Patent GB-953174-A (GB)
Title: General purpose transistorised function generator
IPC: G06G7/28
Filed: 1960-08-09
Abstract: 953,174. Electric analogue calculating. TECHNION RESEARCH & DEVELOPMENT FOUNDATION Ltd. Aug. 9,1960 [Sept. 2, 1959], No. 27597/60. Heading G4G. A function f(x) is approximated by a further function F(x) given by where and x is an independent variable Ax is a constant spacing of i sampling points x i  is a value of x at an i-th discrete sampling point Max, Min are operators selecting the respectively smallest and largest of the quantities upon which they operate. and the values of f i  chosen so that The function #<SP>1</SP> [x - x i ] (Fig. 1) is triangular in form with the height representing #x and the absassal displacement between the apex and the ends of the base given by 2#x, while the function F(x) is represented by the additive combination of the products of constants and a plurality of triangular functions whose bases extend along the abassan from 0 to 2#x, #x to 3#xx, 2#x to 4#x, &c. and whose altitudes are determined by constants A of suitable values (Fig. 2). Fig. 5 shows a function generator wherein an input voltage representing x is applied over terminal Tin<SP>+</SP> to input unit A<SP>+</SP> and over a unity gain phase changing amplifier to terminal Tin of input unit A<SP>-</SP> 1  yielding voltages representing (x-x i )+ #x at output terminals T 1 <SP>+</SP>, T 2 <SP>+</SP> .... T i <SP>+</SP>... T n <SP>+</SP> and voltages representing -(x - x i ) + #x at output terminals T 1 <SP>-</SP>, T 2 <SP>-</SP>, ... T i <SP>-</SP>... T n <SP>-</SP> where x i  = x o  +  i #x  and i is an integer. Voltages T i <SP>+</SP>, T i <SP>-</SP> are applied to respective triangular function generators B i  to produce output voltages given by eo = k i  #<SP>1</SP>[x - x i ] at terminal t i  which are connectible over a range of switches s, either to the input t i <SP>+</SP> or t i <SP>-</SP> of synchanging addition circuits 46,47 respectively. The outputs of 46 and a constant voltage over terminal 48 are applied to the input of 47 which develops at its output T a signal representing F(x) in equation (1). Switches S i  permit selection of positive and negative values of f i . Unit A<SP>+</SP> comprises (Fig. 12) a train of series potentiometers Rs<SP>+</SP> i ...Rs<SP>+</SP> n  connected between positive and negative constant voltages at 53 and 54, with their respective sliders connected over resistors R p1 <SP>+</SP> ... R pi <SP>+</SP> ... R p <SP>+</SP> n  to the appropriate output terminals T 1 <SP>+</SP> ... T n <SP>+</SP> which are also returned through parallel RC networks R bi <SP>+</SP>, C i <SP>+</SP>; R bn <SP>+</SP>, C n <SP>+</SP> to the output of an impedance converting amplifier 51 also fed with the input x voltage over terminal 50; the potentiometers R<SP>+</SP> si  and resistances R<SP>+</SP> pi  being scaled so that the outputs represent (x - x i ) + #x as required for a succession of sampling points. Unit A- operates similarly in response to input voltage T in <SP>-</SP> to produce successive outputs t i  representing -(x - x,)+ #x. Triangle function generators B i  are identical (Fig. 6), and each comprise terminals 21,22 accepting signals representing (x - x,)+ #x and -(x - x i )+ #x from corresponding outputs of units A<SP>+</SP> and A- through parallel RC networks 23,24 and 25,26 (which may be eliminated when the supply is taken from the circuit of Fig. 12) to the bases B of PNP transistors 27, 28 which are also connected to a D. C. bias source 33 over limiting diodes 34, 35. The collectors care grounded and the emitters E are connected in common over resistance 29 of valve R to a positive D. C. source 28 and also to a potentiometer 30 returned at 32 to ground or a constant compensating voltage. Slider 31 derives an output representing f i  F, #<SP>1</SP> (x-x i ) where f i  is a constant dependent on the slider setting. For production of the negative triangle function (Fig. 7 not shown) NPN transistors are used with reversal of the limiting diodes and the voltages at 28,32,33. The transistors of Fig. 6 may be reduced to combinations of diodes, current sources and resistors (Fig. 8) where a is the transistor current amplification factor, Ie the emitter current, and r b , r e  and r c  the internal base, emitter, and collector resistances, and for an ideal transistor a = 1, r e  = 0 and r c  is large so that for positive inputs 1i 1 , 1i 2 , the potentials at F 1 , F 2  are equal to 1i 1  1i 2  respectively. The emitter diode of the channel with the lower input voltage conducts while that of the other channel is cut off, so that the output voltage 1 0  equals the smaller of 1i 1  and 1i 2 . Positive values of 1i 1  and 1i 2  thus defined the region QQ<SP>1</SP> of the triangle function (Fig. 1) while negative values shunt F 1  to ground to define the regions P<SP>1</SP> Q<SP>1</SP> and Q P... Given that the resistance R 1 , R 2  of 24,26 are equal and R  1 (3) while r c  is large compared with all their circuit resistances, where m = 1 or 2 for 1i 1  < 1i 2  or 1i 2  < 1i 1  and V is the voltage at 29, so that the output is always equal to one of the input signals over region QQ<SP>1</SP>. Fig. 9 shows an approximation to the required triangle function in which the apex and shoulders K 1 Q 1  Q' are rounded and the regions PQ, P<SP>1</SP>Q are not horizontal and zero due to the curved emitter current/ input voltage characteriztics of the transistors (Fig. 11 not shown) from which errors in the form of peaks in the transfer characteristic of the function generator arise (Fig. 10 not shown). It is shown that these errors are removed by increasing the rounding of the apex of the triangle function, which compensates for the rounding of the shoulders, by means of the limiting diodes 34,35 (Figs. 6, 8) which also operate to limit the base voltage of each transistor so as to increase the permissible range of input voltage. A single limiting diode connected to the common emitter E may replace the diodes 34, 35. The regions PQ and P<SP>1</SP>Q<SP>1</SP> may be restored to zero by applying a positive bias to the potentiometer return 32 (Fig. 6) or a negative bias to the common collector return. Representative component values are quoted.