Patent GB-751602-A (GB)
Title: Improvements in electrical analogue-computer devices
IPC: G06G7/16
Filed: 1952-05-27
Abstract: 751,602. Electric analogue calculating systems. SOC. D'ELECTRONIQUE ET D'AUTOMATISME. May 27,1952 [May 28, 1951; Sept. 19, 1951; April 5, 1952], No. 13408/52. Class 37. Apparatus for deriving an electrical analogue voltage simulating an arbitrary function of a variable which is reducible to a combination of plural straight line elementary functions of the variable having adjustable slopes, comprises a balanced direct voltage source representing the input variable energizing a pair of positive and negative feeders, a degenerative summation amplifier delivering the analogue voltage, and a multiple array of elementary transfer networks interconnecting the feeders and the input of the amplifier; each transfer network having a linear characteristic of positive or negative slope and resistance attenuating means whereby the appropriate straight line elementary function is represented in polarity and gradient, and selective transfer networks incorporating adjustable limiter circuits to restrict their outputs to voltages equivalent to the maximum numerical values attainable by the corresponding straight line elementary functions. Fig. 1 shows the curve A of an arbitrary function y=fx which is closely approximated by curve B, composed of successive elementary straight line portions Oy 1 , y 1  y 2 , y 2  y 3 , y 3  y 4 , Y 4  Y 5  of respective slopes a 1 , a 2 , - a 3 , O, a 4  with regard to the X-axis, connecting the points of the curve corresponding to abscissµ x 1  ... x 5 . It is shown that the approximation to the functional curve may be derived from the combination of the following elementary curves having the general equation y=x tan a. I. A straight line of slope a 1  joining (o, o) to (y 1 , x 1 ) and thereafter limited to y 1 . II. A straight line of slope a 2 , joining (o, x 1 ) to (y<SP>1</SP> 2 , x 2 ) and thereafter limited to y<SP>1</SP> 2 , comprising the combination of a line II<SP>1</SP> of slope a 2  joining (o, o) to (y<SP>11</SP> 2 , x 2 ) and thereafter limited to y<SP>11</SP> 2  with a line II<SP>11</SP> of slope -a 2  joining (o, o) to (y<SP>111</SP> 2 , x 1 ) and thereafter limited to y<SP>111</SP> 2 . III. A straight line of slope - a 3  joining (o, x 2 ) to (y<SP>1</SP> 3 , x 3 ) and thereafter limited to y<SP>1</SP> 3 , comprising the combination of a line III<SP>1</SP> of slope -a 3  from (o, o) to (y<SP>11</SP> 3 , x 3 ) and thereafter limited to y<SP>11</SP> 3  with a line III<SP>11</SP> of slope a 3  from (o, o) to (y<SP>111</SP> 3 , x 2 ) and thereafter limited to y<SP>111</SP> 3.  IV. A straight line of slope a 4  joining (o, x,) to (y<SP>1</SP> 5 , x 5 ) and thereafter limited to y<SP>1</SP> 5 , comprising the combination of a line IV<SP>1</SP> of slope a 4  from (o, o) to (y<SP>11</SP> 5,  x 5 ) and thereafter limited to y<SP>11</SP> 5  with a line IV<SP>11</SP> of slope - a 4  from (o, o) to (y<SP>111</SP> 5,  x 4 ) and thereafter limited to y<SP>111</SP> 5 . Fig. 2 shows for the above synthesis a circuit comprising a plurality of transfer networks wherein oppositely poled feeders 3, 4 and 1, 2 are respectively energized by a balanced variable unidirectional abscissa voltage x and a balanced fixed unidirectional reference voltage X, and preset potentiometers 9 1  to 9 7  are connected between earth and either feeder 1, 2 through switches 11 1  to 11 7 , while preset potentiometers 10 1  to 10 7  are connected between earth and either feeder 3, 4 through switches 12 1  to 12 7 . The slider of each potentiometer 9 1  to 9 7  is connected to one cathode and plate of a corresponding pair of opposed limiting diodes or germanium rectifiers 15 1  to 15 7 ; 16 1  to 16 7 . The remaining cathode and plate of each diode pair are selectively connected through switches 20 1  to 20 7  ganged with the associated switches 11 1  to 11 7 ; 12 1  to 12 7  of the corresponding networks to the junction of resistances 17 1  to 17 7 ; 18 1  to 18 7  having equal values R, the former of which is connected to the slider of the associated potentiometer 10 1  to 10 7  of the corresponding transfer network while the latter is commoned with the corresponding resistances of the other transfer networks to the input of a linear amplifier 22 having variable degeneration over resistance 23 of value 2R. Potentiometers 9 1 -9 7  are preset to develop diode bias voltages defining the limiting values y 1 , y<SP>11</SP> 2 , y<SP>111</SP> 2 , y<SP>111</SP> 3 , y<SP>11</SP> 3 , y<SP>11</SP> 5  and y<SP>111</SP> 5 , and potentiometers 10 1 -10 7  are preset to represent the appropriate co-efficients tan a 1 , tan a 2 , tan (- a 2 ), tan a 3 , tan (- a 3 ), tan a 4 , and tan (-a 4 ), for the several component curves shown in Fig. 1, the correct polarities being obtained by appropriately setting the corresponding ganged switches 9 1  to 9 7 ; 10 1  to 10 7 ; 20 1  to 20 7 , A voltage x linearly increasing with time is derived from a Miller integrator (Fig. 4, not shown), and applied to the feeders 3, 4, so that the several initially non- conductive transfer networks are operative successively at preset inputs to develop linearly increasing output voltages which are subsequently and successively limited to predetermined steady values. The combined variable voltage at the output 24 of amplifier 22 is the analogue of the approximation B to the curve A of the required arbitrary function. The device is usuable as an electric table in which known discrete voltages are applicable to feeders 3, 4 to produce at 24 the voltage analogue of the corresponding functional value, and to combine the preset arbitrary function with another arbitrary function according to which the voltage on feeders 3, 4 varies with time. In modifications (Figs. 3, 5) the pair of diodes in each transfer network is replaceable by a single diode 25 connectible in the appropriate polarity by a ganged switch 26, 27, and the potentiometers 9, 10 of each transfer network may be replaced by potentiometers 13, 14 connected directly between the appropriate oppositely poled feeders 1, 2 and 3, 4 with the elimination of the associated polarity switch sections 11 and 12. To accommodate curves of functions whose elementary straight line portions have slopes a > 45 i.e. tan a >1, (Fig. 6, not shown), the value of the degeneration resistance and thus the gain of amplifier 22 is multiplied by the tangent of the greatest slope to be accommodated, while the values set into the potentiometers 9 1  to 9 7 , and 10 1  to 10 7  are divided by the same factor (tan a max) to effectively reduce all the slope and limiting values and impose a contraction on the resultant curve, which is expanded by multiplying the amplifier gain by the same factor (tan a max). Alternatively in those transfer networks representing components for which tan a < 1 the co-efficients and limiting voltages are set in unaltered and the resistances 17 1  to 17 7 ; 18 1  to 18 7  are increased by the factor (tan a max) together with the amplifier gains, while in networks for which tan a >1 the co-efficients and limiting voltages are reduced by the factor (tan a max) while the resistor values are left unaltered; thus achieving a similar result. The transfer networks modified as above to accommodate components for which tan a>1 and <1 may be separately grouped together (Fig. 7, not shown) or the resistances 17 1  to 17 7 ; 18 1  to 18 7  of each transfer network may be provided with multiple tappings adapted to accommodate them to a range of components for which tan a >1 (Fig. 8, not shown). If the reference voltage is replaced by a second variable voltage z it is shown that the function defined by the system is and if the voltages z and x are similarly varied the apparatus will define voltage analogues of a family of homothetic curves. If in a series of transfer networks of the kind shown in Fig. 5 above, the reference voltage X is replaced by a variable voltage z and a voltage bz derived from an additional potentiometer across variable voltage z is added into the input of the summation amplifier, the system defines a function and if the additional potentiometer is connected across variable voltage x, the function becomes (Fig. 9, not shown). In Fig. 10, feeders 3, 4 of a series of transfer networks is energized by a variable voltage x, and a voltage bz derived from potentiometer 61 across feeders 5, 6 energized by variable voltage z is combined with the outputs of the successive transfer networks at the input of the summation amplifier 22, whose output is fed back through an inverter amplifier 64 to energize feeders 1, 2 with a variable voltage output y. It is shown that the output voltage y is the solution of the equation If the potentiometer 61 is energized by variable voltage x and feeders 1, 2 by variable voltage z (Fig. 11, not shown), it is shown that the output voltage y is the solution of the equation If the transfer network characteristics are made parabolic of order n (Fig. 12, not shown), and the respective feeders are energized by variable voltages x and z, the output voltage y is given by so that if n=¢ y=xz<SP>¢</SP> and if n=z, y=x<SP>2</SP>z<SP>-1</SP> so that for x=1 y=<SP>1</SP>/ z . In Fig. 13 two function simulator units as described, respectively comprising groups of transfer networks having respective parabolic characteristics of the nth and mth orders are cascaded. The feeders 1, 2 and 3, 4 of the first unit are supplied with variable voltages z, x and the feeders 1<SP>1</SP>2<SP>1</SP> and 3<SP>1</SP>4<SP>1</SP> of the second unit are supplied with a variable voltage z 1 , and the output voltage y of the first unit, through an inverter amplifier 64 of gain - 1. Then it is shown that Similarly, if feeders 1<SP>1</SP>, 2<SP>1</SP> of the 2nd unit (Fig. 14, not shown) are energized from the output of the 1st unit and feeders 31, 41 of the 2nd unit are energized by a variable voltage x 1  so that if x, z, x 1  are successively made = 1, In a modification (