Radio broadcast .. (1922-30)

sistance How Your Filament Rheostats Value May Be Altered to Accommodate New Tubes — Combining Fixed and Variable Condensers to Qive a Required Capacity The Range of the Accompanying Charts May Be Extended By HOMER S. DAVIS RESISTANCES ALIGNMENT or calculation charts have long been in use among engineers for the easy solution of mathematical formulas. By their means, difficult calculations are avoided. The drawing of one or two straight lines with a pencil and a ruler is the only effort necessary to arrive at an answer when such charts are utilized, and that answer is more likely to be correct since the possibility of numerical errors is eliminated. A knowledge of advanced mathematics is not at all necessary. In the March, 1926, number of RADIO BROADCAST, such a chart was presented by means of which the reader was enabled to design a single-layer inductance coil to cover a given frequency range with a given size of tuning condenser. A wavelength-frequency conversion chart appeared in the February, 1926, RADIO BROADCAST. In the present article charts have been further applied to the solution of resistances in parallel and of capacities in series. Additional charts dealing with other problems in the design of radio apparatus and receivers are now in preparation. It is suggested that the reader preserve these charts for future reference. When resistance units, such as rheostats, grid leaks, coupling resistors, are connected together in series, the resultant resistance of the combination is the sum of the individual values. Thus, if a rheostat or grid leak is found to be too small, and the correct size not available, the required additional resistance may be connected in series with it. But when they are connected in parallel, or shunt, an entirely different relation holds. The resultant resistance is then less than that of any one component, and in the case of only two resistances, is given by the formula: R=-l!ll when R = the resultant resistance and r, ra, the resistances in parallel. By virtue of this property, a resistor may be reduced in value by shunting it with another. Two charts are presented for resistances in parallel, based on the above formula, the first, A, covering the range of 5 to 100 ohms, the second, B, 100 to 10,000 ohms. Their correct use is best illustrated by working out one or two examples. Suppose that two rheostats, one of 30 ohms, the other 10 ohms, are at hand, and it is desired to know their resultant resistance when connected in parallel. Draw a straight line between 10 on one outside scale of Chart A, and 30 on the other outside scale; the point where this line cuts the center scale marks the value of the resultant resistance, 7.5 ohms in this case. To find the resistance necessary to shunt across an existing resistance to bring it down to any desired size, draw a line from the known value on an outside scale to the desired resultant value on the center scale, and continue the line to intersect the other outside scale, reading the answer at this point. The range of either of these two charts may be extended by considering the values on each of the three scales as multiplied by some constant. For instance, if the values on Chart B are multiplied by 1000, the range then will be from 100,000 to 10,000,000 ohms, or o. i to 10 megohms. To take an example, the resultant resistance of a 5OO,ooo-ohm (0.5 megohms) and a i ,ooo,ooo-ohm (i.o megohm) resistor in parallel may be found by drawing a line between 500 and 1000 on the outside scales, the intersection with the center scale at 330 giving the answer as 330,000 ohms (0.33 megohm). In extending the range of a chart in this way, the reader should be careful to use the same multiplier on all three scales. Resistance units are coming into more extensive use every day, some of the more recent applications being as coupling resistors, stabilizers for radio-frequency amplifiers, regeneration controls, volume regulators in audio-frequency amplifiers, and voltage regulators for battery eliminators. A knowledge of how to combine them to obtain different values of resistance should be of value to the constructor in avoiding delays and affecting savings in his outlay of parts. CONDENSERS CONDENSERS may also be connected ^ in series or in parallel to obtain any desired value of capacity, but here the case is reversed from that of resistance units. That is, if two or more condensers are in parallel, their capacities are added to obtain the resultant; but if they are connected in series, the resultant capacity is then less than that of any one of them, and in the case of only two condensers, is given by the formula: where C is the resultant capacity, and c, C2, etc., the various capacities in series. Charts for this formula are presented, again in two ranges. Values in microfarads and in micromicrofarads have been plotted on opposite sides of the scales. To work out an example illustrating their use, suppose that a radio-frequency transformer is to be used which requires a o.ooo3-mfd. tuning condenser to coyer the broadcast band of frequencies, and that a o.ooo5-mfd. condenser is the only one at hand. To use this condenser would be undesirable, since it would crowd the tuning toward the lower end of the scale, and a considerable portion of the upper end would be unusable. This may be remedied by connecting a high grade mica fixed condenser in series with the tuning condenser to bring its maximum capacity down to 0.0003 mfd. The size of the fixed condenser may be found with the calculation chart by drawing a straight line from 0.0005 on an outside scale through 0.0003 on the center, or "resultant," scale, and extending it to meet the other outside scale; this point indicates 0.00075 as the required size of the fixed condenser. If this size is not available commercially, it may be made up by connecting together a 0.00025 ar>d a o.ooo5-mfd. condenser in parallel. To take another example, it is desired to know the resultant capacity of a 0.00025 and a o.ooo5-mfd. condenser in series. Connect these values on the outside scales and read the answer, 0.000168 mfd., at the intersection with the middle scale. The ranges of these charts may be extended by the use of a suitable multiplier as was done with the resistance charts.