Letters of a Radio-Engineer to His Son Part 8

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.

[Ill.u.s.tration: 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 relations.h.i.+p. 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.

[Ill.u.s.tration: 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 pa.s.sed 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 s.h.i.+p 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, s.h.i.+ps 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 s.h.i.+p 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.

[Ill.u.s.tration: 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_.

[Ill.u.s.tration: 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."

[Ill.u.s.tration: 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 pa.s.s 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 s.p.a.ce 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 s.p.a.ce 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.