US 2704305 A Description (OCR text may contain errors) March 15, 1955 D. J. MCLAUGHLIN ETAL 2,70 ,305 RESISTIVE SURFACE VOLTAGE DIVIDER NETWORK Filed June 9, 1954 2 Shets-Sheet 1 IELE= J. EXC I TATION DETECTION DISPLAY INVENTORS DONALD J. MC LAUGHLIN HARVEY G. TALMADGEAR. ATTORNEYS March 1955 D. J. MCLAUGHLIN ETAL 2,704,305 RESISTIVE SURFACE VOLTAGE DIVIDER NETWORK Filed June 9. 1.954 2 Sheets-Sheet 2 cdq d c d g d 8 g 5 g 8 8m 6E2; Q g 5 a My Q Pvww W3}: I 3 9 W W J g m 8 8 no m (D (D m \g a m o In 9 s S "WA/w r r 9 In N N N "M 8 S W; m "M 9 u\ v N v flan: 2 l AIAAANJ v N m r m lo q- M I: am en ml 0': 8 m a; co cocci IO N D F] F m I r0 10 m Mm M H INVENTOR5 I. DONALD J. MG LAUGHLIN HARVEY G. TALMADGE,JR. ATTORNEY: United States Patent RESISTIVE SURFACE VOLTAGE DIVIDER NETWORK Donald J. McLaughlin, Washington, D. C., and Harvey G. Talmadge, Jr., Clinton, Md., assignors to the United States of America as represented by the Secretary of the Navy Application June 9, 1954, Serial No. 435,652 8 Claims. (Cl. 178-18) (Granted under Title 35, U. S. Code (1952), see. 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 in general to the provision of an improved electrical writing tablet for use in telautograph systems and in particular to the provision of means for uniformly energizing a resistive surface. It is common in telautograph systems to employ a plane resistive surface as a writing tablet by energizing the surface across the x and y axes of the surface to develop a field of x and y coordinate voltage information. la the prior art the resistive surface has been energized for x and y coordinate information by the application of voltages across parallel elongated electrodes located at opposite ends of the x and y axes respectively. It has been recognized that the x and y potential gradients produced by such an energization system are uniformly distributed only in the region of the axes of the tablet and are non-uniformly distributed about the edges of the tablet. Thus the accurate writing area, which is the area of parallel equipotential lines, comprises only the centermost portion of the energized square. It is frequently desirable to utilize a larger writing area without enlarging the energized surface. Also in certain applications, such as the data transfer systems for use with radar indicators or other cathode ray tube devices, a transparent resistive surface substantially the size and shape of a cathode ray tube screen may be used, thereby further complicating the problem of providing parallel equipotential lines over a large writing area. It is an object of this invention to provide a uniformly energized writing surface for telautograph systems. It is another object of this invention to provide a uniformly energized circular writing surface which may be superimposed on a data plotting cathode ray tube indicator such as used in PPI radar systems. It is still another object of this invention to extend the useful writing area of telautograph writing tablets. Other objects will become apparent from a complete understanding of the invention for which reference is had to the accompanying drawings and description of the invention. Figure 1 is a block diagram of a typical telautograph system incorporating the energized writing surface of this invention. Figure 2 is a schematic diagram of one embodiment of the energized writing surface shown in the block diagram of Figure 1. Figure 3 is a more detailed schematic diagram of the embodiment shown in Fig. 2. Briefly, this invention provides a means for applying it and y voltage coordinate information on a resistive writing tablet by alternately energizing the surface in a predetermined manner at each of a plurality of points arranged in a circular locus about the center of the surface. This energization is obtained by applying in alternate order separate predetermined voltages to each of the points on the surface for respective x and y axes ener-, gizations. In particular, a single voltage source operat-' ing through a low impedance multiple tap voltage divider network is used to establish the two predetermined voltages at each point. Figure 1 depicts a typical telautograph system utilizing a rectangular coordinate excitation system for the resistive writing surface to permit the detection of x and y coordinate information. in this system the x and y excitation may be applied in alternate order from a single excitation source as in the embodiments of the invention discussed herein. A probe, which is indicated in the drawings by an arrowhead, is provided to contact the surface at any point anti to PICK onvoltage information at this point representative of its position on the surface. 'lhe probe is connected to a detection means also shown in OlOCK diagram wherein the x and y VOitage inforination is separately distinguished and is then applied to the orthogonal denection system of a cathode ray tube type display means as shown. For a further understanding or me utility of this invention reference is had to the co-pending application of D. J. McLaughlin et al. for a 'leiautograph System, Serial No. 413,734, tiled on March 2, i954. rigure z is a simplified schematic diagram and Figure 3 is a more detailed schematic diagram of the energized writing surface of this invention which, for purposes of illustration only, incorporates a transparent resistive film on a glass base and a resistance voltage divider network in a u. C. voltage energization system. The transparent resistive element in this embodiment is commercially known as N653. or Electropane glass, and comprises a thin metallic iilm of copper, silver, or gold on a siliceous base. by investigation, this type of element has been found to have a linear resistive variation between two points on the surface in accordance with the distance between the two points only when the current paths surrounding the two points are uninterrupted by edge discontinuities, or when the two points are on an infinite suriace. Since infinite surfaces are not of practical concent, a resistance per square rating has been adopted for this type of surface. This "resistance per square has been round to be substantially constant for a given surface within any square area whether the square is one inch on a side or one foot on a side. The embodiment or this invention shown in the drawings is concerned with the non-linear point-to-point resistance gradient of a circular configuration and in particular the energization of this non-linear resistance gradient to produce a linear voltage gradient on the surface. More particularly, in Figure 2. a circular transparent resistive surface 39 which may be conveniently positioned before the screen of a cathode ray tube has been shown. This circular surface has, by way of example, 24 consecutively numbered (1-24) equally spaced peripheral contact points. in this embodiment, for purposes of simplit'ying the description, only 8 of the peripheral points are shown as being energized. Each of these eight points are connected through a unique voltage dividing resistance network to at least one of four external terminals A, B, C, and D. Said terminals are separately connected in pairs A and C, B and D, through two SPDT synchronous operating switches 25 and 26 to a D. C. voltage source, whereby the surface is alternately energized across the y axis through terminals A and C and across the x axis through terminals B and D. The D. C. voltage source preferably comprises two low impedance, high current capacity, equal voltage supplies 37 and 38 connected in series with their center connection grounded to establish a convenient zero voltage point at the center of the surface and, as hereinafter made apparent, zero or ground potential at any point on the x axis during the y axis energization and likewise ground potential at any point on the y axis of the surface during x axis energization. Said switches 25 and 26 permit the energization of said surface across orthogonal axes by a single voltage source, however, it may be seen that switches 25 and 26 could be eliminated in telautograph systems employing separately distinguishable energization of orthogonal axes. To establish a linear x and y voltage gradient over a circular area with zero voltage at the center, two predetermined voltages must be alternately applied to each point on the periphery of the circle. It may be seen by trigonometry that these voltages must vary alternately as the sine and cosine functions of the radius angle as: Vpy=V1n Sill 0 and V92=Vm C08 0 where V is the voltage at any given point on the periphery of the surface during the y axis energization, vpx is the voltage at the same point during the x axis energization, Vm is the maximum voltage on the surface (at the energization axis), and 6 is the angle the radius to the point makes with the horizontal or x axis. For example, considering Vm= volts, point 8, the first peripheral point away from the vertical axis (where 24 points spaced at 15 intervals are used), must be at 15 (sin 75") or 14.5 volts during y axis energization and at 15 (cosine 75) or 3.9 volts during the x axis energlzation. Referring in particular to the drawing it will be seen that each of the 45 points, 4, 10, 16 and 22, is connected through identical resistance elements to each of two adjacent terminals, A, B, C or D, of energization. More specifically, point 10 is connected through resistances 33 and 43 to terminals A and B, respectively; point 16 through resistances 53 and 63 to terminals B and C, respectively; point 22 through resistances 73 and 83 to terminals C and D, respectively; and finally point 4 through resistances 93 and 103 to terminals D and A, respectively. In the connection all of the resistances 33,43, 53, 63, 73, 83, 93 and 103 are equal which thereby places all the 45 points at points of absolute symmetry in the external voltage divider network. That is, due to the equality of the resistances connecting the four 45 points 4, 10, 16 and 22 to the terminals A, B, C and D, fixed voltages of a predetermined magnitude will be impressed at these points regardless of which pair of terminals, A and C or B and D, are being energized. To illustrate this point take the case where the synchronous switches 25 and 26 are in their down position and terminals A and C are being energized corresponding to a y axis energization. Neglecting for the moment the surface resistance of surface 39, terminals B and D will be at ground potential, points 4 and 10 at one-half the potential of source 37 above ground and points 16 and 22 at one-half the potential of source 38 below ground. During the alternate energization where synchronous switches 25 and 26 are in their up position and terminals B and D are being energized, corresponding to an x axis energization, then (still neglecting the resistance of the surface 39) terminals A and C will be at ground potential, points 10 and 16 will be at onehalf the potential of source 37 above ground and points 4 and 22 at one-half the potential of source 38 below ground. Accordingly, since sources 37 and 38 are equal, the magnitude of the potential at the 45 points will remain constant regardless of the direction of energization and points 4 and 22 merely change signs with the changes in the direction of energization. As will be explained in more detail hereafter, when the resistance of the surface is taken into consideration the magnitude of the voltage at the 45 points on the surface will be decreased but will still remain equal in both energizations. Once the voltage at the 45 points 4, 10, 16 and 22 have been established it may be seen from the trigonometric relation that the desired maximum voltage on the surface Vm will be 1.414 times the 45 point voltage. The maximum voltage in the x and y axes energizations are established across points 1 and 13, and 7 and 19, respectively. The points 1 and 13 are each connected through single equal valued resistances 86 and 46 to one terminal D and B, respectively. Likewise the points 7 and 19 are each connected through similar equal valued resistances 36, and 66 to one terminal A and C, respectively. The points 1, 7, 13 and 19 are also serially interconnected in bridge fashion by other equal valued resistances 27, 28, 29 and 30. Still neglecting the resistance of the surface 39, these interconnecting resistances 27, 28, 29 and 30, together with the terminal connected resistances, 86 and 46, and, 36 and 66, form another voltage divider network which establishes the maximum voltage Vm on the surface for both the x and y axes energizations. Thus both the maximum voltage and the 45 point voltage are established on the surface by these two separate voltage divider networks. In addition, the symmetrically evaluated resistances in one network serves to establish a zero voltage at the unenergized terminals, as previously mentioned, and the other network establishes a zero voltage at the unenergized axes on the surface for a resulting zero voltage drop across the terminal connected resistance at the unenergized axes. As mentioned, the foregoing discussion neglects the shunting relative to point resistance of the surface 39. Thus it will be seen the external voltage divider network is the principal factor in the described voltage divisions. For precision calculation in the external network, the shunting effect of the resistive surface cannot be completely neglected and therefore its part in the voltage division will now be considered. In the first described voltage division, involving the 45 points, it will be seen that the terminal connected resistances 33, 43, etc., are each alternately in series or parallel with the surface resistance of surface 39, whereas in the second described voltage division, involving the ordinate points 1, 7, 13 and 19, it will be seen that the terminal connected resistances are only in series with the surface resistance and but two of the four terminal connected resistances 36, 46, 66 and 86 are in the voltage division at any one time. Consequently, each terminal connected resistance, 33, 43, 53, etc., in the first described voltage division is employed alternatively as a voltage dropping resistance and as a bleeder current resistance in what might be termed a reciprocal voltage division. In the second described voltage division the terminal connected resistances 36, 46, etc., are employed as voltage dropping resistances and only the bridge connected resistances 27, 28, etc., act as bleeder current resistances. It is readily apparent that the disclosed symmetry in both voltage division networks is essential to the alternate energization of the surface across x and y axes by a single source. Further considering the resistance of the surface in the voltage division, it is apparent that the resistive surface provides innumerable additional current paths between points and that in the energization of the surface at several points an indeterminate number of current paths are established in the voltage divider network. Thus the variation of any one resistance in the external voltage division network may afiect the voltage at all points on the surface to some degree by changing the current distribution in the network. To maintain a particular current distribution it is important in adjusting the voltage division networks to vary all described equal valued resistances the same amount, at the same time. As pointed out above, in the embodiment of Figure 2 the voltages at points 1, 4, 7, 10, 13, 16, 19 and 22 are substantially stabilized by their provision of heavy bleeder current through the external resistance in parallel with the surface resistance. By the use of resistances of the lowest value commensurate with the current load capacity of the voltage source, the resistive effect of the surface is minimized and surfaces of varying resistance per square may be substituted in the invention. And as a further consequence, any slight resistive irregularities on the surface will have a negligible eflfect on the uniformity of the equipotential field on the surface. In the illustration of Figure 2 a typical resistive surface 39 is shown which has a resistance per square rating of 125 ohms, and elfective resistance to ground at the 45 points 4, 10, 16 and 22 of 415 ohms and an effective resistance to ground at the end of the energization axes 1, 7, 13 and 19 of 530 ohms. For this particular surface, the voltage dropping resistances and the bleeder current resistances 33, 43, 53, etc., in the first described voltage divider network are each ohms. In the second described network the terminal connected voltage dropping resistances 36, 46, 66 and 86 and the interconnecting bleeder current resistances 27, 28, 29 and 30 are 12 ohms and 47 ohms, respectively. Again it is pointed out that to stabilize the voltages at the energization points on the surface and to provide the maximum voltage on the surface, the external resistances of the voltage divider should have as low a value as is commensurate with the current carrying capacity of the source. Therefore if a voltage source having a higher current carrying capacity were used it would be desirable to employ lower valued resistances in the voltage divider networks. The embodiment of Figure 2 depicts a basic resistive surface voltage divider network for producing a uniform voltage gradient on the resistive surface. This illustrated embodiment provides a reasonably linear voltage gradient over the surface which is satisfactory for most writing or tracing applications. However, in this embodiment the voltage field which is produced on the surface produces a somewhat scalloped pattern about its periphery. It will be seen that the scalloping will be less objectionable and a larger writing area will be provided by increasing the number of energization points about the periphery. In Figure 3 the same resistive surface 39 is shown with all 24 peripheral pointsconnected in an energization systern similar to that discussed with respect to Figure 2. In this embodiment, the maximum voltage and the 45 point voltage are both established in a manner identical to that discussed in respect to Figure 2. The voltages at intermediate points are determined, of course, by means of the same trigonometric relation used before and each of these intermediate points are connected to two terminals through two separate resistances in like manner to the connection of the 45 points 4, 10, 16 and 22. Specifically, points 2 and 6 are connected through resistances 95 and 91, and 101 and 105, to terminals D and A, respectively; points 8 and 12 are connected through resistances 35 and 31, and 41 and 45, to terminals A and B, respectively; points 14 and 18 are connected through resistances 55 and 51, and 61 and 65, to terminals B and C, respectively; and points 20 and 24 are connected through resistances 75 and 71, and 81 and 85, to terminals C and D, respectively. Likewise, points 3 and 5 are connected through resistances 94 and 92, and 102 and 104, to terminals D and A, respectively; points 9 and 11 are connected through resistances 34 and 32, and 42 and 44, to terminals A and B, respectively; points 15 and 17 are connected through resistances 54 and 52, and 62 and 64, to terminals B and C, respectively; and points 21 and 23 are connected through resistances 74 and 72, and 82 and 84, to terminals C and D, respectively. In the calculation of resistance values at these intermediate points, it is important to remember that while the effective resistance to ground is the same in both energizations at the ordinate points 1, 7, 13 and 19 and at the 45 points, it is not the same in both energizations at the intermediate points. Obviously, this complicates the calculation of resistance values and in view of this complication, the voltage division at the intermediate points must effect a compromise of the two voltages desired at these points. Again, it is important to preserve symmetry in the voltage divider network to permit a linear energization across orthogonal axes by a single source. In Figure 3 the equal valued resistances are identifiable by the same last integer in their identifying numbers. By way of illustration, resistances 31, 41, 51, etc., are each 510 ohms; resistances 32, 42, 52, etc., are each 220 ohms; resistances 34, 44, 54, etc., are each 130 ohms; and resistances 35, 45, 55, etc., are each 160 ohms. As in the previous embodiment, resistances 33, 43, 53, etc., are each 100 ohms; resistances 36, 46, 56, etc., are each 12 ohms and the resistances 27, 28, 29 and 30 interconnecting the points 1, 7, 13 and 19 are each 47 ohms. As the adjustment of impedance values in the external network is extremely complex the specific resistance values disclosed in this application, while assumed to be optimum values for the present consideration, are not thus to be considered limiting factors in this invention to any degree. This specification has disclosed a system for the uniform energization of a circular area on a resistive surface by means of a plurality of points. Twenty-four peripheral points has been arbitrarily selected as the optimum number and most advantageous arrangement for the present embodiment but, dependent on the useable writing area desired, a greater or a lesser number of points and a different arrangement of points might be chosen. It is apparent that other resistive surfaces of substantially uniform resistance per square over the surface area may be substituted as the centermost resistance element of the voltage divider network of this invention provided their diiference in resistivity is within a reasonable range. For example, any surface having a resistance per square rating between 70 and 170 ohms might be incorporated in the described embodiment. It is understood that other surface configurations than the disclosed circular surface may be used in this invention without exceeding the scope of the invention, and that these surfaces may also be energized at a plurality of points through a similarly devised voltage divider network to permit the rotation of parallel equipotential lines. Furthermore, it is understood that a carbon plate or any other substantially uniform resistive surface may be used in this invention. Although only certain specific embodiments of our invention have been disclosed it must be understood that we are fully aware of the many modifications possible thereof. Therefore, it must be understood that the present invention is to be limited only in and to the extent indicated by the spirit of the disclosure. What is claimed is: 1. In a device for alternately energizing a plane resistive surface across the x and y axes of a rectangular coordinate system, the combination comprising, a plurality of contact points disposed along a circular locus about a center point on said surface, with one pair of points being disposed at diametrically opposite positions on the x axis and another pair of said points being disposed at diametrically opposite positions on the y axis of the two coordinate system, first and second pairs of voltage input terminals arranged to receive a suitable energizing voltage across each pair of terminals in alternation, a balanced resistive bridge network interconnecting the diametrically opposite contact points lying on the x and y axes of the two coordinate system, separate and equal resistance elements connecting each diametrically opposite point on both x and y axis to a respective terminal of said first and second pairs of input terminals, a separate pair of resistances connecting each of the remaining contact points in each quadrant of the two coordinate system to one terminal of each of said pairs of input terminals with the contact points of one quadrant being connected to a terminal of each pair different than the contact points in its diametrically opposing quadrant, said last named resistances being proportioned to establish a potential distribution along said contact points that varies in magnitude as a sine function of the radius angle described by the contact point and the instantaneous axes of energlzation. 2. In a device for alternately energizing a plane resistive surface across x and y axes of the surface in a rectangular coordinate system, the combination comprising a plurality of contact points disposed along a circular locus about a center point of said surface with one pair of points being disposed at diametrically opposite positions on the x axis and another pair of said points being disposed at diametrically opposite positions on the y axis of the two coordinate system, a balanced resistive bridge network interconnecting the diametrically opposite contact points lying on the x and y axes of the two coordinate system, a first pair of voltage input terminals connected across one pair of junction points of the bridge and a second pair of voltage input terminals adapted to be energized in alternation with the first pair of voltage input terminals connected across the other pair of junction points of the bridge, a separate pair of resistances connecing each of the remaining contact points in each quadrant of the two coordinate system to one terminal of each of said pairs of input terminals with the contact points of one quadrant being connected to a terminal of each pair different than the contact points of its diametrically opposite quadrant, said last named resistances being proportioned to establish a potential distribution along said contact points that varies in magnitude as a sine function of the radius angle described by the contact point and the instantaneous axes of energization. 3. In a device for alternately energizing a plane resistive surface across x and y axes on the surface in a rectangular coordinate system, the combination comprising a plurality of contact points disposed along a circular locus about a center point on said surface, with one pair of points being disposed at diametrically opposite positions on the x axis and another pair of said points being disposed at diametrically opposite positions on the y axis of the two coordinate system, first and second pairs of voltage input terminals arranged to receive a suitable energizing voltage across each pair of terminals in alternation, a balanced resistive bridge network interconnecting the diametrically opposite contact points lying on the x and y axes of the two coordinate system, separate and equal resistance elements connecting each junction point in the bridge network to a respective terminal of said first and second pairs of input terminals, a separate pair of resistances connecting each of the remaining contact points in each quadrant of the two coordinate system to one terminal of each of said pairs of input terminals with the contact points of one quadrant being connected to a terminal of each pair different than the contact points of its diametrically opposite quadrant, said last named resistances being proportioned so that diametrically opposite points are connected to opposing input terminals of the same input terminal pair through identical valued resistances to establish a potential distribution along said contact points that varies in magnitude as a sinefunction of the radius angle described by the contact point and the instantaneous axes of energization. 4. In a device for alternately energizing a plane resistive surface across x and y axes on the surface in a! rectangular coordinate system, the combination comprising a plurality of contact points disposed along a circular locus about a center point on said surface with one pair of points being disposed at diametrically opposite positions on the x axis and another pair of said points being disposed at diametrically opposite positions on the y axis of the two coordinate system, a balanced resistive bridge network interconnecting the diametrically opposite contact points lying on the x and y axes of the two coordinate system, a first pair of voltage input terminals connected across one pair of junction points of the bridge and a second pair of voltage input terminals adapted to be energized in alternation with the first pair of voltage input terminals connected across the other pair of junction points of the bridge, a separate pair of resistances connecting each of the remaining contact points in each quadrant of the two coordinate system to one terminal of each of said pairs of input terminals with the contact points of one quadrant being connected to a terminal of each pair different than the contact points of its diametrically opposite quadrant, said last named resistances being proportioned so that diametrically opposite points are connected to opposing input terminals of the same input terminal pair through identical valued resistances to establish a potential distribution along said contact points that varies in magnitude as a sine function of the radius angle described by the contact point and the instantaneous axis of energization. 5. In a device for alternately energizing a plane resistive surface across the x and y axes on the surface in a rectangular coordinate system, the combination comprising a plurality of pairs of energization points encompassing an area on said surface, the points in each of said pairs being diametrically disposed with each point in said pairs equally spaced with respect to the center of the surface, with one pair of points being disposed on the x axis and another of said pair of points being disposed on the y axis of the two coordinate system, first and second pairs of voltage input terminals arranged to receive a suitable energizing voltage across each pair of terminals in alternation, a balanced resistive bridge network interconnecting the pairs of points lying on the x and y axes of the two coordinate system, separate and equal resistance elements connecting each junction point in the bridge network to a respective terminal of said first and second pairs of input terminals, a separate pair of resistances connecting each of the remaining energization points in each quadrant of the two coordinate system to one terminal of each of said pairs of input terminals with the energization points of one quadrant being connected to a terminal of each pair of terminals different than the energization points in its diametrically opposite quadrant, said last named resistance being in proportion to establish a potential distribution along said points that varies in magnitude as a sine function of the radius angle described by the energization point and the instantaneous axis of energization. 6. In a device for alternately energizing a plane resistive surface across x and y axes on the surface in a rectangular coordinate system, the combination comprising a plurality of pairs of energization points encompassing an area on said surface, the point in said pairs of points being diametrically disposed with each point equally spaced with respect to the center of the surface, one pair of points being disposed on the x axis and another pair of points being disposed on the y axis of the two coordinate system, a balanced resistive bridge network interconnecting the pairs of points lying on the x and y axes of the two coordinate system, a first pair of voltage input terminals connected across one pair of junction points of the bridge and a second pair of voltage input terminals adapted to be energized in alternation with the first pair of voltage input terminals connected across the other pair of junction points of the bridge, a separate pair of resistances connecting each of the remaining energization points in each quadrant of the two coordinate system to' one terminal of each of said pairs of input terminals with the energization points of one quadrant being connected to a terminal of each pair of input terminals different than the energization points in its diametrically opposite quadrant, said last named resistances being in proportion so that each point in said pairs of points is connected to opposing input terminals of the same input terminal pair through identical valued resistances to establish a potential distribution along said points that varies in magnitude as a sine function of the radius angle described by the energization point and the instantaneous axes of energization. 7. In a device for alternately energizing a plane resistive surface across x and y axes on the surface in a rectangular coordinate system, the combination comprising a plurality of pairs of energization points diametrically disposed about a center point to encompass a circular area on said surface, one pair of points being disposed on the x axis and another pair of points being disposed on the y axis of the two coordinate system, first and second pairs of voltage input terminals arranged to receive a suitable energizing voltage across each pair of terminals in alternation, a balanced impedance bridge network interconnecting the pairs of points lying on the x and y axes of the two coordinate system, separate and equal valued impedance elements connecting each junction point in the bridge network to a respective terminal of said first and second pairs of input terminals, a third and fourth pair of points in said plurality equally spaced with respect to the pairs of points on the x and y axes so that each point in said third and fourth pair of points is disposed in a different quadrant of the two coordinate system, a separate pair of impedances connecting each of the energization points in said last named pair of points to one terminal of each of said pairs of input terminals, so that said contact point in each quadrant is connected to a terminal of each pair of terminals dilferentthan the contact point in its diametrically opposite quadrant, said last named impedances being equal valued and all other impedances being proportioned in respect to the point potential established thereby to establish a potential distribution along the energization points that varies in magnitude as a sine function of the radius angle described by the energization points and the instantaneous axes of energization. 8. In a device for alternately energizing a plane resistive surface across x and y axes on the surface in a rectangular coordinate system, the combination comprising a plurality of pairs of energization points diametrically disposed about a center point on said surface, the points in each of said pairs of points being equally spaced with respect to adjacent points, one pair of points being d sposed on the x axis and another pair of points being disposed on the y axis of the two coordinate system, first and second pairs of voltage input terminals arranged to receive a suitable energizing voltage across each pair of terminals in alternation, a balanced resistive bridge network interconnecting the pairs of points lying on the x and y axes of the two coordinate system, separate resistance elements connecting each junction point in the bridge network to a respective terminal of said first and second pairs of input terminals, a separate pair of resistances connecting each of the remaining energization points in each quadrant of the two coordinate system to one terminal of each of said pairs of input terminals with the energization points of one quadrant being connected to a terminal of each pair of input terminals different than the energization points of its diametrically opposite References Cited in the file of this patent UNITED STATES PATENTS Handrick Dec. Moodey Jan. Kopfmuller et al. Jan Levin Aug Patent Citations
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