Patent GB-1273526-A (GB)
Title: Improvements relating to function generators
Inventor: FRANKLIN DONALD PETER
IPC: G06G7/28
Filed: 1968-05-03
Abstract: 1,273,526. Function generators. E.M.I. Ltd. 2 July, 1969 [3 May, 1968], No. 20997/68. Heading G4G. In a function generator of the type in which, for different values of the input, different resistance networks are connected by diodes to an inverting amplifier, the error arising from voltage drop across the operative (conducting) diode or diodes is compensated by a non-linear device (e.g. a diode) in the feedback path of the amplifier. In the single example described, the function generated is (x<SP>2</SP>+y<SP>2</SP>)¢, where, if x=r cos # and y = r sin #, r = (x<SP>2</SP>+y<SP>2</SP>)¢ and # = arc tan y/x. The value of a linear function ax + by can be expressed as Kr cos #.cos α + Kr sin #.sin α = Kr cos (#-α), by putting a = K cos α, b = K sin α, α being constant. If α approximates to #, (ar+by) # Kr, and Fig. 1 shows, for values of # in the range 0 to 90 degrees, curves A, B, C, D, E of r cos (#-α) where α is respectively 9, 45, 81, 27, 36 degrees. The horizontal chain line represents r and the curves approximate to r with less than 1À5% error. Fig. 2 shows an elementary network comprising resistors 3, 4, 6 having respectively conductance values g x , g y , g e . If voltages x, y are applied respectively between terminals 1, 2 and earth, the output at terminal 7 is xg x /g + yg y /g where g = g x  + g y  + g e . This expression can be made equivalent to the expression for (ax+by) above by putting g x = Kg cos α and g y  = Kg sin α, from which g e  = g[1-K(cos α + sin α)]. If g e  is not to be negative K must be less than 0À707. It can be shown that the network of Fig. 2 is equivalent to a voltage of value Kr cos (#-α) associated with a series conductance g and in Figs. 3, 4 (Fig. 3, not shown), the elementary networks corresponding to Fig. 2 are shown as equivalent conductances g across which the equivalent voltages are applied. The conductances are connected by diodes 16, 17, 18 to a series conductance 19 (a shunt conductance is shown in Fig. 3) having a value ng. It is shown in the Specification that n may be chosen so that when one diode is conducting the voltage follows one of the curves A, B, C (for which α = 9, 45, 81 degrees respectively) and when two diodes are conducting the voltage follows one of the curves D and E. The small forward resistance of the diodes causes an error voltage to appear and, according to the invention, this is compensated by the feedback circuit of inverter amplifier 23 consisting of conductances g, ng and a diode 26 of the same type as diodes 16, 17, 18. A further diode 27 is provided to prevent the output of the amplifier from becoming accidentally positive. Figs. 7 and 8 (Fig. 7, not shown) are circuits for accepting + ve and -ve values of an input x or y and producing | x | or | y | as inputs for the function generator. They comprise a differential amplifier 39 with inverting input 45. For - ve signals, diode 36 conducts and holds input terminal 44 to zero whereby + ve signals appear at output 41. For +ve signals, diode 35 conducts and the signal is applied to input 44 so that a + ve signal again appears at terminal 41. A current i is supplied to a further diode 42 and diodes 35, 36 when conducting, also take a current i, the voltage across diodes 35, 36 being compensated by that appearing across diode 42. The Specification describes (Figs. 5 and 6, not shown) two practical examples of a generator giving values for networks of the kind shown in Fig. 2. An impedance-matching resistance is connected from the cathode of diode 26 to earth.