US3084862A - Input converter and sign discriminator for multipliers - Google Patents

Input converter and sign discriminator for multipliers Download PDF

Info

Publication number
US3084862A
US3084862A US782497A US78249758A US3084862A US 3084862 A US3084862 A US 3084862A US 782497 A US782497 A US 782497A US 78249758 A US78249758 A US 78249758A US 3084862 A US3084862 A US 3084862A
Authority
US
United States
Prior art keywords
input signals
input
sign
quadrant
multiplier
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Lifetime
Application number
US782497A
Inventor
Nathan Amos
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Individual
Original Assignee
Individual
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Individual filed Critical Individual
Priority to US782497A priority Critical patent/US3084862A/en
Application granted granted Critical
Publication of US3084862A publication Critical patent/US3084862A/en
Anticipated expiration legal-status Critical
Expired - Lifetime legal-status Critical Current

Links

Images

Classifications

    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06GANALOGUE COMPUTERS
    • G06G7/00Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/12Arrangements for performing computing operations, e.g. operational amplifiers
    • G06G7/16Arrangements for performing computing operations, e.g. operational amplifiers for multiplication or division

Definitions

  • This invention relates to an input converter and sign discriminator for electronic multipliers. More specifically, this invention relates to a device which, when connected to the input of any two-quadrant electronic multiplier, or to the input of some one-quadrant multipliers, permits four-quadrant operation. This invention also provides a unit which, when fed 'by two voltages, generates an output voltage whose sign is equal to the sign of the product of the two input voltages.
  • an electronic multiplier is a device, which when fed with input voltages x and y, generates an output voltage which is proportional to xy.
  • a multiplier is said to operate in the first quadrant, if x20, ygtl; in the second quadrant, if xO, 3'50; in the third quadrant, if x50, ytl; and in the fourth quadrant if x20, ygO.
  • -A multiplier is said to have one quadrant or two quadrant operation if the permissible input range is restricted to one quadrant or to two adjacent quadrants, respectively.
  • the prior art provides input converters for oneor twoquadrant multiplication whose operation is such, that the correct sign of the output of the multiplier is not always preserved. For example, in a converter for a one quadrant multiplier operative in the first quadrant, x is converted into the modulus of x, ]x[, and y is converted into [y]. In this case the sign of multiplier output is always non-negative.
  • FIGURE 1A is a three dimensional plot of converter output 1 as a function of its inputs x and y;
  • FIGURE 1B is a three dimensional plot of converter output .5 as a function of its inputs x andy;
  • FIGURE 2 is a circuit diagram of one embodiment of the converter and sign discriminator of this invention
  • Any pair of non-zero values of x and y having differing moduli must of necessity satisfy one, and only one, of the following four conditions:
  • the multiplier need only be of the two quadrant type, whereas the converter accepts inputs in four quadrants.
  • the part of the converter generating the .5 signal is a sign discriminator for the sign of xy, as tollows from (iv), above.
  • FIGURE 2 is a schematic diagram of one embodiment of the device for the generation of 5 and 7;.
  • T and T are the input terminals for input signals x and y, respectively.
  • Input signal x is fed to sign changer A whose output signal x appears at output terminal T
  • Input signal y is fed to sign changer A whose output signal -y appears at output terminal T
  • the anodes of diodes D D D D are connected to terminals T T T T respectively. Their cathodes are joined at terminal T which is also connected to a negative D.C.
  • diodes D D D D conducts at a time; there thus appears at terminal T a signal approximately equal to 1 If the diodes have a voltage drop equal to s when conducting, the voltage at T will be equal to +6.
  • e is of the order of 0 .1 to 1.0 volt.
  • diode D of the same type as diodes D to D is connected with its cathode to T The anode of D is connected to output terminal T and to a positive D.C.
  • Some types of diodes have considerable spread of voltage drops from diode to diode, when conducting.
  • the errors thus introduced into the converter can be eliminated by first determining the voltage drop of that diode which has the largest drop, 6, when conducting, and then adding resistors of suitable values in series with each of the other diodes so that the drop across each series combination of said resistors and diodes is made equal to e when the diodes are conducting. This compensation should be carried out for all diodes of the converter.
  • the cathodes of diodes D D D D are connected to terminals T T T T respectively.
  • the anodes of D and D are joined to T which is also connected to a positive D.C. voltage, through a resistor R At T thus appears a signal equal to min.(x, y)+e.
  • the anodes of diodes D and D are joined at T, which is also connected to a. positive D.C. voltage, through resistor R At T; thus appears a signal equal to
  • the anodes of diodes D D are connected to T T respectively.
  • Their cathodes are joined at terminal T which is also connected to a negative voltage, shown at through resistor R At '1; thus appears a signal equal to g.
  • a two quadrant multiplier, or a single quadrant multiplier whose inputs lie within-the quadrant yglxl, can therefore be connected to terminals T and T,
  • No compensating diodes are required for the offset voltages of the diodes associated with the circuit for generating :3, because, by virtue of the configuration, the offset voltages cancel.
  • the device generating 5 heretofore described is based on the expression Analogously, a device with identical functions can be constructed, based on the given equivalent form for .5
  • FIGURE 3 shows one embodiment of the use of the sign discriminator of this invention to convert a one quadrant multiplier to four quadrant operation.
  • T T T T are the terminals which are at voltages x, x, y, y, respectively, as in the device described in connection with FIGURE 2.
  • Terminal T is at voltage 5.
  • This voltage is generated by use of the part of the converter generating 5, as heretofore described, i.e. by use of the device shown in FIGURE 2 less that part of it consisting of D D D D R and T1,, and their interconnections.
  • M is a one quadrant multiplier whose input terminals are T and T T T T are fed with volta es ]x[, ]y[, respec tively.
  • the anodes of diodes D D are connected to T T respectively; their cathodes are connected to T T is also connected to a negative D.C. voltage, through resistor R the voltage of T is approximately equal to Diode D is provided in order to compensate for the voltage drop in D and D and to compensate for diode drift.
  • the cathode of D is connected to T and its anode is connected to T which is also connected to a positive DC. voltage, through resistor R T is thus at a voltage equal to
  • the anodes of diodes D D are connected to T T respectively; their cathodes are connected to T which is also connected to a negative D.C.
  • Voltage 5 is fed from terminal T to a polarized relay whose actuating mechanism R connects terminal T of its change-over switch S to T or T for positive or negative values of 5, respectively.
  • R actuating mechanism
  • C is a capacitor, connected between T and ground; C is required in some applications, depending upon the circuit fed from T in order effectively to ground T during the switching over of S.
  • the relay consisting of R and S and their associated circuits is by way of illustration only; it can be replaced, in particular, by an electronic switching device.
  • a half quadrant multiplier can be converted into a four quadrant multiplier.
  • a multiplier operative in the half quadrant 3 2x20 said multiplier can be fed with signals I5] and 1;.
  • this can be done by omitting D D D R and R and their interconnections, and feeding T T T with E, 5, and 1 respectively, Where 5 and 1 are generated as described above, whereas 5 can be obtained from 5 by sign changing means, or directly from x, x, y, -y from the expression
  • the circuit for the generation of 5 according to this later expression is therefore identical with the circuit of FIGURE 2 for the generation of 5, except that anode and cathode connections of each of diodes D to D and the positive and negative voltages at and respectively, must be interchanged, and, because of the loading of the circuits generating a and 5, in the circuit generating 5 resistor R and the negative voltage to which it connects must be omitted, and in the circuit generating 5
  • All diodes are silicon junction diodes
  • inputs x and/or 2 are restricted, or the multiplier has special input characteristics. It is then not always required to realize the complete surfaces of FIGURES 1A and 1B.
  • multiplier is such that it can accept only inputs x and y for which ygx, the later restriction defining a particular two quadrant multiplier, said two quadrants covering half of the first, the whole second, and half of the third quadrants.
  • One embodiment of the modification sufficient in the latter case consists of the unit of FIGURE 2 with the omission of the following components: A A D D D D D and R and their interconnections.
  • the converter is described above as an input unit to a multiplier, it can also be used as an input unit to a two dimensional function generator, or to any two inputs of a multidimensional function'generator; in the latter case several converters can be used as input units, each converter serving as input unit to one pair of input terminals of the function generator or its other input con-' verters, or to a pair of terminals one of which is an input terminal of the function generator and the other one is an input terminal of an input converter, all this, provided the function generated has the same symmetry properties and/ or the same input restrictions as a multiplier.
  • f(x, y) is the function generated by the function generator when it is fedwith voltages at and y, at its two input terminals
  • [-5 I and a can be used as input signals and output switching must be provided, as described above in connection with the conversion of a half quadrant multiplier to four quadrant operation.
  • FIGURE 2 uses diodes as non-linear elements. It is to be understood that the use of diodes is by way of example only; in particular, the diodes can be replaced by transistors connected in a so-called diode logic connection. The manner of said replacement will be described in connection with FIGURES 4A to 4D, in which FIGURE 4A represents the diagram of a typical diode, such as D D D D D or D of FIGURE 2, together with resistor R connected to its cathode, which corresponds to R or R in the case of D D D D or D D respectively.
  • FIGURE 4A represents the diagram of a typical diode, such as D D D D D or D of FIGURE 2
  • resistor R connected to its cathode, which corresponds to R or R in the case of D D D D or D D respectively.
  • FIGURE 4B shows the corresponding transistor connection, in which terminals 1, 2, 3 are identical with terminals 1, 2, 3, of FIGURE 4A.
  • TR is an NPN transistor.
  • the parallel connection of resistor R and capacitor 6 serves as input network to the base of the transistor.
  • the base is also connected to bias voltage V at terminal 4 through resistor R
  • the emitter is connected to terminal 2 which is also connected to a negative D.C.
  • FIGURE 40 corresponds to one of the diodes such as D D D D D in the embodiment of FIGURE 2, and consists of FIGURE 4A with diode 5, replaced by diode 1 5 where D is D with interchanged terminals, and with voltage V of reversed sign.
  • FIGURE 4D shows the transistor equivalent to FIGURE 4C and is identical to FIGURE 4B except for the substitution of PNP transistor TR for TR and the reversal of sign of voltages V V and V Combinations of transistors and diode elements can be used.
  • D 10, D may be diodes, all othernon-linear elements being transistors.
  • the use of transistors has the main advantages of providing impedance conversion, from a higher input to a lower output value, and of improving the frequency response; its main disadvantage is the restriction of, the useful voltage range of input voltages at and y.
  • An input converter for a one or two quadrant multiplier or like function generator comprising means for accepting first and second input signals, first means connected to said accepting means for producing from said input signals a first output signal corresponding with the maximum of the moduli of said input signals, and second means connected to said accepting means for producing a second output signal having a modulus equal to the minimum of the moduli of the input signals, said second means including means for generating a sign for said second output signal wherein said sign is equal to the sign of the product of the input signals; said accepting means including means for generating a plurality of secondary output signals greater in number than said input signals; at least one of said secondary output signals being equal in mag nitude and opposite in sign to one of said input signals; said first and second means being adapted to employ said secondary output signals to generate appropriate moduli signals.
  • the input converter of claim 1 wherein the means for producing the first output signal comprises first and second sign changer means for producing first and second secondary input signals equal to the inverses of the first and second input signals, and third means for selecting the maximum of said first and second input signals and said first and second secondary input signals.
  • An input converter for a one or two quadrant multiplier or like function generator comprising means for accepting first and second input signals, first and second sign changer means for producing first and second secondary input signals equal to the inverse of the respective input signals, means for selecting the maximum of said first and second input signals and said first and second secondary input signals, means for selecting the minimum of said first and second input signals, means for selecting the minimum of said first and second secondary input signals, and means for selecting the maximum of the two minima so selected.
  • a four quadrant multiplier comprising means for accepting first and second input signals, means for deriving the moduli of said input signals, a single quadrant multiplier for multiplying said moduli to produce a first output signal, sign changer means to produce a second output signal equal to the inverse of said first output signal, and changeover means for selecting one of said first and second output signals as final output signal, said changeover means being responsive to the sign of a control signal derived from said input signals so that the output signal selected has the sign as well as the modulus of the product of the input signals.
  • a four quadrant multiplier comprising means for accepting first and second input signals, means for deriving the moduli of said input signals, means for multiplying said moduli to produce a first output signal, means for changing the sign of said first output to produce a second output signal, means for deriving a control signal having the sign of the product of the input signals, and changeover means, responsive to said control signal, for selecting that one of said first and second output signals having the sign of said control signal.
  • a four quadrant multiplier or like function generator comprising means for accepting first and second input signals, means for deriving a first secondary signal equal to the maximum of the moduliof the input signals, means for deriving a second secondary signal equal to the minimum of the moduli of the input signals, a half quadrant multiplier or like function generator .producing a first output signal from said secondary signals, sign changer means to produce a second output signal equal to the inverse of said first output signal, and changeover means for selecting one of said first and second output signals as final output signal, said changeover means being responsive to the sign of a control signal derived from said input signals so that the output signal selected has the sign of the product of the input signals.
  • a multiplier or function generator for the generation of the modulus of a product or of another function comprising means for accepting first and second input signals, means for deriving a first secondary signal equal to the maximum of the moduli of the input signals, means for deriving a second setiondary signal equal to the mini- 8 mum of the moduli of the input signals, a halt quadrant multiplier or like function generator producing an output signal from said secondary signals, said output signal being the required modulus.
  • a multiplier as set forth in claim 5 wherein the means for deriving said control signal comprises first and second sign changer means for producing first and second secondary input signals equal to the inverses of the first and second input signals respectively, means for selecting the minimum of said first and second input signals, means for selecting theminimum of said first and second secondary input signals and means for selecting the maximum of the minima so selected, said maximum being the required control signal.
  • means for deriving a signal with the same sign as the product of two input signals comprising first and second sign changer means for producing first and second secondary input signals equal to the inverses' of the first and second input signals respectively, means for selecting the minimum of said first and second input signals, means for selecting the minimum of said first and second secondary input signals and means for selecting the maximum of the minima so selected, said maximum being the required signal.
  • a sign discriminator for use in multipliers or similarly symmetrical function generators comprising means for accepting first and second input signals, first and second sign changer means for producing first and second secondary input signals equal to the inverses of the first and second input signals respectively, means for selecting the minimum of said first and second input signals, means for selecting the minimum of said first and second secondary input signals, and means for selecting the maximum of the minima so selected, said maximum having the sign of the product of the two input signals.
  • An input converter for a one or two quadrant multiplier or like function generator comprising means for accepting first and second input signals, means for producing from said input signals a first output signal correspond-ing with the maximum of the moduli of said input signals, and means for producing a second output signal having a modulus equal to the minimum of the moduli of the input signals and a sign equal to the sign of the product of the input signals, the means for producing the second output signal comprising first and second sign changer means for producing first and second secondary input signals equal to the inverses of the first and second' input signals respectively, means for selecting the minimum of said first and second input signals, means for selecting the minimum of said first and second secondary input signals and means for selecting the maximum of the minima so selected, said maximumbeing the required second output signal.
  • An input converter for a one or two quadrant multiplier or like function generator comprising means for accepting first and second input signals, means for producing from said input signals a first output signal corresponding with the maximum of the moduli of said input signals, and means for producing a second output signal having a modulus equal to the minimum of the moduli of the input signals and a'sign equal to the sign of the product of the input signals, the means for producing the second output signal comprising first and second sign changer means for producing first and second secondary input signals equal to the inverse of the first and second input signals respectively, means for selecting the maximum of said first input signal and said secondary input signal, means for selecting the maximum of said second input signal and said first secondary input signal and means for selecting the minimum of the maxima so selected, said minimum being the required second output signal.

Description

April 1963 A. NATHAN 3,084,862
INPUT CONVERTER AND SIGN DISCRIMINATOR FOR MULTIPLIERS Filed Dec. 23, 1958 2 Sheets-Sheet 1 FIG. 2
A ril 9, 1963 A. NATHAN 3,084,862
INPUT CONVERTER AND SIGN DISCRIMINATOR FOR MULTIPLIERS Filed Dec. 25, 1958 2 Sheets-Sheet 2 FIG. 3
United States Patent 3,084,862 INPUT CQNVERTER AND SIGN DISCRRMINATGR FOR MULTIPLIERS Amos Nathan, 17 Lamed Heir Ave, Ramoth Rernez, Haifa, Israel Filed Dec. 23, 1958, Ser. No. 782,497 12 Claims. (Cl. 235194) This invention relates to an input converter and sign discriminator for electronic multipliers. More specifically, this invention relates to a device which, when connected to the input of any two-quadrant electronic multiplier, or to the input of some one-quadrant multipliers, permits four-quadrant operation. This invention also provides a unit which, when fed 'by two voltages, generates an output voltage whose sign is equal to the sign of the product of the two input voltages.
In general, an electronic multiplier is a device, which when fed with input voltages x and y, generates an output voltage which is proportional to xy. The following terminology is used to describe some aspects of the input ranges of multipliers: A multiplier is said to operate in the first quadrant, if x20, ygtl; in the second quadrant, if xO, 3'50; in the third quadrant, if x50, ytl; and in the fourth quadrant if x20, ygO.
-A multiplier is said to have one quadrant or two quadrant operation if the permissible input range is restricted to one quadrant or to two adjacent quadrants, respectively.
The prior art provides input converters for oneor twoquadrant multiplication whose operation is such, that the correct sign of the output of the multiplier is not always preserved. For example, in a converter for a one quadrant multiplier operative in the first quadrant, x is converted into the modulus of x, ]x[, and y is converted into [y]. In this case the sign of multiplier output is always non-negative.
It is an object of this invention to provide an input converter, which, when connected to the input terminals of any electronic multiplier, preserves both the value and the sign of the output of the multiplier and extends the operative range of one or both of the input variables in the case of multipliers which do not have four quadrant operation.
. In particular, it is an object of this invention to provide two quadrant input voltages to an electronic multiplier, when fed with four quadrant inputs.
It is another object of this invention to provide means for producing an output voltage whose sign is equal to the sign of the product of two input voltages.
It is a further object of this invention to provide a device which, when used with conventional additional circuits, converts any one quadrant multiplier into a four quadrant multiplier.
It is yet another object of this invention to provide a device which, when used with additional conventional circuits, converts some half quadrant multipliers into four quadrant multipliers.
It is another object of this invention to provide an input converter for multidimensional function generators with certain symmetry properties. A
yF-urther objects and advantages of this invention will become apparent from the following description of a practical realization of the invention taken in connection with the accompanying drawings, in which- FIGURE 1A is a three dimensional plot of converter output 1 as a function of its inputs x and y;
FIGURE 1B is a three dimensional plot of converter output .5 as a function of its inputs x andy;
FIGURE 2 is a circuit diagram of one embodiment of the converter and sign discriminator of this invention; FIGURE/3 is a schematic diagram of one embodiment 3,084,862 Patented Apr. 9, 1963 1= l l I I or, equivalently, as
using the sign dis- In FIGUR-E 1B the equation representing plane EOF is =x; the equation representing plane FOG is 5: the equation representing plane GOH is =x; and the equation representing plane HOE is .5: y. Surface EFGHO can therefore be represented as The terms maximum and minimum are used in this specification to denote selection operators; thus max. (a, b, c is equal to the greatest of a, b, c, and min. (a, b, c, is equal to the least of a, b, c,
' Any pair of non-zero values of x and y having differing moduli must of necessity satisfy one, and only one, of the following four conditions:
(a) y cg y x y y y y y Evaluating the functions 5 and 1 for each of these cases separately there is obtained respectively:
It follows, for all values of x and y,
(iv) The sign'of .5 is equal to the sign of xy A device generating g, 1 as output signals when fed' with x, y as input signals can therefore be used as an input converter for a multiplier, 5 and 1 being the input,
signals to the multiplier; because from (i), above, the
output of the multiplier is not affected by the introductionof such a converter in the said manner. Moreover, because of (ii), above, the multiplier need only be of the two quadrant type, whereas the converter accepts inputs in four quadrants. The multiplier can actually be of an even more restricted type, for (iii), above shows that input signals 5, 7 lie within one quadrant only, said quadrant being limited by the lines 23:1; and .=-a7. The part of the converter generating the .5 signal is a sign discriminator for the sign of xy, as tollows from (iv), above.
FIGURE 2 is a schematic diagram of one embodiment of the device for the generation of 5 and 7;. T and T are the input terminals for input signals x and y, respectively. Input signal x is fed to sign changer A whose output signal x appears at output terminal T Input signal y is fed to sign changer A whose output signal -y appears at output terminal T The anodes of diodes D D D D are connected to terminals T T T T respectively. Their cathodes are joined at terminal T which is also connected to a negative D.C. voltage, at through resistor R Except for a small transitional interval, only one of diodes D D D D conducts at a time; there thus appears at terminal T a signal approximately equal to 1 If the diodes have a voltage drop equal to s when conducting, the voltage at T will be equal to +6. When using silicon or germanium diodes or transistors, e is of the order of 0 .1 to 1.0 volt. To correct for this offset voltage and for diode drift, diode D of the same type as diodes D to D is connected with its cathode to T The anode of D is connected to output terminal T and to a positive D.C. voltage, shown at through resistor R The offset voltage of D cancels the offset voltages of diodes D to D and voltage 1; thus appears at T This compensation device, comprising D and R is needed only when high accuracy is required. Another way of compensating for said offset voltage consists of replacing D by a resistor having a resistance which is equal to the resistance of D when conducting.
Some types of diodes have considerable spread of voltage drops from diode to diode, when conducting. The errors thus introduced into the converter can be eliminated by first determining the voltage drop of that diode which has the largest drop, 6, when conducting, and then adding resistors of suitable values in series with each of the other diodes so that the drop across each series combination of said resistors and diodes is made equal to e when the diodes are conducting. This compensation should be carried out for all diodes of the converter.
The cathodes of diodes D D D D are connected to terminals T T T T respectively. The anodes of D and D are joined to T which is also connected to a positive D.C. voltage, through a resistor R At T thus appears a signal equal to min.(x, y)+e. The anodes of diodes D and D are joined at T, which is also connected to a. positive D.C. voltage, through resistor R At T; thus appears a signal equal to The anodes of diodes D D are connected to T T respectively. Their cathodes are joined at terminal T which is also connected to a negative voltage, shown at through resistor R At '1; thus appears a signal equal to g. A two quadrant multiplier, or a single quadrant multiplier whose inputs lie within-the quadrant yglxl, can therefore be connected to terminals T and T,, No compensating diodes are required for the offset voltages of the diodes associated with the circuit for generating :3, because, by virtue of the configuration, the offset voltages cancel.
The device generating 5 heretofore described is based on the expression Analogously, a device with identical functions can be constructed, based on the given equivalent form for .5
The description above is to be understood by way of example only.
FIGURE 3 shows one embodiment of the use of the sign discriminator of this invention to convert a one quadrant multiplier to four quadrant operation. In FIGURE 3, T T T T are the terminals which are at voltages x, x, y, y, respectively, as in the device described in connection with FIGURE 2. Terminal T; is at voltage 5. This voltage is generated by use of the part of the converter generating 5, as heretofore described, i.e. by use of the device shown in FIGURE 2 less that part of it consisting of D D D D R and T1,, and their interconnections. 111 FIGURE 3, M is a one quadrant multiplier whose input terminals are T and T T T are fed with volta es ]x[, ]y[, respec tively. The anodes of diodes D D are connected to T T respectively; their cathodes are connected to T T is also connected to a negative D.C. voltage, through resistor R the voltage of T is approximately equal to Diode D is provided in order to compensate for the voltage drop in D and D and to compensate for diode drift. The cathode of D is connected to T and its anode is connected to T which is also connected to a positive DC. voltage, through resistor R T is thus at a voltage equal to The anodes of diodes D D are connected to T T respectively; their cathodes are connected to T which is also connected to a negative D.C. voltage, through resistor R The cathode of compensating diode D is connected to T and its anode is connected to terminal T which is also connected to a negative D.C. voltage, through resistor R T is therefore at a voltage equal to |y|. M is therefore fed with non-negative voltages and can be of one quadrant operation. At the output terminal T of M thus appears a voltage equal to klxy], where k is a positive constant. Analogous considerations apply when k is negative constant. This voltage is fed to sign changer A whose output terminal T is therefore at voltage kIxy]. Voltage 5 is fed from terminal T to a polarized relay whose actuating mechanism R connects terminal T of its change-over switch S to T or T for positive or negative values of 5, respectively. At T therefore appears the required output voltage kxy. C is a capacitor, connected between T and ground; C is required in some applications, depending upon the circuit fed from T in order effectively to ground T during the switching over of S. The relay consisting of R and S and their associated circuits is by way of illustration only; it can be replaced, in particular, by an electronic switching device.
Similarly, a half quadrant multiplier can be converted into a four quadrant multiplier. For example, to convertto four quadrant operation a multiplier operative in the half quadrant 3 2x20, said multiplier can be fed with signals I5] and 1;. Referring again to FIGURE 3, this can be done by omitting D D D R and R and their interconnections, and feeding T T T with E, 5, and 1 respectively, Where 5 and 1 are generated as described above, whereas 5 can be obtained from 5 by sign changing means, or directly from x, x, y, -y from the expression The circuit for the generation of 5 according to this later expression is therefore identical with the circuit of FIGURE 2 for the generation of 5, except that anode and cathode connections of each of diodes D to D and the positive and negative voltages at and respectively, must be interchanged, and, because of the loading of the circuits generating a and 5, in the circuit generating 5 resistor R and the negative voltage to which it connects must be omitted, and in the circuit generating 5 resistor R must be halved. E or E are also used as control signals for output selection.
Alternatively [til can be generated according to expressions such as for example, .and the manner of said generations will be quite clear from the above description.
In one embodiment of the invention the following components and component values were used:
All diodes are silicon junction diodes;
All voltages marked are 250 volts D.C.;
All voltages marked are 250 volts D.C.
In the device described in connection with FIGURE 2,
In the device described in connection with FIGURE 3,
R =R =2S0 kilohms R7=Rg=500 kilohms C 200' picofarads In some applications, inputs x and/or 2 are restricted, or the multiplier has special input characteristics. It is then not always required to realize the complete surfaces of FIGURES 1A and 1B.
For example, if input variable y is always non-negative, 3720, the previous expressions for 1; and 5 simplify to and the elements D D and A may be omitted from the device of FIGURE 2.
Another example which realizes only a part of each of the surfaces of FIGURE 1 is required if the multiplier is such that it can accept only inputs x and y for which ygx, the later restriction defining a particular two quadrant multiplier, said two quadrants covering half of the first, the whole second, and half of the third quadrants.
One embodiment of the modification sufficient in the latter case consists of the unit of FIGURE 2 with the omission of the following components: A A D D D D D and R and their interconnections.
Other modifications, realizing other parts of the surfaces of FIGURE 1 are obtained by the omission of selected components of the embodiment of this invention described in connection with FIGURE 2. 1
While the converter is described above as an input unit to a multiplier, it can also be used as an input unit to a two dimensional function generator, or to any two inputs of a multidimensional function'generator; in the latter case several converters can be used as input units, each converter serving as input unit to one pair of input terminals of the function generator or its other input con-' verters, or to a pair of terminals one of which is an input terminal of the function generator and the other one is an input terminal of an input converter, all this, provided the function generated has the same symmetry properties and/ or the same input restrictions as a multiplier.
For example, if f(x, y) is the function generated by the function generator when it is fedwith voltages at and y, at its two input terminals, and if fi y)=f(y )=f( y)=f(y the unmodified input converter can be used and only one quadrant of f(x, y) need be realized in the function generator, said quadrant lying partly in the first and partly in the second quadrants, between x=y and x: y.
As a second example, if (x, y) =f(y, x), the modification of this invention described above in connection with multipliers for which ygx can be used as an input converter to the function generator and only two quadrants of f(x, y) need be realized in the function generator, said two quadrants lying partly in the first and third quadrants, and covering the whole second quadrant, their limit being given by the line x=y.
As a third example, if
[-5 I and a can be used as input signals and output switching must be provided, as described above in connection with the conversion of a half quadrant multiplier to four quadrant operation.
The embodiments of this invention and its modifications which have been described in connection with FIGURE 2 use diodes as non-linear elements. It is to be understood that the use of diodes is by way of example only; in particular, the diodes can be replaced by transistors connected in a so-called diode logic connection. The manner of said replacement will be described in connection with FIGURES 4A to 4D, in which FIGURE 4A represents the diagram of a typical diode, such as D D D D D or D of FIGURE 2, together with resistor R connected to its cathode, which corresponds to R or R in the case of D D D D or D D respectively. 3 is the terminal of the constant negative voltage, FIGURE 4B shows the corresponding transistor connection, in which terminals 1, 2, 3 are identical with terminals 1, 2, 3, of FIGURE 4A. TR is an NPN transistor. The parallel connection of resistor R and capacitor 6 serves as input network to the base of the transistor. The base is also connected to bias voltage V at terminal 4 through resistor R The emitter is connected to terminal 2 which is also connected to a negative D.C. voltage V at terminal 3, through resistor R The collector is connected to terminal 5 which is at the constant voltage V FIGURE 40 corresponds to one of the diodes such as D D D D D in the embodiment of FIGURE 2, and consists of FIGURE 4A with diode 5, replaced by diode 1 5 where D is D with interchanged terminals, and with voltage V of reversed sign. FIGURE 4D shows the transistor equivalent to FIGURE 4C and is identical to FIGURE 4B except for the substitution of PNP transistor TR for TR and the reversal of sign of voltages V V and V Combinations of transistors and diode elements can be used. For example, D 10, D may be diodes, all othernon-linear elements being transistors.
, The use of transistors has the main advantages of providing impedance conversion, from a higher input to a lower output value, and of improving the frequency response; its main disadvantage is the restriction of, the useful voltage range of input voltages at and y.
, Typical values for the embodiments of FIGURES 4B and 4 D are as follows: Rf =50 kilohms; R =2.0 kilohms; E =10O kilohms; 0:570 picofarads. Typical voltages in the embodiment of FIGURE 48 are as follows; V =22.5 volts; V =7 volts; V =2 volts. In the embodiment of FIGURE 4D the same voltage values with reversed sign are used. The gain from input to output was found to be 0.98. The permissible voltage range at terminal Zwas 3 volts to +3 volts. Adjustment for zero output voltage with zero input voltage is obtained by a slight variation of V For this purpose adjustable V is provided.
As an alternative way of carrying out the invention, 5 as given above and 1;=min.(x, -x, y, -y) may be used, or, for example, realization of and 7 according to the expressions, which require only one sign-changer,
andthe manner of their generation will be quite clear from the above description.
.What I claim is:
1. An input converter for a one or two quadrant multiplier or like function generator, comprising means for accepting first and second input signals, first means connected to said accepting means for producing from said input signals a first output signal corresponding with the maximum of the moduli of said input signals, and second means connected to said accepting means for producing a second output signal having a modulus equal to the minimum of the moduli of the input signals, said second means including means for generating a sign for said second output signal wherein said sign is equal to the sign of the product of the input signals; said accepting means including means for generating a plurality of secondary output signals greater in number than said input signals; at least one of said secondary output signals being equal in mag nitude and opposite in sign to one of said input signals; said first and second means being adapted to employ said secondary output signals to generate appropriate moduli signals.
2. The input converter of claim 1 wherein the means for producing the first output signal comprises first and second sign changer means for producing first and second secondary input signals equal to the inverses of the first and second input signals, and third means for selecting the maximum of said first and second input signals and said first and second secondary input signals.
'3. An input converter for a one or two quadrant multiplier or like function generator, comprising means for accepting first and second input signals, first and second sign changer means for producing first and second secondary input signals equal to the inverse of the respective input signals, means for selecting the maximum of said first and second input signals and said first and second secondary input signals, means for selecting the minimum of said first and second input signals, means for selecting the minimum of said first and second secondary input signals, and means for selecting the maximum of the two minima so selected.
4. A four quadrant multiplier comprising means for accepting first and second input signals, means for deriving the moduli of said input signals, a single quadrant multiplier for multiplying said moduli to produce a first output signal, sign changer means to produce a second output signal equal to the inverse of said first output signal, and changeover means for selecting one of said first and second output signals as final output signal, said changeover means being responsive to the sign of a control signal derived from said input signals so that the output signal selected has the sign as well as the modulus of the product of the input signals.
5. A four quadrant multiplier comprising means for accepting first and second input signals, means for deriving the moduli of said input signals, means for multiplying said moduli to produce a first output signal, means for changing the sign of said first output to produce a second output signal, means for deriving a control signal having the sign of the product of the input signals, and changeover means, responsive to said control signal, for selecting that one of said first and second output signals having the sign of said control signal.
6. A four quadrant multiplier or like function generator comprising means for accepting first and second input signals, means for deriving a first secondary signal equal to the maximum of the moduliof the input signals, means for deriving a second secondary signal equal to the minimum of the moduli of the input signals, a half quadrant multiplier or like function generator .producing a first output signal from said secondary signals, sign changer means to produce a second output signal equal to the inverse of said first output signal, and changeover means for selecting one of said first and second output signals as final output signal, said changeover means being responsive to the sign of a control signal derived from said input signals so that the output signal selected has the sign of the product of the input signals.
7. A multiplier or function generator for the generation of the modulus of a product or of another function, comprising means for accepting first and second input signals, means for deriving a first secondary signal equal to the maximum of the moduli of the input signals, means for deriving a second setiondary signal equal to the mini- 8 mum of the moduli of the input signals, a halt quadrant multiplier or like function generator producing an output signal from said secondary signals, said output signal being the required modulus.
8. A multiplier as set forth in claim 5 wherein the means for deriving said control signal comprises first and second sign changer means for producing first and second secondary input signals equal to the inverses of the first and second input signals respectively, means for selecting the minimum of said first and second input signals, means for selecting theminimum of said first and second secondary input signals and means for selecting the maximum of the minima so selected, said maximum being the required control signal.
9. In a multiplier or like function generator, means for deriving a signal with the same sign as the product of two input signals, comprising first and second sign changer means for producing first and second secondary input signals equal to the inverses' of the first and second input signals respectively, means for selecting the minimum of said first and second input signals, means for selecting the minimum of said first and second secondary input signals and means for selecting the maximum of the minima so selected, said maximum being the required signal.
'10. A sign discriminator for use in multipliers or similarly symmetrical function generators, comprising means for accepting first and second input signals, first and second sign changer means for producing first and second secondary input signals equal to the inverses of the first and second input signals respectively, means for selecting the minimum of said first and second input signals, means for selecting the minimum of said first and second secondary input signals, and means for selecting the maximum of the minima so selected, said maximum having the sign of the product of the two input signals.
11. An input converter for a one or two quadrant multiplier or like function generator, comprising means for accepting first and second input signals, means for producing from said input signals a first output signal correspond-ing with the maximum of the moduli of said input signals, and means for producing a second output signal having a modulus equal to the minimum of the moduli of the input signals and a sign equal to the sign of the product of the input signals, the means for producing the second output signal comprising first and second sign changer means for producing first and second secondary input signals equal to the inverses of the first and second' input signals respectively, means for selecting the minimum of said first and second input signals, means for selecting the minimum of said first and second secondary input signals and means for selecting the maximum of the minima so selected, said maximumbeing the required second output signal.
12. An input converter for a one or two quadrant multiplier or like function generator, comprising means for accepting first and second input signals, means for producing from said input signals a first output signal corresponding with the maximum of the moduli of said input signals, and means for producing a second output signal having a modulus equal to the minimum of the moduli of the input signals and a'sign equal to the sign of the product of the input signals, the means for producing the second output signal comprising first and second sign changer means for producing first and second secondary input signals equal to the inverse of the first and second input signals respectively, means for selecting the maximum of said first input signal and said secondary input signal, means for selecting the maximum of said second input signal and said first secondary input signal and means for selecting the minimum of the maxima so selected, said minimum being the required second output signal.
(References on following page) References Cited in the file of this patent UNITED STATES PATENTS Van Allen Oct. 8, 1957 OTHER REFERENCES Electronic Analog Computer, GAP/R K2 Series, Philbrick Researches, Inc., received in Scientific Library 10 Sept. 29, 1958. FIG. 1.1, p. 10 and FIG. 4.3, p. 23 relied on.
Electronic Analog Computer (Korn and K0111), 1952, McGraw-Hill Book Company, Inc, N.Y., FIG. 6.2, page 212 showing adaptation of two-quadrant multipliers to four-quadrant multiplication of interest.

Claims (1)

1. AN INPUT CONVERTER FOR A ONE OR TWO QUADRANT MULTIPLIER OR LIKE FUNCTION GENERATOR, COMPRISING MEANS FOR ACCEPTING FIRST AND SECOND INPUT SIGNALS, FIRST MEANS CONNECTED TO SAID ACCEPTING MEANS FOR PRODUCING FROM SAID INPUT SIGNALS A FIRST OUTPUT SIGNAL CORRESPONDING WITH THE MAXIMUM OF THE MODULI OF SAID INPUT SIGNALS, AND SECOND MEANS CONNECTED TO SAID ACCEPTING MEANS FOR PRODUCING A SECOND OUTPUT SIGNAL HAVING A MODULUS EQUAL TO THE MINIMUM OF THE MODULI OF THE INPUT SIGNALS, SAID SECOND MEANS INCLUDING MEANS FOR GENERATING A SIGN FOR SAID SECOND OUTPUT SIGNAL WHEREIN SAID SIGN IS EQUAL TO THE SIGN OF THE PRODUCT OF THE INPUT SIGNALS; SAID ACCEPTING MEANS INCLUDING MEANS FOR GENERATING A PLURALITY OF SECONDARY OUTPUT SIGNALS GREATER IN NUMBER THAN SAID INPUT SIGNALS; AT LEAST ONE OF SAID SECONDARY OUTPUT SIGNALS BEING EQUAL IN MAGNITUDE AND OPPOSITE IN SIGN TO ONE OF SAID INPUT SIGNALS; SAID FIRST AND SECOND MEANS BEING ADAPTED TO EMPLOY SAID SECONDARY OUTPUT SIGNALS TO GENERATE APPROPRIATE MODULI SIGNALS.
US782497A 1958-12-23 1958-12-23 Input converter and sign discriminator for multipliers Expired - Lifetime US3084862A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
US782497A US3084862A (en) 1958-12-23 1958-12-23 Input converter and sign discriminator for multipliers

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
US782497A US3084862A (en) 1958-12-23 1958-12-23 Input converter and sign discriminator for multipliers

Publications (1)

Publication Number Publication Date
US3084862A true US3084862A (en) 1963-04-09

Family

ID=25126234

Family Applications (1)

Application Number Title Priority Date Filing Date
US782497A Expired - Lifetime US3084862A (en) 1958-12-23 1958-12-23 Input converter and sign discriminator for multipliers

Country Status (1)

Country Link
US (1) US3084862A (en)

Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3710087A (en) * 1971-03-24 1973-01-09 Kistler Instr Corp Calculation of approximate magnitude of a physical vector quantity
US5367610A (en) * 1988-09-28 1994-11-22 Omron Tateisi Electronics Co. Fuzzy controller for selecting an input signal
US10594334B1 (en) 2018-04-17 2020-03-17 Ali Tasdighi Far Mixed-mode multipliers for artificial intelligence
US10700695B1 (en) 2018-04-17 2020-06-30 Ali Tasdighi Far Mixed-mode quarter square multipliers for machine learning
US10819283B1 (en) 2019-06-04 2020-10-27 Ali Tasdighi Far Current-mode analog multipliers using substrate bipolar transistors in CMOS for artificial intelligence
US10832014B1 (en) 2018-04-17 2020-11-10 Ali Tasdighi Far Multi-quadrant analog current-mode multipliers for artificial intelligence
US11416218B1 (en) 2020-07-10 2022-08-16 Ali Tasdighi Far Digital approximate squarer for machine learning
US11467805B1 (en) 2020-07-10 2022-10-11 Ali Tasdighi Far Digital approximate multipliers for machine learning and artificial intelligence applications

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2808990A (en) * 1956-10-31 1957-10-08 Roland L Van Allen Polarity responsive voltage computing means

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US2808990A (en) * 1956-10-31 1957-10-08 Roland L Van Allen Polarity responsive voltage computing means

Cited By (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3710087A (en) * 1971-03-24 1973-01-09 Kistler Instr Corp Calculation of approximate magnitude of a physical vector quantity
US5367610A (en) * 1988-09-28 1994-11-22 Omron Tateisi Electronics Co. Fuzzy controller for selecting an input signal
USRE36421E (en) * 1988-09-28 1999-11-30 Omron Corporation Fuzzy controller for selecting an input signal
US10594334B1 (en) 2018-04-17 2020-03-17 Ali Tasdighi Far Mixed-mode multipliers for artificial intelligence
US10700695B1 (en) 2018-04-17 2020-06-30 Ali Tasdighi Far Mixed-mode quarter square multipliers for machine learning
US10832014B1 (en) 2018-04-17 2020-11-10 Ali Tasdighi Far Multi-quadrant analog current-mode multipliers for artificial intelligence
US10819283B1 (en) 2019-06-04 2020-10-27 Ali Tasdighi Far Current-mode analog multipliers using substrate bipolar transistors in CMOS for artificial intelligence
US11275909B1 (en) 2019-06-04 2022-03-15 Ali Tasdighi Far Current-mode analog multiply-accumulate circuits for artificial intelligence
US11449689B1 (en) 2019-06-04 2022-09-20 Ali Tasdighi Far Current-mode analog multipliers for artificial intelligence
US11416218B1 (en) 2020-07-10 2022-08-16 Ali Tasdighi Far Digital approximate squarer for machine learning
US11467805B1 (en) 2020-07-10 2022-10-11 Ali Tasdighi Far Digital approximate multipliers for machine learning and artificial intelligence applications

Similar Documents

Publication Publication Date Title
US2459106A (en) Computing apparatus
US3084862A (en) Input converter and sign discriminator for multipliers
US3736515A (en) Non-linear function generator
US3982115A (en) Electronically programmable function generator
US3646428A (en) Symmetrical voltage regulator
US4563670A (en) High speed multiplying digital to analog converter
US3422306A (en) Distortion correction circuitry
US3532868A (en) Log multiplier with logarithmic function generator connected in feedback loop of operational amplifier
US3585487A (en) High-speed precision rectifier
US3368066A (en) Fast multiplier employing fieldeffect transistors
US3106639A (en) Electronic function generator with interpolating resistors
US2841707A (en) Information handling system
US3448297A (en) Analog multiplier
US3311835A (en) Operational rectifier
US3371224A (en) High accuracy electronic function generator
US2842664A (en) Electronic switches
US3393308A (en) Electronic function generator
US3806758A (en) Dynamic focus generator
US3783304A (en) Constant pulse width generator
US3308334A (en) Trace distortion correction
US3389340A (en) Common mode rejection differential amplifier
US3480794A (en) Parallel operational rectifiers
US3259758A (en) Sum and difference circuit
US2600264A (en) Geometrical computer
US2682607A (en) Amplifier