Radio Broadcast (May 1928-Apr 1929)

RADIO BROADCAST No. 19 Radio Broadcast's Home-Study Sheets April 1929 Fundamental Radio Theory '"THERE is a simple formula that must be used -1 very generally if one is going to plan or experiment in a quantitative way with radio circuits. Its use need not involve any tedious mathematical reductions, as the results of this formula have been reduced to tabular form. The application of this formula is so fundamental that every student of the' subject should have a clear understanding of the simple manner in which it is derived. It is, in fact, the connecting link, so to speak, between two very different electrical manifestations — the alternating current that lights our homes and the faint' radio waves that find their way to the antenna. It is assumed that the reader is already possessed of an elementary knowledge of electricity and is familiar with the fundamental units involved in expressing such quantities, as voltage (E), current (I), resistance (R), capacity (C), and inductance (L). The last term is the only one that usually presents any difficulty, but it will become clear as the work proceeds. Ohm's law, I = =-, (See Home Study Sheet No. K, 3) expresses the relation of current, voltage, and -Tuning 60-cycle 110-volt supply resistance in a direct-current circuit. The corresponding formula for an alternating-current circuit is: in which f is the frequency of the alternations. Now it requires scarcely an elementary knowledge of algebra to see that if the two terms inclosed within the brackets in the denominator can be made to equal one another, their difference will be zero, and the equation becomes. E VR2 + ° which is Ohm's law. When this condition exists the circuit is said to be tuned. The essential point to be observed is the fact that the denominator of the equation will be a minimum, and therefore the value of the current is maximum, only when 2irfL = 2xfc or wnen ^ 2x -y/LC. An experimental application of this important formula may be had readily if there are at hand one or two coils wound with fine wire on iron cores — the primary of an old high-ratio audio transformer, for example — and some condensers, such as are used as part of filters or by-pass equipment. Connect a ten or fifteen-watt lamp to the 110-volt alternating-current house supply in series with a coil and a condenser, as indicated in Fig. 1. When approximately the proper values for L and C for a 60-cycle current are secured, it will be found that when the condenser is short-circuited the lamp will burn less brightly, thus indicating that less current is flowing. To arrive at appropriate values of L and C for striking results, it may be necessary to use two coils in series, or two condensers in parallel, all depending on the equipment at hand. But the experiment is quite worth while, particularly to one whose experience has been largely with direct current, as it demonstrates so clearly that a condenser, which is a non-conductor in the case of direct current, is not only a conductor for alternating current, but may actually increase the flow of current. To apply our formula to this experiment, let it be supposed that a 1-mfd. filter condenser is used. This is one-millionth of a farad, which is the primary unit. A simple calculation will then show that for the usual frequency of 60 cycles per second an inductance of approximately 7 henries will be required to tune the circuit to produce the maximum current flow. No matter how different it may seem, radio is simply a manifestation of an alternating current of high frequency, the difference being purely one of degree and not of kind. The velocity at which a disturbance, say sound or light, travels depends on the medium through which it is transmitted. Thus, sound has one velocity in water (about 4900 feet per second) and another in air (about 1100 feet per second), but for either medium the velocity of all sounds is equal. That is, a note from the upper end of a piano will reach a distant observer as soon as one from the lower end. As both light and radio are dependent for their transmission on the same medium called the ether, they, in accordance with all other observed wave phenomena, travel at the same velocity. This velocity, is approximately 300,000,000 meters a second. As the velocity of propagation is constant, and as this velocity is equal to the length of one wave multiplied by the number of waves per second, or the frequency, f, it necessarily follows that f = 300,000,000 .... I . . i r and d t = ,z-r; , waveleugth = 2lt wavelength 2x -y/LC ^CL X 300,000,000 or if microhenries and microfarads are used wavelength = 1884 -\/LC fre159.2. quency in kc. = ^/lq These relations have been worked out for a great many wavelengths, and a few are presented in the following table. Its value to the experimenter will be evident. With a given coil and condenser, it is only necessary to multiply the inductance of one by the capacity of the other, to find the wavelength to which they will respond. If a condenser of a certain capacity is at hand, a simple division will tell us what the inductance must be to tune to a given wavelength. As the experimenter begins to get his laboratory together, he will soon find himself determining the inductances and capacities of his various coils and condensers, and, with the table at hand, he may always keep informed as to the wavelength or frequency of the current he is handling. Meters f L X C 100 3,000,000 0.00282 200 1,500,000 0.01126 300 1,000,000 0 . 0253 400 750,000 0 . 0450 500 600,000 0.0704 600 500,000 0.1013 700 429,000 0.1379 800 375,000 0 . 1801 900 333,000 0.228 1000 300,000 0.282 The experimenter will find a complete table of L C products in Principles Underlying Radio Communication, the Signal Corps book, and he should either get such a table or work out one for himself. The following rule will be helpful: For smaller values, divide meters by 10 and Lx C by 100 ; for larger values, multiply meters by 10 and LxC by 100. Mechanial Analogies The following mechanical analogy may aid in giving a little clearer view of the phenomena involved. The weight, L, in Fig. 2 is mounted on the upper end of an arm, the lower end of which is pivoted at the floor. A spring, C, is connected to the weight and to a rigid support, and is of such a length that the weight stands directly over the pivot when the spring is neither compressed nor extended. If the weight is pulled to one side and released it will vibrate back and forth at a certain definite frequency, depending on the size of the weight and the nature of the spring. The same frequency can be obtained by making the weight heavier and shortening the spring, or by reducing the weight and lengthening the spring. In the above example the frequency depends on the product of two factors, and this is precisely the case in radio oscillations. We can continue to tune to a certain wavelength by increasing the inductance and reducing the capacity, or vice versa. The spring is a rather apt analogy for a condenser, for the reason that when the latter is charged, the electrons are supposed to be displaced from their normal positions, to which they rebound when the condenser is discharged. Similarly appropriate is weight or mass in representing inductance, which may be considered as electrical inertia. Just as mass tends to retard the beginning of motion and to continue the motion when the applied force is withdrawn, so inductance opposes a sudden increase of current after the applied voltage ceases. The analogy may be carried further by considering the resistance of the air on the weight as corresponding to electrical resistance. Let it be supposed that the spring and weight were set up in a room from which the air has been exhausted, and that a fine thread attached to the weight is intermittently pulled exactly in tune with the natural period of oscillation. After a little time the oscillations will become very violent, and if the spring were of highly elastic material, it is quite possible that the repetition of a very minute force would finally break it. In other words, the internal forces generated within the spring may many times exceed the applied force, and this is exactly what occurs in a tuned electrical circuit when the resistance is greatly reduced, the voltage across the condenser being many times the impressed voltage. Hence it is that often a condenser tested to withstand a high voltage will break down in a resonant circuit, although no high voltage was outwardly applied. The voltage across a coil in a resonant circuit is 2 TC f L times the current, but, as has already been pointed out, the current in a tuned circuit is in consequence of which the voltage across the coil will be That is, under given conditions, the Jt\ voltage developed across the coil will be greater as the ratio 5 is increased. In other words, the desira ble thing in a radio coil is to secure the most inductance per ohm of resistance. Another point in the analogy may be mentioned. The ability of a minute force to generate oscillations in the weight and spring would obviously disappear if the resistance were greatly increased by immersing the system in water or molasses, for example. As the resistance of an electrical circuit is increased, not only will the amplitude of the oscillations diminish, but the variations due to moderate changes on the frequency of the applied force will become less and less. In other words, with increasing resistance the system loses its selectivity, precisely as in electrical circuits. Our analogy also illustrates a point that puzzles many beginners, and that is how the current in a condenser can be said to be 90°, that is one-quarter cycle, out of phase with the voltage (see "Home Study Sheets No. 7 and 8"). It will be observed that when the weight is at the point of maximum velocity, that is at the midpoint of its path, the spring is idle, that is, it is neither extended nor compressed. And when the weight is completely at rest at either end of its path, the spring is at that moment under its greatest stress. Similarly, when the current is at its greatest value, the condenser is at the instant of changing from one polarity to the other and so has no voltage, but when the current has just ceased flowing in, the electrons in the dielectric are under their greatest stress, so that when there is no current flowing the voltage is a maximum. Finally, it may be pointed out, the action of the weight and spring exemplifies what is referred to in radio as damping. Suppose the weight was quite heavy and t he spring rather short. If the weight were given an initial impulse the oscillations would continue for some time, though gradually diminishing in amplitude. Now suppose the weight were made Fig. 2 — Mechanical analogy of an oscillating current very light and the spring lengthened considerably so that the frequency remained the same. Then the air resistance would increase in importance and the oscillations would die out very quickly. The corresponding change in a radio circuit would be to reduce the inductance and increase the capacity, the resistance remaining constant, and when this is done an oscillation once started is quickly damped. To recapitulate: We have learned that the current in a radio circuit reaches its greatest value when the wavelength equals 1884 |/LC. That this fact is readily derivable from the fundamental equation for alternating-current circuits. That when this condition exists, Ohm's law is applicable to the circuit. That the voltage across the coil or condenser in a resonant circuit may very greatly exceed the applied voltage. That the most efficient radio coil is that which has the greatest inductance per ohm resistance. That the sharpness of tuning increases as the resistance is reduced. • april, 1929 page 397 •