Patent GB-740071-A (GB)
Title: Improvements relating to computing apparatus
Inventor: SPENCER ROLF EDMUND
IPC: G06G7/22
Filed: 1950-01-28
Abstract: 740,071. Electric analogue calculating systems. ELECTRIC & MUSICAL INDUSTRIES, Ltd. Jan. 15, 1951 [Jan. 28, 1950], No. 2262/50. Class 37. In an apparatus for the synthesis of exponential and trigonometrical functions, the initial terms of Taylor's Series are employed. The expressions used are, for the exponential case: and for the trigonometrical case: The terms involving differential coefficients of the function in the Taylor's Series are obtained by adding to the selected signal either an incremental signal involving the selected signal or a feed-back output signal of the apparatus. By an adaption of the trigonometrical case, coordinates may be transformed from the Cartesian to the Polar form. In Fig. 1, particular values of f(x) are set up at tappings bo, b1 ... br of potentiometer 1 which are scanned by the slowspeed selector 4, 5, the displacement of which represents the instantaneous value of x. The potentiometer 6 is scanned by high-speed brush 7, 8, the displacement of which represents the instantaneous value of #x. Brush 7, 8 is supplied with a signal f(x) from 4, 5; 6 is fed with a voltage equal to f(x) multiplied by a constant a and hence the output at 9 is as in equation A. In the sine-cosine computing apparatus, Fig. 2, voltages representative of particular values of sin x n , i.e. the first term of equation B, are developed at the tappings bo to br of potentiometer 10 scanned by the slow-speed brushes 11, 12, the displacement of which represents the instantaneous value of xn. Linearly tapped potentiometer 19 is fed inductively from 20 with a voltage representative of cos x from the output terminal 21 and is scanned by the high-speed brushes 15, 16, the displacement of which represents the instantaneous value of #x. The voltage at each tap represents #x. cos x, i.e. the second term of equation B, and between it and the studs scanned by 15, 16 two further voltages are injected by the transformers 24, 25 corresponding to : which are used to form the third and fourth terms of equation B. Devices 24, 25 each consist of a primary winding which is supplied with a feed-back voltage from the output terminals 23, 21 and a set of secondary windings in series with the leads between 19 and 15, 16. In 24 the number of turns on each secondary is representative of #x<SP>2</SP> and in 25 is representative of #x<SP>3</SP>. The cosine terms are synthesized in a similar way from the tappings Co to Cr scanned by the slow-speed brushes 13, 14 connected to the high-speed brushes 17, 18 which scan the linearly tapped potentiometer 22 fed from the sine output terminal 23. In transforming coordinates from Cartesian to Polar, Fig. 3, use is made of the equations : where Rn and # n  are the Polar co-ordinates and X and Y are the Cartesian co-ordinates. In the apparatus Rn and U are evaluated by expressing each in the form of the Taylor Series and U is maintained at zero by a feedback arrangement and thus : The values X, Y are applied to the apparatus in the form of voltages and the outputs R, # appear as a voltage and shaft displacement respectively. In equation C, Rn is derived at 28, 29 and applied to high-speed scanning switch 31, 32 where it is added to a signal at quadrilaterally tapped winding 30, representing the second term R./2 ##<SP>2</SP> to produce the electrical output signal R. To form the second term a voltage corresponding to R/2 is applied from the primary winding 33 to the quadrilaterally tapped winding 30 where the voltage developed between each tapping and the lower end of the winding is proportional to R. ##<SP>2</SP> / 2 where ## is represented by the angular displacement of the scanning brushes 31, 32. Devices 28, 29 are similar to potentiometer 10 of Fig. 2, the scanning switches of which are driven together with 31, 32, 36, 37 by motor 51. In equation D, Un is derived at 28, 29 and applied to scanning switch 36, 37 where it is added to a signal at the linearly tapped secondary winding 35 representing the second term R. ##. To form the second term a voltage corresponding to R is generated in the winding 35 the tappings of which are scanned by 36, 37 the angular displacement of which represents ##. The third term R.##<SP>3</SP> / 6, is injected into each lead from 35 by the transformer 38. The primary of 38 is energized by a voltage of R/6 from winding 50 while the secondary winding in each lead produces a voltage corresponding to - ##<SP>3</SP>, where ## has a value corresponding to the respective stud of 36, 37. The signal U is applied to the servo motor 51 which drives the brush shafts until U is zero and the Polar angle is given by the sum of the angles of the shafts in 28, 29 and that driving 31, 32, 36, 37. In a modification of Fig. 3, not shown, the variable U is brought accurately to zero by the injection, by means of a transformer, of a further voltage between 31, 32 and winding 30. Specification 734,829 is referred to.