Patent GB-1147806-A (GB)
Title: Apparatus and method for producing an electrical signal having a square-law relationship with an input electrical signal
IPC: G06G7/164
Filed: 1966-08-23
Abstract: 1,147,806. Squaring circuits. ZELTEX Inc. 23 Aug., 1966 [27 Aug., 1965], No. 37649/66. Heading G4G. A quarter squares electric analog multiplier (Fig. 1, not shown) comprises summation circuits receiving pairs of signals representing x, y; -x, -y; x, -y; -x, y to produce signals representing +(x + y), - (x + y), + (x-y), - (x-y) the first pair of which are fed to a positive absolute value network and the second pair to a negative absolute value network whose outputs representing a (x + y) and - a (x - y) respectively are applied to positive and negative squaring circuits whose outputs b (x + y)<SP>2</SP> and -b (x-y)<SP>2</SP> are added to produce a signal representing c. x y. In the squaring circuits + B and - B (Fig. 5), it is shown that an approximate segmental parabolic output characteristic is generated according to S = ¢(n<SP>2</SP>-n) where S denotes ordinate and n denotes abscissa over a range of, e.g. 16 units by summation of plural P symmetrical triangular halfwave functions S 1 , S 2 , S 3 , S 4  (Fig. 2, not shown) in serial relationship with a frequency progression of 2<SP>P</SP>; the base break point of each being coincident with the peak of the next higher order function, and the successive peak amplitudes related so as to produce a constant change in slope between successive segments of the parabola. Thus function S 4  extends (Fig. 2, not shown) from abscissal units 1 to 3, 5 to 7, 9 to 11, 13 to 15; function S 3  extends from abscissal units 2 to 6; 10 to 14; function S 2  extends from abscissal units 4 to 12; function S 1  extends from abscissal units 8 to a maximum at abscissal unit 16, with zero signal values at other abscissal values; and the slopes of S 1 , S 2 , S 3 , S 4  are related as 1: 3: 7: 15 i.e. their differences increase by successive powers of 2 and if the base break points of the triangun lar functions are traversed - towards the origin, 2 the parabola becomes S = ¢ (n<SP>2</SP>-“) while accuracy is increased by generating function S 4  as a fullwave and feeding it through a passive squaring diode network to obtain a parabolic error curve added to S 1 , S 2  and S 3  (Fig. 3, not shown). Squaring networks ŒB (Fig. 5) are supplied with input signals ŒX, ŒY over positive and negative input summing and absolute value networks to supply inputs - (X+Y), (X-Y) respectively to the active squaring networks. In network +B to which -B is similar but for polarity, an input signal S in  is applied over resistor R 1  to a first operational amplifier with feedback over diode CR 1  and resistor R 25  on positive output and over diode CR 2  on negative output; appropriate graded bias SB 1  being applied from potentiometer R 19  to 224 over resistor R 2 , together with a compensating signal over resistor R 3  for the voltage drops across the diodes of the input network (-A) derived from signals ŒX, Y applied to compensating diode network (+C). It is shown that when and in combination with the bias SB 1  a ramp signal SO 1  representing function S 1  (Fig. 2d, not shown) extending from a predetermined break point is established at the output for negative going input signals; its slope being determined by resistors R 1 , R 25 . A second operational amplifier receives its input sin over resistor R 4 , the output SO 1  over resistor R 5 , a graded bias voltage SB 2  over resistor R 6 , and a compensating voltage over resistor R 8 , output SO 1  over resistor R 9 , output SO 2  over resistor R 10 , graded bias SB 3  over resistor R 11  and a compensating voltage over resistor R 12 ; the combined outputs SO 2 , SO 3  representing the triangular waveforms S 2 , S 3  (Figs. 2b, 2c, not shown). A fourth operational amplifier having resistive feedback over R 28  receives input sin over resistor R 13 , output SO 1  over resistor R 14 , output SO 2  over resistor R 15 , output SO 3  over resistor R 16 , graded bias over resistor R 17  and compensating voltage over resistor R 18  produces a fullwave triangular waveform (Fig. 3, not shown) which is applied to a passive diode squaring network comprising parallel branches 77 to 83 each having a diode in series with a resistance, sequentially biased from potential divider 84 to provide an output voltage representing a sequential parabolic correction waveform. The additively combined outputs are amplified at 9 in combination with the additively combined outputs of the corresponding squaring network -B responsive to X, Y variables of opposite sign, to produce an output signal representing the product X Y. A theoretical analysis is given.