Patent GB-800071-A (GB)
Title: Improvements relating to voltage function interpolating devices
Inventor: SPENCER ROLF EDMUND
IPC: G05B19/4105
Filed: 1954-04-28
Abstract: 800,071. Electric analogue calculating systems. ELECTRIC & MUSICAL INDUSTRIES, Ltd. April 28, 1955 [April 28, 1954], No. 12384/54. Class 37. An A.C. voltage analogue function generator providing for continuous variation of the output function voltage with input, by combination of interpolating voltages with a range of discrete function voltages corresponding to discrete input values; comprises plural conductors representing discrete values of the input variable, auto-transformer means for injecting into the conductors first voltages representing function values for corresponding discrete values of the variable, transformer means for injecting into the conductors second voltages representing numerical quantities having as factors the values of the first derivative of the function for corresponding discrete input values, further transformer means for injecting into the conductors third voltages representing numerical quantities having as factors the values of the second derivative of the function for corresponding discrete input values, and variable transformer means for regulating the second and third voltages independence on the differences between an arbitrary value of the input variable and the selected discrete value, so that the resultant voltage on the conductor corresponding to such discrete value represents the value of the function for the arbitrary value of the input variable, which is defined by a variable tapping selecting successive conductors for different discrete values and simultaneously geared to operate the variable transformer means. In Fig. 1 an autotransformer 1 energized from a reference A. C. source 2 is provided with appropriately positioned tappings connected by conductors a1, a2, a3 ... &c. to a range of contact studs b1, b2, b3 ... &c. of a switch comprising a makebefore-break slider 3 rotatably traversed in accordance with the input variable x to derive discrete voltages representing the function values corresponding to discrete values of x, such that yn =f(x n ), from the combination of the respective tap voltages with fraction correction voltages derived from an injector 4 comprising multiple secondary windings in series with the respective conductors, wound on a toroidal core having a primary winding 5 energized from a subsidiary secondary 6 of the autotransformer. Alternate conductors are connected in series with corresponding secondaries of injectors 7, 8 similar to 4, whose primary windings are respectively energized with voltages proportional to #x from 180 degrees spaced brushes 10, 14 rotatable by shaft 13 over the winding of a semi-circular autotransformer 11 energized from a further subsidiary secondary 12 of autotransformer 1, so that the voltage between either end of autotransformer 11 and its grounded midpoint = ¢ #x, where x is the voltage interval between adjacent discrete values of x. Shaft 13 is geared to the operating mechanism of slider 3 to rotate 180 degrees for each contact step of the latter, brushes 10 and 13 being respectively at the grounded midpoint of the transformer 11 when brush 3 is symmetrically aligned with one of the odd (b1, b3, &c.) or even (b2, b4, &c.) studs. Injectors 7, 8 are wound so that secondary voltages are introduced into the respective conductors proportionate to the values of the first derivative (dy/dx) of the function y for the corresponding discrete values of x. Further similar injectors 15, 16 are provided whose corresponding secondaries are connected in series with alternate conductors and whose primaries are energized respectively from sliders 17, 19 driven by shaft 13 over semi-circular variable autotransformers 18, 20 which are centre tapped to earth and energized from sliders 10, 13 of variable autotransformer 11 with voltages proportional to #x<SP>2</SP> ; the injectors being wound so that secondary voltages are introduced into the respective conductors proportionate to the second derivative (¢ d<SP>2</SP>y/dx<SP>2</SP>) of the function y for corresponding discrete values of x. It is shown that the voltage picked up by slider 3 at any instant is proportional to : where n is the value of x corresponding to the midpoint of the stud contacted by slider 3 and #x is the difference between the arbitrary input value of the variable and the discrete value x n  corresponding to the stud, the expression representing the first 3 terms of a Taylor series, so that if higher terms of the series are negligible the voltage on slider 3 represents continuously the value of the function y for any arbitrary value of the input variable x. The several injectors may each comprise multiple toroidal cores wound with single primaries and secondaries, the former being interconnected as described in Specification 734,829. The primaries of injectors 15, 16 may be energized from a single quadratically tapped autotransformer, energized from a subsidiary winding of autotransformer 1, with tappings connected to a semicircular array of studs traversed by 180 degrees spaced brushes driven by shaft 13 as before; one end of the autotransformer being earthed and connected to the centre stud of the array and subsequent tappings being connected to further studs spaced sequentially and symmetrically on each side of the central stud (Fig. 2, not shown). Fig. 3 shows apparatus operating on the principle of Fig. 1 for generating the analogue voltage of a function Z of two variables x and y which is derived from a semicircular matrix of plural rows of contact studs a11, a21 ... &c., a12, a22 ... &c., of which the " row " studs correspond to successive discrete values of x for a particular value of y and the " column " studs correspond to successive discrete values of y for a particular value of x. The rows are scanned by an array of sliders 24<SP>1</SP>, 24<SP>2</SP>, &c., rotatable by a shaft whose angular displacement represents the instantaneous value of x, while the required analogue voltage of Z is derived from a slider 25 rotatable by a shaft angularly displaceable to represent the instantaneous value of y over a range of studs d1, d2, &c., interconnected to corresponding sliders 24<SP>1</SP>, 24<SP>1</SP>, &c. A tapped autotransformer 26 energized from a reference A.C. source supplies a range of voltages to each row of studs corresponding to the discrete values of the function Z for the several discrete values of Z and the discrete value of y corresponding to the row. The conductors are connected in series with the respective secondaries of a correction injector 27 (similar to 4 in Fig. 1) energized from an auxiliary winding of transformer 26 and alternately in series with corresponding secondaries of injectors 28, 29 energized by 180 degree spaced rotary taps on a variable autotransformer 40 which is centre tapped to earth and excited from a further auxiliary winding; with corresponding secondaries of injectors 30, 31 energized by rotary taps on variable autotransformers 41, 42 which are centre tapped to earth and excited respectively from 180 degree spaced taps on autotransformer 40; with corresponding secondaries of injectors 32, 33 energized by 180 degree spaced rotary taps on a variable autotransformer 43 which is centre tapped to earth and excited from a further auxiliary winding on transformer 26; with corresponding secondaries of injectors 34, 35 energized respectively from rotary taps on variable autotransformers 44, 45 which are centre tapped to earth and excited from the 180 degree spaced taps of autotransformer 43, and with corresponding secondaries of injectors 36, 37, 38, 39 respectively energized from 180 degree spaced rotary taps on variable autotransformers 46, 47 which are centre-tapped to earth and respectively excited from the taps on autotransformer 40. The operating shafts of autotransformers 40, 41, 42 are ganged for rotation with the operating shaft of sliders 241, 24<SP>2</SP>, &c., while the operating shafts of autotransformers 43 to 47 are ganged for rotation with the operating shaft of slider 25 so that injectors 28, 29 are excited analogously to #x, injectors 30, 31 to #x<SP>2</SP>, injectors 32, 33 to #y, injectors 34, 35 to #y<SP>2</SP> and injectors 36, 37, 38, 39 are excited analogously to #x#y. The voltage arising on stud a11 represents the value of Z for (x 1  + #x), (y 1  + #y), that on stud a21 represents the value of Z for (x 2  + #x), (y 1  + 8y), that on stud a12 represents the value of Z for (x 1  + #x), (y 2  + #y), that on stud a22 represents the value of Z for (x 2  + #x), (y 2  + #y), and in general the voltage on any stud a ij  represents the value of Z for (x i  + #x), (yj + #y) ; the injectors 28, 29 introducing #Z voltages representing -, injectors 30, 31 intro- #x #<SP>2</SP>Z #Z ducing ¢-, injectors 32, 33 introducing -, in- #x2 #y #<SP>2</SP>Z jectors 34, 35 introducing ¢-, and injectors 36 #y2 #<SP>2</SP>Z to 39 introducing cross-functions - so that 8x8y the analogue voltage finally appearing at slider 25 represents any arbitrary value of f (x, y) determined by the continuous values of (x, y) set in by rotation of the shafts operating sliders 241, 24<SP>2</SP> together with autotransformers 40-42, and slider 25 together with autotransformers 43 to 47.