[Ill.u.s.tration: 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 s.p.a.ce for electrons is increased.
[Ill.u.s.tration: Pl. VI.--Low-power Transmitting Tube, U V 202 (Courtesy of Radio Corporation of America).]
[Ill.u.s.tration: 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.
[Ill.u.s.tration: Fig 43]
[Ill.u.s.tration: 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.
[Ill.u.s.tration: 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 trespa.s.sing.
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.
[Ill.u.s.tration: Fig 46a]
[Ill.u.s.tration: 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.
[Ill.u.s.tration: 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.
[Ill.u.s.tration: 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.
[Ill.u.s.tration: 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.
[Ill.u.s.tration: Fig 47c]
Remove the battery and connect the charged condenser to the resistance as in Fig. 47c. The electrons rush home. They b.u.mp 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.
[Ill.u.s.tration: 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 b.u.mp and jostle, but some of them are stopped or else diverted so that they go b.u.mping 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."
[Ill.u.s.tration: 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.
[Ill.u.s.tration: Fig 49]
Now take away this coil _ab_ with its battery and subst.i.tute 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 a.s.sociated 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.
[Ill.u.s.tration: 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.