Patent GB-940677-A (GB)
Title: Electronic function generators with resistive interpolation
IPC: G06G7/28
Filed: 1960-08-09
Abstract: 940,677. Electric analogue calculating. A. NATHAN. Aug. 9, 1960 [Sept. 2, 1959], No. 27599/60. Heading G4G. An electronic generator for a function of one or more variables comprises plural input means for plural input potential signals of which one at least is a function of said variables; plural interpolating conductive means at least one of which is non- linear connected to the input means and to a common output connection at which a potential signal represents the generated function for the instantaneous values of said variables; and generating means connected to the common output connection for supplying current to at least one interpolating means at any instant; the interpolating means having resistive values such that at least two of them are simultaneously supplied with current by the generating means for suitable values of said variables; while the generating means supplies the total current from the common connection into any one interpolating means at any instant, such current depending on the relative potentials of the input means so as to cause the function generator to produce at the common connection an output signal which is a nonlinear function of the variables when two of the interpolating means; are simultaneously supplied with current by the current means. A generator for a convex function of one or more variables comprises (Fig. 5) plural inputs 1, 2, 3 receiving voltages e i1 , e i2 , e i3  which are functions of a parameter x which are connected over respective resistances r 1 , r 2 , r 3  in series with diodes D 1 , D 2 , D 3  connected to a common output 4 from which a current i 1  is withdrawn by a generator 5. When output voltage e 0  < e i1 , diode D 1  conducts and (1) e 0  = e i1  - i r1  when e 0  < e i2 , D 2  only conducts and (2) e 0  = e 12  - i r2  while in the interval, D 1  and D 2  conduct simultaneously so that and the output voltage is given by similar expressions for conductivity of D 2  and D 3  in combination and of D 3  only, so that the required function is represented by the output voltages as an approximation represented by the combination in succession of the voltages developed when D 1  only is conductive, D 1  and D 2  are both conductive, D 2  only is conductive, D 2  and D 3  are both conductive, and D 3  only is conductive;with curvilinear transitions. More than two diodes may be arranged to conduct simultaneously, and the input voltages may represent nonlinear functions of parameter x. For a concave function of x, the diode polarities are reversed (Fig. 6 not shown) and for a concaveconvex function the respective circuits may be combined. In a modification (Fig. 7) the generator 5 (Fig. 5) is replaced by a source 11 of constant negative voltage V connected to output 4 over a resistance R large by comparison with the diode series resistances r 1 , r 2  &c. such that so that when D 1  conducts when D 1  and D 2  conduct simultaneously and when D 2  conducts Fig. 8 shows the variation of the output analog voltage e 0  as a function of x linearly represented by e i1  and e i2 , wherein e 0  = (e i1  - i r1 ) while D 1  only is conducting until point A<SP>1</SP> is reached at which e 0  = e i2 . D 1  and D 2  then both conduct, the latter introducing an output voltage e 0  (e i2  - i r2 ) so that in combination the output voltages are represented by interpolated segment A<SP>1</SP> B<SP>1</SP> until D 1  ceases to conduct at point B<SP>1</SP>, at which e 0  = e i1 . Thereafter, e 0  is given by (e i2  - i r2 ). In general, for a total of n diodes and their series resistances, the output voltage contains (2n - 1) linear segments, so that by using sufficient diodes a close approximation to any desired function may be achieved. Functions of two discrete variables may be produced e.g. by applying to the inputs 1, 2 of Fig. 7 the voltages given by (8) e i1  = a 1 x + b 1 y +c 1  (9) e i2  = a 2 x + b 2 y + c 2  where a 1 , b 1 , c 1 , a 2 , b 2 , c 2  are constant coefficients and the output voltage e 0  is given by equations 5, 6, 7 above as a combination of three successive domains representing the corresponding linear functions of x and y in combination. Specification 940, 676 is referred to. The diodes may be replaced by PNP or NPN transistors; the input voltages being applied to the bases over feed resistors shunted by capacitances, the emitters being connected to the output over series resistances, and the collectors being returned to constant voltage sources (Figs. 9,10 not shown). Voltage drops across the diodes may be compensated by adding appropriate voltages to the input or to the output voltages, while errors due to drift in such voltage drops are correctible by replacing generator 5 by generator 17 withdrawing current i + i<SP>1</SP> from terminal 4, which is connected to the output 19 over diode D 9  oppositely poled to diodes D 1 , D 2  (Fig. 11). A further generator 18 feeds a current i<SP>1</SP> to terminal 19 so that diode D 9  is maintained conducting. When i<SP>1</SP> = i, drift compensation is complete when one diode D 1  or D 2  only conducts, and partial when both diodes D 1 , D 2  conduct, while the value i<SP>1</SP> = 0.75i for r 1  = r 2  gives satisfactory compensation over the range of the output function voltage. The diode series resistances may be nonlinear e.g. their values may be monotonously decreasing functions of the current i m  therein, whereby the interpolated segments of the approximation to the required function are made curvilinear (Fig. 12 not shown). In the generation of a sinusoidal function of a variable x (Fig. 13 not shown) over the range 0 to # using the device shown in Fig. 6, the diodes are silicon and the resistances r 6 , r 7 , and r 8  each comprise a linear resistance in parallel with a non- linear resistance of law E = C i <SP>#</SP> where E is the developed voltage i is the current therein C, # are constants Circuit values are given. It is stated that for limited ranges of variation a diode may be omitted when a nonlinear resistance is used in the particular circuit branch.