Patent GB-1074623-A (GB)
Title: An electrical function generator
Inventor: MILES SYDNEY FRANK
IPC: G06F1/03
Filed: 1963-02-28
Abstract: 1,074,623. Electric analogue calculating. SOLARTRON ELECTRONIC GROUP Ltd. May 21, 1964 [Feb. 28, 1963], No. 8169/63. Heading G4G A function generator comprises first apparatus responsive to a variable voltage representing an independent variable to derive two intermediate voltage functions each varying linearly from 0 to a fixed limit and back to 0 periodically with variation of the independent variable; the values of this at functional values of 0 or limit being defined as break points and the two functions being out of phase so that when one is at limit the other is at 0; a second apparatus multiplying the first intermediate function by successive coefficients corresponding to the respective odd numbered break points over successive ranges from one odd numbered break point to the next odd numbered break point, and multiplying the second intermediate function by successive coefficients corresponding to the respective even numbered break points over successive ranges from one even numbered break point to the next even numbered breakpoint; and a third apparatus summing the intermediate functions multiplied by the respective coefficients so that the generated function varies linearly from one break point to the next and has accurate values at the break points with approximate values formed by interpolation between the break points. Fig. 1 shows the progression of functions A(x), B(x) which are triangular periodic waveforms of slopes Œ 1 over a range of positive values of x = n divided into p subranges each of unit voltage, wherein x = n + k, where n is a +ve integer and 0<k<1 A(x) = k for even values of n 1-k for odd values of n B(x)=k k for odd values of n 1-k for even values of n If y n  is the value of a dependent variable y at points having x=n and is set into the function generator for each value of n, and the function A is multiplied over the range n - 1 to n + 1 for odd values of n by coefficient y n  while the function B is multiplied over the range n to n + 2 for odd values of n by coefficient y n + 1, the value of function y for any value of x is obtained by adding the coefficient multiplied functions A yn , B yn Œ 1 to give an approximate interpolated value of y between x=n - 1, n, n+ 1 &c. while for integral values of x an accurate value of y is obtained (Fig. 2). Fig. 3 shows a device for generating intermediate functions A, B wherein two high gain amplifiers 21, 22 develop output voltages Vo given by -V o /R o =V 1 /R 1  where R 0  is the feedback resistance across the amplifier and an input voltage V 1  develops input current across input resistance R 1 . A digital to analogue converter 23 connects a selected combination of a set of resistances 11, 12, 13 of values forming a geometrical progression of ratio ¢ to the input of amplifier 21 while grounding the remainder, and similarly a selected combination of a set of resistances 15, 16, 17 to the input of amplifier 22; the resistances shown as multiples of a standard value R being returned to a standard voltage V R , so that the current at the input of each amplifier is given by where each coefficient a o  to a p  has value of 0 or 1, so that the total input current is variable VR VR from 0 to - (2<SP>P</SP> + 1 - 1) in steps of -. The R R output of each amplifier feeds a limit detector 25, 26 comprising, e.g. a Schmitt trigger, so that when either output voltage representing A or B reaches a unity limit value, the detector pulses to change the state of a bi-stable circuit 18. A first stable state exists during the intervals x=o to x=1; x=2 to x=3; x= 4 to R x = 5; &c. during which relay - is inoperative, 3 as shown, while a second stable state exists during intervening intervals x = 1 to x =2; R x=3 to x=4 &c. during which relayis 3 operated. Contacts R 1  alternatively connect either the output of amplifier 21 or a reference voltage + 1 to the input of amplifier 22 over R resistance 32 of valve -; contacts R 2  alterna- 2 tively connect the output of B limit detector 26 to the reverse or forward input of reversible counter 24, and contacts R 3  disconnect or connect the output of amplifier 22 from or to the input of amplifier 21 over resistor 29 of value R -. Whenever the B voltage function attains 2 the limit value + 1, unity is added to the count when the limit value is approached from below with x increasing, since the relay is then operated as x lies between an odd integral value n and an even value n + 1, and conversely whenever the limit value is approached from above with x decreasing, unity is subtracted from the count ; the state of the counter being shown as in Fig. 1 and being applied to control a digital analogue converter 23 switching resistances 11, 12, 13, 15, 16, 17 to earth for count 0; resis- R tances 13, 17 of valueto reference voltage 2 +1 for count 1; resistances 12, 16 of value R - to + 1 reference voltage for count 2; resis- 4 tances 13, 12, 17, 16 to reference voltage +1 for count 3 and so on in a binary scale; further resistances being usable as necessary. A permanent reference voltage of -1 is applied over resistance 33 to the input of amplifier 22, and a voltage - x is applied over resistances 27, 30 of value R to the inputs of amplifiers 21, 22. In operation, as - x decreases from 0, converter 23 is inoperative so that amplifier 21 at A receives input current - x to produce output voltage x, and amplifier 22 receives input currents of - x, + 2x from the output of 21 over contact R 1  and resistance 32, and -1 from the reference source, to produce an output voltage (1 - x) at B. When the output at A reaches + 1, R limit detector 25 operates relay -, so that 3 contacts R 1 , R 2 , R 3  change over, and the inputs toamplifier22arex, +2 over R 1  and resistance 32 of value R/2, and -1 over resistance 33. The input current to 22 is thus 1 - x and the output voltage is x - 1 varying form 0 to 1 over range x=1 to x=2. The input currents to 21 are now - x and + 2(x - 1) from output of 22 R over R 3  and resistance 29 of value -, so that 2 the output voltage is 2 - x falling from 1 to 0. As the output of amplifier 22 rises to +1,   limit detector 26 operates to restore relay R/3 and contacts R 1 , R 2 , R 3  to their initial condition, so that the outputs of both amplifiers are at their initial values for input x = 2 and the counter is pulsed from the limit detector to register state 1, and to operate converter 23 to apply an input of +2 to both amplifiers over R resistances 13, 17 of value -, so that the 2 current inputs are restored to those at x = 0. The sequence continues indefinitely while there are digits in the counter, generating the intermediate functions A, B (Fig. 1). Such functions A, B are multiplied by the appropriate coefficients (Fig. 4) by applying their analogue voltages to lines 41, 42 respectively which energize potentiometer groups 51, 53, 55 and 52, 54, 56 returned to earth. The sliders are connected over respective switches 61, 63, 65; 62, 64, 66 to a summation amplifier 43 and the sliders of 51, 53, 55 are set to represent appropriate multiplying coefficient values y n  for odd n values; the sliders of 52, 54, 56 are set to represent appropriate multiplying coefficient values y n  for even n values; and a required potentiometer is selected by closure of the appropriate switch. The switches are operated under control of counter 24 and bi-stable circuit 18, so that with counter in state 1 switch 62 is closed and switches 61, 63 are prepared for closure; with counter in state 2 switch 64 is closed and switches 63, 65 are prepared for closure; and so on; the state of the bi-stable circuit 18 determining which of switches 61, 63; 63; 65; and so on is closed. Then for function A the switches 61, 63, 65 &c. are closed in sequence, one for each interval between successive even values of x; the sequence being from lower to higher switch numbers when x is increasing or vice versa. Similarly, for function B, switches 62, 64, 66 &c. are closed in sequence one for each interval between successive odd values of x; the sequence being as before from lower to higher switch numbers when x is increasing, or vice versa. Fig. 1 shows the required switch closure intervals. Fig. 5 shows alternative apparatus for multiplying the intermediate function A and B by the necessary coefficients; the analogue voltages of functions A and B being carried by lines 79, 80 energizing digital to analogue converters 77, 78 comprising a series of resistances 91 to 96 whose values form a geometric series of ratio ¢ selectible by switches 100 to 105 responsive to punched card information of the required coefficients yn. The value of the latter for any value of n is punched on card 75, an individual card corresponding to a particular function, and a column of holes 85 corresponds to values of n while the holes 851, 85<SP>2</SP> &c. determine the values of yn. On energization of any sensing contact 71 to 74 the corresponding contact 87 is energized through a hole. 85 of the card and energizes all the contacts 88 connected in row to it, which contacts register with further holes of a series representing value of y n  for the particular value of n corresponding to the position of the energized contact 87. Circuits are completed through such holes to contacts 86 or 81 to energize selected transistors of switching circuits 82, 83 causing the converters 77, 78 to select the appropriate resistances from series 91 to 96. Contacts 86 control the function B converter and contacts 81 the function A converter, and in general even numbered rows of contacts control the function A converter and odd numbered rows the function B converter. The appropriate two contacts of 71 to 74 are selectively energized by switches 111 to 114 operated as in Fig. 4.