US 2954517 A Description (OCR text may contain errors) Sept. 27, 1960 w. A. MENZEL 2,954,517 VOLTAGE DIVIDER Filed Jan. 8, 1953 2 Sheets-Sheet 2 2L I i I ZNVENTOR 0 V V2 l WOLFGANG A. MENZEL ATTORNEYS United States Patent VOLTAGE DIVIDER Wolfgang A. Menzel, Silver Spring, Md., assignor to the United States of America as represented by the Secretary of the Navy Filed Jan. 8, 1953, Ser. No. 330,366 Claims. (Cl. 323-74) (Granted under Title 35, US. 'Code (1952), sec. 266) The invention described herein may be manufactured and used by or for the government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor. This invention relates to a voltage divider and more particularly to a potentiometer designed to produce two voltages having a ratio varying according to an exponential function. For many purposes in electrical circuits the voltage change is desired to be exponential. For example, an analysis of the electric stabilized time fuze circuit shows that a linear time setting requires an exponential change in the ratio of two voltages. Heretofore, this has been accomplished by dividing a multiple turns potentiometer into equal segments and by inserting suitable parallel resistances converting the divider to the desired exponential ratio. This structure is delicate and expensive and does not provide suflicient accuracy. The presently disclosed voltage divider provides a means for obtaining an exponential ratio between two voltages by combining a plurality of normally linear potentiometers. It consists of four potentiometers arranged on a single axis and having the contact arms connected in such a manner as to give two output voltages, the ratio of which follows the exponential'function with an accuracy of one part in two million for range e x varying from 0 to 1. An object of the present invention is to provide a voltage divider which produces an exponential ratio between the resulting voltages. A further object of this invention is to provide a voltage divider employing four linear potentiometers of such values that the resulting voltages vary according to an exponential ratio. Other objects and many of the attendant advantages of this invention will be readily appreciated as the same 0 becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings wherein: Fig. 1 shows one form of a voltage divider constructed according to the present invention; Fig. 2 illustrates another species of this invention; Fig. 3 shows the preferred embodiment of a voltage divider; and Fig. 4 is a graph showing the variation of 3 from e where x varies from 0 to 1 by employing the voltage divider of Fig. 3. Referring now to the drawings and more specifically to Fig. 1 it can be seen that there is provided a voltage divider having ganged wiper contacts, or sliders 1 and 2. Output voltages E and E, are obtained across wiper contact 1 and the common output, or reference, point 12, and across wiper contact 2 and reference point 12, respectively. There are provided resistances R R and R disice posed in series as shown and across which is impressed a voltage E which can be supplied by any suitable source, such as battery 13. When x=0 the sliders are in the upper position and when x=1 the sliders are in the lower position. E is accepted as a fixed voltage as shown in Fig. 1. Accordingly when x: 1, E =E and and x=l. The accuracy of the ratio l +1 E 'E.B,. will be calculated for the case in which E and E vary through one half the total range of e". By definition of the exponential function in E, E0 E, 13 From this equation E is found equal to The values of A and B may be evaluated when 4:1 as A=E E and Substituting the derived value of E into the original equation the final equation for the voltage divider shown in Fig. 1 becomes: E 1 +xh Z 1] E3 lW x e From this equation the ratio of may be calculated for various values of x yielding the following results: Table I 1 [1 X T: Ratio E meets the theoretical values for x=0, x=1 and .-==.5. The maximum error is dx=.004. With XII/7', this means a maximum timing error of 120 milliseconds for 'r=30 seconds. In other words a time fuze for 30 seconds maximum time has no error due to the voltage divider at settings of 0, 15, 30 seconds, but the deviation is +120 milliseconds at 7.5 seconds and -120 milliseconds at 22.5 seconds. Whilethis accuracy is suflicient for many purposes, it is not adequate for fuze application. . In Fig. 1, E is accepted as a constant. However, it can be shown that E varies between when x =0 and when x=1. The deviation of E from a linear function between these values is slight and therefore a linear potentiometer may be provided to vary E as E; and E are varied. Such a voltage divider is shown in Fig. 2. There The voltage divider of Fig. 1 yields the general equation to meet the curve e at three points. If x=0, .5 and l are the meeting points then a and b can be calculated and the resulting equation gives coincidence at these points. In order to improve the accuracy of the voltage divider it would be necessary to increase the number of points ofcoincidence thereby increasing the order of the rational function by which is expressed. This gives the equation I 1+a x+ b x E3 1 llg$+ 17 50 In this case the coefficients a [7 a b must be determined to give coincidence points with the curve e Assuming these points to be at x=0, .25, .5, .75 and 1 then: a =.5411S855 b =.10755897 a =.45871O32 b =.06523960 Comparing with e with the above calculated coefficients gave values shown in the following table: I II are provided sliders 4, 5 and 6 which are ganged as shown. Tab e I Slider 5 serves the function of impressing at point 7 a varying voltage corresponding to a linear variation of E 5 A Ratio E M1016 X E The output voltages E and B are obtained across wiper 3 arm 4 and reference point 12, and across wiper arm 6 [1] [2] and reference point 12, respectively. This voltage divider may beexpressed by the following equation: 0.0 1.000000000 1.000000000 1.000000000 0.0000 0.1 1. 105170018 1.105105522 1. 000004882 +4. 882 m 1] 0.2 1 221402758 1221400527 1.000001820 +1.826 [1:z;] [1-:c]+a; 0.3 1 340858808 1.349860571 0. 000008003 l.307 El-erl 101803 301880 200080 .1053 E3 +'E 0Z0 1:82211880O 1:5322115631 11000001730 +11 730 -1 e 0.7 2. 013752707 2013750077 1. 000001300 +1300 08 2.225540028 2225545003 0000008108 -1.332 e 0. 0 2. 450003111 2. 450015131 0. 000005113 -4. 887 1+z[-[ -2]+x 1- 1.0 2. 718281828 2. 718281828 1.000000000 0.000 2e 1 e 1x[2 +0 1- for or by the general equation El 1 5 2 l-i-Ax-l-Cx E3 1 (1 16+ 17210 2 1 a =().54115855 b =0.1075589 This equation yields the following results: =0 45 871()32 b =0.06523960 Table 11 ,It is apparent that the voltage divider of Fig. 1 must El [1] be modified to include a potentiometer arrangement vary- X '5 Ratiom i140 ing proportional to mx The voltage divider of Fig. 3 provides such an arrangement. There are provided [11 I21 00 sliders 8 9 10 and 11 which are I 1 ganged as shown. In thi od' lta E E are oh- 000 1.000000000 1.000000000 1.000000000 0.0000 t Z the outgut 2 gas 1 altld t 3 t 0.1 1.105170018 1.105140020 1000022523 +0.2252 ame acmss P all common P P0111 100003 130080 133020 1200 andwipwm2800330323230212,383- 014 l:491824698 11401550042 11000184141 +11 8414 lively; Sliders 10 With 'lesistofs 5 alld 4 gg %.ggg'figg l pggtgggggg wgggg igg ig-g spectively are added to yield the square function hereggwgwgg g? .lIIbGfOl'fi I'BfGITEd t0. voltage dlVldfil' gives the 01- 55 00 5 2 0.0 2. 450003111 2, 450523370 1. 000032417 +0. 324 lpwmg who for 1.0 2. 718281828 2. 71828182 1.000000000 +0. 0000 1 E2 for R R e 1 2. 0 [21+ 8 [121111212 E V :0 e1 :0 E3 2M 3 R1+ R3 xR1+x $10 R The coefiicients of this equation must equal the methcients a b a b previously calculated. However, all resistance values can be expressed in terms of the single resistor R; as follows: With there is: Since r and r;, are close to 1, for simplification purposes R may be assumed equal to R and R;,. A voltage divider with R =R =R gives good accuracy with an error of not more than .0043 percent. This invention with the foregoing calculations demonstrates that a combination of five linear resistance units, four of which are potentiometers assembled on one axis can produce output voltages having a ratio which follows the exponential function with an accuracy of one part in two million for the range e [x:0 1]. Obviously many modifications and variations of the present invention are possible in the light of the above teachings. It is therefore to be understood that within the scope of the appended claims the invention may be practiced otherwise than as specifically described. What is claimed as new and desired to be secured by Letters Patent is: 1. An electrical circuit comprising a potential energy source, a plurality of series connected linear resistance elements connected across said source, a common output terminal defined in the electrical circuit, and ganged wiper contacts individually coupled to two of said resistance elements, the instantaneous potentials appearing across each of said ganged contacts and said common output terminal as said contacts are moved across their respective resistance elements exhibiting an exponential relationship therebetween. 2. An electrical circuit comprising a potential energy source, a plurality of series connected linear resistance elements connected across said source, a common output terminal defined in the electrical circuit, ganged wiper contacts individually coupled to two adjoining resistance elements of said plurality of resistance elements, the effective resistance between said adjoining resistance elements being selectively varied by said contacts being electrically isolated from each other, the movement of said ganged wiper contact in a manner to provide instantaneous output potentials between each of said ganged contacts and said common terminal exhibiting an exponential relationship therebetween. 3. An electrical circuit comprising a potential energy source, a bank having a plurality of serially connected linear resistance elements connected across said source, a common output terminal defined by one juncture between said source and said bank, a first movable output terminal electrically coupled to one of said elements for developing a variable output potential between said first and said common output terminals correlative to the movement of said first terminal on said one element, a second movable output terminal electrically coupled to the resistance element adjoining said one element for developing a variable output potential between said second and said common output terminals correlative to the movement of said second terminal on said adjoining element, said movable output terminals being ganged for movement in unison on their respective resistance elements in a manner to selectively vary the effective resistance between the adjoining elements to effect an exponential relationship between said output potentials. 4. An electrical circuit comprising a potential energy source, a first bank of a plurality of serially connected linear resistance elements connected across said source, a second bank of a plurality of serially connected linear resistance elements connected across said source, a common output terminal defined by one juncture between said first bank and said source, a first movable output terminal electrically coupled to one of the elements in said first bank for developing a variable output potential between said first and said common terminals correlative to the movement of said first terminal on said one element, a second movable output terminal electrically coupled to the element adjoining said one element in said first bank for developing a variable output potential between said second and said common terminals correlative to the movement of said second terminal on said adjoining element, a movable contact electrically coupled to one of the elements in said second bank and to the juncture between said one and adjoining elements on said first bank, said movable contact and terminals being ganged for movement in unison on their respective elements to effect an exponential relationship between said output potentials. 5. An electrical circuit comprising a potential energy source, a bank of interconnected linear resistance elements coupled across said source, said bank including a plurality of serially connected elements and one element connected in parallel with one of said serially connected elements, a movable contact electrically coupled to the one serially connected element and to said parallel connected element, a first movable output terminal electrically coupled to one of said plurality of serially connected elements for developing a variable output potential between said first terminal and a common terminal correlative to the movement of said first terminal on the one element, a second movable output terminal electrically coupled to the element adjoining said one of said serially connected elements for developing a variable output potential between said second terminal and a common terminal correlative to the movement of said second terminal on said adjoining element, a movable common terminal electrically coupled to said parallel connected element, said movable contact and terminals being ganged for movement in unison on their respective elements to effect an exponential relationship between said output terminals. References Cited in the file of this patent UNITED STATES PATENTS 1,858,364 Koenig May 17, 1932 2,417,442 Parkinson Mar. 18, 1947 2,448,885 Hooven Sept. 7, 1948 2,453,462 Sellers Nov. 9, 1948 2,573,280 Schmidt Oct. 30, 1951 FOREIGN PATENTS 698,560 Germany Nov. 13, 1940 Patent Citations
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