Radio Broadcast (May 1929-Apr 1930)

RADIO BROADCAST No. 21 Radio Broadcast's Home-Study Sheets THE USE OF A BRIDGE May 1929 'T'HE usual method of measuring the inductance of a coil is to compare it with a coil whose inductance is known — either having been calculated, or compared to some other standard. One method by which this comparison may take place is indicated in "Home-Study Sheet" No. 15. Another, and more often used method, is to employ a Wheatstone bridge by which the unknown inductance, or capacity, may be compared directly to a known inductance or capacity. Such a bridge may be a simple affair, like the one illustrated in this "Home-Study Sheet," or it may be much more complicated and costly. As this piece of apparatus probably has a more Fig. 1 — Connections for a simple slide-wire bridge. varied field of usefulness than any other single piece of equipment in the laboratory, the experimenter will be well repaid for any effort expended in its construction. The simplest form and one with which a great deal of practical work may be done is the slide-wire bridge — a type that is greatly improved by the use of a wire of one of the modern high-resistance alloys, such as number 36 nichrome, which has a resistance of about 25 ohms per foot. The reader is doubtless familiar with the connections as set forth in Fig. 1, in which condenser C is being compared with condenser c, the relation being expressed by the simple proportion — = — ' It is, of course, unnecessary to know the absolute values of R and r. If, for example, the scale has 300 uniform divisions, and the sound in the telephone receiver vanishes at a point on the wire 100 divisions from the left, the — = ^~ or 2, which tells us that r 100 the capacity of C is twice that of c. Practical work may be done by using about two feet of the wire referred to above, stretching it between metal connecting blocks and providing a paper scale. If the scale has twenty divisions to the inch, under proper conditions, it should be readily possible to read to the nearest division, which means a possible accuracy of a fraction of 1 per cent. Those who have had some experience in lettering and drafting will have no difficulty in producing an accurate and professional-looking scale. Procure a piece of durable and smooth-surfaced card. Mark out the lines for the scale, but do not cut off the required strip until the work is complete. To subdivide, use a steel rule, holding it on edge and running the sharp point of a hard pencil down each engraved division line. This procedure will result in a series of fine dots, more accurately spaced in this mechanical manner than could possibly be done were the pencil point directed by the eye. A straight edge may now be placed parallel to the length of the scale, and, by using a small triangle against it, just as a T square is used against the edge of a drawing board, the division lines may be drawn in readily with a right-line pen and waterproof drawing ink. When the numerals have been lettered, the scale may be -given a coat of transparent radio varnish or lacquer. The chances of error due to inequalities in the wire, which are never very serious, can be reduced greatly by dividing the wire into two equal parts as shown in Fig. 2. When a reading has eeen taken, connections A and B may be reversed and another reading taken. If the two results differ materially, one or both wires should be replaced. When approximately the same reading is obtained on either side, it is evident that a mean between the two will be quite accurate. For the measurement of resistance where inductance is also involved, as in the case of a coil, direct current must be employed, and a galvanometer used to locate the zero point on the slide-wire. For capacity measurements, alternating current is required and should also be used for non-inductive resistance determinations (e.g., grid leaks), as the telephone receiver is much more sensitive and more convenient than the usual galvanometer. For practical work a very satisfactory source of alternating current is a fairly high-pitched buzzer. In Fig. 1 the bridge wire is connected across the two contact points. Another method is to connect it directly across the buzzer coil, and sometimes the bridge, battery, and buzzer are all placed in series. For any given buzzer the best plan may be determined by using the bridge to compare two variable air condensers, preferably of the same make or type. The buzzer connection that results in most completely eliminating all residual sound from the telephone receiver when the bridge is balanced is the best. Make the test in a quiet room at different adjustments of the buzzer tone and at different points on the slide-wire. It is very important to have a buzzer that will produce practically no residual sound under the foregoing conditions, as it enables one to identify defective condensers. If one of the air condensers referred to is replaced with a small fixed condenser which may have a poor dielectric, the sound in the telephone receiver cannot be made to disappear completely when the bridge is balanced, and the amount of this residual sound is a measure of the quality of the dielectric. The faint note that remains in the telephone receiver is simply due to what is termed phase difference. This may be made clear by referring to the mechanical analogy illustrated in Fig. 2, "Home-Study Sheet" No. 19, in connection with which it was pointed out that the spring had its maximum velocity at the moment when it was free from all stress, and that the stress was at a maximum when the velocity was zero. Representing the complete cycle of the spring, one extension and one compression, as 360°, it will be evident that velocity and stress are 90° out of phase. Similarly, in a perfect air condenser, the voltage and current are said to differ 90° in phase. In the mechanical analogy a perfect spring is assumed— one that responds instantly to any difference in pressure. If, however, the spring were made of a sluggish or faulty material that required a little time to conform to the pressure, the phase difference would no longer be exactly 90°. Similarly, with a poor dielectric, the phase difference is not precisely 90°, as it is in a perfect air condenser. When a condenser with a poor dielectric is balanced against an air condenser, the bridge will determine the point at which the opposing voltages balance, but as the phase of the current on one side is not exactly the same as on the other side, there will be a slight but unavoidable flow of current. After the experimenter has become familiar with the action of his bridge, he will be surprised to note the marked differences in fixed condensers, not only in regard to the quality of the dielectric, but also as to their stated capacities. Fig. 3 illustrates a slide-wire bridge which, though it may be somewhat more elaborate than the reader may care to construct, will be described briefly, as certain features may prove suggestive. It is built on a strip of wood }" thick, 3" wide, and 21" long. On one end is a buzzer and on the other a galvanometer. One or two dry cells are used, and, by throwing the six-arm switch, the telephone receiver and buzzer are disconnected and the galvanometer and battery are connected directly to the slide-wire. The slide-wire is in two sections, which are connected through two brass blocks and a taper plug. By removing this plug, two large equal and noninductive resistances may be placed across the binding posts indicated at B-B, thus greatly increasing the resistance of the bridge at the 1 :1 ratio. This ratio is very generally used in measuring capacities within the range of a calibrated variable condenser, the balance being accomplished by varying the latter. The use of the high resistance in the two arms adds greatly to the sensitivity of the bridge. At the two free ends of the slide-wire is a switch, which reverses the arms of the bridge, so that a mean of two readings may be used. The movable contact should have a fine point and be mounted in an insulating handle, and is connected through a flexible conductor to a small binding post at A, which is in connection with a small switch arm. When the bridge is being used at the 1:1 ratio, this switch is placed on the inner contact point, which makes the desired connection to the mid-point permanent. At B, provision is made for throwing in a high resistance in the lead to the galvanometer in order that the deflections will not be violent while attempting to find the point of balance. When this has been determined approximately, this resistance may be switched out. A. piece of card heavily coated with pencil lead will answer and may be slipped readily under a pair of spring clips. The wiring is all done on the underside, appropriate grooves being cut for the necessary leads. These should not be larger than No. 22 or 24 wire, except for the two short connections between the reversing switch at the end of the slide-wires and the two binding posts, which connections should be made with No. 14 or 16 wire in order that no extra resistance will be interposed beyond the points where the current divides. The galvanometer used will be referred to later when the subject of galvanometers is taken up, and the necessary resistance units will be considered in a separate "Home-Study Sheet." Using the Bridge In practice one lead of the unknown capacity, inductance, or resistance is attached to the binding post X, one lead of the standard to which this unknown is being compared is connected to the post A D B U Fig. 2 — A double slide-wire tends to eliminate error. Y, and the remaining two leads are both attached to the post to the right of these two posts. Then the slider is moved until silence is secured in the head phones — it may be necessary to use an audio amplifier between the phones and the bridge if the room is noisy — the value of the unknown resistance or inductance is equal to the standard times the ratio of the two resistances, thus, Lx = Ly X B/r and Bx = By X B/r but if two capacities are being compared, the ratio of the resistances (the lengths of the slide wire on either side of the slider) must be inverted; thus Cx = Cy r/B because the larger the capacity the smaller its reactance. Fig. 3 — Diagram of a reversible slide-wire bridge which may be used with either direct or alternating current. m may, 1929 page 29 •