Radio Broadcast (May 1928-Apr 1929)

136 JULY, 1928 Radio Broadcast's Home Study Sheets Determining the Capacity and Inductance of a Radio Circuit /"•OILS and condensers are the foundation on which every radio circuit is erected. The coils possess an electrical quantity known as Inductance, and as every radio experimenter knows, the quantity that makes a condenser use'ful is its Capacity for storing electricity. When a current flows through the coil, lines of force surround it ; the sum total of these lines is known as an electromagnetic field. The word magnetic is important heie, for a compass — which normally points one end of its swinging needle toward the earth's north magnetic pole — will be deflected when brought near such a coil. When a current flows through a condenser, lines of force surround it. The total of these lines is known as the electrostatic field. It can be detected, not by a compass needle or any other device using the magnetic principle, but by a i.'.'iir^i/bodysuchasasmall bit ofpaper which had been rubbed on the sleeve. The unit of capacity is the farad, named after Michael Faraday, a distinguished English experimenter. In radio circuits, however, the millionth of a farad, a microfarad, is ordinarily the quantity dealt with, or even the micro-microfarad, the million-millionth of a farad. The unit of inductance is the henry, named from Joseph Henry, a famous American experimenter. In radio circuits the unit dealt with is the milli or microhenry, thousandths or millionths of henries. The table on this page shows how to convert farads and henries to microfarads or milli or microhenries. For example, to change henries to millihenries, you multiply by one thousand. To convert mmfd. to mfd. you divide by one thousand; and so on. It is the size of the coil and the condenser that controls the wavelength or frequency to which a circuit tunes. The designer of the world's best receiver must know within very close limits what the inductance of his coils must be; he knows how large a capacity he must have to cover a certain band of frequencies. It is always important to know the exact value of these two electrical quantities, capacity and inductance. The following experiment will enable anyone to find out the capacity of a condenser, and the inductance of a coii. APPARATUS REQUIRED 1. A coil of wire. The dimensions of the coil used in the Laboratory are given in Fig. 1 . 2. A variable condenser fitted with a dial. About 500 mmfd. is the best size of condenser. 3. A radio receiver, preferably with an oscillating detector; or a tube wavemeter. ' PROCEDURE 1. Connect the coil and condenser across each other and bring the coil near the coil in the receiver or that of the tube wavemeter. 2. Tune the receiver to a known station near the center of the broadcast band, or if a wavemeter is used, set its wavelength to about 300 meters. 3. Change the setting of the variable condenser across the coil whose inductance is unknown, until resonance with the receiver is indicated by a decrease in signal strength, or by a click if the oscillating detector is used, or by a dip in the indicating needle of the tube wavemeter. A good meter is the modulated oscillator in the June, 1927, Radio Broadcast. 4. ' Tune the receiver, or wavemeter, to other wavelengths above and below the first medium wavelength setting until the whole of the condenser has been used, at each wavelength noting down the data as is shown in Table 1 . s. Compute the inductance of the coil from the following formula — which is one used bv Professor Hazeltine. Inductance in Microhenries = — 0.2 X d X N2 3d +ob where d is the diameter of the coil in inches N is the number of turns of wire b is the length of the winding in inches As an example below is the manner in which the inductance of the coil illustrated in Fig. 1 is calculated. Inductance =* 0.2 X 3062 X 642 .2 X 38400 3X306 + 9X1.875 9.18+16.85 7o1o 26.03 292 [Ah 6. Compute the capacity of the condenser at each of several of the long v..nelength settings from the formula wavelength =1884 V L X C where L is the inductance in microhenries C is the capacity in microfarads For example, the 202-microhenry inductance tuned to S27 meters at 55° on the condenser dial. What is the capacity of the condenser at that point? To simplify the problem let us change the above formula to read (wavelength)2 = 3.54 X io« X L X C 527s = 3.54 X 106 X 292 X C C 527' 3.54 X 106 X 292 = 270 mmfd. To provide additional examples, the capacity column in the data Table 1 has been left blank. 7. Plot this data as shown in Fig. 1 8. Make a tap at the center of the coil and repeat the above calculations and experiment. 9. Pick out some condenser setting on each set of calculations, say 60 degrees, and see how nearly the calculated capacities check. DISCUSSION In the experiment we have demonstrated the phenomenon known as resonance; that is, a circuit composed of inductance and capacity absorbing energy from another also composed of inductance and capacity, to which it is properly tuned. We have calculated the inductance of a coil by means of a formula which will give us a result accurate to within two or three per cent., provided, a. we measure the dimensions of the coil accurately; b. we make no mistake in our arithmetic, and c. provided the length and diameter of the coil are not too different in dimensions. The formula will be most accurate when the length of winding equals the diameter of the coil. We have demonstrated that knowing the wavelength to which a coilcondenser combination tunes, and knowing the inductance, we may calculate the capacity. This is one means of calibrating a condenser, that is, determining the relation between dial degrees or divisions and microfarads of capacity. The accuracy with which we determine the capacity by this method is none too great, but for all practical purposes it is good enough provided, a. we make no error in our arithmetic; b. we know the wavelength accurately; c. we can set the condenser dial accurately to the wavelength of the receiver or wavemeter. and d. the capacities being measured are fairly large, say 250 mmfd. and more. This latter proviso is because the actual capacity across the coil is made up not only of the capacity of the condenser but of the leads connecting coil and condenser and the distributed capacity of the coil. This latter capacity is a bothersome factor in all experimenters' calculations and experiments. It is discussed in the Signal Corps book. Principles Underlying Radio Communication, page 244, in the Bureau of Standards Bulletin 74 on pages 137-8 and in Morecroft's Principles 0/ Radio Communication, page 230-235. The capacity of the condenser used in the Laboratory, a General Radio "tin can" Type 247E, was actually 300 mmfd. at 550 while our calculations showed it to be 270 mmfd. — an accuracy of 10 per cent. The coil as measured on a bridge had an inductance of 280 microhenries instead of 292 as calculated — an accuracy of 95.6 per cent. TABLE 1 condenser setting in decrees 78.5 55.0 41.0 32.0 26.5 22.0 condenser capacity in mmfd. (calculated) 270 wavelength in meters 621 527 458 408 370 338 frequency (wavelength)2 in kilocycles 483 568 655 735 810 385,000 277,000 210,000 133,700 114,000 TABLE 2 Name of unit farad microfarad micromicrofarad henry millihenry microhenry TABLE 3 abbreviation f. mfd. mmfd. h. mh. [J.h. f. one million mfd. 106 mfd. f. one million million mmfd. 10]2 mmfd. mfd. one million mmfd. 106 mmfd. mfd. one millionth f. 10 6 f. mmfd. one millionth mfd. 106 mfd. mmfd. one million millionth f. IO-12 f. h. one thousand mh. W mh. h. one million [Ah. 10" u.n. mh. one thousand [Ah. 10' [Ah. mh. one thousandth h. 10-3 n. [Ah. one thousandth mh. 10 ~3 mh. [Ah. one millionth h. 10 -« h. 1300 [lilfM 0,,j >m\ 1 N=64 t#26d.c.c. 1 1 1 I mm1 1 Sill I 20 30 40 50 CONDENSER DEGREES FIG. I 60 80 PROBLEMS 1. Calculate the inductance of two coils which have the same diameter and length of winding, but of which one has twice as many turns as the other, obtained by using smaller wire. 2. The coil used in the Laboratory was too large to cover the broadcast band effectively with a 500-mmfd. condenser. Half the number of turns is too few. What is the correct number of turns, providing the diameter and length of winding is the same? 3. With a condenser whose maximum capacity is 150 mmfd. what is the coil inductance required to tune to 40 meters, 80 meters? 4. How many microhenries is 0.370 millihenries? 5. How many microfarads is 500 mmfd.? 6. If the minimum wavelength a broadcast receiver can be tuned to is 240 meters, and if the condenser has a minimum capacity of 5 mmfd. and at 500 mmfd. the receiver tunes to, 600 meters, what is wrong? Why will not the receiver tune to shorter waves?