Patent GB-855303-A (GB)
Title: Improvements in or relating to electric circuits for generating an output voltage which is approximately proportional to a function of an input voltage where the function is proportional or analogous to the sum of a convergent power series
IPC: G06G7/22
Filed: 1957-07-17
Abstract: 855,303. Valve non-linear circuits. GENERAL ELECTRIC CO. Ltd., and BROWN, E. July 15, 1958 [July 17, 1957], No. 22603/57. Class 40(6). [Also in Group XXXVI] A convergent power series function generator comprising an adding circuit including a feedback amplifier, first means arranged to supply to said adding circuit a current which is proportional to the first term or to the sum of the first and second terms of the series and second means, including at least one non-linear resistor arranged to supply to said adding circuit a second current proportional to the sum of the second or third successive terms of the power series. A circuit (Fig. 1) the output voltage of which (at 7) represents the sine of an input voltage # uses the series for sine # i.e. sine # = # - #3/3<SP>1</SP> + #5/5<SP>1</SP>   and comprises a feedback adding amplifier 5 having two input paths, the first comprising a linear resistance 16 providing a current component proportional to # while the second path 2 comprises two non-linear silicon carbide resistors 9, 11 of the type obeying the law I = Kv<SP>α</SP>, the current at 4 from this path being proportional to the sum of the other terms of the series. Path 2 also comprises a sign changer 13 and series and parallel resistors 10, 12 for the non-linear resistors 9, 11 to vary their power law as desired since with a series resistor for the combination varies as the input voltage increases to unity while the reverse is the case for parallel resistor, choice of the non-linear resistors being dependent principally upon the power of the second term of the series as is the current appearing at 4 due to path 2. A circuit for cos (1 - #2/2<SP>1</SP> + #4/4<SP>1</SP> ..) is shown in Fig. 3 in which an input terminal 18 is maintained at a constant potential and connected to the amplifier input through a resistance 38 (the linear path 17) to provide the first term of the series, the non-linear path 20 providing the second current component proportional to the sum of the other terms comprising two non-linear resistances 34, 36 as before and two parallel branches containing a sign-changer 26, a diode 30 and a diode 32 respectively to ensure that the voltage at 25 will be positive whatever the sign of the input voltage. Other trigonometrical function generators may be similarly constructed. A tangent function generator is shown in Fig. 4 (tan # = # + #3/3<SP>1</SP> + #/5<SP>1</SP> ..) and comprises a (tan 0 = # + #3/3<SP>1</SP> + #5/5<SP>1</SP> ..) and comprises a linear path 39 and a non linear path 40, consisting of a potential divider 48 and a non-linear resistor 4, in parallel. An inverse sine function generator may be formed by including circuit 51 (Fig. 1) in the feedback path of amplifier 5, dispensing with the amplifier feedback resistor and providing an input path through a resistor directly to the amplifier, (Fig. 5, not shown) a similar construction from an inverse tangent function generator being also described (Fig. 7, not shown). An inverse cosine function generator to operate in one quadrant only is also described, the sign changer and diodes being omitted from the circuit shown in Fig. 3 and now included in the amplifier feedback path (Fig. 6, not shown). An exponential series function generator (e<SP>x</SP> = 1 + x/1 + x<SP>2</SP>/2<SP>1</SP> + x<SP>3</SP>/3<SP>1</SP> + ..) is shown in Fig. 8   and comprises a linear path 62 and a non-linear path 63 connected in parallel between input terminal 64 and a point 65; a second input 69 kept at a constant positive potential being provided through a resistor 70 to provide the constant term of the series, the second term and third and subsequent terms being again provided by the linear and non-linear path respectively.