US2872109A - Multiplier-integrator circuit - Google Patents

Description

Feb. 3, 1959 B, D, sMl'n-l,v JR 2,872,109

MULTIPLIER-INTEGRATOR CIRCUIT Filed Oct. 29, 1955 United States Patent() 2,872,109 MULTIPLIER-INTEGRATOR CIRCUIT Blanchard D. Smith, Jr., Alexandria,

United States of America as tary of the Air Force Va., assgnor to the represented by the Secre- It is the object of this invention to provide a circuit capable of producing an output voltage that is proportional to the integral over a period of time of the product of two voltages that are functions of time.

The circuit consists essentially of a condenser and means for initially charging the condenser to a predetermined starting voltage. The condenser is arranged to discharge through a device the current iiow through which is substantially independent of condenser voltage but proportional to one of the input signals. Such a device may be a high gain amplifier tube, such as a pentode, employing current negative feedback. Conduction through the above device, however, is prevented except during periodically occurring intervals the durations of which are pro portional to the second input voltage. At the end of the period of integration the condenser potential is less than its initial value and this difference is proportional to the integral of the product of the two input signals.

A more detailed description of the invention will be given in connection with the accompanying drawings, in which Fig. l is a schematic circuit diagram of the multiplierintegrator; and

Fig. 2 illustrates the performance of the a single integration.

Referring to Fig. l, the multiplier-integrator circuit is provided with input terminals 1 and 2 to which input signals E1=f1() and E4=f2(t) are applied. The value of the integral of the product of these two functions over a period of time appears at terminals 3 and equals E2E Ep being substantially equal to Ec as will be seen later. Tube 4 is a high gain peutode having its screen grid G2 at a fixed potential E3. The anode-cathode circuit of the tube contains condenser C, which supplies the anode voltage for the tube during integration, resistor R and input signal source E1. Resistor R and source E1 are also ineluded in the grid-cathode circuit of the tube so that the common resistor provides a current negative feedback to the input circuit of the tube. A source E2 and switch S1 are provided for initially charging condenser C. Grid G3, the suppressor grid, has applied to it a series of rectangular pulses which are width modulated so that the ratio w/ T is proportional to E4 and has a maximum value not exceeding unity. This modulation is accomplished by the pulse Width modulator 5 which may be a circuit of the phantastron type, such as described on pages 195- 204, vol. 19, Radiation Laboratory Series, McGraw-Hill, or any other known circuit capable of performing the required pulse modulation. Certain of these circuits require trigger pulses which for this reason are illustrated as being applied to terminal 6. The circuit is so adjusted that conduction between anode and cathode in tube 4 can take place only during the interval w of the square wave applied to G3. In the example shown the voltage of the square wave is zero during time w and negative at all other times.

To perform an integration, condenser C is irst charged to a voltage E2 by momentarily closing S1. The concircuit during ICC- denser charges rapidly due to the low resistance of the grid-cathode space path of tube 4. The functions represented by the voltages E1 and E4 are then applied to terminals 1 and 2 for the interval of integration t. At the end of this interval the voltage Ez-Ep at terminals 3 represents the value of the integral K f ofElEzdt.

To analyze the operation of the circuit lirst consider the situation in which E4=0. For this condition w=0 and plate conduction in tube 4 can not occur at any time during the interval of integration. Therefore C can not discharge and its voltage at the end of the interval remains at the value E2. Further, the voltage of G1 is substantially zero since it cannot exceed that of the cathode because of R and grid-cathode conduction. The voltage at terminals 3, which represents the value of the integral, is therefore zero. For the condition E1=0, the discharge of C is likewise prevented and the value of the integral is zero. The reason for this is that any attempt for C t0 discharge through the anode-cathode path of tube 4 and resistor R is opposed by the resulting negative potential on G1 due to R, or, in other words, by the resulting negative feedback. If the amplication of the tube is high the impedance offered to the discharge current is high and substantially no change in condenser voltage takes place during the integration interval. The voltage of G1 remains substantially zero in this condition also since, with E1=O, there is nothing to drive it in a positive direction and the high mutual conductance of the grid prevents any appreciable movement in the negative direction due to anode current flow in R.

vThe usual condition is that in which both E, and E4 are greater than zero. In this condition also, the presence of R and the high mutual conductance of G1 prevent this grid from departing by any appreciable amount from the cathode potential, so that its potential is always substantially zero. Considering the operation during the period w, condenser C discharges through the anode-cathode path of tube 4, source E1 and resistor R. Due to the negative feedback produced by R and the high mutual conductance of G1 the discharge current through R is substantially independent of the condenser voltage Ec and is proportional to El. During the time interval w, therefore, the charge on condenser C is decreased by an amount proportional to w and the discharge current. Since w is proportional to E4 and the discharge current, as stated above, is proportional to E1, the decrement in condenser voltage Ec during each pulse on G3 is proportional to the product EIEAX. During the time when the voltage on G3 is negative and the anode current of tube 4 is cut otf, C cannot discharge and Ec remains constant. The voltage Ec therefore decreases in steps during the integration interval, each decrement being proportional to EIE., at the time, so that the total decrement at the end of the interval is proportional to the integral of BIE, over that period of time. This decrement may be measured across terminals 3 since, as has been stated, G1 remains at substantially zero or ground potential. so that EZ-EpzKfofElEldL The constant K is a function of RC and the degree of pulse width modulation caused by E4. The frequency of the pulses modulated by E4 should be high enough to accurately follow the envelope of E4.

The above process is illustrated in Fig. 2. The square wave of voltage applied to G3 is shown along the horizontal axis. As is evident, the decrement in Ec, AEC, during each interval w is proportional to the slope of the linear discharge curve and to the size of w. This decrement is therefore proportional to E1E4 since the slope is proportional to El and w is proportional to E4.

l claim:

l. A circuit for reducing the charge in a condenser by an amount proportional to the integral of the product of two varying signal voltages over a desired integration Patented Feb. 3, 1959` germes interval, said circuit comprising means operative during said interval for periodically discharging said condenser through a device the current through which is substantially independent of the condenser voltage and is proportional to one of said signal voltages, and means for controlling the durations of the periodic discharges in proportion to the other of said signal voltages.

2. A circuit for producing a voltage proportional to the integral of the product ot twotvoltages over a desired integration interval, said circuit comprising a condenser, means for initially charging said condenser to a predetermined potential, means operative during said interval for periodically discharging said condenser through a device the current through which is substantially independent of the condenser voltage and is proportional to one of said signal voltages, means for controlling the durations of the periodic discharges in proportion to the other of said signal voltages, and means for deriving the difference between said predetermined potential and the potential across said condenser at the end of said interval.

3. A circuit for reducing the charge on a condenser by an amount proportional to the integral of the product of two varying voltages over a desired integration interval, said circuit comprising a high gain amplifier tube having an anode, a cathode and a control grid; means connecting said condenser, a resistor and one of said two voltages in series between the anode and cathode of said tube; means for also connecting said resistor and said one voltage between the control grid and cathode of said tube; and means for blocking anode conduction in said tube except during periodically occurring discharge periods within said interval the lengths of which are proportional to the other of said two voltages.

4. Apparatus as claimed in claim 3 in which said last named means comprises a second grid in said tube located between the anode and said control grid, means for applying a rectangular Vvoltage wave to said second grid of such voltage relative to the cathode of said tube that anode conduction is prevented except during the positivegoing portions of said wave, and means for controlling the durations of said positive-going portions in proportion to the other of said two voltages.

5, A circuit for producing a voltage proportional to the integral of the product of two voltages over a desired integration interval, said circuit comprising a condenser; a high gain amplitier tube having an anode, a cathode and a control grid; means connecting said condenser a resistor and one of said two voltages in series between the anode and cathode of said tube; means for also connecting said resistor and said one voltage between the control grid and cathode of said tube; means for blocking anode conduction in said tube except during periodically occurring discharge periods within said interval the lengths ot which are proportional to the other of said two voltages; means for momentarily applying a direct voitage between said anode and cathode for initially charging said condenser; and means for deriving the difference between said direct voltage and the voltage of said anode at the end of said integration interval.

References Cited in the file of this patent UNlTED STATES PATENTS 2,491,779 Y Swantzel June ll, 1946 2,433,237 Rajchman Dec. 23, 1947 2,486,068 Shishini Oct. 25, 1949 2,643,819 Lee et al. June 30, i953 2,675,469 Harker Apr. 13, 1954 OTHER REFERENCES Korn and Korn Electronic Analog Computers, Mc- Graw-Hill Book Co., New York, Toronto, Canada 1952, Electronic Engineering, August 1948, pages 244-246.

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