Radio Broadcast (May 1928-Apr 1929)

7Z_ RADIO BROADCAST No. 20 Radio Broadcast' 's Home-Study Sheets Inductance Standards April 1929 THE applications of the principles in "HomeStudy Sheet No. 19" are far-reaching and will afford an interesting field for experiment, but before this may be undertaken, certain standards must be acquired, as one cannot measure without some sort of a yardstick. This will, however, require many hours at the workbench, but before rolling up our sleeves, it would be well to dispose of the inductance standards, for the reason that for the value of these we are dependent on calculation. Function of Inductance The inductance of a coil has the same function in regard to the motion of the electrons that constitute an electric current, as weight has in regard to the motion of a material body. When the current is uniform, as in the case of direct current, inductance has no effect, just as the mass of a body is without effect in a mechanical motion of constant velocity. On the other hand, any change in the strength of an electric current, whether it be an increase or decrease, is opposed by inductance, and, as radio currents are continually changing with extreme rapidity from a maximum strength in one direction to a maximum in the other, inductance becomes a very important item. A circuit is said to have an inductance of one henry when a current changing at the rate of one ampere per second induces therein an e.m.f. of one volt. In such a coil, there being no iron core, a current variation of two amperes would induce an e.m.f. of two volts. Inductance may therefore be considered as the ratio of the e.m.f. induced to current variation per second. The reason for this e.m.f. lies in the fundamental fact that a conductor has a voltage induced in it when it cuts the lines of force of a magnetic field. When the current isstarted Fig. 1 — Demonstrating the counter direction of the e.m.f. of self-induction. in a coil the magnetic lines radiate outward from the center, thus cutting the turns of wire and inducing therein an e.m.f., which is always in such a direction, that it tends to delay the applied current in reaching its maximum value. Similarly, when the applied current ceases, the magnetic lines collapse towards the center, inducing an e.m.f. which now tends to maintain the current flow in the coil. By coiling a length of wire, the resulting magnetic field will be concentrated into a smaller space and, as a consequence, this counter e.m.f. increases. Inductance is a property which depends on the number of turns, size, and shape of a coil. Laboratory Demonstrations Tha counter direction of the induced current may be demonstrated by connecting up a coil, galvanometer, or compass and dry-cell battery as illustrated in Fig. 1. When the switch is closed the current will flow as indicated by the arrows in the diagram on the left. If the galvanometer needle is now restored to the zero point and held there with a pin or small weight, it will be deflected in the reverse direction when the switch is opened. This indicates a reversal of current through the galvanometer, and demonstrates the important fact that the current induced in the coil after breaking the circuit passed in the same direction through the coil as did the battery current. Obviously the reverse must have been the case when the connection was first made, as the magnetic lines proceeded outward instead of collapsing toward the center. That the direction of a current induced when a circui t is closed is opposite to that induced when the circuit is opened may be demonstrated easily by connecting up an audio transformer to a galvanometer and dry-cell battery as illustrated in Fig. 2. When the circuit is closed the galvanometer will show a brief deflection, returning to zero when the primary current has reached its full value. When the circuit is opened, the deflection will be in the opposite direction, again returning to zero after the magnetic field has completely disappeared. Inductance formulas have been developed for coils of a great many forms, but as our present Fig. 2 — Closing and opening the circuit induces two opposite currents purpose is to acquire certain suitable standards, attention will be confined to the single-layer cylindrical form called the solenoid. The inductance of any coil of more complex winding may then be determined by comparison. Coil Formulas For a single-layer winding the Bureau of Standards gives the following simple formula. The significance of the terms a and b are illustrated in Fig. 3. N is the number of turns and K is a factor depending on the ratio of diameter to length, and is given in Table I. 0.03948a2N2K microhenries All dimensions are in centimeters, and while they may be made in inches by changing the formula to 1.0028 a2N2K microhenries such a change is not advised for the reason that the metric system is now used so generally in scientific work that the experimenter should aim to acquire some familiarity with it. If a centimeter scale is available, it is just as easy to measure in centimeters as in inches, and in any subsequent computations, there will be less chance of error in handling the decimals of the metric system than with the awkward fractions of the inch. In planning a coil for a standard, procure a tube of durable material, as near a perfect cylinder as possible, two or three inches in diameter and about twice as long. Apply one layer of number 18 d.c.c. wire. If a winding jig is not available, attach one end of the wire securely to the wall and stretch it out full length, removing all kinks and bends by pulling it lightly through a towel held in the hands. When the free end has been fastened to the tube, the process of winding may be accomplished quickly by turning the tube with the hands, always keeping the wire under tension. Before beginning the winding, however, provide suitable means for securing the two ends of the wire in place. A satisfactory way of doing this is to bore two small holes in the tube for each end and to pass the wire through in the manner indicated in Fig. 4. Place these holes so that the winding will have a whole number of turns — no fractions. If binding posts are desired, they should be very small, as large ones will add to the distributed capacity of the coil. Measuring Coils In counting the turns, be careful not to start counting until after the completion of the first turn is reached. Care must also be exercised in determining the length b, which, it will be noted in Fig. 3, is not the exact physical length of the coil but the length plus one turn, or the number of complete turns multiplied by the distance between the turns, that is b-N X D For an inductance standard based on computation it is usually best to have the coil long rather than short, although the inductance will not be quite so great. The reason for this is that the formula may be applied more accurately, and the distributed capacity will not be as large. For this latter reason also, the coil should not be coated with any liquid preparation. Usually the experimenter will have on hand one or more single-layer coils, and by applying the formula to these their inductance may be readily determined. These will then serve as standards until one's requirements become known more definitely through further experiment. Accuracy It must be borne in mind that the accuracy of the determination cannot be greater than that with which the physical measurements of the coil are taken, and among these the diameter will probably present the greatest trouble, particularly if the tube is not truly cylindrical. Under these conditions it is a good plan to wrap a strip of smooth thin paper tightly around the tube until the ends overlap. A sharp knife point should then be made to pierce the two overlapping ends, after which the strip may be laid flat and the distance between the two marks made may be measured accurately. By repeating the process after the tube is wound, the outside circumference may be determined, and then by taking an average of the two, the required diameter may be computed. Fig. 4 — Securing the end of the wire Spaced Turns It is sometimes desirable to reduce the distributed capacity to a minimum by using a spaced winding, which may be accomplished by cutting a shallow thread on the cylinder or by winding a string between the turns. If a high degree of accuracy is desired in the computation of the inductance of a spaced winding, a slight correction may be made for the spacing by adjusting the value calculated by the formula given above by an amount equal to — .01257Na (A + B) the proper values of A and B are given on page 284 of the Bureau of Standards Circular Number 74, Radio Instruments and Measurements. In planning a coil, the experimenter will now be in a position to calculate the inductance quite closely in advance. If the wire is already at hand, estimate the total number of turns by counting the number that can be wound on one inch of the length of a lead pencil. If the size of wire has been determined, the number of turns that will go into a certain space may be estimated by referring to a wire table. Estimates obtained from wire tables are necessarily approximate as there are slight variations in the specified sizes of bare wire and in the thickness of the insulation, and further differences may result according to the tension under which the wire is wound. Conclusion Before leaving the present subject, the reader should be impressed with the necessity of maintaining a laboratory notebook in which to enter his calculations and observations in a clear and orderly manner. As the work proceeds, two facts will become evident: one will frequently have occasion to refer to some earlier record, and that memory cannot be trusted to retain experimental data. Diameter length Table I— Values of K K Diameter length Fig. 3 — Essential coil dimensions 0 . 9588 0.9201 0 . 8838 0 . 8499 0.8181 0 7885 0.7 0.8 0.9 1.0 1.5 2.0 0.7609 0.8351 0.7710 0 6884 0.5950 0 . 5255 • april, 1929 . . . page 398 •