Radio Broadcast (May 1929-Apr 1930)

RADIO BROADCAST. No. 24 Radio Broadcast's Home-Study Sheets June 1929 MEASURING CAPACITY The essential pabts of every tuned circuit, of which radio receivers are made, are capacities and inductances. " Home-Study Sheet" No. 20 told how to build a standard inductance for the home laboratory or shop; this "Home-Study Sheet" gives some of the fundamental facts about condensers. Capacity Measurements Eliminating the slight effect of the edges, the capacity of two opposing conducting surfaces, as in Fig. 1, is given by the simple equation: _ 0.0885 S . , . ( . = — — micromicrotarads S is the area of one plate, and T the distance apart, both in centimeters. If the dimensions are in inches, the formula is: C = ^Tjr^ S micromicrofarads If the space between the plates is occupied by any other insulator (called the dielectric) than air, the above values must be multiplied by the dielectric constant of the material used. For mica this constant may vary from 4 to 8, for glass from 3 to 10, and for waxed paper from 3.5 to 3.75. For example, the capacity of the condenser in Fig. 1 is 88.5 mmfd. To the experimenter these formulas have little practical application except to afford some means of estimating capacities. In the usual form of variable air condenser accurate measurements would be extremely difficult, if not impossible. We are, therefore, dependent on some known capacity for a standard. No reliance whatever can be placed in the stated capacities of the many small fixed condensers on the market, the error not infrequently being as great as 50 per cent. The G.B. 347 variable condenser may be had at a reasonable cost, and carries a scale reading directly in micromicrofarads from zero to 500 or 1000. The upper end of the scale of this condenser could be accepted with assurance of a very fair degree of accuracy, and the instrument is well adapted to laboratory work as it is inclosed in a metal shield. In any case, see to it that the condenser chosen is of the straight-capacity-line type, has a maximum capacity of not less than 500 (preferably 1000) micromicrofarads, has very durable bearings, has no stop to prevent the plates from revolving completely, and has the dial firmly secured to the shaft. It is also desirable to have a condenser with some sort of fine vernier that can be disconnected, as many times the condenser will be used for approximate determinations when a vernier would be quite inconvenient. At other times, when using loose coupling and absolute resonance is necessary, the vernier cannot be too sensitive. If the experimenter is fortunately in a position to have his chosen condenser calibrated for him at about ten points, his troubles may be ended quickly. A curve should then be laid out on squared paper having ten lines to the inch. The resulting capacity readings may then be tabulated opposite each of the one hundred points of the dial, such a tabulating being much more convenient fot general use than a curve. Standard Condensers Standard laboratory condensers of the variable type generally carry a label stating the values at ten different points. If access can be gained to one of these at a near-by college, school, or electrical establishment, the values should be transferred to the new condenser by capacities A and B in series is the reciprocal of the sum of the reciprocals or 1 A X B Fig. 2 — Two calibrated variable condensers. The teninch slide rule shows their comparative size and the chart shows the usual type of calibration curve. means of the substitution method. Set the standard condenser on one of the points at which it has been calibrated. Connect it to terminals "Y" of the bridge ("Home-Study Sheet" No. 21) and then balance it with an extra variable condenser connected to the "X" terminals at a 1:1 ratio, or, if a third condenser is not available, use a fixed condenser and the slide-wire. When a perfect balance is secured, replace the standard (connected to "Y") with the new condenser, and adjust it carefully until it is in balance; i.e., until its capacity equals the known value of the standard condenser. Have the leads to the condensers fairly long, and k 10 cm Fig. 1 — Schematic drawing of a simple condenser. Fig. 3 — The circuit used in problem No. 3. maintain them in the same relation throughout the comparison in order that their capacities will remain constant. The new condenser should be compared at least twice to each of the known values of the standard condenser, using different settings of the slide-wire and capacity. The advantage of this method is that its accuracy is not affected by any errors in the bridge. When making measurements of capacities on a bridge, the laboratory worker must remember that a condenser has a negative reactance, and so the ratio used in determining the capacity of a condenser in terms of a standard must be reversed. Thus, if resistance or inductances were measured on a bridge, and the two lengths of a slide-wire which gave the ratio between the standard and the unknown resistance or capacity were A/B, when capacities are measured and the balance is obtained, the proper ratio to use is B/A. Thus, if the lengths of slide-wire to balance two inductances, Lx and Ls, are 4/5, L. 4 5 =— — r or L.x = 7 Ls Lx 5 4 when capacities are balanced by this ratio, the correct value of Cx=|Cs At this point it would be appropriate for the experimenter to familiarize himself a little further with his equipment and at the same time experimentally verify the rule for combining two condensers in parallel or series. Formulas In the first case the capacities are merely added, and the demonstration of this fact simply requires the measurement, of the two capacities separately and then comparing their addition with the measured capacity of the two connected in parallel. The resultant capacity of two condensers of +-1 A B A + B Thus, if both capacities are 1, then the resultant is obviously To verify this, measure each capacity separately, and then compute the resultant, which may then be compared with the measured value of the two condensers connected in series. While the expression, the reciprocal of the sum of the reciprocals, sounds rather deep, the reason for it is very simple, and requires no mathematical demonstration to show why it should be so. The reactance of a condenser is decreased as the capacity is increased, so that the reciprocal is proportionate to the reactance. The sum of the reciprocals then is, therefore, simply adding two series resistances, as it were, and represents the total reactance. To get this back into terms of capacity again, we merely turn the expression upside down. While a variable condenser of 0.001 mfd. will generally be found sufficient, it is desirable to calibrate two or three fixed condensers of larger values, for which purpose the usual square mica condensers, securely held together by two eyelets, are satisfactory. In making such determinations do not use the slide-wire at too great a ratio — say not over 5:1. When the measurement of large values is necessary, it is better to measure a condenser of intermediate value, and then proceed from it to the higher value. For the measurement of a very small capacity, such as the minimum of a variable condenser, it is advisable to connect it in parallel with the calibrated condenser, set at about half capacity. With the bridge, balance this combination against any available condenser, and note the dial reading. Disconnect the small condenser, and balance again. The difference between the two readings will be the desired capacity. Problems Problem 1: Two condensers, each of 200 mmfd., are connected in parallel. What is the resultant capacity? If one is 200 and one is 400 mmfd., what is the resultant capacity? Problem 2: The condensers described above are connected in series. What is the resultant capacity? Problem 3: In a certain receiver circuit it is necessary to ground the tuning condenser to the filament of the tube but it is not permissible to ground the coil. This can be done by connecting another condenser into the tuned circuit, as in Fig. 3. Must C2 be large or small compared to Ci, so that the tuning range of the circuit will not be altered appreciably? For example, if Ci is 500 mmfd., how large should C2 be? Problem 4: An antenna has an effective capacity of 0.0002 mfd. How much capacity must be added in series to reduce this capacity to 0.00015 mfd.? If the inductance in the antenna has not been changed, what is its natural wavelength now? Problem 5: Two plates 10 cm on a side are separated by 3 mm of dry air. What is the capacity of the condenser? Suppose a sheet of mica, dielectric constant = 6, is put between the plates. What is the capacity now? Problem 6: A fixed condenser across a given inductance has a capacity of 1000 mmfd. and tunes the inductance to 1000 meters. A variable condenser having a maximum capacity of 1000 and a minimum capacity of 25 mmfd. is placed in series with it. Plot the wavelength against added series capacity. (Note. Wavelength in meters = 1.884 LC where L = (J.h and C = mmfd.) Ci iic2 C,xC2 _ c3 = Cl+C2 — + — Ci C2 Fig. 4 — Capacity formula for condettsers in series. C3= Ci+C2 Fig. 5 — Capacity formula for condensers iti parallel. 106 • • JUNE 1929 •