of the sulphate +ions which are in that neighborhood. During the mix-up electrons are +carried away from the plate and that leaves it positive. + +The result of all this is a little lead sulphate on each plate, a +negative plate where the spongy lead was, and a positive plate where the +lead peroxide was. + +Notice very carefully that I said "a little lead sulphate on each +plate." The sort of thing I have been describing doesn't go on very +long. If it did the battery would run down inside itself and then when +we came to start our automobile we would have to get out and crank. + +How long does it go on? Answer another question first. So far we haven't +connected any wire between the two plates of the battery, and so none of +the electrons on the negative plate have any way of getting around to +the positive plate where electrons are badly needed. Every time a +negative sulphate ion combines with the spongy lead of the negative +plate there are two more electrons added to that plate. You know how +well electrons like each other. Do they let the sulphate ions keep +giving that plate more electrons? There is the other question; and the +answer is that they do not. Every electron that is added to that plate +makes it just so much harder for another sulphate ion to get near enough +to do business at all. That's why after a few extra electrons have +accumulated on the spongy lead plate the actions which I was describing +come to a stop. + +Do they ever begin again? They do just as soon as there is any reduction +in the number of electrons which are hopping around in the negative +plate trying to keep out of each other's way. When we connect a wire +between the plates we let some of these extra electrons of the negative +plate pass along to the positive plate where they will be welcome. And +the moment a couple of them start off on that errand along comes another +sulphate ion in the solution and lands two more electrons on the plate. +That's how the battery keeps on discharging. + +We mustn't let it get too much discharged for the lead sulphate is not +soluble, as I just told you, and it will coat up that plate until there +isn't much chance of getting the process to reverse. That's why we are +so careful not to let the discharge process go on too long before we +reverse it and charge. That's why, when the car battery has been used +pretty hard to start the car, I like to run quite a while to let the +generator charge the battery again. When the battery charges, the +process reverses and we get spongy lead on the negative plate and lead +peroxide on the positive plate. + +You've learned enough for one day. Write me your questions and I'll +answer and then go on in my next letter to tell how the audion works. +You know about conduction of electricity in wires; that is, about the +electron stream, and about batteries which can cause the stream. Now you +are ready for the most wonderful little device known to science: the +audion. + + + + +LETTER 5 + +GETTING ELECTRONS FROM A HEATED WIRE + + +DEAR SON: + +I was pleased to get your letter and its questions. Yes, a proton is a +speck of electricity of the kind we call positive and an electron is of +the kind we call negative. You might remember this simple law; "Like +kinds of electricity repel, and unlike attract." + +The word ion[2] is used to describe any atom, or part of a molecule +which can travel by itself and has more or less than its proper number +of electrons. By proper number of electrons I mean proper for the number +of protons which it has. If an ion has more electrons than protons it is +negative; if the inequality is the other way around it is positive. An +atom or molecule has neither more nor less protons than electrons. It is +neutral or "uncharged," as we say. + +No, not every substance which will dissolve will dissociate or split up +into positive and negative ions. The salt which you eat will, but the +sugar will not. If you want a name for those substances which will +dissociate in solution, call them "electrolytes." To make a battery we +must always use an electrolyte. + +Yes, it is hard to think of a smooth piece of metal or a wire as full +of holes. Even in the densest solids like lead the atoms are quite far +apart and there are large spaces between the nuclei and the planetary +electrons of each atom. + +I hope this clears up the questions in your mind for I want to get along +to the vacuum tube. By a vacuum we mean a space which has very few atoms +or molecules in it, just as few as we can possibly get, with the best +methods of pumping and exhausting. For the present let's suppose that we +can get all the gas molecules, that is, all the air, out of a little +glass bulb. + +The audion is a glass bulb like an electric light bulb which has in it a +thread, or filament, of metal. The ends of this filament extend out +through the glass so that we may connect a battery to them and pass a +current of electricity through the wire. If we do so the wire gets hot. + +What do we mean when we say "the wire gets hot?" We mean that it feels +hot. It heats the glass bulb and we can feel it. But what do we mean in +words of electrons and atoms? To answer this we must start back a little +way. + +In every bit of matter in our world the atoms and molecules are in very +rapid motion. In gases they can move anywhere; and do. That's why odors +travel so fast. In liquids most of the molecules or atoms have to do +their moving without getting out of the dish or above the surface. Not +all of them stay in, however, for some are always getting away from the +liquid and going out into the air above. That is why a dish of water +will dry up so quickly. The faster the molecules are going the better +chance they have of jumping clear away from the water like fish jumping +in the lake at sundown. Heating the liquid makes its molecules move +faster and so more of them are able to jump clear of the rest of the +liquid. That's why when we come in wet we hang our clothes where they +will get warm. The water in them evaporates more quickly when it is +heated because all we mean by "heating" is speeding up the molecules. + +In a solid body the molecules can't get very far away from where they +start but they keep moving back and forth and around and around. The +hotter the body is, the faster are its molecules moving. Generally they +move a little farther when the body is hot than when it is cold. That +means they must have a little more room and that is why a body is larger +when hot than when cold. It expands with heating because its molecules +are moving more rapidly and slightly farther. + +When a wire is heated its molecules and atoms are hurried up and they +dash back and forth faster than before. Now you know that a wire, like +the filament of a lamp, gets hot when the "electricity is turned on," +that is, when there is a stream of electrons passing through it. Why +does it get hot? Because when the electrons stream through it they bump +and jostle their way along like rude boys on a crowded sidewalk. The +atoms have to step a bit more lively to keep out of the way. These more +rapid motions of the atoms we recognize by the wire growing hotter. + +That is why an electric current heats a wire through which it is +flowing. Now what happens to the electrons, the rude boys who are +dodging their way along the sidewalk? Some of them are going so fast and +so carelessly that they will have to dodge out into the gutter and off +the sidewalk entirely. The more boys that are rushing along and the +faster they are going the more of them will be turned aside and plunge +off the sidewalks. + +The greater and faster the stream of electrons, that is the more current +which is flowing through the wire, the more electrons will be "emitted," +that is, thrown out of the wire. If you could watch them you would see +them shooting out of the wire, here, there, and all along its length, +and going in every direction. The number which shoot out each second +isn't very large until they have stirred things up so that the wire is +just about red hot. + +What becomes of them? Sometimes they don't get very far away from the +wire and so come back inside again. They scoot off the sidewalk and on +again just as boys do in dodging their way along. Some of them start +away as if they were going for good. + +If the wire is in a vacuum tube, as it is in the case of the audion, +they can't get very far away. Of course there is lots of room; but they +are going so fast that they need more room just as older boys who run +fast need a larger play ground than do the little tots. By and by there +gets to be so many of them outside that they have to dodge each other +and some of them are always dodging back into the wire while new +electrons are shooting out from it. + +When there are just as many electrons dodging back into the wire each +second as are being emitted from it the vacuum in the tube has all the +electrons it can hold. We might say it is "saturated" with electrons, +which means, in slang, "full up." If any more electrons are to get out +of the filament just as many others which are already outside have to go +back inside. Or else they have got to be taken away somewhere else. + +What I have just told you about electrons getting away from a heated +wire is very much like what happens when a liquid is heated. The +molecules of the liquid get away from the surface. If we cover a dish of +liquid which is being heated the liquid molecules can't get far away and +very soon the space between the surface of the liquid and the cover gets +saturated with them. Then every time another molecule escapes from the +surface of the liquid there must be some molecule which goes back into +the liquid. There is then just as much condensation back into liquid as +there is evaporation from it. That's why in cooking they put covers over +the vessels when they don't want the liquid all to "boil away." + +Sometimes we speak of the vacuum tube in the same words we would use in +describing evaporation of a liquid. The molecules of the liquid which +have escaped form what is called a "vapor" of the liquid. As you know +there is usually considerable water vapor in the air. We say then that +electrons are "boiled out" of the filament and that there is a "vapor of +electrons" in the tube. + +That is enough for this letter. Next time I shall tell you how use is +made of these electrons which have been boiled out and are free in the +space around the filament. + +[Footnote 2: If the reader has omitted Letters 3 and 4 he should omit +this paragraph and the next.] + + +LETTER 6 + +THE AUDION + + +DEAR SON: + +In my last letter I told how electrons are boiled out of a heated +filament. The hotter the filament the more electrons are emitted each +second. If the temperature is kept steady, or constant as we say, then +there are emitted each second just the same number of electrons. When +the filament is enclosed in a vessel or glass bulb these electrons which +get free from it cannot go very far away. Some of them, therefore, have +to come back to the filament and the number which returns each second is +just equal to the number which is leaving. You realize that this is what +is happening inside an ordinary electric light bulb when its filament is +being heated. + +[Illustration: Fig 4] + +An ordinary electric light bulb, however, is not an audion although it +is like one in the emission of electrons from its filament. That reminds +me that last night as I was waiting for a train I picked up one of the +Radio Supplements which so many newspapers are now running. There was a +column of enquiries. One letter told how its writer had tried to use an +ordinary electric light bulb to receive radio signals. + +He had plenty of electrons in it but no way to control them and make +their motions useful. In an audion besides the filament there are two +other things. One is a little sheet or plate of metal with a connecting +wire leading out through the glass walls and the other is a little wire +screen shaped like a gridiron and so called a "grid." It also has a +connecting wire leading through the glass. Fig. 4 shows an audion. It +will be most convenient, however, to represent an audion as in Fig. 5. +There you see the filament, _F_, with its two terminals brought out +from the tube, the plate, _P_, and between these the grid, +_G_. + +[Illustration: Fig 5] + +These three parts of the tube are sometimes called "elements." Usually, +however, they are called "electrodes" and that is why the audion is +spoken of as the "three-electrode vacuum tube." An electrode is what we +call any piece of metal or wire which is so placed as to let us get at +electrons (or ions) to control their motions. Let us see how it does so. + +To start with, we shall forget the grid and think of a tube with only a +filament and a plate in it--a two-electrode tube. We shall represent it +as in Fig. 6 and show the battery which heats the filament by some lines +as at _A_. In this way of representing a battery each cell is +represented by a short heavy line and a longer lighter line. The heavy +line stands for the negative plate and the longer line for the positive +plate. We shall call the battery which heats the filament the "filament +battery" or sometimes the "A-battery." As you see, it is formed by +several battery cells connected in series. + +[Illustration: Fig 6] + +Sometime later I may tell you how to connect battery cells together and +why. For the present all you need to remember is that two batteries are +in series if the positive plate of one is connected to the negative +plate of the other. If the batteries are alike they will pull an +electron just twice as hard as either could alone. + +[Illustration: Pl. IV.--Radiotron (Courtesy of Radio Corporation of +America).] + +To heat the filament of an audion, such as you will probably use in your +set, will require three storage-battery cells, like the one I described +in my fourth letter, all connected in series. We generally use storage +batteries of about the same size as those in the automobile. If you will +look at the automobile battery you will see that it is made of three +cells connected in series. That battery would do very well for the +filament circuit. + +By the way, do you know what a "circuit" is? The word comes from the +same Latin word as our word "circus." The Romans were very fond of +chariot racing at their circuses and built race tracks around which the +chariots could go. A circuit, therefore, is a path or track around which +something can race; and an electrical circuit is a path around which +electrons can race. The filament, the A-battery and the connecting wires +of Fig. 6 form a circuit. + +[Illustration: Fig 7] + +Let us imagine another battery formed by several cells in series which +we shall connect to the tube as in Fig. 7. All the positive and negative +terminals of these batteries are connected in pairs, the positive of one +cell to the negative of the next, except for one positive and one +negative. The remaining positive terminal is the positive terminal of +the battery which we are making by this series connection. We then +connect this positive terminal to the plate and the negative terminal to +the filament as shown in the figure. This new battery we shall call the +"plate battery" or the "B-battery." + +Now what's going to happen? The B-battery will want to take in electrons +at its positive terminal and to send them out at its negative terminal. +The positive is connected to the plate in the vacuum tube of the figure +and so draws some of the electrons of the plate away from it. Where do +these electrons come from? They used to belong to the atoms of the plate +but they were out playing in the space between the atoms, so that they +came right along when the battery called them. That leaves the plate +with less than its proper number of electrons; that is, leaves it +positive. So the plate immediately draws to itself some of the electrons +which are dodging about in the vacuum around it. + +Do you remember what was happening in the tube? The filament was +steadily going on emitting electrons although there were already in the +tube so many electrons that just as many crowded back into the filament +each second as the filament sent out. The filament was neither gaining +nor losing electrons, although it was busy sending them out and +welcoming them home again. + +When the B-battery gets to work all this is changed. The B-battery +attracts electrons to the plate and so reduces the crowd in the tube. +Then there are not as many electrons crowding back into the filament as +there were before and so the filament loses more than it gets back. + +Suppose that, before the B-battery was connected to the plate, each tiny +length of the filament was emitting 1000 electrons each second but was +getting 1000 back each second. There was no net change. Now, suppose +that the B-battery takes away 100 of these each second. Then only 900 +get back to the filament and there is a net loss from the filament of +100. Each second this tiny length of filament sends into the vacuum 100 +electrons which are taken out at the plate. From each little bit of +filament there is a stream of electrons to the plate. Millions of +electrons, therefore, stream across from filament to plate. That is, +there is a current of electricity between filament and plate and this +current continues to flow as long as the A-battery and the B-battery do +their work. + +The negative terminal of the B-battery is connected to the filament. +Every time this battery pulls an electron from the plate its negative +terminal shoves one out to the filament. You know from my third and +fourth letters that electrons are carried through a battery from its +positive to its negative terminal. You see, then, that there is the same +stream of electrons through the B-battery as there is through the vacuum +between filament and plate. This same stream passes also through the +wires which connect the battery to the tube. The path followed by the +stream of electrons includes the wires, the vacuum and the battery in +series. We call this path the "plate circuit." + +We can connect a telephone receiver, or a current-measuring instrument, +or any thing we wish which will pass a stream of electrons, so as to let +this same stream of electrons pass through it also. All we have to do is +to connect the instrument in series with the other parts of the plate +circuit. I'll show you how in a minute, but just now I want you to +understand that we have a stream of electrons, for I want to tell you +how it may be controlled. + +Suppose we use another battery and connect it between the grid and the +filament so as to make the grid positive. That would mean connecting the +positive terminal of the battery to the grid and the negative to the +filament as shown by the C-battery of Fig. 8. This figure also shows a +current-measuring instrument in the plate circuit. + +What effect is this C-battery, or grid-battery, going to have on the +current in the _plate circuit_? Making the grid positive makes it +want electrons. It will therefore act just as we saw that the plate did +and pull electrons across the vacuum towards itself. + +[Illustration: Fig 8] + +What happens then is something like this: Electrons are freed at the +filament; the plate and the grid both call them and they start off in a +rush. Some of them are stopped by the wires of the grid but most of them +go on by to the plate. The grid is mostly open space, you know, and the +electrons move as fast as lightning. They are going too fast in the +general direction of the grid to stop and look for its few and small +wires. + +When the grid is positive the grid helps the plate to call electrons +away from the filament. Making the grid positive, therefore, increases +the stream of electrons _between filament and plate_; that is, +increases the current in the plate circuit. + +We could get the same effect so far as concerns an increased plate +current by using more batteries in series in the plate circuit so as to +pull harder. But the grid is so close to the filament that a single +battery cell in the grid circuit can call electrons so strongly that it +would take several extra battery cells in the plate circuit to produce +the same effect. + +[Illustration: Fig 9] + +If we reverse the grid battery, as in Fig. 9, so as to make the grid +negative, then, instead of attracting electrons the grid repels them. +Nowhere near as many electrons will stream across to the plate when the +grid says, "No, go back." The grid is in a strategic position and what +it says has a great effect. + +When there is no battery connected to the grid it has no possibility of +influencing the electron stream which the plate is attracting to itself. +We say, then, that the grid is uncharged or is at "zero potential," +meaning that it is zero or nothing in possibility. But when the grid is +charged, no matter how little, it makes a change in the plate current. +When the grid says "Come on," even though very softly, it has as much +effect on the electrons as if the plate shouted at them, and a lot of +extra electrons rush for the plate. But when the grid whispers "Go +back," many electrons which would otherwise have gone streaking off to +the plate crowd back toward the filament. That's how the audion works. +There is an electron stream and a wonderfully sensitive way of +controlling the stream. + + + + +LETTER 7 + +HOW TO MEASURE AN ELECTRON STREAM + + +(This letter may be omitted on the first reading.) + +DEAR YOUTH: + +If we are to talk about the audion and how its grid controls the current +in the plate circuit we must know something of how to measure currents. +An electric current is a stream of electrons. We measure it by finding +the rate at which electrons are traveling along through the circuit. + +What do we mean by the word "rate?" You know what it means when a +speedometer says twenty miles an hour. If the car should keep going just +as it was doing at the instant you looked at the speedometer it would go +twenty miles in the next hour. Its rate is twenty miles an hour even +though it runs into a smash the next minute and never goes anywhere +again except to the junk heap. + +It's the same when we talk of electric currents. We say there is a +current of such and such a number of electrons a second going by each +point in the circuit. We don't mean that the current isn't going to +change, for it may get larger or smaller, but we do mean that if the +stream of electrons keeps going just as it is there will be such and +such a number of electrons pass by in the next second. + +In most of the electrical circuits with which you will deal you will +find that electrons must be passing along in the circuit at a most +amazing rate if there is to be any appreciable effect. When you turn on +the 40-watt light at your desk you start them going through the filament +of the lamp at the rate of about two and a half billion billion each +second. You have stood on the sidewalk in the city and watched the +people stream past you. Just suppose you could stand beside that narrow +little sidewalk which the filament offers to the electrons and count +them as they go by. We don't try to count them although we do to-day +know about how many go by in a second if the current is steady. + +If some one asks you how old you are you don't say "About five hundred +million seconds"; you tell him in years. When some one asks how large a +current is flowing in a wire we don't tell him six billion billion +electrons each second; we tell him "one ampere." Just as we use years as +the units in which to count up time so we use amperes as the units in +which to count up streams of electrons. When a wire is carrying a +current of one ampere the electrons are streaming through it at the rate +of about 6,000,000,000,000,000,000 a second. + +Don't try to remember this number but do remember that an ampere is a +unit in which we measure currents just as a year is a unit in which we +measure time. An ampere is a unit in which we measure streams of +electrons just as "miles per hour" is a unit in which we measure the +speed of trains or automobiles. + +If you wanted to find the weight of something you would take a scale and +weigh it, wouldn't you? You might take that spring balance which hangs +out in the kitchen. But if the spring balance said the thing weighed +five pounds how would you know if it was right? Of course you might take +what ever it was down town and weigh it on some other scales but how +would you know those scales gave correct weight? + +The only way to find out would be to try the scales with weights which +you were sure were right and see if the readings on the scale correspond +to the known weights. Then you could trust it to tell you the weight of +something else. That's the way scales are tested. In fact that's the way +that the makers know how to mark them in the first place. They put on +known weights and marked the lines and figures which you see. What they +did was called "calibrating" the scale. You could make a scale for +yourself if you wished, but if it was to be reliable you would have to +find the places for the markings by applying known weights, that is, by +calibration. + +How would you know that the weights you used to calibrate your scale +were really what you thought them to be? You would have to find some +place where they had a weight that everybody would agree was correct and +then compare your weight with that. You might, for example, send your +pound weight to the Bureau of Standards in Washington and for a small +payment have the Bureau compare it with the pound which it keeps as a +standard. + +That is easy where one is interested in a pound. But it is a little +different when one is interested in an ampere. You can't make an ampere +out of a piece of platinum as you can a standard pound weight. An ampere +is a stream of electrons at about the rate of six billion billion a +second. No one could ever count anywhere near that many, and yet +everybody who is concerned with electricity wants to be able to measure +currents in amperes. How is it done? + +First there is made an instrument which will have something in it to +move when electrons are flowing through the instrument. We want a meter +for the flow of electrons. In the basement we have a meter for the flow +of gas and another for the flow of water. Each of these has some part +which will move when the water or the gas passes through. But they are +both arranged with little gear wheels so as to keep track of all the +water or gas which has flowed through; they won't tell the rate at which +the gas or water is flowing. They are like the odometer on the car which +gives the "trip mileage" or the "total mileage." We want a meter like +the speedometer which will indicate at each instant just how fast the +electrons are streaming through it. + +There are several kinds of meters but I shall not try to tell you now of +more than one. The simplest to understand is called a "hot-wire meter." +You already know that an electron stream heats a wire. Suppose a piece +of fine wire is fastened at the two ends and that there are binding +posts also fastened to these ends of the wire so that the wire may be +made part of the circuit where we want to know the electron stream. Then +the same stream of electrons will flow through the fine wire as through +the other parts of the circuit. Because the wire is fine it acts like a +very narrow sidewalk for the stream of electrons and they have to bump +and jostle pretty hard to get through. That's why the wire gets heated. + +You know that a heated wire expands. This wire expands. It grows longer +and because it is held firmly at the ends it must bow out at the center. +The bigger the rate of flow of electrons the hotter it gets; and the +hotter it gets the more it bows out. At the center we might fasten one +end--the short end--of a little lever. A small motion of this short end +of the lever will mean a large motion of the other end, just like a +"teeter board" when one end is longer than the other; the child on the +long end travels further than the child on the short end. The lever +magnifies the motion of the center of the hot wire part of our meter so +that we can see it easier. + +[Illustration: Fig 10] + +There are several ways to make such a meter. The one shown in Fig. 10 is +as easy to understand as any. We shape the long end of the lever like a +pointer. Then the hotter the wire the farther the pointer moves. + +If we could put this meter in an electric circuit where we knew one +ampere was flowing we could put a numeral "1" opposite where the pointer +stood. Then if we could increase the current until there were two +amperes flowing through the meter we could mark that position of the +pointer "2" and so on. That's the way we would calibrate the meter. +After we had done so we would call it an "ammeter" because it measures +amperes. Years ago people would have called it an "amperemeter" but no +one who is up-to-date would call it so to-day. + +[Illustration: Fig 11] + +If we had a very carefully made ammeter we would send it to the Bureau +of Standards to be calibrated. At the Bureau they have a number of +meters which they know are correct in their readings. They would put one +of their meters and ours into the same circuit so that both carry the +same stream of electrons as in Fig. 11. Then whatever the reading was on +their meter could be marked opposite the pointer on ours. + +Now I want to tell you how the physicists at the Bureau know what is an +ampere. Several years ago there was a meeting or congress of physicists +and electrical engineers from all over the world who discussed what they +thought should be the unit in which to measure current. They decided +just what they would call an ampere and then all the countries from +which they came passed laws saying that an ampere should be what these +scientists had recommended. To-day, therefore, an ampere is defined by +law. + +To tell when an ampere of current is flowing requires the use of two +silver plates and a solution of silver nitrate. Silver nitrate has +molecules made up of one atom of silver combined with a group of atoms +called "nitrate." You remember that the molecule of copper sulphate, +discussed in our third letter, was formed by a copper atom and a group +called sulphate. Nitrate is another group something like sulphate for it +has oxygen atoms in it, but it has three instead of four, and instead of +a sulphur atom there is an atom of nitrogen. + +When silver nitrate molecules go into solution they break up into ions +just as copper sulphate does. One ion is a silver atom which has lost +one electron. This electron was stolen from it by the nitrate part of +the molecule when they dissociated. The nitrate ion, therefore, is +formed by a nitrogen atom, three oxygen atoms, and one extra electron. + +If we put two plates of silver into such a solution nothing will happen +until we connect a battery to the plates. Then the battery takes +electrons away from one plate and gives electrons to the other. Some of +the atoms in the plate which the battery is robbing of electrons are +just like the silver ions which are moving around in the solution. +That's why they can go out into the solution and play with the nitrate +ions each of which has an extra electron which it stole from some silver +atom. But the moment silver ions leave their plate we have more silver +ions in the solution than we do sulphate ions. + +The only thing that can happen is for some of the silver ions to get out +of the solution. They aren't going back to the positive silver plate +from which they just came. They go on toward the negative plate where +the battery is sending an electron for every one which it takes away +from the positive plate. There start off towards the negative plate, not +only the ions which just came from the positive plate, but all the ions +that are in the solution. The first one to arrive gets an electron but +it can't take it away from the silver plate. And why should it? As soon +as it has got this electron it is again a normal silver atom. So it +stays with the other atoms in the silver plate. That's what happens +right along. For every atom which is lost from the positive plate there +is one added to the negative plate. The silver of the positive plate +gradually wastes away and the negative plate gradually gets an extra +coating of silver. + +Every time the battery takes an electron away from the positive plate +and gives it to the negative plate there is added to the negative plate +an atom of silver. If the negative plate is weighed before the battery +is connected and again after the battery is disconnected we can tell how +much silver has been added to it. Suppose the current has been perfectly +steady, that is, the same number of electrons streaming through the +circuit each second. Then if we know how long the current has been +running we can tell how much silver has been deposited each second. + +The law says that if silver is being deposited at the rate of 0.001118 +gram each second then the current is one ampere. That's a small amount +of silver, only about a thousandth part of a gram, and you know that it +takes 28.35 grams to make an ounce. It's a very small amount of silver +but it's an enormous number of atoms. How many? Six billion billion, of +course, for there is deposited one atom for each electron in the stream. + +In my next letter I'll tell you how we measure the pull which batteries +can give to electrons, and then we shall be ready to go on with more +about the audion. + + + + +LETTER 8 + +ELECTRON-MOVING-FORCES + + +(This letter may be omitted on the first reading.) + +DEAR YOUNG MAN: + +I trust you have a fairly good idea that an ampere means a stream of +electrons at a certain definite rate and hence that a current of say 3 +amperes means a stream with three times as many electrons passing along +each second. + +In the third and fourth letters you found out why a battery drives +electrons around a conducting circuit. You also found that there are +several different kinds of batteries. Batteries differ in their +abilities to drive electrons and it is therefore convenient to have some +way of comparing them. We do this by measuring the electron-moving-force +or "electromotive force" which each battery can exert. To express +electromotive force and give the results of our measurements we must +have some unit. The unit we use is called the "volt." + +The volt is defined by law and is based on the suggestions of the same +body of scientists who recommended the ampere of our last letter. They +defined it by telling how to make a particular kind of battery and then +saying that this battery had an electromotive force of a certain number +of volts. One can buy such standard batteries, or standard cells as they +are called, or he can make them for himself. To be sure that they are +just right he can then send them to the Bureau of Standards and have +them compared with the standard cells which the Bureau has. + +I don't propose to tell you much about standard cells for you won't have +to use them until you come to study physics in real earnest. They are +not good for ordinary purposes because the moment they go to work +driving electrons the conditions inside them change so their +electromotive force is changed. They are delicate little affairs and are +useful only as standards with which to compare other batteries. And even +as standard batteries they must be used in such a way that they are not +required to drive any electrons. + +[Illustration: Fig 12] + +Let's see how it can be done. Suppose two boys sit opposite each other +on the floor and brace their feet together. Then with their hands they +take hold of a stick and pull in opposite directions. If both have the +same stick-motive-force the stick will not move. + +Now suppose we connect the negative feet--I mean negative terminals--of +two batteries together as in Fig. 12. Then we connect their positive +terminals together by a wire. In the wire there will be lots of free +electrons ready to go to the positive plate of the battery which pulls +the harder. If the batteries are equal in electromotive force these +electrons will stay right where they are. There will be no stream of +electrons and yet we'll be using one of the batteries to compare with +the other. + +That is all right, you think, but what are we to do when the batteries +are not just equal in e. m. f.? (e. m. f. is code for electromotive +force). I'll tell you, because the telling includes some other ideas +which will be valuable in your later reading. + +[Illustration: Fig 13] + +Suppose we take batteries which aren't going to be injured by being made +to work--storage batteries will do nicely--and connect them in series as +in Fig. 13. When batteries are in series they act like a single stronger +battery, one whose e. m. f. is the sum of the e. m. f.'s of the separate +batteries. Connect these batteries to a long fine wire as in Fig. 14. +There is a stream of electrons along this wire. Next connect the +negative terminal of the standard cell to the negative terminal of the +storage batteries, that is, brace their feet against each other. Then +connect a wire to the positive terminal of the standard cell. This wire +acts just like a long arm sticking out from the positive plate of this +cell. + +[Illustration: Fig 14] + +Touch the end of the wire, which is _p_ of Fig. 14, to some point +as _a_ on the fine wire. Now what do we have? Right at _a_, of +course, there are some free electrons and they hear the calls of both +batteries. If the standard battery, _S_ of the figure, calls the +stronger they go to it. In that case move the end _p_ nearer the +positive plate of the battery _B_, so that it will have a chance to +exert a stronger pull. Suppose we try at _c_ and find the battery +_B_ is there the stronger. Then we can move back to some point, say +_b_, where the pulls are equal. + +To make a test like this we put a sensitive current-measuring instrument +in the wire which leads from the positive terminal of the standard cell. +We also use a long fine wire so that there can never be much of an +electron stream anyway. When the pulls are equal there will be no +current through this instrument. + +As soon as we find out where the proper setting is we can replace +_S_ by some other battery, say _X_, which we wish to compare +with _S_. We find the setting for that battery in the same way as +we just did for _S_. Suppose it is at _d_ in Fig. 14 while the +setting for _S_ was at _b_. We can see at once that _X_ +is stronger than _S_. The question, however, is how much stronger. + +Perhaps it would be better to try to answer this question by talking +about e. m. f.'s. It isn't fair to speak only of the positive plate +which calls, we must speak also of the negative plate which is shooing +electrons away from itself. The idea of e. m. f. takes care of both +these actions. The steady stream of electrons in the fine wire is due to +the e. m. f. of the battery _B_, that is to the pull of the +positive terminal and the shove of the negative. + +If the wire is uniform, that is the same throughout its length, then +each inch of it requires just as much e. m. f. as any other inch. Two +inches require twice the e. m. f. which one inch requires. We know how +much e. m. f. it takes to keep the electron stream going in the part of +the wire from _n_ to _b_. It takes just the e. m. f. of the +standard cell, _S_, because when that had its feet braced at +_n_ it pulled just as hard at _b_ as did the big battery +_B_. + +Suppose the distance _n_ to _d_ (usually written _nd_) is +twice as great as that from _n_ to _b_ (_nb_). That means +that battery _X_ has twice the e. m. f. of battery _S_. You +remember that _X_ could exert the same force through the length of +wire _nd_, as could the large battery. That is twice what cell +_S_ can do. Therefore if we know how many volts to call the e. m. +f. of the standard cell we can say that _X_ has an e. m. f. of +twice as many volts. + +If we measured dry batteries this way we should find that they each had +an e. m. f. of about 1.46 volts. A storage battery would be found to +have about 2.4 volts when fully charged and perhaps as low as 2.1 volts +when we had run it for a while. + +That is the way in which to compare batteries and to measure their e. m. +f.'s, but you see it takes a lot of time. It is easier to use a +"voltmeter" which is an instrument for measuring e. m. f.'s. Here is how +one could be made. + +First there is made a current-measuring instrument which is quite +sensitive, so that its pointer will show a deflection when only a very +small stream of electrons is passing through the instrument. We could +make one in the same way as we made the ammeter of the last letter but +there are other better ways of which I'll tell you later. Then we +connect a good deal of fine wire in series with the instrument for a +reason which I'll tell you in a minute. The next and last step is to +calibrate. + +We know how many volts of e. m. f. are required to keep going the +electron stream between _n_ and _b_--we know that from the e. +m. f. of our standard cell. Suppose then that we connect this new +instrument, which we have just made, to the wire at _n_ and +_b_ as in Fig. 15. Some of the electrons at _n_ which are so +anxious to get away from the negative plate of battery _B_ can now +travel as far as _b_ through the wire of the new instrument. They +do so and the pointer swings around to some new position. Opposite that +we mark the number of volts which the standard battery told us there was +between _n_ and _b_. + +[Illustration: Fig 15] + +If we move the end of the wire from _b_ to _d_ the pointer +will take a new position. Opposite this we mark twice the number of +volts of the standard cell. We can run it to a point _e_ where the +distance _ne_ is one-half _nb_, and mark our scale with half +the number of volts of the standard cell, and so on for other positions +along the wire. That's the way we calibrate a sensitive +current-measuring instrument (with its added wire, of course) so that it +will read volts. It is now a voltmeter. + +If we connect a voltmeter to the battery _X_ as in Fig. 16 the +pointer will tell us the number of volts in the e. m. f. of _X_, +for the pointer will take the same position as it did when the voltmeter +was connected between _n_ and _d_. + +There is only one thing to watch out for in all this. We must be careful +that the voltmeter is so made that it won't offer too easy a path for +electrons to follow. We only want to find how hard a battery can pull an +electron, for that is what we mean by e. m. f. Of course, we must let a +small stream of electrons flow through the voltmeter so as to make the +pointer move. That is why voltmeters of this kind are made out of a long +piece of fine wire or else have a coil of fine wire in series with the +current-measuring part. The fine wire makes a long and narrow path for +the electrons and so there can be only a small stream. Usually we +describe this condition by saying that a voltmeter has a high +resistance. + +[Illustration: Fig 16] + +Fine wires offer more resistance to electron streams than do heavy wires +of the same length. If a wire is the same diameter all along, the longer +the length of it which we use the greater is the resistance which is +offered to an electron stream. + +You will need to know how to describe the resistance of a wire or of any +part of an electric circuit. To do so you tell how many "ohms" of +resistance it has. The ohm is the unit in which we measure the +resistance of a circuit to an electron stream. + +I can show you what an ohm is if I tell you a simple way to measure a +resistance. Suppose you have a wire or coil of wire and want to know its +resistance. Connect it in series with a battery and an ammeter as shown +in Fig. 17. The same electron stream passes through all parts of this +circuit and the ammeter tells us what this stream is in amperes. Now +connect a voltmeter to the two ends of the coil as shown in the figure. +The voltmeter tells in volts how much e. m. f. is being applied to force +the current through the coil. Divide the number of volts by the number +of amperes and the quotient (answer) is the number of ohms of resistance +in the coil. + +[Illustration: Fig 17] + +Suppose the ammeter shows a current of one ampere and the voltmeter an +e. m. f. of one volt. Then dividing 1 by 1 gives 1. That means that the +coil has a resistance of one ohm. It also means one ohm is such a +resistance that one volt will send through it a current of one ampere. +You can get lots of meaning out of this. For example, it means also that +one volt will send a current of one ampere through a resistance of one +ohm. + +How many ohms would the coil have if it took 5 volts to send 2 amperes +through it. Solution: Divide 5 by 2 and you get 2.5. Therefore the coil +would have a resistance of 2.5 ohms. + +Try another. If a coil of resistance three ohms is carrying two amperes +what is the voltage across the terminals of the coil? For 1 ohm it would +take 1 volt to give a current of 1 ampere, wouldn't it? For 3 ohms it +takes three times as much to give one ampere. To give twice this current +would take twice 3 volts. That is, 2 amperes in 3 ohms requires 2x3 +volts. + +Here's one for you to try by yourself. If an e. m. f. of 8 volts is +sending current through a resistance of 2 ohms, how much current is +flowing? Notice that I told the number of ohms and the number of volts, +what are you going to tell? Don't tell just the number; tell how many +and what. + + + + +LETTER 9 + +THE AUDION-CHARACTERISTIC + + +MY DEAR YOUNG STUDENT: + +Although there is much in Letters 7 and 8 which it is well to learn and +to think about, there are only three of the ideas which you must have +firmly grasped to get the most out of this letter which I am now going +to write you about the audion. + +First: Electric currents are streams of electrons. We measure currents +in amperes. To measure a current we may connect into the circuit an +ammeter. + +Second: Electrons move in a circuit when there is an +electron-moving-force, that is an electromotive force or e. m. f. We +measure e. m. f.'s in volts. To measure an e. m. f. we connect a +voltmeter to the two points between which the e. m. f. is active. + +Third: What current any particular e. m. f. will cause depends upon the +circuit in which it is active. Circuits differ in the resistance which +they offer to e. m. f.'s. For any particular e. m. f. (that is for any +given e. m. f.) the resulting current will be smaller the greater the +resistance of the circuit. We measure resistance in ohms. To measure it +we find the quotient of the number of volts applied to the circuit by +the number of amperes which flow. + +In my sixth letter I told you something of how the audion works. It +would be worth while to read again that letter. You remember that the +current in the plate circuit can be controlled by the e. m. f. which is +applied to the grid circuit. There is a relationship between the plate +current and the grid voltage which is peculiar or characteristic to the +tube. So we call such a relationship "a characteristic." Let us see how +it may be found and what it will be. + +Connect an ammeter in the plate- or B-circuit, of the tube so as to +measure the plate-circuit current. You will find that almost all books +use the letter "_I_" to stand for current. The reason is that +scientists used to speak of the "intensity of an electric current" so +that "_I_" really stands for intensity. We use _I_ to stand +for something more than the word "current." It is our symbol for +whatever an ammeter would read, that is for the amount of current. + +[Illustration: Fig 18] + +Another convenience in symbols is this: We shall frequently want to +speak of the currents in several different circuits. It saves time to +use another letter along with the letter _I_ to show the circuit to +which we refer. For example, we are going to talk about the current in +the B-circuit of the audion, so we call that current _I_{B}_. We +write the letter _B_ below the line on which _I_ stands. That +is why we say the _B_ is subscript, meaning "written below." When +you are reading to yourself be sure to read _I_{B}_ as "eye-bee" or +else as "eye-subscript-bee." _I_{B}_ therefore will stand for the +number of amperes in the plate circuit of the audion. In the same way +_I_{a}_ would stand for the current in the filament circuit. + +We are going to talk about e. m. f.'s also. The letter "_E_" stands +for the number of volts of e. m. f. in a circuit. In the filament +circuit the battery has _E_{A}_ volts. In the plate circuit the e. +m. f. is _E_{B}_ volts. If we put a battery in the grid circuit we +can let _E_{C}_ represent the number of volts applied to the +grid-filament or C-circuit. + +The characteristic relation which we are after is one between grid +voltage, that is _E_{C}_, and plate current, that is _I_{B}_. +So we call it the _E_{C}_--_I_{B}_ characteristic. The dash +between the letters is not a subtraction sign but merely a dash to +separate the letters. Now we'll find the "ee-see-eye-bee" +characteristic. + +Connect some small dry cells in series for use in the grid circuit. Then +connect the filament to the middle cell as in Fig. 19. Take the wire +which comes from the grid and put a battery clip on it, then you can +connect the grid anywhere you want along this series of batteries. See +Fig. 18. In the figure this movable clip is represented by an arrow +head. You can see that if it is at _a_ the battery will make the +grid positive. If it is moved to _b_ the grid will be more +positive. On the other hand if the clip is at _o_ there will be no +e. m. f. applied to the grid. If it is at _c_ the grid will be made +negative. + +Between grid and filament there is placed a voltmeter which will tell +how much e. m. f. is applied to the grid, that is, tell the value of +_E_{C}_, for any position whatever of the clip. + +We shall start with the filament heated to a deep red. The manufacturers +of the audion tell the purchaser what current should flow through the +filament so that there will be the proper emission of electrons. There +are easy ways of finding out for one's self but we shall not stop to +describe them. The makers also tell how many volts to apply to the +plate, that is what value _E_{B}_ should have. We could find this +out also for ourselves but we shall not stop to do so. + +[Illustration: Fig 19] + +Now we set the battery clip so that there is no voltage applied to the +grid; that is, we start with _E_{C}_ equal to zero. Then we read the +ammeter in the plate circuit to find the value of _I_{B}_ which +corresponds to this condition of the grid. + +Next we move the clip so as to make the grid as positive as one battery +will make it, that is we move the clip to _a_ in Fig. 19. We now +have a different value of _E_{C}_ and will find a different value +of _I_{B}_ when we read the ammeter. Next move the clip to apply +two batteries to the grid. We get a new pair of values for _E_{C}_ +and _I_{B}_, getting _E_{C}_ from the voltmeter and _I_{B}_ from the +ammeter. As we continue in this way, increasing _E_{C}_, we find that +the current _I_{B}_ increases for a while and then after we have +reached a certain value of _E_{C}_ the current _I_{B}_ stops +increasing. Adding more batteries and making the grid more positive +doesn't have any effect on the plate current. + +[Illustration: Fig 20] + +Before I tell you why this happens I want to show you how to make a +picture of the pairs of values of _E_{C}_ and _I_{B}_ which we +have been reading on the voltmeter and ammeter. + +Imagine a city where all the streets are at right angles and the north +and south streets are called streets and numbered while the east and +west thorofares are called avenues. I'll draw the map as in Fig. 20. +Right through the center of the city goes Main Street. But the people +who laid out the roads were mathematicians and instead of calling it +Main Street they called it "Zero Street." The first street east of Zero +St. we should have called "East First Street" but they called it +"Positive 1 St." and the next beyond "Positive 2 St.," and so on. West +of the main street they called the first street "Negative 1 St." and so +on. + +When they came to name the avenues they were just as precise and +mathematical. They called the main avenue "Zero Ave." and those north of +it "Positive 1 Ave.," "Positive 2 Ave." and so on. Of course, the +avenues south of Zero Ave. they called Negative. + +The Town Council went almost crazy on the subject of numbering; they +numbered everything. The silent policeman which stood at the corner of +"Positive 2 St." and "Positive 1 Ave." was marked that way. Half way +between Positive 2 St. and Positive 3 St. there was a garage which set +back about two-tenths of a block from Positive 1 Ave. The Council +numbered it and called it "Positive 2.5 St. and Positive 1.2 Ave." Most +of the people spoke of it as "Plus 2.5 St. and Plus 1.2 Ave." + +Sometime later there was an election in the city and a new Council was +elected. The members were mostly young electricians and the new Highway +Commissioner was a radio enthusiast. At the first meeting the Council +changed the names of all the avenues to "Mil-amperes"[3] and of all the +streets to "Volts." + +Then the Highway Commissioner who had just been taking a set of +voltmeter and ammeter readings on an audion moved that there should be a +new road known as "Audion Characteristic." He said the road should pass +through the following points: + + Zero Volt and Plus 1.0 Mil-ampere + Plus 2.0 Volts and Plus 1.7 Mil-amperes + Plus 4.0 Volts and Plus 2.6 Mil-amperes + Plus 6.0 Volts and Plus 3.4 Mil-amperes + Plus 8.0 Volts and Plus 4.3 Mil-amperes + +And so on. Fig. 21 shows the new road. + +[Illustration: Fig 21] + +One member of the Council jumped up and said "But what if the grid is +made negative?" The Commissioner had forgotten to see what happened so +he went home to take more readings. + +He shifted the battery clip along, starting at _c_ of Fig. 22. At +the next meeting of the Council he brought in the following list of +readings and hence of points on his proposed road. + + Minus 1.0 Volts and Plus 0.6 Mil-ampere + " 2.0 " " " 0.4 " " + " 3.0 " " " 0.2 " " + " 4.0 " " " 0.1 " " + " 5.0 " " " 0.0 " " + +Then he showed the other members of the Council on the map of Fig. 23 +how the Audion Characteristic would look. + +[Illustration: Fig 22] + +There was considerable discussion after that and it appeared that +different designs and makes of audions would have different +characteristic curves. They all had the same general form of curve but +they would pass through different sets of points depending upon the +design and upon the B-battery voltage. It was several meetings later, +however, before they found out what effects were due to the form of the +curve. Right after this they found that they could get much better +results with their radio sets. + +Now look at the audion characteristic. Making the grid positive, that is +going on the positive side of the zero volts in our map, makes the plate +current larger. You remember that I told you in Letter 6 how the grid, +when positive, helped call electrons away from the filament and so made +a larger stream of electrons in the plate circuit. The grid calls +electrons away from the filament. It can't call them out of it; they +have to come out themselves as I explained to you in the fifth letter. + +[Illustration: Fig 23] + +You can see that as we make the grid more and more positive, that is, +make it call louder and louder, a condition will be reached where it +won't do it any good to call any louder, for it will already be getting +all the electrons away from the filament just as fast as they are +emitted. Making the grid more positive after that will not increase the +plate current any. That's why the characteristic flattens off as you see +at high values of grid voltage. + +The arrangement which we pictured in Fig. 22 for making changes in the +grid voltage is simple but it doesn't let us change the voltage by less +than that of a single battery cell. I want to show you a way which will. +You'll find it very useful to know and it is easily understood for it is +something like the arrangement of Fig. 14 in the preceding letter. + +[Illustration: Fig 24] + +Connect the cells as in Fig. 24 to a fine wire. About the middle of this +wire connect the filament. As before use a clip on the end of the wire +from the grid. If the grid is connected to _a_ in the figure there +is applied to the grid circuit that part of the e. m. f. of the battery +which is active in the length of wire between _o_ and _a_. The +point _a_ is nearer the positive plate of the battery than is the +point _o_. So the grid will be positive and the filament negative. + +On the other hand, if the clip is connected at _b_ the grid will be +negative with respect to the filament. We can, therefore, make the grid +positive or negative depending on which side of _o_ we connect the +clip. How large the e. m. f. is which will be applied to the grid +depends, of course, upon how far away from _o_ the clip is +connected. + +Suppose you took the clip in your hand and slid it along in contact with +the wire, first from _o_ to _a_ and then back again through +_o_ to _b_ and so on back and forth. You would be making the +grid _alternately_ positive and negative, wouldn't you? That is, +you would be applying to the grid an e. m. f. which increases to some +positive value and then, decreasing to zero, _reverses_, and +increases just as much, only to decrease to zero, where it started. If +you do this over and over again, taking always the same time for one +round trip of the clip you will be impressing on the grid circuit an +"_alternating e. m. f._" + +What's going to happen in the plate circuit? When there is no e. m. f. +applied to the grid circuit, that is when the grid potential +(possibilities) is zero, there is a definite current in the plate +circuit. That current we can find from our characteristic of Fig. 23 for +it is where the curve crosses Zero Volts. As the grid becomes positive +the current rises above this value. When the grid is made negative the +current falls below this value. The current, _I_{B}_, then is made +alternately greater and less than the current when _E_{C}_ is zero. + +You might spend a little time thinking over this, seeing what happens +when an alternating e. m. f. is applied to the grid of an audion, for +that is going to be fundamental to our study of radio. + +[Footnote 3: A mil-ampere is a thousandth of an ampere just as a +millimeter is a thousandth of a meter.] + + + + +LETTER 10 + +CONDENSERS AND COILS + + +DEAR SON: + +In the last letter we learned of an alternating e. m. f. The way of +producing it, which I described, is very crude and I want to tell how to +make the audion develop an alternating e. m. f. for itself. That is what +the audion does in the transmitting set of a radio telephone. But an +audion can't do it all alone. It must have associated with it some coils +and a condenser. You know what I mean by coils but you have yet to learn +about condensers. + +A condenser is merely a gap in an otherwise conducting circuit. It's a +gap across which electrons cannot pass so that if there is an e. m. f. +in the circuit, electrons will be very plentiful on one side of the gap +and scarce on the other side. If there are to be many electrons waiting +beside the gap there must be room for them. For that reason we usually +provide waiting-rooms for the electrons on each side of the gap. Metal +plates or sheets of tinfoil serve nicely for this purpose. Look at Fig. +25. You see a battery and a circuit which would be conducting except for +the gap at _C_. On each side of the gap there is a sheet of metal. +The metal sheets may be separated by air or mica or paraffined paper. +The combination of gap, plates, and whatever is between, provided it is +not conducting, is called a condenser. + +Let us see what happens when we connect a battery to a condenser as in +the figure. The positive terminal of the battery calls electrons from +one plate of the condenser while the negative battery-terminal drives +electrons away from itself toward the other plate of the condenser. One +plate of the condenser, therefore, becomes positive while the other +plate becomes negative. + +[Illustration: Fig 25] + +You know that this action of the battery will go on until there are so +many electrons in the negative plate of the condenser that they prevent +the battery from adding any more electrons to that plate. The same thing +happens at the other condenser plate. The positive terminal of the +battery calls electrons away from the condenser plate which it is making +positive until so many electrons have left that the protons in the atoms +of the plate are calling for electrons to stay home just as loudly and +effectively as the positive battery-terminal is calling them away. + +When both these conditions are reached--and they are both reached at the +same time--then the battery has to stop driving electrons around the +circuit. The battery has not enough e. m. f. to drive any more +electrons. Why? Because the condenser has now just enough e. m. f. with +which to oppose the battery. + +It would be well to learn at once the right words to use in describing +this action. We say that the battery sends a "charging current" around +its circuit and "charges the condenser" until it has the same e. m. f. +When the battery is first connected to the condenser there is lots of +space in the waiting-rooms so there is a great rush or surge of +electrons into one plate and away from the other. Just at this first +instant the charging current, therefore, is large but it decreases +rapidly, for the moment electrons start to pile up on one plate of the +condenser and to leave the other, an e. m. f. builds up on the +condenser. This e. m. f., of course, opposes that of the battery so that +the net e. m. f. acting to move electrons round the circuit is no longer +that of the battery, but is the difference between the e. m. f. of the +battery and that of the condenser. And so, with each added electron, the +e. m. f. of the condenser increases until finally it is just equal to +that of the battery and there is no net e. m. f. to act. + +What would happen if we should then disconnect the battery? The +condenser would be left with its extra electrons in the negative plate +and with its positive plate lacking the same number of electrons. That +is, the condenser would be left charged and its e. m. f. would be of +the same number of volts as the battery. + +[Illustration: Fig 26] + +Now suppose we connect a short wire between the plates of the condenser +as in Fig. 26. The electrons rush home from the negative plate to the +positive plate. As fast as electrons get home the e. m. f. decreases. +When they are all back the e. m. f. has been reduced to zero. Sometimes +we say that "the condenser discharges." The "discharge current" starts +with a rush the moment the conducting path is offered between the two +plates. The e. m. f. of the condenser falls, the discharge current grows +smaller, and in a very short time the condenser is completely +discharged. + +[Illustration: Fig 27] + +That's what happens when there is a short conducting path for the +discharge current. If that were all that could happen I doubt if there +would be any radio communication to-day. But if we connect a coil of +wire between two plates of a charged condenser, as in Fig. 27, then +something of great interest happens. To understand you must know +something more about electron streams. + +Suppose we should wind a few turns of wire on a cylindrical core, say on +a stiff cardboard tube. We shall use insulated wire. Now start from one +end of the coil, say _a_, and follow along the coiled wire for a +few turns and then scratch off the insulation and solder onto the coil +two wires, _b_, and _c_, as shown in Fig. 28. The further end +of the coil we shall call _d_. Now let's arrange a battery and +switch so that we can send a current through the part of the coil +between _a_ and _b_. Arrange also a current-measuring instrument so as +to show if any current is flowing in the part of the coil between _c_ +and _d_. For this purpose we shall use a kind of current-measuring +instrument which I have not yet explained. It is different from the +hot-wire type described in Letter 7 for it will show in which direction +electrons are streaming through it. + +The diagram of Fig. 28 indicates the apparatus of our experiment. When +we close the switch, _S_, the battery starts a stream of electrons +from _a_ towards _b_. Just at that instant the needle, or +pointer, of the current instrument moves. The needle moves, and thus +shows a current in the coil _cd_; but it comes right back again, +showing that the current is only momentary. Let's say this again in +different words. The battery keeps steadily forcing electrons through +the circuit _ab_ but the instrument in the circuit _cd_ shows +no current in that circuit except just at the instant when current +starts to flow in the neighboring circuit _ab_. + +[Illustration: Fig 28] + +One thing this current-measuring instrument tells us is the direction of +the electron stream through itself. It shows that the momentary stream +of electrons goes through the coil from _d_ to _c_, that is in +the opposite direction to the stream in the part _ab_. + +Now prepare to do a little close thinking. Read over carefully all I +have told you about this experiment. You see that the moment the battery +starts a stream of electrons from _a_ towards _b_, something causes +a momentary, that is a temporary, movement of electrons from _d_ to +_c_. We say that starting a stream of electrons from _a_ to _b_ sets +up or "induces" a stream of electrons from _d_ to _c_. + +What will happen then if we connect the battery between _a_ and _d_ +as in Fig. 29? Electrons will start streaming away from _a_ towards +_b_, that is towards _d_. But that means there will be a momentary +stream from _d_ towards _c_, that is towards _a_. Our stream from +the battery causes this oppositely directed stream. In the usual +words we say it "induces" in the coil an opposing stream of electrons. +This opposing stream doesn't last long, as we saw, but while it does +last it hinders the stream which the battery is trying to establish. + +[Illustration: Fig 29] + +The stream of electrons which the battery causes will at first meet an +opposition so it takes a little time before the battery can get the +full-sized stream of electrons flowing steadily. In other words a +current in a coil builds up slowly, because while it is building up it +induces an effect which opposes somewhat its own building up. + +Did you ever see a small boy start off somewhere, perhaps where he +shouldn't be going, and find his conscience starting to trouble him at +once. For a time he goes a little slowly but in a moment or two his +conscience stops opposing him and he goes on steadily at his full pace. +When he started he stirred up his conscience and that opposed him. +Nobody else was hindering his going. It was all brought about by his +own actions. The opposition which he met was "self-induced." He was +hindered at first by a self-induced effect of his own conscience. If he +was a stream of electrons starting off to travel around the coil we +would say that he was opposed by a self-induced e. m. f. And any path +in which such an effect will be produced we say has "self-inductance." +Usually we shorten this term and speak of "inductance." + +There is another way of looking at it. We know habits are hard to form +and equally hard to break. It's hard to get electrons going around a +coil and the self-inductance of a circuit tells us how hard it is. The +harder it is the more self-inductance we say that the coil or circuit +has. Of course, we need a unit in which to measure self-inductance. The +unit is called the "henry." But that is more self-inductance than we can +stand in most radio circuits, so we find it convenient to measure in +smaller units called "mil-henries" which are thousandths of a henry. + +You ought to know what a henry[4] is, if we are to use the word, but it +isn't necessary just now to spend much time on it. The opposition which +one's self-induced conscience offers depends upon how rapidly one +starts. It's volts which make electrons move and so the conscience which +opposes them will be measured in volts. Therefore we say that a coil has +one henry of inductance when an electron stream which is increasing one +ampere's worth each second stirs up in the coil a conscientious +objection of one volt. Don't try to remember this now; you can come back +to it later. + +There is one more effect of inductance which we must know before we can +get very far with our radio. Suppose an electron stream is flowing +through a coil because a battery is driving the electrons along. Now let +the battery be removed or disconnected. You'd expect the electron stream +to stop at once but it doesn't. It keeps on for a moment because the +electrons have got the habit. + +[Illustration: Fig 28] + +If you look again at Fig. 28 you will see what I mean. Suppose the +switch is closed and a steady stream of electrons is flowing through the +coil from _a_ to _b_. There will be no current in the other +part of the coil. Now open the switch. There will be a motion of the +needle of the current-measuring instrument, showing a momentary current. +The direction of this motion, however, shows that the momentary stream +of electrons goes through the coil from _c_ to _d_. + +Do you see what this means? The moment the battery is disconnected there +is nothing driving the electrons in the part _ab_ and they slow +down. Immediately, and just for an instant, a stream of electrons starts +off in the part _cd_ in the same direction as if the battery was +driving them along. + +Now look again at Fig. 29. If the battery is suddenly disconnected there +is a momentary rush of electrons in the same direction as the battery +was driving them. Just as the self-inductance of a coil opposes the +starting of a stream of electrons, so it opposes the stopping of a +stream which is already going. + +[Illustration: Fig 29] + +So far we haven't said much about making an audion produce alternating +e. m. f.'s and thus making it useful for radio-telephony. Before radio +was possible all these things that I have just told you, and some more +too, had to be known. It took hundreds of good scientists years of +patient study and experiment to find out those ideas about electricity +which have made possible radio-telephony. + +Two of these ideas are absolutely necessary for the student of +radio-communication. First: A condenser is a gap in a circuit where +there are waiting-rooms for the electrons. Second: Electrons form +habits. It's hard to get them going through a coil of wire, harder than +through a straight wire, but after they are going they don't like to +stop. They like it much less if they are going through a coil instead of +a straight wire. + +In my next letter I'll tell you what happens when we have a coil and a +condenser together in a circuit. + +[Footnote 4: The "henry" has nothing to do with a well-known automobile. +It was named after Joseph Henry, a professor years ago at Princeton +University.] + + + + +LETTER 11 + +A "C-W" TRANSMITTER + + +DEAR SON: + +[Illustration: Fig 28] + +Let's look again at the coils of Fig. 28 which we studied in the last +letter. I have reproduced them here so you won't have to turn back. When +electrons start from _a_ towards _b_ there is a momentary +stream of electrons from _d_ towards _c_. If the electron +stream through _ab_ were started in the opposite direction, that is +from _b_ to _a_ the induced stream in the coil _cd_ would +be from _c_ towards _d_. + +[Illustration: Fig 30] + +It all reminds me of two boys with a hedge or fence between them as in +Fig. 30. One boy is after the other. Suppose you were being chased; you +know what you'd do. If your pursuer started off with a rush towards one +end of the hedge you'd "beat it" towards the other. But if he started +slowly and cautiously you would start slowly too. You always go in the +opposite direction, dodging back and forth along the paths which you are +wearing in the grass on opposite sides of the hedge. If he starts to the +right and then slows up and starts back, you will start to your right, +slow up, and start back. Suppose he starts at the center of the hedge. +First he dodges to the right, and then back through the center as far to +the left, then back again and so on. You follow his every change. + +[Illustration: Fig 31] + +I am going to make a picture of what you two do. Let's start with the +other fellow. He dodges or alternates back and forth. Some persons would +say he "oscillates" back and forth in the same path. As he does so he +induces you to move. I am on your side of the hedge with a +moving-picture camera. My camera catches both of you. Fig. 31 shows the +way the film would look if it caught only your heads. The white circle +represents the tow-head on my side of the hedge and the black circle, +young Brown who lives next door. Of course, the camera only catches you +each time the shutter opens but it is easy to draw a complete picture of +what takes place as time goes on. See Fig. 32. + +[Illustration: Fig 32] + +Now suppose you are an electron in coil _cd_ of Fig. 33 and +"Brownie" is one in coil _ab_. Your motions are induced by his. +What's true of you two is true of all the other electrons. I have +separated the coils a little in this sketch so that you can think of a +hedge between. I don't know how one electron can affect another on the +opposite side of this hedge but it can. And I don't know anything really +about the hedge, which is generally called "the ether." The hedge isn't +air. The effect would be the same if the coils were in a vacuum. The +"ether" is just a name for whatever is left in the space about us when +we have taken out everything which we can see or feel--every molecule, +every proton and every electron. + +[Illustration: Fig 33] + +Why and how electrons can affect one another when they are widely +separated is one of the great mysteries of science. We don't know any +more about it than about why there are electrons. Let's accept it as a +fundamental fact which we can't as yet explain. + +[Illustration: Fig 34] + +And now we can see how to make an audion produce an alternating current +or as we sometimes say "make an audion oscillator." We shall set up an +audion with its A-battery as in Fig. 34. Between the grid and the +filament we put a coil and a condenser. Notice that they are in +parallel, as we say. In the plate-filament circuit we connect the +B-battery and a switch, _S_, and another coil. This coil in the +plate circuit of the audion we place close to the other coil so that the +two coils are just like the coils _ab_ and _cd_ of which I +have been telling you. The moment any current flows in coil _ab_ +there will be a current flow in the coil _cd_. (An induced electron +stream.) Of course, as long as the switch in the B-battery is open no +current can flow. + +The moment the switch _S_ is closed the B-battery makes the plate +positive with respect to the filament and there is a sudden surge of +electrons round the plate circuit and through the coil from _a_ to +_b_. You know what that does to the coil _cd_. It induces an +electron stream from _d_ towards _c_. Where do these electrons +come from? Why, from the grid and the plate 1 of the condenser. Where do +they go? Most of them go to the waiting-room offered by plate 2 of the +condenser and some, of course, to the filament. What is the result? The +grid becomes positive and the filament negative. + +[Illustration: Fig 35] + +This is the crucial moment in our study. Can you tell me what is going +to happen to the stream of electrons in the plate circuit? Remember that +just at the instant when we closed the switch the grid was neither +positive nor negative. We were at the point of zero volts on the audion +characteristic of Fig. 35. When we close the switch the current in the +plate circuit starts to jump from zero mil-amperes to the number of +mil-amperes which represents the point where Zero Volt St. crosses +Audion Characteristic. But this jump in plate current makes the grid +positive as we have just seen. So the grid will help the plate call +electrons and that will make the current in the plate circuit still +larger, that is, result in a larger stream of electrons from _a_ to +_b_. + +This increase in current will be matched by an increased effect in the +coil _cd_, for you remember how you and "Brownie" behaved. And that +will pull more electrons away from plate 1 of the condenser and send +them to the waiting-room of 2. All this makes the grid more positive and +so makes it call all the more effectively to help the plate move +electrons. + +[Illustration: Pl. V.--Variometer (top) and Variable Condenser (bottom) +of the General Radio Company. Voltmeter and Ammeter of the Weston +Instrument Company.] + +We "started something" that time. It's going on all by itself. The grid +is getting more positive, the plate current is getting bigger, and so +the grid is getting more positive and the plate current still bigger. Is +it ever going to stop? Yes. Look at the audion characteristic. There +comes a time when making the grid a little more positive won't have any +effect on the plate-circuit current. So the plate current stops +increasing. + +There is nothing now to keep pulling electrons away from plate 1 and +crowding them into waiting-room 2. Why shouldn't the electrons in this +waiting-room go home to that of plate 1? There is now no reason and so +they start off with a rush. + +Of course, some of them came from the grid and as fast as electrons get +back to the grid it becomes less and less positive. As the grid becomes +less and less positive it becomes less and less helpful to the plate. + +If the grid doesn't help, the plate alone can't keep up this stream of +electrons. All the plate can do by itself is to maintain the current +represented by the intersection of zero volts and the audion +characteristic. The result is that the current in the plate circuit, +that is, of course, the current in coil _ab_, becomes gradually less. +About the time all the electrons, which had left the grid and plate 1 +of the condenser, have got home the plate current is back to the value +corresponding to _E_{C}_=_0_. + +The plate current first increases and then decreases, but it doesn't +stop decreasing when it gets back to zero-grid value. And the reason is +all due to the habit forming tendencies of electrons in coils. To see +how this comes about, let's tell the whole story over again. In other +words let's make a review and so get a sort of flying start. + +[Illustration: Fig 34] + +When we close the battery switch, _S_ in Fig. 34, we allow a +current to flow in the plate circuit. This current induces a current in +the coil _cd_ and charges the condenser which is across it, making +plate 1 positive and plate 2 negative. A positive grid helps the plate +so that the current in the plate circuit builds up to the greatest +possible value as shown by the audion characteristic. That's the end of +the increase in current. Now the condenser discharges, sending electrons +through the coil _cd_ and making the grid less positive until +finally it is at zero potential, that is neither positive nor negative. + +While the condenser is discharging the electrons in the coil _cd_ +get a habit of flowing from _c_ toward _d_, that is from plate +2 to plate 1. If it wasn't for this habit the electron stream in +_cd_ would stop as soon as the grid had reduced to zero voltage. +Because of the habit, however, a lot of electrons that ought to stay on +plate 2 get hurried along and land on plate 1. It is a little like the +old game of "crack the whip." Some electrons get the habit and can't +stop quickly enough so they go tumbling into waiting-room 1 and make it +negative. + +That means that the condenser not only discharges but starts to get +charged in the other direction with plate 1 negative and plate 2 +positive. The grid feels the effect of all this, because it gets extra +electrons if plate 1 gets them. In fact the voltage effective between +grid and filament is always the voltage between the plates of the +condenser. + +The audion characteristic tells us what is the result. As the grid +becomes negative it opposes the plate, shooing electrons back towards +the filament and reducing the plate current still further. But you have +already seen in my previous letter what happens when we reduce the +current in coil _ab_. There is then induced in coil _cd_ an +electron stream from _c_ to _d_. This induced current is in +just the right direction to send more electrons into waiting-room 1 and +so to make the grid still more negative. And the more negative the grid +gets the smaller becomes the plate current until finally the plate +current is reduced to zero. Look at the audion characteristic again and +see that making the grid sufficiently negative entirely stops the plate +current. + +When the plate current stops, the condenser in the grid circuit is +charged, with plate 1 negative and 2 positive. It was the plate current +which was the main cause of this change for it induced the charging +current in coil _cd_. So, when the plate current becomes zero there +is nothing to prevent the condenser from discharging. + +Its discharge makes the grid less and less negative until it is zero +volts and there we are--back practically where we started. The plate +current is increasing and the grid is getting positive, and we're off on +another "cycle" as we say. During a cycle the plate current increases to +a maximum, decreases to zero, and then increases again to its initial +value. + +[Illustration: Fig 36] + +This letter has a longer continuous train of thought than I usually ask +you to follow. But before I stop I want to give you some idea of what +good this is in radio. + +What about the current which flows in coil _cd_? It's an +alternating current, isn't it? First the electrons stream from _d_ +towards _c_, and then back again from _c_ towards _d_. + +Suppose we set up another coil like _CD_ in Fig. 36. It would have +an alternating current induced in it. If this coil was connected to an +antenna there would be radio waves sent out. The switch _S_ could +be used for a key and kept closed longer or shorter intervals depending +upon whether dashes or dots were being set. I'll tell you more about +this later, but in this diagram are the makings of a "C-W Transmitter," +that is a "continuous wave transmitter" for radio-telegraphy. + +It would be worth while to go over this letter again using a pencil and +tracing in the various circuits the electron streams which I have +described. + + + + +LETTER 12 + +INDUCTANCE AND CAPACITY + + +DEAR SIR: + +In the last letter I didn't stop to draw you a picture of the action of +the audion oscillator which I described. I am going to do it now and you +are to imagine me as using two pencils and drawing simultaneously two +curves. One curve shows what happens to the current in the plate +circuit. The other shows how the voltage of the grid changes. Both +curves start from the instant when the switch is closed; and the two +taken together show just what happens in the tube from instant to +instant. + +Fig. 37 shows the two curves. You will notice how I have drawn them +beside and below the audion characteristic. The grid voltage and the +plate current are related, as I have told you, and the audion +characteristic is just a convenient way of showing the relationship. If +we know the current in the plate circuit we can find the voltage of the +grid and vice versa. + +As time goes on, the plate current grows to its maximum and decreases to +zero and then goes on climbing up and down between these two extremes. +The grid voltage meanwhile is varying alternately, having its maximum +positive value when the plate current is a maximum and its maximum +negative value when the plate current is zero. Look at the two curves +and see this for yourself. + +[Illustration: Fig 37] + +Now I want to tell you something about how fast these oscillations +occur. We start by learning two words. One is "cycle" with which you are +already partly familiar and the other is "frequency." Take cycle first. +Starting from zero the current increases to a maximum, decreases to +zero, and is ready again for the same series of changes. We say the +current has passed through "a cycle of values." It doesn't make any +difference where we start from. If we follow the current through all its +different values until we are back at the same value as we started with +and ready to start all over, then we have followed through a cycle of +values. + +Once you get the idea of a cycle, and the markings on the curves in Fig. +31 will help you to understand, then the other idea is easy. By +"frequency" we mean the number of cycles each second. The electric +current which we use in lighting our house goes through sixty cycles a +second. That means the current reverses its direction 120 times a +second. + +In radio we use alternating currents which have very high frequencies. +In ship sets the frequency is either 500,000 or 1,000,000 cycles per +second. Amateur transmitting sets usually have oscillators which run at +well over a million cycles per second. The longer range stations use +lower frequencies. + +You'll find, however, that the newspaper announcements of the various +broadcast stations do not tell the frequency but instead tell the "wave +length." I am not going to stop now to explain what that means but I am +going to give you a simple rule. Divide 300,000,000 by the "wave length" +and you'll have the frequency. For example, ships are supposed to use +wave lengths of 300 meters or 600 meters. Dividing three hundred million +by three hundred gives one million and that is one of the frequencies +which I told you were used by ship sets. Dividing by six hundred gives +500,000 or just half the frequency. You can remember that sets +transmitting with long waves have low frequencies, but sets with short +waves have high frequencies. The frequency and the wave length don't +change in the same way. They change in opposite ways or inversely, as we +say. The higher the frequency the shorter the wave length. + +I'll tell you about wave lengths later. First let's see how to control +the frequency of an audion oscillator like that of Fig. 38. + +[Illustration: Fig 38] + +It takes time to get a full-sized stream going through a coil because of +the inductance of the coil. That you have learned. And also it takes +time for such a current to stop completely. Therefore, if we make the +inductance of the coil small, keeping the condenser the same, we shall +make the time required for the current to start and stop smaller. That +will mean a higher frequency for there will be more oscillations each +second. One rule, then, for increasing the frequency of an audion +oscillator is to decrease the inductance. + +Later in this letter I shall tell you how to increase or decrease the +inductance of a coil. Before I do so, however, I want to call your +attention to the other way in which we can change the frequency of an +audion oscillator. + +Let's see how the frequency will depend upon the capacity of the +condenser. If a condenser has a large capacity it means that it can +accommodate in its waiting-room a large number of electrons before the +e. m. f. of the condenser becomes large enough to stop the stream of +electrons which is charging the condenser. If the condenser in the grid +circuit of Fig. 38 is of large capacity it means that it must receive in +its upper waiting-room a large number of electrons before the grid will +be negative enough to make the plate current zero. Therefore, the +charging current will have to flow a long time to store up the necessary +number of electrons. + +You will get the same idea, of course, if you think about the electrons +in the lower room. The current in the plate circuit will not stop +increasing until the voltage of the grid has become positive enough to +make the plate current a maximum. It can't do that until enough +electrons have left the upper room and been stored away in the lower. +Therefore the charging current will have to flow for a long time if the +capacity is large. We have, therefore, the other rule for increasing the +frequency of an audion oscillator, that is, decrease the capacity. + +These rules can be stated the other way around. To decrease the +frequency we can either increase the capacity or increase the inductance +or do both. + +But what would happen if we should decrease the capacity and increase +the inductance? Decreasing the capacity would make the frequency higher, +but increasing the inductance would make it lower. What would be the net +effect? That would depend upon how much we decreased the capacity and +how much we increased the inductance. It would be possible to decrease +the capacity and then if we increased the inductance just the right +amount to have no change in the frequency. No matter how large or how +small we make the capacity we can always make the inductance such that +there isn't any change in frequency. I'll give you a rule for this, +after I have told you some more things about capacities and inductances. + +First as to inductances. A short straight wire has a very small +inductance, indeed. The longer the wire the larger will be the +inductance but unless the length is hundreds of feet there isn't much +inductance anyway. A coiled wire is very different. + +A coil of wire will have more inductance the more turns there are to it. +That isn't the whole story but it's enough for the moment. Let's see +why. The reason why a stream of electrons has an opposing conscience +when they are started off in a coil of wire is because each electron +affects every other electron which can move in a parallel path. Look +again at the coils of Figs. 28 and 29 which we discussed in the tenth +letter. Those sketches plainly bring out the fact that the electrons in +part _cd_ travel in paths which are parallel to those of the +electrons in part _ab_. + +[Illustration: Fig 39] + +If we should turn these coils as in Fig. 39 so that all the paths in +_cd_ are at right angles to those in _ab_ there wouldn't be +any effect in _cd_ when a current in _ab_ started or stopped. +Look at the circuit of the oscillating audion in Fig. 38. If we should +turn these coils at right angles to each other we would stop the +oscillation. Electrons only influence other electrons which are in +parallel paths. + +When we want a large inductance we wind the coil so that there are many +parallel paths. Then when the battery starts to drive an electron along, +this electron affects all its fellows who are in parallel paths and +tries to start them off in the opposite direction to that in which it is +being driven. The battery, of course, starts to drive all the electrons, +not only those nearest its negative terminal but those all along the +wire. And every one of these electrons makes up for the fact that the +battery is driving it along by urging all its fellows in the opposite +direction. + +It is not an exceptional state of affairs. Suppose a lot of boys are +being driven out of a yard where they had no right to be playing. +Suppose also that a boy can resist and lag back twice as much if some +other boy urges him to do so. Make it easy and imagine three boys. The +first boy lags back not only on his own account but because of the +urging of the other boys. That makes him three times as hard to start as +if the other boys didn't influence him. The same is true of the second +boy and also of the third. The result is the unfortunate property owner +has nine times as hard a job getting that gang started as if only one +boy were to be dealt with. If there were two boys it would be four times +as hard as for one boy. If there were four in the group it would be +sixteen times, and if five it would be twenty-five times. The difficulty +increases much more rapidly than the number of boys. + +Now all we have to do to get the right idea of inductance is to think of +each boy as standing for the electrons in one turn of the coil. If there +are five turns there will be twenty-five times as much inductance, as +for a single turn; and so on. You see that we can change the inductance +of a coil very easily by changing the number of turns. + +I'll tell you two things more about inductance because they will come in +handy. The first is that the inductance will be larger if the turns are +large circles. You can see that for yourself because if the circles were +very small we would have practically a straight wire. + +The other fact is this. If that property owner had been an electrical +engineer and the boys had been electrons he would have fixed it so that +while half of them said, "Aw, don't go; he can't put you off"; the other +half would have said "Come on, let's get out." If he did that he would +have a coil without any inductance, that is, he would have only the +natural inertia of the electrons to deal with. We would say that he had +made a coil with "pure resistance" or else that he had made a +"non-inductive resistance." + +[Illustration: Fig 40] + +How would he do it? Easy enough after one learns how, but quite +ingenious. Take the wire and fold it at the middle. Start with the +middle and wind the coil with the doubled wire. Fig. 40 shows how the +coil would look and you can see that part of the way the electrons are +going around the coil in one direction and the rest of the way in the +opposite direction. It is just as if the boys were paired off, a +"goody-goody" and a "tough nut" together. They both shout at once +opposite advice and neither has any effect. + +I have told you all except one of the ways in which we can affect the +inductance of a circuit. You know now all the methods which are +important in radio. So let's consider how to make large or small +capacities. + +First I want to tell you how we measure the capacity of a condenser. We +use units called "microfarads." You remember that an ampere means an +electron stream at the rate of about six billion billion electrons a +second. A millionth of an ampere would, therefore, be a stream at the +rate of about six million million electrons a second--quite a sizable +little stream for any one who wanted to count them as they went by. If a +current of one millionth of an ampere should flow for just one second +six million million electrons would pass along by every point in the +path or circuit. + +That is what would happen if there weren't any waiting-rooms in the +circuit. If there was a condenser then that number of electrons would +leave one waiting-room and would enter the other. Well, suppose that +just as the last electron of this enormous number[5] entered its +waiting-room we should know that the voltage of the condenser was just +one volt. Then we would say that the condenser had a capacity of one +microfarad. If it takes half that number to make the condenser oppose +further changes in the contents of its waiting-rooms, with one volt's +worth of opposition, that is, one volt of e. m. f., then the condenser +has only half a microfarad of capacity. The number of microfarads of +capacity (abbreviated mf.) is a measure of how many electrons we can get +away from one plate and into the other before the voltage rises to one +volt. + +What must we do then to make a condenser with large capacity? Either of +two things; either make the waiting-rooms large or put them close +together. + +If we make the plates of a condenser larger, keeping the separation +between them the same, it means more space in the waiting-rooms and +hence less crowding. You know that the more crowded the electrons become +the more they push back against any other electron which some battery is +trying to force into their waiting-room, that is the higher the e. m. f. +of the condenser. + +The other way to get a larger capacity is to bring the plates closer +together, that is to shorten the gap. Look at it this way: The closer +the plates are together the nearer home the electrons are. Their home is +only just across a little gap; they can almost see the electronic games +going on around the nuclei they left. They forget the long round-about +journey they took to get to this new waiting-room and they crowd over to +one side of this room to get just as close as they can to their old +homes. That's why it's always easier, and takes less voltage, to get the +same number of electrons moved from one plate to the other of a +condenser which has only a small space between plates. It takes less +voltage and that means that the condenser has a smaller e. m. f. for the +same number of electrons. It also means that before the e. m. f. rises +to one volt we can get more electrons moved around if the plates are +close together. And that means larger capacity. + +There is one thing to remember in all this: It doesn't make any +difference how thick the plates are. It all depends upon how much +surface they have and how close together they are. Most of the electrons +in the plate which is being made negative are way over on the side +toward their old homes, that is, toward the plate which is being made +positive. And most of the homes, that is, atoms which have lost +electrons, are on the side of the positive plate which is next to the +gap. That's why I said the electrons could almost see their old homes. + +[Illustration: Fig 41] + +All this leads to two very simple rules for building condensers. If you +have a condenser with too small a capacity and want one, say, twice as +large, you can either use twice as large plates or bring the plates you +already have twice as close together; that is, make the gap half as +large. Generally, of course, the gap is pretty well fixed. For example, +if we make a condenser by using two pieces of metal and separating them +by a sheet of mica we don't want the job of splitting the mica. So we +increase the size of the plates. We can do that either by using larger +plates or other plates and connecting it as in Fig. 41 so that the total +waiting-room space for electrons is increased. + +[Illustration: Pl. VI.--Low-power Transmitting Tube, U V 202 +(Courtesy of Radio Corporation of America).] + +[Illustration: Fig 42] + +If you have got these ideas you can understand how we use both sides of +the same plate in some types of condensers. Look at Fig. 42. There are +two plates connected together and a third between them. Suppose +electrons are pulled from the outside plates and crowded into the middle +plate. Some of them go on one side and some on the other, as I have +shown. The negative signs indicate electrons and the plus signs their +old homes. If we use more plates as in Fig. 43 we have a larger +capacity. + +[Illustration: Fig 43] + +[Illustration: Fig 44] + +What if we have two plates which are not directly opposite one another, +like those of Fig. 44? What does the capacity depend upon? Imagine +yourself an electron on the negative plate. Look off toward the positive +plate and see how big it seems to you. The bigger it looks the more +capacity the condenser has. When the plates are right opposite one +another the positive plate looms up pretty large. But if they slide +apart you don't see so much of it; and if it is off to one side about +all you see is the edge. If you can't see lots of atoms which have lost +electrons and so would make good homes for you, there is no use of your +staying around on that side of the plate; you might just as well be +trying to go back home the long way which you originally came. + +That's why in a variable plate condenser there is very little capacity +when no parts of the plates are opposite each other, and there is the +greatest capacity when they are exactly opposite one another. + +[Illustration: Fig 45] + +While we are at it we might just as well clean up this whole business of +variable capacities and inductances by considering two ways in which to +make a variable inductance. Fig. 45 shows the simplest way but it has +some disadvantages which I won't try now to explain. We make a long coil +and then take off taps. We can make connections between one end of the +coil and any of the taps. The more turns there are included in the part +of the coil which we are using the greater is the inductance. If we want +to do a real job we can bring each of these taps to a little stud and +arrange a sliding or rotating contact with them. Then we have an +inductance the value of which we can vary "step-by-step" in a convenient +manner. + +Another way to make a variable inductance is to make what is called a +"variometer." I dislike the name because it doesn't "meter" anything. If +properly calibrated it would of course "meter" inductance, but then it +should be called an "inducto-meter." + +Do you remember the gang of boys that fellow had to drive off his +property? What if there had been two different gangs playing there? How +much trouble he has depends upon whether there is anything in common +between the gangs. Suppose they are playing in different parts of his +property and so act just as if the other crowd wasn't also trespassing. +He could just add the trouble of starting one gang to the trouble of +starting the other. + +It would be very different if the gangs have anything in common. Then +one would encourage the other much as the various boys of the same gang +encourage each other. He would have a lot more trouble. And this extra +trouble would be because of the relations between gangs, that is, +because of their "mutual inductance." + +On the other hand suppose the gangs came from different parts of the +town and disliked each other. He wouldn't have nearly the trouble. Each +gang would be yelling at the other as they went along: "You'd better +beat it. He knows all right, all right, who broke that bush down by the +gate. Just wait till he catches you." They'd get out a little easier, +each in the hope the other crowd would catch it from the owner. There's +a case where their mutual relations, their mutual inductance, makes the +job easier. + +That's true of coils with inductance. Suppose you wind two inductance +coils and connect them in series. If they are at right angles to each +other as in Fig. 46a they have no effect on each other. There is no +mutual inductance. But if they are parallel and wound the same way like +the coils of Fig. 46b they will act like a single coil of greater +inductance. If the coils are parallel but wound in opposite directions +as in Fig. 46c they will have less inductance because of their mutual +inductance. You can check these statements for yourself if you'll refer +back to Letter 10 and see what happens in the same way as I told you in +discussing Fig. 28. + +[Illustration: Fig 46a] + +[Illustration: Fig 46b] + +If the coils are neither parallel nor at right angles there will be some +mutual inductance but not as much as if they were parallel. By turning +the coils we can get all the variations in mutual relations from the +case of Fig. 46b to that of Fig. 46c. That's what we arrange to do in a +variable inductance of the variometer type. + +[Illustration: Fig 46c] + +There is another way of varying the mutual inductance. We can make one +coil slide inside another. If it is way inside, the total inductance +which the two coils offer is either larger than the sum of what they can +offer separately or less, depending upon whether the windings are in the +same direction or opposite. As we pull the coil out the mutual effect +becomes less and finally when it is well outside the mutual inductance +is very small. + +Now we have several methods of varying capacity and inductance and +therefore we are ready to vary the frequency of our audion oscillator; +that is, "tune" it, as we say. In my next letter I shall show you why we +tune. + +Now for the rule which I promised. The frequency to which a circuit is +tuned depends upon the product of the number of mil-henries in the coil +and the number of microfarads in the condenser. Change the coil and the +condenser as much as you want but keep this product the same and the +frequency will be the same. + +[Footnote 5: More accurately the number is 6,286,000,000,000.] + + + + +LETTER 13 + +TUNING + + +DEAR RADIO ENTHUSIAST: + +I want to tell you about receiving sets and their tuning. In the last +letter I told you what determines the frequency of oscillation of an +audion oscillator. It was the condenser and inductance which you studied +in connection with Fig. 36. That's what determines the frequency and +also what makes the oscillations. All the tube does is to keep them +going. Let's see why this is so. + +[Illustration: Fig 47a] + +Start first, as in Fig. 47a, with a very simple circuit of a battery and +a non-inductive resistance, that is, a wire wound like that of Fig. 40 +in the previous letter, so that it has no inductance. The battery must +do work forcing electrons through that wire. It has the ability, or the +energy as we say. + +[Illustration: Fig 47b] + +Now connect a condenser to the battery as in Fig. 47b. The connecting +wires are very short; and so practically all the work which the battery +does is in storing electrons in the negative plate of the condenser and +robbing the positive plate. The battery displaces a certain number of +electrons in the waiting-rooms of the condenser. How many, depends upon +how hard it can push and pull, that is on its e. m. f., and upon how +much capacity the condenser has. + +[Illustration: Fig 47c] + +Remove the battery and connect the charged condenser to the resistance +as in Fig. 47c. The electrons rush home. They bump and jostle their way +along, heating the wire as they go. They have a certain amount of energy +or ability to do work because they are away from home and they use it +all up, bouncing along on their way. When once they are home they have +used up all the surplus energy which the battery gave them. + +Try it again, but this time, as in Fig. 47d, connect the charged +condenser to a coil which has inductance. The electrons don't get +started as fast because of the inductance. But they keep going because +the electrons in the wire form the habit. The result is that about the +time enough electrons have got into plate 2 (which was positive), to +satisfy all its lonely protons, the electrons in the wire are streaming +along at a great rate. A lot of them keep going until they land on this +plate and so make it negative. + +[Illustration: Fig 47d] + +That's the same sort of thing that happens in the case of the inductance +and condenser in the oscillating audion circuit except for one important +fact. There is nothing to keep electrons going to the 2 plate except +this habit. And there are plenty of stay-at-home electrons to stop them +as they rush along. They bump and jostle, but some of them are stopped +or else diverted so that they go bumping around without getting any +nearer plate 2. Of course, they spend all their energy this way, getting +every one all stirred up and heating the wire. + +Some of the energy which the electrons had when they were on plate 1 is +spent, therefore, and there aren't as many electrons getting to plate 2. +When they turn around and start back, as you know they do, the same +thing happens. The result is that each successive surge of electrons is +smaller than the preceding. Their energy is being wasted in heating the +wire. The stream of electrons gets smaller and smaller, and the voltage +of the condenser gets smaller and smaller, until by-and-by there isn't +any stream and the condenser is left uncharged. When that happens, we +say the oscillations have "damped out." + +[Illustration: Fig 48] + +That's one way of starting oscillations which damp out--to start with a +charged condenser and connect an inductance across it. There is another +way which leads us to some important ideas. Look at Fig. 48. There is an +inductance and a condenser. Near the coil is another coil which has a +battery and a key in circuit with it. The coils are our old friends of +Fig. 33 in Letter 10. Suppose we close the switch _S_. It starts a +current through the coil _ab_ which goes on steadily as soon as it +really gets going. While it is starting, however, it induces an electron +stream in coil _cd_. There is only a momentary or transient current +but it serves to charge the condenser and then events happen just as +they did in the case where we charged the condenser with a battery. + +[Illustration: Fig 49] + +Now take away this coil _ab_ with its battery and substitute the +oscillator of Fig. 36. What's going to happen? We have two circuits in +which oscillations can occur. See Fig. 49. One circuit is associated +with an audion and some batteries which keep supplying it with energy so +that its oscillations are continuous. The other circuit is near enough +to the first to be influenced by what happens in that circuit. We say it +is "coupled" to it, because whatever happens in the first circuit +induces an effect in the second circuit. + +Suppose first that in each circuit the inductance and capacity have such +values as to produce oscillations of the same frequency. Then the moment +we start the oscillator we have the same effect in both circuits. Let me +draw the picture a little differently (Fig. 50) so that you can see this +more easily. I have merely made the coil _ab_ in two parts, one of +which can affect _cd_ in the oscillator and the other the coil +_L_ of the second circuit. + +But suppose that the two circuits do not have the same natural +frequencies, that is the condenser and inductance in one circuit are so +large that it just naturally takes more time for an oscillation in that +circuit than in the other. It is like learning to dance. You know about +how well you and your partner would get along if you had one frequency +of oscillation and she had another. That's what happens in a case like +this. + +[Illustration: Fig 50] + +If circuit _L-C_ takes longer for each oscillation than does +circuit _ab_ its electron stream is always working at cross +purposes with the electron stream in _ab_ which is trying to lead +it. Its electrons start off from one condenser plate to the other and +before they have much more than got started the stream in _ab_ +tries to call them back to go in the other direction. It is practically +impossible under these conditions to get a stream of any size going in +circuit _L-C_. It is equally hard if _L-C_ has smaller capacity and +inductance than _ab_ so that it naturally oscillates faster. + +I'll tell you exactly what it is like. Suppose you and your partner are +trying to dance without any piano or other source of music. She has one +tune running through her head and she dances to that, except as you drag +her around the floor. You are trying to follow another tune. As a couple +you have a difficult time going anywhere under these conditions. But it +would be all right if you both had the same tune. + +If we want the electron stream in coil _ab_ to have a large guiding +effect on the stream in coil _L-C_ we must see that both circuits +have the same tune, that is the same natural frequency of oscillation. + +[Illustration: Fig 51] + +This can be shown very easily by a simple experiment. Suppose we set up +our circuit _L-C_ with an ammeter in it, so as to be able to tell +how large an electron stream is oscillating in that circuit. Let us also +make the condenser a variable one so that we can change the natural +frequency or tune of the circuit. Now let's see what happens to the +current as we vary this condenser, changing the capacity and thus +changing the tune of the circuit. If we use a variable plate condenser +it will have a scale on top graduated in degrees and we can note the +reading of the ammeter for each position of the movable plates. If we +do, we find one position of these plates, that is one setting, +corresponding to one value of capacity in the condenser, where the +current in the circuit is a maximum. This is the setting of the +condenser for which the circuit has the same tune or natural frequency +as the circuit _cd_. Sometimes we say that the circuits are now in +resonance. We also refer to the curve of values of current and condenser +positions as a "tuning curve." Such a curve is shown in Fig. 51. + +[Illustration: Fig 52] + +That's all there is to tuning--adjusting the capacity and inductance of +a circuit until it has the same natural frequency as some other circuit +with which we want it to work. We can either adjust the capacity as we +just did, or we can adjust the inductance. In that case we use a +variable inductance as in Fig. 52. + +If we want to be able to tune to any of a large range of frequencies we +usually have to take out or put into the circuit a whole lot of +mil-henries at a time. When we do we get these mil-henries of inductance +from a coil which we call a "loading coil." That's why your friends add +a loading coil when they want to tune for the long wave-length stations, +that is, those with a low frequency. + +When our circuit _L-C_ of Fig. 49 is tuned to the frequency of the +oscillator we get in it a maximum current. There is a maximum stream of +electrons, and hence a maximum number of them crowded first into one and +then into the other plate of the condenser. And so the condenser is +charged to a maximum voltage, first in one direction and then in the +other. + +[Illustration: Fig 53] + +Now connect the circuit _L-C_ to the grid of an audion. If the +circuit is tuned we'll have the maximum possible voltage applied between +grid and filament. In the plate circuit we'll get an increase and then a +decrease of current. You know that will happen for I prepared you for +this moment by the last page of my ninth letter. I'll tell you more +about that current in the plate circuit in a later letter. I am +connecting a telephone receiver in the plate circuit, and also a +condenser, the latter for a reason to be explained later. The +combination appears then as in Fig. 53. That figure shows a C-W +transmitter and an audion detector. This is the sort of a detector we +would use for radio-telephony, but the transmitter is the sort we would +use for radio-telegraphy. We shall make some changes in them later. + +[Illustration: Fig 54] + +Whenever we start the oscillating current in the transmitter we get an +effect in the detector circuit, of which I'll tell you more later. For +the moment I am interested in showing you how the transmitter and the +detector may be separated by miles and still there will be an effect in +the detector circuit every time the key in the transmitter circuit is +closed. + +This is how we do it. At the sending station, that is, wherever we +locate the transmitter, we make a condenser using the earth, or ground, +as one plate. We do the same thing at the receiving station where the +detector circuit is located. To these condensers we connect inductances +and these inductances we couple to our transmitter and receiver as shown +in Fig. 54. The upper plate of the condenser in each case is a few +horizontal wires. The lower plate is the moist earth of the ground and +we arrange to get in contact with that in various ways. One of the +simplest methods is to connect to the water pipes of the city +water-system. + +Now we have our radio transmitting-station and a station for receiving +its signals. You remember we can make dots and dashes by the key or +switch in the oscillator circuit. When we depress the key we start the +oscillator going. That sets up oscillations in the circuit with the +inductance and the capacity formed by the antenna. If we want a +real-sized stream of electrons up and down this antenna lead (the +vertical wire), we must tune that circuit. That is why I have shown a +variable inductance in the circuit of the transmitting antenna. + +What happens when these electrons surge back and forth between the +horizontal wires and the ground, I don't know. I do know, however, that +if we tune the antenna circuit at the receiving station there will be a +small stream of electrons surging back and forth in that circuit. + +Usually scientists explain what happens by saying that the transmitting +station sends out waves in the ether and that these waves are received +by the antenna system at the distant station. Wherever you put up a +receiving station you will get the effect. It will be much smaller, +however, the farther the two stations are apart. + +I am not going to tell you anything about wave motion in the ether +because I don't believe we know enough about the ether to try to +explain, but I shall tell you what we mean by "wave length." + +Somehow energy, the ability to do work, travels out from the sending +antenna in all directions. Wherever you put up your receiving station +you get more or less of this energy. Of course, energy is being sent out +only while the key is depressed and the oscillator going. This energy +travels just as fast as light, that is at the enormous speed of 186,000 +miles a second. If you use meters instead of miles the speed is +300,000,000 meters a second. + +Now, how far will the energy which is sent out from the antenna travel +during the time it takes for one oscillation of the current in the +antenna? Suppose the current is oscillating one million times a second. +Then it takes one-millionth of a second for one oscillation. In that +time the energy will have traveled away from the antenna one-millionth +part of the distance it will travel in a whole second. That is +one-millionth of 300 million meters or 300 meters. + +The distance which energy will go in the time taken by one oscillation +of the source of that energy is the wave length. In the case just given +that distance is 300 meters. The wave length, then, of 300 meters +corresponds to a frequency of one million. In fact if we divide 300 +million meters by the frequency we get the wave length, and that's the +same rule as I gave you in the last letter. + +In further letters I'll tell you how the audion works as a detector and +how we connect a telephone transmitter to the oscillator to make it send +out energy with a speech significance instead of a mere dot and dash +significance, or signal significance. We shall have to learn quite a +little about the telephone itself and about the human voice. + + + + +LETTER 14 + +WHY AND HOW TO USE A DETECTOR + + +DEAR SON: + +In the last letter we got far enough to sketch, in Fig. 54, a radio +transmitting station and a receiving station. We should never, however, +use just this combination because the transmitting station is intended +to send telegraph signals and the receiving station is best suited to +receiving telephonic transmission. But let us see what happens. + +[Illustration: Fig 54] + +When the key in the plate circuit of the audion at the sending station +is depressed an alternating current is started. This induces an +alternating current in the neighboring antenna circuit. If this antenna +circuit, which is formed by a coil and a condenser, is tuned to the +frequency of oscillations which are being produced in the audion circuit +then there is a maximum current induced in the antenna. + +As soon as this starts the antenna starts to send out energy in all +directions, or "radiate" energy as we say. How this energy, or ability +to do work, gets across space we don't know. However it may be, it does +get to the receiving station. It only takes a small fraction of a second +before the antenna at the receiving station starts to receive energy, +because energy travels at the rate of 186,000 miles a second. + +The energy which is received does its work in making the electrons in +that antenna oscillate back and forth. If the receiving antenna is tuned +to the frequency which the sending station is producing, then the +electrons in the receiving antenna oscillate back and forth most widely +and there is a maximum current in this circuit. + +The oscillations of the electrons in the receiving antenna induce +similar oscillations in the tuned circuit which is coupled to it. This +circuit also is tuned to the frequency which the distant oscillator is +producing and so in it we have the maximum oscillation of the electrons. +The condenser in that circuit charges and discharges alternately. + +The grid of the receiving audion always has the same voltage as the +condenser to which it is connected and so it becomes alternately +positive and negative. This state of affairs starts almost as soon as +the key at the sending station is depressed and continues as long as it +is held down. + +Now what happens inside the audion? As the grid becomes more and more +positive the current in the plate circuit increases. When the grid no +longer grows more positive but rather becomes less and less positive the +current in the plate circuit decreases. As the grid becomes of zero +voltage and then negative, that is as the grid "reverses its polarity," +the plate current continues to decrease. When the grid stops growing +more negative and starts to become less so, the plate current stops +decreasing and starts to increase. + +All this you know, for you have followed through such a cycle of changes +before. You know also how we can use the audion characteristic to tell +us what sort of changes take place in the plate current when the grid +voltage changes. The plate current increases and decreases alternately, +becoming greater and less than it would be if the grid were not +interfering. These variations in its intensity take place very rapidly, +that is with whatever high frequency the sending station operates. What +happens to the plate current on the average? + +The plate current, you remember, is a stream of electrons from the +filament to the plate (on the inside of the tube), and from the plate +back through the B-battery to the filament (on the outside of the tube). +The grid alternately assists and opposes that stream. When it assists, +the electrons in the plate circuit are moved at a faster rate. When the +grid becomes negative and opposes the plate the stream of electrons is +at a slower rate. The stream is always going in the same direction but +it varies in its rate depending upon the changes in grid potential. + +[Illustration: Fig 55] + +When the grid is positive, that is for half a cycle of the alternating +grid-voltage, the stream is larger than it would be if the plate current +depended only on the B-battery. For the other half of a cycle it is +less. The question I am raising is this: Do more electrons move around +the plate circuit if there is a signal coming in than when there is no +incoming signal? To answer this we must look at the audion +characteristic of our particular tube and this characteristic must have +been taken with the same B-battery as we use when we try to receive the +signals. + +There are just three possible answers to this question. The first answer +is: "No, there is a smaller number of electrons passing through the +plate circuit each second if the grid is being affected by an incoming +signal." The second is: "The signal doesn't make any difference in the +total number of electrons which move each second from filament to +plate." And the third answer is: "Yes, there is a greater total number +each second." + +[Illustration: Fig 56] + +Any one of the three answers may be right. It all depends on the +characteristic of the tube as we are operating it, and that depends not +only upon the type and design of tube but also upon what voltages we are +using in our batteries. Suppose the variations in the voltage of the +grid are as represented in Fig. 55, and that the characteristic of the +tube is as shown in the same figure. Then obviously the first answer is +correct. You can see for yourself that when the grid becomes positive +the current in the plate circuit can't increase much anyway. For the +other half of the cycle, that is, while the grid is negative, the +current in the plate is very much decreased. The decrease in one +half-cycle is larger than the increase during the other half-cycle, so +that on the average the current is less when the signal is coming in. +The dotted line shows the average current. + +Suppose that we take the same tube and use a B-battery of lower voltage. +The characteristic will have the same shape but there will not be as +much current unless the grid helps, so that the characteristic will be +like that of Fig. 56. This characteristic crosses the axis of zero volts +at a smaller number of mil-amperes than does the other because the +B-batteries can't pull as hard as they did in the other case. + +[Illustration: Fig 57] + +You can see the result. When the grid becomes positive it helps and +increases the plate current. When it becomes negative it opposes and +decreases the plate current. But the increase just balances the +decrease, so that on the average the current is unchanged, as shown by +the dotted line. + +On the other hand, if we use a still smaller voltage of B-battery we get +a characteristic which shows a still smaller current when the grid is at +zero potential. For this case, as shown in Fig. 57, the plate current is +larger on the average when there is an incoming signal. + +If we want to know whether or not there is any incoming signal we will +not use the tube in the second condition, that of Fig. 56, because it +won't tell us anything. On the other hand why use the tube under the +first conditions where we need a large plate battery? If we can get the +same result, that is an indication when the other station is signalling, +by using a small battery let's do it that way for batteries cost money. +For that reason we shall confine ourselves to the study of what takes +place under the conditions of Fig. 57. + +We now know that when a signal is being sent by the distant station the +current in the plate circuit of our audion at the receiving station is +greater, on the average. We are ready to see what effect this has on the +telephone receiver. And to do this requires a little study of how the +telephone receiver works and why. + +[Illustration: Fig 58] + +I shall not stop now to tell you much about the telephone receiver for +it deserves a whole letter all to itself. You know that a magnet +attracts iron. Suppose you wind a coil of insulated wire around a bar +magnet or put the magnet inside such a coil as in Fig. 58. Send a stream +of electrons through the turns of the coil--a steady stream such as +comes from the battery shown in the figure. The strength of the magnet +is altered. For one direction of the electron stream through the coil +the magnet is stronger. For the opposite direction of current the magnet +will be weaker. + +[Illustration: Fig 59] + +Fig. 59 shows a simple design of telephone receiver. It is formed by a +bar magnet, a coil about it through which a current can flow, and a thin +disc of iron. The iron disc, or diaphragm, is held at its edges so that +it cannot move as a whole toward the magnet. The center can move, +however, and so the diaphragm is bowed out in the form shown in the +smaller sketch. + +Now connect a battery to the receiver winding and allow a steady stream +of electrons to flow. The magnet will be either strengthened or +weakened. Suppose the stream of electrons is in the direction to make it +stronger--I'll give you the rule later. Then the diaphragm is bowed out +still more. If we open the battery circuit and so stop the stream of +electrons the diaphragm will fly back to its original position, for it +is elastic. The effect is very much that of pushing in the bottom of a +tin pan and letting it fly back when you remove your hand. + +Next reverse the battery. The magnet does not pull as hard as it would +if there were no current. The diaphragm is therefore not bowed out so +much. + +Suppose that instead of reversing the current by reversing the battery +we arrange to send an alternating current through the coil. That will +have the same effect. For one direction of current flow, the diaphragm +is attracted still more by the magnet but for the other direction it is +not attracted as much. The result is that the center of the diaphragm +moves back and forth during one complete cycle of the alternating +current in the coil. + +The diaphragm vibrates back and forth in tune with the alternating +current in the receiver winding. As it moves away from the magnet it +pushes ahead of it the neighboring molecules of air. These molecules +then crowd and push the molecules of air which are just a little further +away from the diaphragm. These in turn push against those beyond them +and so a push or shove is sent out by the diaphragm from molecule to +molecule until perhaps it reaches your ear. When the molecules of air +next your ear receive the push they in turn push against your eardrum. + +In the meantime what has happened? The current in the telephone receiver +has reversed its direction. The diaphragm is now pulled toward the +magnet and the adjacent molecules of air have even more room than they +had before. So they stop crowding each other and follow the diaphragm in +the other direction. The molecules of air just beyond these, on the way +toward your ear, need crowd no longer and they also move back. Of +course, they go even farther than their old positions for there is now +more room on the other side. That same thing happens all along the line +until the air molecules next your ear start back and give your eardrum a +chance to expand outward. As they move away they make a little vacuum +there and the eardrum puffs out. + +That goes on over and over again just as often as the alternating +current passes through one cycle of values. And you, unless you are +thinking particularly of the scientific explanations, say that you "hear +a musical note." As a matter of fact if we increase the frequency of the +alternating current you will say that the "pitch" of the note has been +increased or that you hear a note higher in the musical scale. + +If we started with a very low-frequency alternating current, say one of +fifteen or twenty cycles per second, you wouldn't say you heard a note +at all. You would hear a sort of a rumble. If we should gradually +increase the frequency of the alternating current you would find that +about sixty or perhaps a hundred cycles a second would give you the +impression of a musical note. As the frequency is made still larger you +have merely the impression of a higher-pitched note until we get up into +the thousands of cycles a second. Then, perhaps about twenty-thousand +cycles a second, you find you hear only a little sound like wind or like +steam escaping slowly from a jet or through a leak. A few thousand +cycles more each second and you don't hear anything at all. + +You know that for radio-transmitting stations we use audion oscillators +which are producing alternating currents with frequencies of several +hundred-thousand cycles per second. It certainly wouldn't do any good to +connect a telephone receiver in the antenna circuit at the receiving +station as in Fig. 60. We couldn't hear so high pitched a note. + +[Illustration: Fig 60] + +Even if we could, there are several reasons why the telephone receiver +wouldn't work at such high frequencies. The first is that the diaphragm +can't be moved so fast. It has some inertia, you know, that is, some +unwillingness to get started. If you try to start it in one direction +and, before you really get it going, change your mind and try to make it +go in the other direction, it simply isn't going to go at all. So even +if there is an alternating current in the coil around the magnet there +will not be any corresponding vibration of the diaphragm if the +frequency is very high, certainly not if it is above about 20,000 cycles +a second. + +The other reason is that there will only be a very feeble current in the +coil anyway, no matter what you do, if the frequency is high. You +remember that the electrons in a coil are sort of banded together and +each has an effect on all the others which can move in parallel paths. +The result is that they have a great unwillingness to get started and an +equal unwillingness to stop. Their unwillingness is much more than if +the wire was long and straight. It is also made very much greater by the +presence of the iron core. An alternating e. m. f. of high frequency +hardly gets the electrons started at all before it's time to get them +going in the opposite direction. There is very little movement to the +electrons and hence only a very small current in the coil if the +frequency is high. + +If you want a rule for it you can remember that the higher the frequency +of an alternating e. m. f. the smaller the electron stream which it can +set oscillating in a given coil. Of course, we might make the e. m. f. +stronger, that is pull and shove the electrons harder, but unless the +coil has a very small inductance or unless the frequency is very low we +should have to use an e. m. f. of enormous strength to get any +appreciable current. + +Condensers are just the other way in their action. If there is a +condenser in a circuit, where an alternating e. m. f. is active, there +is lots of trouble if the frequency is low. If, however, the frequency +is high the same-sized current can be maintained by a smaller e. m. f. +than if the frequency is low. You see, when the frequency is high the +electrons hardly get into the waiting-room of the condenser before it is +time for them to turn around and go toward the other room. Unless there +is a large current, there are not enough electrons crowded together in +the waiting-room to push back very hard on the next one to be sent along +by the e. m. f. Because the electrons do not push back very hard a small +e. m. f. can drive them back and forth. + +Ordinarily we say that a condenser impedes an alternating current less +and less the higher is the frequency of the current. And as to +inductances, we say that an inductance impedes an alternating current +more and more the higher is the frequency. + +Now we are ready to study the receiving circuit of Fig. 54. I showed you +in Fig. 57 how the current through, the tube will vary as time goes on. +It increases and decreases with the frequency of the current in the +antenna of the distant transmitting station. We have a picture, or +graph, as we say, of how this plate current varies. It will be necessary +to study that carefully and to resolve it into its components, that is +to separate it into parts, which, added together again will give the +whole. To show you what I mean I am going to treat first a very simple +case involving money. + +Suppose a boy was started by his father with 50 cents of spending money. +He spends that and runs 50 cents in debt. The next day his father gives +him a dollar. Half of this he has to spend to pay up his yesterday's +indebtedness. This he does at once and that leaves him 50 cents ahead. +But again he buys something for a dollar and so runs 50 cents in debt. +Day after day this cycle is repeated. We can show what happens by the +curve of Fig. 61a. + +[Illustration: Fig 61a] + +On the other hand, suppose he already had 60 cents which, he was saving +for some special purpose. This he doesn't touch, preferring to run into +debt each day and to pay up the next, as shown in Fig. 61a. Then we +would represent the story of this 60 cents by the graph of Fig. 61b. + +[Illustration: Fig 61b] + +Now suppose that instead of going in debt each day he uses part of this +60 cents. Each day after the first his father gives him a dollar, just +as before. He starts then with 60 cents as shown in Fig. 61c, increases +in wealth to $1.10, then spends $1.00, bringing his funds down to 10 +cents. Then he receives $1.00 from his father and the process is +repeated cyclically. + +[Illustration: Fig 61c] + +If you saw the graph of Fig. 61c you would be able to say that, whatever +he actually did, the effect was the same as if he had two pockets, in +one of which he kept 60 cents all the time as shown in Fig. 61b. In his +other pocket he either had money or he was in debt as shown in Fig. 61a. +If you did that you would be resolving the money changes of Fig. 61c +into the two components of Figs. 61a and b. + +That is what I want you to do with the curve of Fig. 57 which I am +reproducing here, redrawn as Fig. 62a. You see it is really the result +of adding together the two curves of Figs. 62b and c, which are shown on +the following page. + +[Illustration: Fig 62a] + +We can think, therefore, of the current in the plate circuit as if it +were two currents added together, that is, two electron streams passing +through the same wire. One stream is steady and the other alternates. + +[Illustration: Fig 62b] + +Now look again at the diagram of our receiving set which I am +reproducing as Fig. 63. When the signal is incoming there flow in the +plate circuit two streams of electrons, one steady and of a value in +mil-amperes corresponding to that of the graph in Fig. 62b, and the +other alternating as shown in Fig. 62c. + +The steady stream of electrons will have no more difficulty in getting +through the coiled wire of the receiver than it would through the same +amount of straight wire. On the other hand it cannot pass the gap of the +condenser. + +The alternating-current component can't get along in the coil because +its frequency is so high that the coil impedes the motion of the +electrons so much as practically to stop them. On the other hand these +electrons can easily run into the waiting-room offered by the condenser +and then run out again as soon as it is time. + +[Illustration: Fig 62c] + +When the current in the plate circuit is large all the electrons which +aren't needed for the steady stream through the telephone receiver run +into one plate of the condenser. Of course, at that same instant an +equal number leave the other plate and start off toward the B-battery +and the filament. An instant later, when the current in the plate +circuit is small, electrons start to come out of the plate and to join +the stream through the receiver so that this stream is kept steady. + +[Illustration: Fig 63] + +This steady stream of electrons, which is passing through the receiver +winding, is larger than it would be if there was no incoming radio +signal. The result is a stronger pull on the diaphragm of the receiver. +The moment the signal starts this diaphragm is pulled over toward the +magnet and it stays pulled over as long as the signal lasts. When the +signal ceases it flies back. We would hear then a click when the signal +started and another when it stopped. + +If we wanted to distinguish dots from dashes this wouldn't be at all +satisfactory. So in the next letter I'll show you what sort of changes +we can make in the apparatus. To understand what effect these changes +will have you need, however, to understand pretty well most of this +letter. + + + + +LETTER 15 + +RADIO-TELEPHONY + + +DEAR LAD: + +Before we start on the important subject matter of this letter let us +make a short review of the preceding two letters. + +An oscillating audion at the transmitting station produces an effect on +the plate current of the detector audion at the receiving station. There +is impressed upon the grid of the detector an alternating e. m. f. which +has the same frequency as the alternating current which is being +produced at the sending station. While this e. m. f. is active, and of +course it is active only while the sending key is held down, there is +more current through the winding of the telephone receiver and its +diaphragm is consequently pulled closer to its magnet. + +What will happen if the e. m. f. which is active on the grid of the +detector is made stronger or weaker? The pull on the receiver diaphragm +will be stronger or weaker and the diaphragm will have to move +accordingly. If the pull is weaker the elasticity of the iron will move +the diaphragm away from the magnet, but if the pull is stronger the +diaphragm will be moved toward the magnet. + +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. + +[Illustration: Fig 64] + +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. + +[Illustration: Fig 65] + +[Illustration: Fig 66] + +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. + +[Illustration: Fig 67a] + +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. + +[Illustration: Fig 67b] + +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. + +[Illustration: Fig 68] + +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. + +[Illustration: Fig 69] + +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. + +[Illustration: Fig 70] + +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. + +[Illustration: 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. + +[Illustration: Fig 72] + +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. + +[Illustration: Fig 73] + +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. + +[Illustration: Fig 74] + +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. + +[Illustration: Fig 75] + +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. + +[Illustration: Fig 77] + +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. + +[Illustration: Pl. VII.--Photographs of Vibrating Strings.] + +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. + +[Illustration: Fig 78] + +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. + +[Illustration: Fig 81] + +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. + +[Illustration: Fig 82] + +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. + +[Illustration: Fig 56] + +[Illustration: Fig 63] + +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. + +[Illustration: Fig 85] + +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. + +[Illustration: Fig 86] + +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. + +[Illustration: Fig 87] + +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. + +[Illustration: 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. + +[Illustration: Fig 89] + +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. + +[Illustration: Pl. VIII.--To Illustrate the Mechanism for the Production +of the Human Voice.] + +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. + +[Illustration: Fig 90] + +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. + +[Illustration: Fig 91] + +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 + + +MY DEAR RECEIVER: + +There is one way of making an audion even more efficient as a detector +than the method described in the last letter. And that is to make it +talk to itself. + +Suppose we arrange a receiving circuit as in Fig. 92. It is exactly like +that of Fig. 90 of the previous letter except for the fact that the +current in the plate circuit passes through a little coil, _L_{t}_, +which is placed near the coil _L_ and so can induce in it an e. m. +f. which will correspond in intensity and wave form to the current in +the plate circuit. + +If we should take out the grid condenser and its leak this circuit would +be like that of Fig. 54 in Letter 13 which we used for a generator of +high-frequency alternating currents. You remember how that circuit +operates. A small effect in the grid circuit produces a large effect in +the plate circuit. Because the plate circuit is coupled to the grid +circuit the grid is again affected and so there is a still larger effect +in the plate circuit. And so on, until the current in the plate circuit +is swinging from zero to its maximum possible value. + +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. + +[Illustration: Fig 92] + +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. + +[Illustration: Fig 93] + +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? + +[Illustration: Fig 94] + +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. + +[Illustration: Fig 95] + +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. + +[Illustration: Fig 96] + +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. + +[Illustration: Fig 97] + +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. + +[Illustration: Fig 98] + +We can't get more work out of the secondary of a transformer than we do +in the primary. If we design the transformer so that there is a greater +pull (e. m. f.) in the secondary the electron stream in the secondary +will be correspondingly smaller. + +You remember how we measure resistance. We divide the e. m. f. (number +of volts) by the current (number of amperes) to find the resistance +(number of ohms). Suppose we do that for the primary and for the +secondary of the transformer of Fig. 98 which we are discussing. See +what happens in the secondary. There is only half as much voltage but +twice as much current. It looks as though the secondary had one-fourth +as much resistance as the primary. And so it has, but we usually call it +"impedance" instead of resistance because straight wires resist but +coils or condensers impede alternating e. m. f.'s. + +[Illustration: Fig 99] + +Before we return to the question of using a transformer in an audion +circuit let us turn this transformer around as in Fig. 99 and send the +current through the side with the larger number of windings. Let's talk +of "primary" and "secondary" just as before but, of course, remember +that now the primary has twice the turns of the secondary. On the +secondary side we shall have only half the current, but there will be +twice the e. m. f. The resistance of the secondary then is four times +that of the primary. + +Now return to the amplifier of Fig. 94 and see what sort of a +transformer should be between the plate circuit of the tube and the +telephone receivers. Suppose the internal resistance of the tube is +12,000 ohms and the resistance of the telephones is 3,000 ohms. Suppose +also that the resistance (really impedance) of the primary side of the +transformer which we just considered is 12,000 ohms. The impedance of +its secondary will be a quarter of this or 3,000 ohms. If we connect +such a transformer in the circuit, as shown, we shall obtain the +greatest output from the tube. + +In the first place the primary of the transformer has a number of ohms +just equal to the internal resistance of the tube. The tube, therefore, +will give its best to that transformer. In the second place the +secondary of the transformer has a resistance just equal to the +telephone receivers so it can give its best to them. The effect of the +transformer is to make the telephones act as if they had four times as +much resistance and so were exactly suited to be connected to the +audion. + +This whole matter of the proper use of transformers is quite simple but +very important in setting up vacuum-tube circuits. To overlook it in +building or buying your radio set will mean poor efficiency. Whenever +you have two parts of a vacuum-tube circuit to connect together be sure +and buy only a transformer which is designed to work between the two +impedances (or resistances) which you wish to connect together. + +There is one more precaution in connection with the purchase of +transformers. They should do the same thing for all the important +frequencies which they are to transmit. If they do not, the speech or +signals will be distorted and may be unintelligible. + +If you take the precautions which I have mentioned your radio receiving +set formed by a detector and one amplifier will look like that of Fig. +94. That is only one possible scheme of connections. You can use any +detector circuit which you wish,[10] one with a grid condenser and leak, +or one arranged for feed-back In either case your amplifier may well be +as shown in the figure. + +[Illustration: Fig 100] + +The circuit I have described uses an audion to amplify the +audio-frequency currents which come from the detector and are capable of +operating the telephones. In some cases it is desirable to amplify the +radio signals before applying them to the detector. This is especially +true where a "loop antenna" is being used. Loop antennas are smaller and +more convenient than aërials 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. + +[Illustration: Fig 101] + +If two parallel wires are carrying steady electron streams in the same +general direction the wires attract each other. If the streams are +oppositely directed the wires repel each other. Fig. 101 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. + +[Illustration: Fig 102] + +These facts, of the attraction of electron streams which are in the same +direction and repulsion of streams in opposite directions, are all that +one need remember to figure out for himself what will happen under +various conditions. For example, if two coils of wire are carrying +currents what will happen is easily seen. Fig. 102 shows the two coils +and a section through them. + +[Illustration: Fig 103] + +Looking at this cross section we seem to have four wires, _1_ and +_2_ of coil _A_ and _3_ and _4_ of coil _B_. You see at once that +if the coils are free to move they will move into the dotted positions +shown in Fig 102, because wire _1_ attracts wire _3_ and repels wire +_4_, while wire _2_ attracts wire _4_ and repels wire _3_. If +necessary, and if they are free to move, the coils will turn +completely around to get to this position. I have shown such a case +in Fig. 103. + +Wires which are not carrying currents do not behave in this way. The +action is due, but how we don't yet know, to the motions of the +electrons. As far as we can explain it to-day, the attraction of two +wires which are carrying currents is due to the attraction of the two +streams of electrons. Of course these electrons are part of the wires. +They can't get far away from the stay-at-home electrons and the nuclei +of the atoms which form the wires. In fact it is these nuclei which keep +the wandering electrons within the wires. The result is that if the +streams of electrons are to move toward each other the wires must go +along with them. + +If the wires are held firmly the electron streams cannot approach one +another for they must stay in the wires. Wires, therefore, perform the +important service of acting as paths for electrons which are traveling +as electric currents. There are other ways in which electrons can be +kept in a path, and other means beside batteries for keeping them going. +It doesn't make any difference so far as the attraction or the repulsion +is concerned why they are following a certain path or why they stay in +it. So far as we know two streams of electrons, following parallel +paths, will always, behave just like the two streams of Fig. 101. + +[Illustration: Fig 104] + +Suppose, for example, there were two atoms which were each formed by a +nucleus and a number of electrons swinging around about the nucleus as +pictured in Fig. 104. The electrons are going of their own accord and +the nucleus keeps them from flying off at a tangent, the way mud flies +from the wheel of an automobile. Suppose these two atoms are free to +turn but not to move far from their present positions. They will turn so +as to make their electron paths parallel just as did the loops of Fig. +102. + +[Illustration: Fig 105] + +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. + +[Illustration: Fig 106] + +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. + +[Illustration: Pl. IX.--Western Electric Loud Speaking Receiver. +Crystal Detector Set of the General Electric Co. Audibility Meter of +General Radio Co.] + +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. + +[Illustration: Fig 107] + +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. + +[Illustration: Fig 33] + +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_. + +[Illustration: Fig 108] + +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_. + +[Illustration: Fig 109] + +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. + +[Illustration: Fig 110] + +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. + +[Illustration: Fig 111] + +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. + +[Illustration: Fig 112] + +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. + +Now buy some more apparatus. You will need a grid condenser of about +0.0002 mf. The grid leaks to go with it you can make for yourself. I +would use a piece of brown wrapping paper and two little metal eyelets. +The eyelets can be punched into the paper. Between them coat the paper +with carbon ink, or with lead pencil marks. A line about an inch long +ought to serve nicely. You will probably wish to make several grid leaks +to try. When you get satisfactory operation in receiving by the +grid-condenser method the leak will probably be somewhere between a +megohm and two megohms. + +For this method you will not want a C-battery, but you will wish to +operate the detector with about as high a voltage as the manufacturers +will recommend for the plate circuit. In this way the incoming signal, +which decreases the plate current, can produce the largest decrease. It +is also possible to start with the grid slightly positive instead of +being as negative as it is when connected to the negative terminal of +the A-battery. There will then be possible a greater change in grid +voltage. To do so connect the grid as in Fig. 115 to the positive +terminal of the A-battery. + +[Illustration: Fig 113] + +About this time I would shop around for two or three small double-pole +double-throw switches. Those of the 5-ampere size will do. With these +you can arrange to make comparisons between different methods of +receiving. Suppose, for example, you connect the switches as shown in +Fig. 113 so that by throwing them to the left you are using the audion +and to the right the crystal as a detector. You can listen for a minute +in one position and then switch and listen for a minute in the other +position, and so on back and forth. That way you can tell whether or not +you really are getting better results. + +If you want a rough measure of how much better the audion is than the +crystal you might see, while you are listening to the audion, how much +you can rob the telephone receiver of its current and still hear as well +as you do when you switch back to the crystal. The easiest way to do +this is to put a variable resistance across the receiver as shown in +Fig. 113. Adjust this resistance until the intensity of the signal when +detected by the audion is the same as for the crystal. You adjust this +variable resistance until it by-passes so much of the current, which +formerly went through the receiver, that the "audibility" of the signal +is reduced until it is the same as for the crystal detector. Carefully +made resistances for such a purpose are sold under the name of +"audibility meters." You can assemble a resistance which will do fairly +well if you will buy a small rheostat which will give a resistance +varying by steps of ten ohms from zero to one hundred ohms. At the same +time you can buy four resistance spools of one hundred ohms each and +perhaps one of 500 ohms. The spools need not be very expensive for you +do not need carefully adjusted resistances. Assemble them so as to make +a rheostat with a range of 0-1000 ohms by steps of 10 ohms. The cheapest +way to mount is with Fahnestock clips as illustrated in Fig. 114. After +a while, however, you will probably wish to mount them in a box with a +rotary switch on top. + +[Illustration: Fig 114] + +To study the effect of the grid condenser you can arrange switches so as +to insert this condenser and its leak and at the same time to cut out +the C-battery. Fig. 115 shows how. You can measure the gain in +audibility at the same time. + +[Illustration: Pl. X.--Audio-frequency Transformer and Banked-wound Coil. +(Courtesy of Pacent Electric Co.)] + +[Illustration: Fig 115] + +After learning to use the audion as a detector, both by virtue of its +curved characteristic and by the grid-condenser method, I would suggest +studying the same tube as an amplifier. First I would learn to use it as +an audio-frequency amplifier. Set up the crystal detector circuit. Use +your audio-frequency transformer the other way around so as to step up +to the grid. Put the telephone in the plate circuit. Choose your +C-battery for amplification and _not detection_ and try to receive. + +You will get better results if you can afford another iron-core +transformer. If you can, buy one which will work between the plate +circuit of one vacuum tube and the grid circuit of another similar tube. +Then you will have the right equipment when you come to make a two-stage +audio-frequency amplifier. If you buy such a transformer use the other +transformer between plate and telephones as you did before and insert +the new one as shown in Fig. 116. This circuit also shows how you can +connect the switches so as to see how much the audion is amplifying. + +[Illustration: Fig 116] + +The next step is to use the audion as an amplifier of the radio-signal +before its detection. Use the proper C-battery for an amplifier, as +determined from the blue print of the tube characteristic. Connect the +tube as shown in Fig. 117. You will see that in this circuit we are +using a choke coil to keep the radio-frequency current out of the +battery part of the plate circuit and a small condenser, another one of +0.002 mf., to keep the battery current from the crystal detector. You +can see from the same figure how you can arrange the switches so as to +find whether or not you are getting any gain from the amplifier. + +Now you are ready to receive those C-W senders at 275 meters. You will +need to wind another coil like the secondary coil you already have. Here +is where you buy another condenser. You will need it later. If before +you bought the 0.0005 size, this time buy the 0.001 size or vice versa. +Wind also a small coil for a tickler. About 20 turns of 26 wire on a +core of 3-1/2 in. diameter will do. Connect the tickler in the plate +circuit of the audion. Connect to the grid your new coil and condenser +and set the audion circuit so that it will induce a current in the +secondary circuit which supplies the crystal. Fig. 118 shows the +hook-up. + +[Illustration: Fig 117] + +You will see that you are now supplying the crystal with current from +two sources, namely the distant source of the incoming signals and the +local oscillator which you have formed. The crystal will detect the +"beat note" between these two currents. + +To receive the 275 meters signals you will need to make several +adjustments at the same time. In the first place I would set the tuning +of the antenna circuit and of the crystal circuit about where you think +right because of your knowledge of the settings for other wave lengths. +Then I would get the local oscillator going. You can tell whether or not +it is going if you suddenly increase or decrease the coupling between +the tickler coil and the input circuit of the audion. If this motion is +accompanied by a click in the receivers the tube is oscillating. + +[Illustration: Fig 118] + +Now you must change the frequency at which it is oscillating by slowly +changing the capacity in the tuned input circuit of the tube. Unless the +antenna circuit is properly tuned to the 275 meter signal you will get +no results. If it is, you will hear an intermittent musical note for +some tune of your local oscillator. This note will have the duration of +dots and dashes. + +You will have to keep changing the tuning of your detector circuit and +of the antenna. For each new setting very slowly swing the condenser +plates in the oscillator circuit and see if you get a signal. It will +probably be easier to use the "stand-by position," which I have +described, with switch _S_ open in the secondary circuit of Fig. +118. In that case you have only to tune your antenna to 275 meters and +then you will pick up a note when your local oscillator is in tune. +After you have done so you can tune the secondary circuit which supplies +the crystal. + +If you adopt this method you will want a close coupling between the +antenna and the crystal circuit. You will always want a very weak +coupling between the oscillator circuit and the detector circuit. You +will also probably want a weaker coupling between tickler and tube input +than you are at first inclined to believe will be enough. Patience and +some skill in manipulation is always required for this sort of +experiment. + +When you have completed this experiment in heterodyne receiving, using a +local oscillator, you are ready to try the regenerative circuit. This +has been illustrated in Fig. 92 of Letter 18 and needs no further +description. You will have the advantage when you come to this of +knowing very closely the proper settings of the antenna circuit and the +secondary tuned circuit. You will need then only to adjust the coupling +of the tickler and make finer adjustments in your tuning. + +After you have completed this series of experiments you will be +something of an adept at radio and are in a position to plan your final +set. For this set you will need to purchase certain parts complete from +reputable dealers because many of the circuits which I have described +are patented and should not be used except as rights to use are obtained +by the purchase of licensed apparatus which embodies the patented +circuits. Knowing how radio receivers operate and why, you are now in a +good condition to discuss with dealers the relative merits and costs of +receiving sets. + +[Illustration: Fig 119] + +Before you actually buy a completed set you may want to increase the +range of frequency over which you are carrying out your experiments. To +receive at longer wave-lengths you will need to increase the inductance +of your antenna so that it will be tuned to a lower frequency. This is +usually called "loading" and can be done by inserting a coil in the +antenna. To obtain smaller wave-lengths decrease the effective capacity +of the antenna circuit by putting another condenser in series with the +antenna. Usually, therefore, one connects into his antenna circuit both +a condenser and a loading coil. By using a variable condenser the +effective capacity of the antenna system may be easily changed. The +result is that this series condenser method becomes the easiest method +of tuning and the slide wire tuner is not needed. Fig. 119 shows the +circuit. + +For quite a range of wave-lengths we may use the same loading coil and +tune the antenna circuit entirely by this series condenser. For some +other range of wave-lengths we shall then need a different loading coil. +In a well-designed set the wave-length ranges overlap. The calculation +of the size of loading coil is quite easy but requires more arithmetic +than I care to impose on you at present. I shall therefore merely give +you illustrations based on the assumption that your antenna has a +capacity of 0.0001 or of 0.0002 mf. and that the condensers which you +have bought are 0.0005 and 0.001 for their maxima. + +In Table I there is given, for each of several values of the inductance +of the primary coil, the shortest and the longest wave-lengths which you +can expect to receive. The table is in two parts, the first for an +antenna of capacity 0.0001 mf. and the second for one of 0.0002 mf. +Yours will be somewhere between these two limits. The shortest +wave-length depends upon the antenna and not upon the condenser which +you use in series with it for tuning. It also depends upon how much +inductance there is in the coil which you have in the antenna circuit. +The table gives values of inductance in the first column, and of minimum +wave-length in the second. The third column shows what is the greatest +wave-length you may expect if you use a tuning condenser of 0.0005 mf.; +and the fourth column the slightly large wave-length which is possible +with the larger condenser. + + TABLE I + + Part 1. (For antenna of 0.0001 mf.) + + Inductance in Shortest wave-length Longest wave-length in meters + mil-henries. in meters. with 0.0005 mf. with 0.001 mf. + + 0.10 103 169 179 + 0.20 146 238 253 + 0.40 207 337 358 + 0.85 300 490 515 + 1.80 400 700 760 + 2.00 420 750 800 + 4.00 600 1080 1130 + 5.00 660 1200 1260 + 10.00 900 1700 1790 + 30.00 1600 2900 3100 + + Part 2. (For antenna of 0.0002 mf.) + + 0.10 169 225 240 + 0.16 210 285 305 + 0.20 240 320 340 + 0.25 270 355 380 + 0.40 340 450 480 + 0.60 420 550 590 + 0.80 480 630 680 + 1.20 585 775 840 + 1.80 720 950 1020 + 3.00 930 1220 1320 + 5.00 1200 1600 1700 + 8.00 1500 2000 2150 + 12.00 1850 2400 2650 + 16.00 2150 2800 3050 + +From Table I you can find how much inductance you will need in the +primary circuit. A certain amount you will need to couple the antenna +and the secondary circuit. The coil which you wound at the beginning of +your experiments will do well for that. Anything more in the way of +inductance, which the antenna circuit requires to give a desired +wave-length, you may consider as loading. In Table II are some data as +to winding coils on straight cores to obtain various values of +inductance. Your 26 s. s. c. wire will wind about 54 turns to the inch. +I have assumed that you will have this number of turns per inch on your +coils and calculated the inductance which you should get for various +numbers of total turns. The first part of the table is for a core of 3.5 +inches in diameter and the second part for one of 5 inches. The first +column gives the inductance in mil-henries. The second gives number of +turns. The third and fourth are merely for convenience and give the +approximate length in inches of the coil and the approximate total +length of wire which is required to wind it. I have allowed for bringing +out taps. In other words 550 feet of the wire will wind a coil of 10.2 +inches with an inductance of 8.00 mil-henries, and permit you to bring +out taps at all the lower values of inductance which are given in the +table. + + Table II + + Part 1. (For a core of 3.5 in. diam.) + + Inductance in Number Length Feet of wire + mil-henries. of turns. in inches. required. + 0.10 25 0.46 25 + 0.16 34 0.63 36 + 0.20 39 0.72 42 + 0.25 44 0.81 49 + 0.40 58 1.07 63 + 0.60 75 1.38 80 + 0.80 92 1.70 100 + 0.85 96 1.78 104 + 1.00 108 2.00 118 + 1.20 123 2.28 133 + 1.80 164 3.03 176 + 2.00 180 3.33 190 + 3.00 242 4.48 250 + 4.00 304 5.62 310 + 5.00 366 6.77 370 + 8.00 550 10.20 550 + + Part 2. (For core of 5.0 in. diam.) + + 2.00 120 2.22 160 + 3.00 158 2.93 215 + 4.00 194 3.58 265 + 5.00 228 4.22 310 + 8.00 324 6.00 450 + 10.00 384 7.10 530 + 12.00 450 8.30 625 + +The coil which you wound at the beginning of your experiment had only 75 +turns and was tapped so that you could, by manipulating the two switches +of Fig. 112, get small variations in inductance. In Table III is given +the values of the inductance which is controlled by the switches of that +figure, the corresponding number of turns, and the wave-length to which +the antenna should then be tuned. I am giving this for two values of +antenna capacity, as I have done before. By the aid of these three +tables you should have small difficulty in taking care of matters of +tuning for all wave-lengths below about 3000 meters. If you want to get +longer waves than that you had better buy a few banked-wound coils. +These are coils in which the turns are wound over each other but in such +a way as to avoid in large part the "capacity effects" which usually +accompany such winding. You can try winding them for yourself but I +doubt if the experience has much value until you have gone farther in +the study of the mathematical theory of radio than this series of +letters will carry you. + + TABLE III + Circuit of Fig. 112 + Number Inductance in Wave length with antenna of + of turns. mil-henries. 0.0001 mf. 0.0002 mf. + 14 0.04 120 170 + 20 0.07 160 220 + 28 0.12 210 290 + 36 0.18 250 360 + 44 0.25 300 420 + 56 0.38 370 520 + 75 0.60 460 650 + +In the secondary circuit there is only one capacity, that of the +variable condenser. If it has a range of values from about 0.00005 mf. +to 0.0005 mf. your coil of 60 turns and 0.42 mf. permits a range of +wave-lengths from 270 to 860 m. Using half the coil the range is 150 to +480 m. With the larger condenser the ranges are respectively 270 to 1220 +and 270 to 670. For longer wave-lengths load with inductance. Four times +the inductance will tune to double these wave-lengths. + +[Footnote 11: If you can afford to buy, or if you can borrow, ammeters +and voltmeters of the proper range you should take the characteristic +yourself.] + + +LETTER 22 + +HIGH-POWERED RADIO-TELEPHONE TRANSMITTERS + + +MY DEAR EXPERIMENTER: + +This letter is to summarize the operations which must be performed in +radio-telephone transmission and reception; and also to describe the +circuit of an important commercial system. + +To transmit speech by radio three operations are necessary. First, there +must be generated a high-frequency alternating current; second, this +current must be modulated, that is, varied in intensity in accordance +with the human voice; and third, the modulated current must be supplied +to an antenna. For efficient operation, of course, the antenna must be +tuned to the frequency which is to be transmitted. There is also a +fourth operation which is usually performed and that is amplification. +Wherever the electrical effect is smaller than desired, or required for +satisfactory transmission, vacuum tubes are used as amplifiers. Of this +I shall give you an illustration later. + +Three operations are also essential in receiving. First, an antenna must +be so arranged and tuned as to receive energy from the distant +transmitting station. There is then in the receiving antenna a current +similar in wave form to that in the transmitting antenna. Second, the +speech significance of this current must be detected, that is, the +modulated current must be demodulated. A current is then obtained which +has the same wave form as the human voice which was the cause of the +modulation at the distant station. The third operation is performed by a +telephone receiver which makes the molecules of air in its neighborhood +move back and forth in accordance with the detected current. As you +already know a fourth operation may be carried on by amplifiers which +give on their output sides currents of greater strength but of the same +forms as they receive at their input terminals. + +In transmitting and in receiving equipment two or more of these +operations may be performed by the same vacuum tube as you will remember +from our discussion of the regenerative circuit for receiving. For +example, also, in any receiving set the vacuum tube which detects is +usually amplifying. In the regenerative circuit for receiving continuous +waves by the heterodyne method the vacuum tube functions as a generator +of high-frequency current and as a detector of the variations in current +which occur because the locally-generated current does not keep in step +with that generated at the transmitting station. + +Another example of a vacuum tube performing simultaneously two different +functions is illustrated in Fig. 120 which shows a simple +radio-telephone transmitter. The single tube performs in itself both the +generation of the radio-frequency current and its modulation in +accordance with the output of the carbon-button transmitter. This audion +is in a feed-back circuit, the oscillation frequency of which depends +upon the condenser _C_ and the inductance _L_. The voice +drives the diaphragm of the transmitter and thus varies the resistance +of the carbon button. This varies the current from the battery, +_B_{a}_, through the primary, _T_{1}_, of the transformer +_T_. The result is a varying voltage applied to the grid by the +secondary _T_{2}_. The oscillating current in the plate circuit of +the audion varies accordingly because it is dependent upon the grid +voltage. The condenser _C_{r}_ offers a low impedance to the +radio-frequency current to which the winding _T_{2}_ of +audio-frequency transformer offers too much. + +[Illustration: Fig 120] + +In this case the tube is both generator and "modulator." In some cases +these operations are separately performed by different tubes. This was +true of the transmitting set used in 1915 when the engineers of the Bell +Telephone System talked by radio from Arlington, near Washington, D. C., +to Paris and Honolulu. I shall not draw out completely the circuit of +their apparatus but I shall describe it by using little squares to +represent the parts responsible for each of the several operations. + +First there was a vacuum tube oscillator which generated a small current +of the desired frequency. Then there was a telephone transmitter which +made variations in a direct-current flowing through the primary of a +transformer. The e. m. f. from the secondary of this transformer and the +e. m. f. from the radio-frequency oscillator were both impressed upon +the grid of an audion which acted as a modulator. The output of this +audion was a radio-frequency current modulated by the voice. The output +was amplified by a two-stage audion amplifier and supplied through a +coupling coil to the large antenna of the U. S. Navy Station at +Arlington. Fig. 121 shows the system. + +[Illustration: Fig 121] + +The audion amplifiers each consisted of a number of tubes operating in +parallel. When tubes are operated in parallel they are connected as +shown in Fig. 122 so that the same e. m. f. is impressed on all the +grids and the same plate-battery voltage on all the plates. As the grids +vary in voltage there is a corresponding variation of current in the +plate circuit of each tube. The total change of the current in the +plate-battery circuit is, then, the sum of the changes in all the +plate-filament circuits of the tubes. This scheme of connections gives a +result equivalent to that of a single tube with a correspondingly larger +plate and filament. + +[Illustration: Fig 122] + +Parallel connection is necessary because a single tube would be +overheated in delivering to the antenna the desired amount of power. You +remember that when the audion is operated as an amplifier the resistance +to which it supplies current is made equal to its own internal +resistance of _R_{p}_. That means that there is in the plate +circuit just as much resistance inside the tube as outside. Hence there +is the same amount of work done each second in forcing the current +through the tube as through the antenna circuit, if that is what the +tube supplies. "Work per second" is power; the plate battery is spending +energy in the tube at the same rate as it is supplying it to the antenna +where it is useful for radiation. + +[Illustration: Pl. XI.--Broadcasting Equipment, Developed by the American +Telephone and Telegraph Company and the Western Electric Company.] + +All the energy expended in the tube appears as heat. It is due to the +blows which the electrons strike against the plate when they are drawn +across from the filament. These impacts set into more rapid motion the +molecules of the plate; and the temperature of the tube rises. There is +a limit to the amount the temperature can rise without destroying the +tube. For that reason the heat produced inside it must not exceed a +certain limit depending upon the design of the tube and the method of +cooling it as it is operated. In the Arlington experiments, which I +mentioned a moment ago, the tubes were cooled by blowing air on them +from fans. + +We can find the power expended in the plate circuit of a tube by +multiplying the number of volts in its battery by the number of amperes +which flows. Suppose the battery is 250 volts and the current 0.02 +amperes, then the power is 5 watts. The "watt" is the unit for measuring +power. Tubes are rated by the number of watts which can be safely +expended in them. You might ask, when you buy an audion, what is a safe +rating for it. The question will not be an important one, however, +unless you are to set up a transmitting set since a detector is usually +operated with such small plate-voltage as not to have expended in it an +amount of power dangerous to its life. + +In recent transmitting sets the tubes are used in parallel for the +reasons I have just told, but a different method of modulation is used. +The generation of the radio-frequency current is by large-powered tubes +which are operated with high voltages in their plate circuits. The +output of these oscillators is supplied to the antenna. The intensity of +the oscillations of the current in these tubes is controlled by changing +the voltage applied in their plate circuits. You can see from Fig. 123 +that if the plate voltage is changed the strength of the alternating +current is changed accordingly. It is the method used in changing the +voltage which is particularly interesting. + +[Illustration: Fig 123] + +The high voltages which are used in the plate circuits of these +high-powered audions are obtained from generators instead of batteries. +You remember from Letter 20 that an e. m. f. is induced in a coil when +the coil and a magnet are suddenly changed in their positions, one being +turned with reference to the other. A generator is a machine for turning +a coil so that a magnet is always inducing an e. m. f. in it. It is +formed by an armature carrying coils and by strong electromagnets. The +machine can be driven by a steam or gas engine, by a water wheel, or by +an electric motor. Generators are designed either to give steady streams +of electrons, that is for d-c currents, or to act as alternators. + +[Illustration: Fig 124] + +Suppose we have, as shown in Fig. 124, a d-c generator supplying +current to a vacuum tube oscillator. The current from the generator +passes through an iron-cored choke coil, marked _L_{a}_ in the figure. +Between this coil and the plate circuit we connect across the line a +telephone transmitter. To make a system which will work efficiently we +shall have to suppose that this transmitter has a high resistance, say +about the same as the internal resistance, _R_{p}_, of the tube and +also that it can carry as large a current. + +Of the current which comes from the generator about one-half goes to +the tube and the rest to the transmitter. If the resistance of the +transmitter is increased it can't take as much current. The coil, +_L_{a}_, however, because of its inductance, tends to keep the same +amount of current flowing through itself. For just an instant then the +current in _L_{a}_ keeps steady even though the transmitter doesn't +take its share. The result is more current for the oscillating tube. On +the other hand if the transmitter takes more current, because its +resistance is decreased, the choke coil, _L_{a}_, will momentarily tend +to keep the current steady so that what the transmitter takes must be +at the expense of the oscillating tube. + +That's one way of looking at what happens. We know, however, from Fig. +123 that to get an increase in the amplitude of the current in the +oscillating tube we must apply an increased voltage to its plate +circuit. That is what really happens when the transmitter increases in +resistance and so doesn't take its full share of the current. The +reason is this: When the transmitter resistance is increased the +current in the transmitter decreases. Just for a moment it looks as +though the current in _L_{a}_ is going to decrease. That's the way it +looks to the electrons; and you know what electrons do in an inductive +circuit when they think they shall have to stop. They induce each other +to keep on for a moment. For a moment they act just as if there was +some extra e. m. f. which was acting to keep them going. We say, +therefore, that there is an extra e. m. f., and we call this an e. m. +f. of self-induction. All this time there has been active on the plate +circuit of the tube the e. m. f. of the generator. To this there is +added at the instant when the transmitter resistance increases, the e. +m. f. of self-induction in the coil, _L_{a}_ and so the total e. m. f. +applied to the tube is momentarily increased. This increased e. m. f., +of course, results in an increased amplitude for the alternating +current which the oscillator is supplying to the transmitting antenna. + +When the transmitter resistance is decreased, and a larger current +should flow through the choke coil, the electrons are asked to speed up +in going through the coil. At first they object and during that instant +they express their objection by an e. m. f. of self-induction which +opposes the generator voltage. For an instant, then, the voltage of the +oscillating tube is lowered and its alternating-current output is +smaller. + +[Illustration: Fig 125] + +For the purpose of bringing about such threatened changes in current, +and hence such e. m. f.'s of self-induction, the carbon transmitter is +not suitable because it has too small a resistance and too small a +current carrying ability. The plate circuit of a vacuum tube will serve +admirably. You know from the audion characteristic that without changing +the plate voltage we can, by applying a voltage to the grid, change the +current through the plate circuit. Now if it was a wire resistance with +which we were dealing and we should be able to obtain a change in +current without changing the voltage acting on this wire we would say +that we had changed the resistance. We can say, therefore, that the +internal resistance of the plate circuit of a vacuum tube can be changed +by what we do to the grid. + +In Fig. 125 I have substituted the plate circuit of an audion for the +transmitter of Fig. 124 and arranged to vary its resistance by changing +the potential of the grid. This we do by impressing upon the grid the e. +m. f. developed in the secondary of a transformer, to the primary of +which is connected a battery and a carbon transmitter. The current +through the primary varies in accordance with the sounds spoken into the +transmitter. And for all the reasons which we have just finished +studying there are similar variations in the output current of the +oscillating tube in the transmitting set of Fig. 125. + +In this latter figure you will notice a small air-core coil, +_L_{R}_, between the oscillator and the modulator tube. This coil +has a small inductance but it is enough to offer a large impedance to +radio-frequency currents. The result is, it does not let the alternating +currents of the oscillating tube flow into the modulator. These currents +are confined to their own circuit, where they are useful in establishing +similar currents in the antenna. On the other hand, the coil _L_{R}_ +doesn't seriously impede low-frequency currents and therefore it does +not prevent variations in the current which are at audio-frequency. It +does not interfere with the changes in current which accompany the +variations in the resistance of the plate circuit of the modulator. +That is, it has too little impedance to act like _L_{a}_ and so it +permits the modulator to vary the output of the oscillator. + +[Illustration: Fig 126] + +The oscillating circuit of Fig. 125 includes part of the antenna. It +differs also from the others I have shown in the manner in which grid +and plate circuits are coupled. I'll explain by Fig. 126. + +The transmitting set which I have just described involves many of the +principles of the most modern sets. If you understand its operation you +can probably reason out for yourself any of the other sets of which you +will hear from time to time. + + + + +LETTER 23 + +AMPLIFICATION AT INTERMEDIATE FREQUENCIES + + +DEAR SON: + +In the matter of receiving I have already covered all the important +principles. There is one more system, however, which you will need to +know. This is spoken of either as the "super-heterodyne" or as the +"intermediate-frequency amplification" method of reception. + +The system has two important advantages. First, it permits sharper +tuning and so reduces interference from other radio signals. Second, it +permits more amplification of the incoming signal than is usually +practicable. + +First as to amplification: We have seen that amplification can be +accomplished either by amplifying the radio-frequency current before +detection or by amplifying the audio-frequency current which results +from detection. There are practical limitations to the amount of +amplification which can be obtained in either case. An efficient +multi-stage amplifier for radio-frequencies is difficult to build +because of what we call "capacity effects." + +Consider for example the portion of circuit shown in Fig. 127. The wires +_a_ and _b_ act like small plates of condensers. What we +really have, is a lot of tiny condensers which I have shown in the +figure by the light dotted-lines. If the wires are transmitting +high-frequency currents these condensers offer tiny waiting-rooms where +the electrons can run in and out without having to go on to the grid of +the next tube. There are other difficulties in high-frequency +amplifiers. This one of capacity effects between parallel wires is +enough for the present. It is perhaps the most interesting because it is +always more or less troublesome whenever a pair of wires is used to +transmit an alternating current. + +[Illustration: Fig 127] + +In the case of a multi-stage amplifier of audio-frequency current there +is always the possibility of the amplification of any small variations +in current which may naturally occur in the action of the batteries. +There are always small variations in the currents from batteries, due to +impurities in the materials of the plates, air bubbles, and other +causes. Ordinarily we don't observe these changes because they are too +small to make an audible sound in the telephone receivers. Suppose, +however, that they take place in the battery of the first tube of a +series of amplifiers. Any tiny change of current is amplified many times +and results in a troublesome noise in the telephone receiver which is +connected to the last tube. + +In both types of amplifiers there is, of course, always the chance that +the output circuit of one tube may be coupled to and induce some effect +in the input circuit of one of the earlier tubes of the series. This +will be amplified and result in a greater induction. In other words, in +a circuit where there is large amplification, there is always the +difficulty of avoiding a feed-back of energy from one tube to another so +that the entire group acts like an oscillating circuit, that is +"regeneratively." Much of this difficulty can be avoided after +experience. + +If a multi-stage amplifier is to be built for a current which does not +have too high a frequency the "capacity effects" and the other +difficulties due to high-frequency need not be seriously troublesome. If +the frequency is not too high, but is still well above the audible +limit, the noises due to variations in battery currents need not bother +for they are of quite low frequency. Currents from 20,000 to 60,000 +cycles a second are, therefore, the most satisfactory to amplify. + +Suppose, however, one wishes to amplify the signals from a +radio-broadcasting station. The wave-length is 360 meters and the +frequency is about 834,000 cycles a second. The system of +intermediate-frequency amplification solves the difficulty and +we shall see how it does so. + +[Illustration: Fig 128] + +At the receiving station a local oscillator is used. This generates a +frequency which is about 30,000 cycles less than that of the incoming +signal. Both currents are impressed on the grid of a detector. The +result is, in the output of the detector, a current which has a +frequency of 30,000 cycles a second. The intensity of this detected +current depends upon the intensity of the incoming signal. The "beat +note" current of 30,000 cycles varies, therefore, in accordance with the +voice which is modulating at the distant sending station. The speech +significance is now hidden in a current of a frequency intermediate +between radio and audio. This current may be amplified many times and +then supplied to the grid of a detector which obtains from it a current +of audio-frequency which has a speech significance. In Fig. 128 I have +indicated the several operations. + +We can now see why this method permits sharper tuning. The whole idea +of tuning, of course, is to arrange that the incoming signal shall cause +the largest possible current and at the same time to provide that any +signals at other wave-lengths shall cause only negligible currents. What +we want a receiving set to do is to distinguish between two signals +which differ slightly in wave-length and to respond to only one of them. + +Suppose we set up a tuned circuit formed by a coil and a condenser and +try it out for various frequencies of signals. You know how it will +respond from our discussion in connection with the tuning curve of Fig. +51 of Letter 13. We might find from a number of such tests that the best +we can expect any tuned circuit to do is to discriminate between signals +which differ about ten percent in frequency, that is, to receive well +the desired signal and to fail practically entirely to receive a signal +of a frequency either ten percent higher or the same amount lower. + +For example, if the signal is at 30,000 cycles a tuned circuit might be +expected to discriminate against an interfering signal of 33,000. If the +signal is at 300,000 cycles a tuned circuit might discriminate against +an interfering signal of 330,000 cycles, but an interference at 303,000 +cycles would be very troublesome indeed. It couldn't be "tuned out" at +all. + +Now suppose that the desired signal is at 300,000 cycles and that there +is interference at 303,000 cycles. We provide a local oscillator of +270,000 cycles a second, receive by this "super-heterodyne" method which +I have just described, and so obtain an intermediate frequency. In the +output of the first detector we have then a current of 300,000--270,000 +or 30,000 cycles due to the desired signal and also a current of +303,000--270,000 or 33,000 cycles due to the interference. Both these +currents we can supply to another tuned circuit which is tuned for +30,000 cycles a second. It can receive the desired signal but it can +discriminate against the interference because now the latter is ten +percent "off the tune" of the signal. + +You see the question is not one of how far apart two signals are in +number of cycles per second. The question always is: How large in +percent is the difference between the two frequencies? The matter of +separating two effects of different frequencies is a question of the +"interval" between the frequencies. To find the interval between two +frequencies we divide one by the other. You can see that if the quotient +is larger than 1.1 or smaller than 0.9 the frequencies differ by ten +percent or more. The higher the frequency the larger the number of +cycles which is represented by a given size of interval. + +While I am writing of frequency intervals I want to tell you one thing +more of importance. You remember that in human speech there may enter, +and be necessary, any frequency between about 200 and 2000 cycles a +second. That we might call the range of the necessary notes in the +voice. Whenever we want a good reproduction of the voice we must +reproduce all the frequencies in this range. + +Suppose we have a radio-current of 100,000 cycles modulated by the +frequencies in the voice range. We find in the output of our +transmitting set not only a current of 100,000 cycles but currents in +two other ranges of frequencies. One of these is above the signal +frequency and extends from 100,200 to 102,000 cycles. The other is the +same amount below and extends from 98,000 to 99,800 cycles. We say there +is an upper and a lower "band of frequencies." + +All these currents are in the complex wave which comes from the +radio-transmitter. For this statement you will have to take my word +until you can handle the form of mathematics known as "trigonometry." +When we receive at the distant station we receive not only currents of +the signal frequency but also currents whose frequencies lie in these +"side-bands." + +No matter what radio-frequency we may use we must transmit and receive +side-bands of this range if we use the apparatus I have described in +the past letters. You can see what that means. Suppose we transmit at a +radio-frequency of 50,000 cycles and modulate that with speech. We +shall really need all the range from 48,000 cycles to 52,000 cycles for +one telephone message. On the other hand if we modulated a 500,000 +cycle wave by speech the side-bands are from 498,000 to 499,800 and +500,200 to 502,000 cycles. If we transmit at 50,000 cycles, that is, at +6000 meters, we really need all the range between 5770 meters and 6250 +meters, as you can see by the frequencies of the side-bands. At 100,000 +cycles we need only the range of wave-lengths between 2940 m. and 3060 +m. If the radio-frequency is 500,000 cycles we need a still smaller +range of wave-lengths to transmit the necessary side-bands. Then the +range is from 598 m. to 603 m. + +In the case of the transmission of speech by radio we are interested in +having no interference from other signals which are within 2000 cycles +of the frequency of our radio-current no matter what their wave-lengths +may be. The part of the wave-length range which must be kept clear from +interfering signals becomes smaller the higher the frequency which is +being modulated. + +You can see that very few telephone messages can be sent in the +long-wave-length part of the radio range and many more, although not +very many after all, in the short wave-length part of the radio range. +You can also see why it is desirable to keep amateurs in the short +wave-length part of the range where more of them can transmit +simultaneously without interfering with each other or with commercial +radio stations. + +There is another reason, too, for keeping amateurs to the shortest +wave-lengths. Transmission of radio signals over short distances is best +accomplished by short wave-lengths but over long distances by the longer +wave-lengths. For trans-oceanic work the very longest wave-lengths are +best. The "long-haul" stations, therefore, work in the frequency range +immediately above 10,000 cycles a second and transmit with wave lengths +of 30,000 m. and shorter. + +[Illustration: Pl. XII.--Broadcasting Station of the American Telephone +and Telegraph Company on the Roof of the Walker-Lispenard Bldg. in New +York City Where the Long-distance Telephone Lines Terminate.] + + + + +LETTER 24 + +BY WIRE AND BY RADIO + + +DEAR BOY: + +The simplest wire telephone-circuit is formed by a transmitter, a +receiver, a battery, and the connecting wire. If two persons are to +carry on a conversation each must have this amount of equipment. The +apparatus might be arranged as in Fig. 129. This set-up, however, +requires four wires between the two stations and you know the telephone +company uses only two wires. Let us find the principle upon which its +system operates because it is the solution of many different problems +including that of wire-to-radio connections. + +[Illustration: Fig 129] + +Imagine four wire resistances connected together to form a square as in +Fig. 130. Suppose there are two pairs of equal resistances, namely +_R_{1}_ and _R_{2}_, and _Z_{1}_ and _Z_{2}_. If we connect a +generator, _G_, between the junctions _a_ and _b_ there will be two +separate streams of electrons, one through the R-side and the other +through the Z-side of the circuit. These streams, of course, will not +be of the same size for the larger stream will flow through the side +which offers the smaller resistance. + +[Illustration: Fig 130] + +Half the e. m. f. between _a_ and _b_ is used up in sending the +stream half the distance. Half is used between _a_ and the points _c_ +and _d_, and the other half between _c_ and _d_ and the other end. It +doesn't make any difference whether we follow the stream from _a_ to +_c_ or from _a_ to _d_, it takes half the e. m. f. to keep this +stream going. Points _c_ and _d_, therefore, are in the same condition +of being "half-way electrically" from _a_ to _b_. The result is that +there can be no current through any wire which we connect between +_c_ and _d_. + +Suppose, therefore, that we connect a telephone receiver between +_c_ and _d_. No current flows in it and no sound is emitted by +it. Now suppose the resistance of _Z_{2}_ is that of a telephone +line which stretches from one telephone station to another. Suppose also +that _Z_{1}_ is a telephone line exactly like _Z_{2}_ except +that it doesn't go anywhere at all because it is all shut up in a little +box. We'll call _Z_{1}_ an artificial telephone line. We ought to +call it, as little children would say, a "make-believe" telephone line. +It doesn't fool us but it does fool the electrons for they can't tell +the difference between the real line _Z_{2}_ and the artificial +line _Z_{1}_. We can make a very good artificial line by using a +condenser and a resistance. The condenser introduces something of the +capacity effects which I told you were always present in a circuit +formed by a pair of wires. + +[Illustration: Fig 131] + +At the other telephone station let us duplicate this apparatus, using +the same real line in both cases. Instead of just any generator of an +alternating e. m. f. let us use a telephone transmitter. We connect the +transmitter through a transformer. The system then looks like that of +Fig. 131. When some one talks at station 1 there is no current through +his receiver because it is connected to _c_ and _d_, while the +e. m. f. of the transmitter is applied to _a_ and _b_. The transmitter +sets up two electron streams between _a_ and _b_, and the stream which +flows through the Z-side of the square goes out to station 2. At this +station the electrons have three paths between _d_ and _b_. I have +marked these by arrows and you see that one of them is through the +receiver. The current which is started by the transmitter at station 1 +will therefore operate the receiver at station 2 but not at its own +station. Of course station 2 can talk to 1 in the same way. + +The actual set-up used by the telephone company is a little different +from that which I have shown because it uses a single common battery at +a central office between two subscribers. The general principle, +however, is the same. + +[Illustration: Fig 132] + +It won't make any difference if we use equal inductance coils, instead +of the R-resistances, and connect the transmitter to them inductively as +shown in Fig. 132. So far as that is concerned we can also use a +transformer between the receiver and the points _c_ and _d_, +as shown in the same figure. + +[Illustration: Fig 133] + +We are now ready to put in radio equipment at station 2. In place of the +telephone receiver at station 2 we connect a radio transmitter. Then +whatever a person at station 1 says goes by wire to 2 and on out by +radio. In place of the telephone transmitter at station 2 we connect a +radio receiver. Whatever that receives by radio is detected and goes by +wire to the listener at station 1. In Fig. 133 I have shown the +equipment of station 2. There you have the connections for wire to radio +and vice versa. + +One of the most interesting developments of recent years is that of +"wired wireless" or "carrier-current telephony" over wires. Suppose that +instead of broadcasting from the antenna at station 2 we arrange to have +its radio transmitter supply current to a wire circuit. We use this same +pair of wires for receiving from the distant station. We can do this if +we treat the radio transmitter and receiver exactly like the telephone +instruments of Fig. 132 and connect them to a square of resistances. One +of these resistances is, of course, the line between the stations. I +have shown the general arrangement in Fig. 134. + +You see what the square of resistances, or "bridge" really does for us. +It lets us use a single pair of wires for messages whether they are +coming or going. It does that because it lets us connect a transmitter +and also a receiver to a single pair of wires in such a way that the +transmitter can't affect the receiver. Whatever the transmitter sends +out goes along the wires to the distant receiver but doesn't affect the +receiver at the sending station. This bridge permits this whether the +transmitter and receiver are radio instruments or are the ordinary +telephone instruments. + +[Illustration: Fig 134] + +By its aid we may send a modulated high-frequency current over a pair of +wires and receive from the same pair of wires the high-frequency current +which is generated and modulated at the distant end of the line. It lets +us send and receive over the same pair of wires the same sort of a +modulated current as we would supply to an antenna in radio-telephone +transmitting. It is the same sort of a current but it need not be +anywhere near as large because we aren't broadcasting; we are sending +directly to the station of the other party to our conversation. + +If we duplicate the apparatus we can use the same pair of wires for +another telephone conversation without interfering with the first. Of +course, we have to use a different frequency of alternating current for +each of the two conversations. We can send these two different modulated +high-frequency currents over the same pair of wires and separate them by +tuning at the distant end just as well as we do in radio. I won't sketch +out for you the tuned circuits by which this separation is made. It's +enough to give you the idea. + +In that way, a single pair of wires can be used for transmitting, +simultaneously and without any interference, several different telephone +conversations. It takes very much less power than would radio +transmission and the conversations are secret. The ordinary telephone +conversation can go on at the same time without any interference with +those which are being carried by the modulations in high-frequency +currents. A total of five conversations over the same pair of wires is +the present practice. + +This method is used between many of the large cities of the U. S. +because it lets one pair of wires do the work of five. That means a +saving, for copper wire costs money. Of course, all the special +apparatus also costs money. You can see, therefore, that this method +wouldn't be economical between cities very close together because all +that is saved by not having to buy so much wire is spent in building +special apparatus and in taking care of it afterwards. For long lines, +however, by not having to buy five times as much wire, the Bell Company +saves more than it costs to build and maintain the extra special +apparatus. + +I implied a moment ago why this system is called a "carrier-current" +system; it is because "the high-frequency currents carry in their +modulations the speech significance." Sometimes it is called a system of +"multiplex" telephony because it permits more than one message at a +time. + +This same general principle is also applied to the making of a multiplex +system of telegraphy. In the multiplex telephone system we pictured +transmitting and receiving sets very much like radio-telephone sets. If +instead of transmitting speech each transmitter was operated as a C-W +transmitter then it would transmit telegraph messages. In the same +frequency range there can be more telegraph systems operated +simultaneously without interfering with each other, for you remember how +many cycles each radio-telephone message requires. For that reason the +multiplex telegraph system which operates by carrier-currents permits as +many as ten different telegraph messages simultaneously. + +You remember that I told you how capacity effects rob the distant end of +a pair of wires of the alternating current which is being sent to them. +That is always true but the effect is not very great unless the +frequency of the alternating current is high. It's enough, however, so +that every few hundred miles it is necessary to connect into the circuit +an audion amplifier. This is true of carrier currents especially, but +also true of the voice-frequency currents of ordinary telephony. The +latter, however, are not weakened, that is, "attenuated," as much and +consequently do not need to be amplified as much to give good +intelligibility at the distant receiver. + +[Illustration: Fig 135] + +In a telephone circuit over such a long distance as from New York City +to San Francisco it is usual to insert amplifiers at about a dozen +points along the route. Of course, these amplifiers must work for +transmission in either direction, amplifying speech on its way to San +Francisco or in the opposite direction. At each of the amplifying +stations, or "repeater stations," as they are usually called, two vacuum +tube amplifiers are used, one for each direction. To connect these with +the line so that each may work in the right direction there are used two +of the bridges or resistance squares. You can see from the sketch of +Fig. 135 how an alternating current from the east will be amplified and +sent on to the west, or vice versa. + +[Illustration: Fig 136] + +There are a large number of such repeater stations in the United States +along the important telephone routes. In Fig. 136 I am showing you the +location of those along the route of the famous "transcontinental +telephone-circuit." This shows also a radio-telephone connection between +the coast of California and Catalina Island. Conversations have been +held between this island and a ship in the Atlantic Ocean, as shown in +the sketch. The conversation was made possible by the use of the vacuum +tube and the bridge circuit. Part of the way it was by wire and part by +radio. Wire and radio tie nicely together because both operate on the +same general principles and use much of the same apparatus. + +[Blank Page] + + + + +INDEX + + A-battery for tubes, 42 + + Accumulator, 29 + + Acid, action of hydrogen in, 7 + + Air, constitution of, 10 + + Ammeter, alternating current, 206; + calibration of, 53; + construction of, 205 + + Ampere, 49, 54 + + Amplification, 182; one stage of, 185 + + Amplitude of vibration, 155 + + Antenna current variation, 141 + + Arlington tests, 233 + + Artificial telephone line, 252 + + Atom, conception of, 6; + nucleus of, 10; + neutral, 34 + + Atomic number, 13 + + Atoms, difference between, 12; + kinds of, 6, 10; + motion of, 35 + + Attenuation of current in wires, 259 + + Audibility meter, 218 + + Audio-frequency amplifier, 185; + limitations of, 185 + + Audion, 35, 40, 42 + + Audion, amplifier, 182; + detector, theory of, 126; + modulator, 232; + oscillator, theory of, 89; + frequency control of, 99 + + B-battery for tubes, 43; + effect upon characteristic, 128 + + Banked wound coils, 228 + + Battery, construction of gravity, 16; + dry, 27; + reversible or storage, 29 + + Band of frequencies, 249 + + Beat note, detection of, 221, 245 + + Bell system, Arlington transmitter, 249 + + Blocking of tube, reason for, 171 + + Blue vitriol, 16 + + Bridge circuit, 255 + + Bureau of Standards, 50 + + C-battery for tubes, 46, 166; + variation of, 75; + for detection, 66 + + Calibration of a receiver, 214 + + Capacity, effect upon frequency, 100; + measurement of, 104; + unit of, 104; + variable, 107 + + Capacity effects, 243; + elimination of, 228 + + Carrier current, modulation of, 146; + telephony, 255 + + Characteristic, of vacuum tube, 68, 74; + effect of B-battery upon, 128; + how to plot a, 70 + + Characteristic curve of transformer, 64 + + Chemistry, 8 + + Choke coils, 210, 221 + + Circuit, A, B, C, 187; + coupled, 115; + defined, 43; + oscillating, 113; + plate, 45; + short, 30; + tune of a, 117 + + Condenser, defined, 77; + charging current of, 78; + discharge current of, 80; + impedance of, 135; + theory of, 78; + tuning, 224 + + Common battery system, 254 + + Connection for wire to radio, 254 + + Continuous waves, 86 + + Copper, atomic number of, 13 + + Copper sulphate, in solution, 21 + + Crystals, atomic structure, 147 + + Crystal detectors, 146; + characteristic of, 148; + circuit of, 150; + theory of, 147 + + Current, transient, 114; + radio, 144 + + Cycle, 94, 97 + + Damped oscillations, 114 + + Demodulation, 231 + + Detection, explained, 146 + + Detectors, audion, 126; + crystal, 146 + + Direct currents, 205 + + Dissociation, 22 + + Distortion, of wave form, 163 + + Dry battery, 27 + + Earth, atomic constitution, 11 + + Effective value, of ampere, 207; + of volt, 207 + + Efficiency, of regenerative circuit, 182 + + Electrical charge, 22 + + Electricity, current of, 15, 16 + + Electrodes, of vacuum tube, 41; + definition of, 41 + + Electrolyte, definition of, 34 + + Electrons, properties of, 4; + planetary, 10, 12; + rate of flow, 48; + vapor of, 39; + wandering of, 14 + + Electron streams, laws of attraction, 200 + + E. M. F., 59; + alternating, 76; + of self-induction, 238 + + Energy, expended in tube, 235; + of electrons, 113; + radiation of, 125 + + Ether, 88 + + Feed-back circuit, 182 + + Frequency, 98, 158; + effect upon pitch, 133; + interval, 247; + natural, 117; + of voice, 163 + + Fundamental note, of string, 157 + + Gravity battery, theory of, 23 + + Grid, action of, 47; + condenser, 169; + current, 173; + leak, 171; + leak, construction, 172, 216; + of audion, 41 + + Harmonics, 160 + + Helium, properties of, 9 + + Henry, 83 + + Heterodyne, 181 + + Hot-wire ammeter, 51 + + Human voice, mechanism of, 152 + + Hydrogen, action of in acid, 7; + atom of, 7 + + Impedance, of coil, 136; + of condenser, 136; + of transformer, 195; + effect of iron core upon, 207; + matching of, 196 + + Intermediate-frequency amplification, 242 + + Inductance, defined, 83; + effect upon frequency, 100; + impedance of, 135; + mutual, 109; + of coils, 101; + self, 83; + table of values, 227; + unit of, 83; + variable, 108 + + Induction, principle of, 208 + + Inducto-meter, 109 + + Input circuit, 187 + + Interference, 249 + + Internal resistance, 191 + + Ion, definition of, 19; + positive and negative, 20, 21 + + Ionization, 20 + + Larynx, 153 + + Laws of attraction, 204 + + Loading coil, 224 + + Loop antenna, 198 + + Magnet, pole of, 203; + of soft iron, 205; + of steel, 205 + + Magnetism, 202 + + Matter, constitution of, 5 + + Megohm, 172 + + Microfarad, 104 + + Mil-ampere, 71 + + Mil-henry, 83 + + Modulation, 145, 230, 237, 239 + + Molecule, kinds of, 6; + motion of, 35 + + [Greek: mu], 190 + + Multiplex telegraphy, 258; + telephony, 258 + + Mutual inductance, 109; + variation of, 110 + + Natural frequency, 161 + + Nitrogen, 10 + + Nucleus of atom, 10, 12 + + Ohm, defined, 64 + + Organ pipe, 160 + + Oscillations, 87; + damped, 114; + to start, 114; + intensity of, 236; + natural frequency of, 117 + + Output circuit, 187 + + Overtones, 159 + + Oxygen, percentage in air, 10 + + Phase, 180 + + Plate, of an audion, 41 + + Plunger type of instrument, 205 + + Polarity of a coil, 204 + + Power, defined, 234; + electrical unit of, 235 + + Proton, properties of, 4 + + Radio current, modulation of, 145 + + Radio-frequency amplification, 243; + limitations, 243 + + Radio-frequency amplifier, 186, 198 + + Radio station connected to land line, 254 + + Rating of tubes, 235 + + Reception, essential operations in, 235 + + Regenerative circuit, 176; + frequency of, 179 + + Repeater stations, 261 + + Resistance, measurement of, 64; + non-inductive, 103; + square, 251 + + Resonance, 161 + + Resonance curve, 117 + + Retard coils, 210 + + Salt, atomic construction of, 17; + crystal structure, 147; + molecule in solution, 19; + percentage in sea water, 11 + + Saturation, 38 + + Sea water, atomic constitution of, 11 + + Self-inductance, 83; + unit of, 83 + + Side bands, 248; + relation to wave lengths, 249 + + Silicon, percentage in earth, 11 + + Sodium chloride, in solution, 19 + + Sound, production of, 152 + + Speech, to transmit by radio, 230 + + Speed of light, 122 + + Standard cell, 58 + + Storage battery, 28, 30 + + Sulphuric acid, 22 + + Super-heterodyne, 242; + advantages of, 242 + + Telephone receiver, 130; + theory of, 131 + + Telephone transmitter, 142 + + Telephony, by wire, 253 + + Tickler coil, 182 + + Transcontinental telephone line, 261 + + Transmission, essential operations in, 230 + + Transmitter, Arlington, 233; + continuous wave, 94, 119; + for high power, 233 + + Transformer, 185; + step-up, 193 + + Tubes, connected in parallel, 234 + + Tuning, curve, 117; + sharp, 214; + with series condenser, 224 + + Undamped waves (see continuous waves), 86 + + Vacuum tube, 35, 40; + characteristics of, 67; + construction of, 205; + modulator, 239; + three-electrode, 41; + two-electrode, 42 + + Variometer, 108 + + Vibrating string, study of, 154 + + Vocal cords, 153 + + Voice frequencies, 163 + + Volt, definition of, 57; + measurement of, 61 + + Voltmeter, calibration of, 62; + construction of, 205 + + Watt, 235 + + Wave form, 182 + + Wave length, relation to frequency, 98, 122; + defined, 122 + + Wire, inductance of, 104 + + Wire, movement of electrons in, 14; + emission of electrons from, 37 + + Wire telephony, 253 + + Wired wireless, 255; + advantages of, 257 + + X-rays, 147 + + Zero coupling, 177 + + Zinc, electrode for battery, 23 + + + + + + +End of the Project Gutenberg EBook of Letters of a Radio-Engineer to His Son, by +John Mills + +*** END OF THIS PROJECT GUTENBERG EBOOK LETTERS--RADIO-ENGINEER TO SON *** + +***** This file should be named 30688-8.txt or 30688-8.zip ***** +This and all associated files of various formats will be found in: + https://www.gutenberg.org/3/0/6/8/30688/ + +Produced by Roger Frank, Robert Cicconetti and the Online +Distributed Proofreading Team at https://www.pgdp.net + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. 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