US3708659A - Function generator - Google Patents

Function generator Download PDF

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Publication number
US3708659A
US3708659A US00182982A US3708659DA US3708659A US 3708659 A US3708659 A US 3708659A US 00182982 A US00182982 A US 00182982A US 3708659D A US3708659D A US 3708659DA US 3708659 A US3708659 A US 3708659A
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Prior art keywords
signal
furnishing
scanning
signals
arrangement
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Expired - Lifetime
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US00182982A
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English (en)
Inventor
G Schirmer
E Fauser
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Robert Bosch GmbH
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Robert Bosch GmbH
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06G—ANALOGUE COMPUTERS
    • G06G7/00—Devices in which the computing operation is performed by varying electric or magnetic quantities
    • G06G7/12—Arrangements for performing computing operations, e.g. operational amplifiers
    • G06G7/26—Arbitrary function generators
    • G06G7/28—Arbitrary function generators for synthesising functions by piecewise approximation

Definitions

  • a first resistance furnishes signals corresponding to theindependent variable values at a plurality of first taps
  • a second resistance furnishes dependent variable signals at a correspond-v ing plurality of second taps.
  • a first and second contact arm respectively scan the first and second resistors simultaneously.
  • a feedback circuit has an input terminal connected to the input furnishing the value of independent variable for which the value of dependent variable is to be found. It has a feedback input connected to receive the signals scanned by the first contact arm- Movement of contactarms is stopped when signal at first contact arm is equal to input signal. Signal at second contact arm then equal to desired value of dependent variable.
  • This invention relates to a function generator for simulating a determined function relating an independent and a dependent variable.
  • it relates to a circuit furnishing for each input value of independent variable, the value of dependent variable related thereto by said determined function.
  • the present invention relates to function generators wherein such approximation of the determined function is carried out step-by-step in accordance with either a linear or other approximation.
  • Known function generators of this type comprise diode function generators. These have the disadvantage that the determined function is approximated by the slope of linear portions between two points x,/y,. If one of the points x,/y, is to be changed, then the slope of the straight line connecting the subsequent and following points, must again be determined and re-set.
  • the present invention comprises a function generator for approximating a determined function relating an independent variable to a dependent variable. It comprises first and second signal furnishing means, respectively furnishing independent variable signals corresponding to values of said independent variable and dependent variable signals, each related to the corresponding one of said independent variable signals by said determined function.
  • the first and second scanning means are simultaneously controlled by closed loop control means.
  • the closed loop control means have a first input connected to receive an input signal signifying the selected value of independent variable, a feedback input connected to said first scanning means, and an output jointly controlling said first and second scanning means until said scanned independent variable signal has a predetermined relationship to said input signal.
  • the scanned second signals scanned at this point correspond to the desired value of dependent variable.
  • the first and second signal furnishing means comprise, for example, first and second resistance means having voltages corresponding to values of X, and Y,, respectively, applied at selected points by use, for example, of calibrated knkbs and furnishing the X, and Y, values between said selected points.
  • The] scanning means may comprise contact or wiper arms sensing the voltages along said resistance means.
  • the first and second scanning means may each comprise a first and second contact arm furnishing sequential values of the independent and dependent variable signals;
  • the scanning means are controlled by the closed loop control circuit in such a manner that the scanning is stopped when the desired value (input signal) of independent variable is within the range signified by the first and second scanned independent variable .signal.
  • Three subtraction means are provided in this embodiment, the first subtracting the scanned independent variable signals one from the other, the second subtracting the scanned dependent variable signals one from the other, and the third subtracting the first scanned independent variable signal from the input signal.
  • Computing means then compute the slope of the curve as a function of the output signal from the first and second subtraction means, and form the product of the slope and the output of the third subtraction means.
  • Adder means are then provided which add the resulting computer output signal to the first scanned dependent variable signal, thereby furnishing an adder output signal corresponding to the value of dependent variable associated by said determined function with the input value of independent variable.
  • FIG. 1 shows a function generator of the present invention using two continuous resistance as signal furnishing means
  • FIG. 2 shows the sistances
  • FIG. 1 shows a function generator having a first and second continuous resistance, 11 and 10, respectively.
  • Resistors 11 and 10 are referred to as first and second signalfurnishin'g means, respectively. These resistances have connecting terminals, namely resistance 10 has.
  • a voltage source has a first voltage furnishing terminal and a second voltage furnishing terminal, herein indicated as ground. Across this source of voltage, are connected resistors 22 through 26 and-27 through 31.
  • a movable wiper arm connects a selected point on resistances 22 through 26 each to one of terminals 12 through 16,
  • the first and second scanning means comprise a contact arm 33 movable along resistance 11 and a contact arm 32 movable along resistance 10, respectively. These contact arms or wiper contacts are mechanically intercoupled and moved simultaneously by output control means, here a motor (preferably a servo motor) 34.
  • the input of the servo motor is connected to the output of a comparator 36 which in turn has a first input connected to an input terminal 37, and a feedback input connected to wiper arm 33.
  • Comparator 36 and motor 34 form the closed loop control means.
  • the dependent variable signals corresponding to points on the curve Y, to Y, are fixed with the aid of resisters 22 through 26.
  • Resistors 27 through 31, or rather the wiper arms associated therewith, serve to fix the coordinates of points X, to X,,. By fixing these points, the value of the function between points is automatically fixed electrically over resistors and 11.
  • the value of independent variable is applied at terminal 37, for example through a potentiometer which is not shown. Input terminal 37 is connected to the first input of comparator means 36.
  • the closed loop control circuit then serves to drive, via motor 34, the wiper arms 33 and 32 until the signal value at wiper arm 33, namely the scanned first signal or scanned independent variable signal, corresponds to the input signal. At this point, the signal appearing at wiper arm 32 corresponds to the desired value of dependent variable and this value is available-at output terminal 35 which is connected to wiper arm 32.
  • the servo motor 34 in the function generator according to FIG. 1 requires a relatively long time for moving the wiper arms over the resistances until a balance is obtained, this response time may for some applications be too long. It may be shortened by use of an embodiment as shown in FIG. 3.
  • the continuous resistances l0 and l l are replaced by a plurality of series-connected resistance means, namely resistors 38. Voltages are again applied at determined points along each other and the number of such terminals exceeds the number of terminals at which the voltages are impressed.
  • the contact arms are operated by first step switch means, namely a switch 39, rather than the servo motor 34 of FIG. 1.
  • the step switch means are operated in dependence upon the output signal of a comparator 36, and the overall functioning of the circuit of FIG. 3 is the same as that of the circuit of FIG. 1.
  • Step switch 39 is of course adapted both for forward and reverse motion.
  • the signal furnishing means are divided into coarse approximation signal furnishing means are divided into coarse approximation signal furnishing means and fine approximation signal furnishing'means.
  • the means applying predetermined voltages which are part of the signal furnishing means for furnishing the independent variable signals comprise a plurality of resistors parallel with a voltage source as in FIG. 3, the wiper arm of each of these resistors here being denoted by terminals 51, 43,44 and 48.
  • the corresponding terminals for the dependent variables are numbered 52,70,71 and 49/
  • Each of the scanning means comprise a pair of contacts which are positioned by a step switch. control 50 to make contact at sequential independent and dependent variable contacts.
  • the contact ismade to the independent variable signal furnishing means at terminals 43 and 44 and to the dependent signal furnishing means at contacts 70 vand 7l.
  • the fine approximation signal furnishing means namely first and second fine resistance means respectively connected between the scanning contacts of the independent and the dependent variable signal furnishing means.
  • the fine resistance means may either be a continuous resistance in which case the scanning means therefore are a wiper arm which travels continuously over the resistances, or they may be series-connected resistances, as shown in FIG. 3 (resistances 38) in which case the wiper arm scanning the series-conv nected resistances is moved by a step switch.
  • the fine the resistance means namely at terminals 18 through 20 and 13 through 15, respectively.
  • the first or independent variable signals are then furnished at terminals 40 which comprise not only terminals 18 through 20,
  • the various connecting points of the individual scanning means for the independent variable are denoted by reference numeral 33, while the fine scanning means for the dependent variable have a reference numeral 32.
  • the movable contact arm 32 is connected to output terminal 35 while the movable arm 33 is connected to the feedback input of a comparator 36, whose first input is connected to input terminal 37 for receiving the independent variable signal for which the corresponding dependent variable signal is to be furnished by this arrangement.
  • the output of comparator 36 is again connected to a switch means 39, which controls the movements of arms 32 and 33 in such a manner as to decrease the difference appearing at the input terminals of comparator 36. Specifically, the switch means move arms 32 and 33 until such time as the difference at the input of comparator 36 is equal to zero.
  • this arrangement has the advantage of requiring much fewerresistors than the arrangement of FIG. 3, since the fine approximation signal fumishing means are switched between pairs of terminals as required, rather than existing between all pairs of the coarse approximation signal furnishing means terminals, as in FIG. 3.
  • the direction of the signal furnished by logic circuit 47 to switch means 50 maybe determined by which of contacts 68 and 69 are contacted by movable contact 33.
  • the logic circuit could furnish a signal whose polarity depends upon the polarity of the output signal of comparator 36 and furnish this signal whenever one of the end contacts 68 or 69 is touched.
  • FIG. 6 A particular example of the logic circuit and the switching means 50 associated therewith is shown in FIG. 6. This Figure will be described now. It is also useful in conjunction with FIG. 5. Specifically, for FIG. 4 I
  • the block labelled 47 shows a first and second comparator, 70, and 71, respectively, each of which has a first input terminal connected to terminal 37.
  • the second input tenninal of comparator 70 is connected to the end terminal 68 at which the minimum value of independent variable for the range is available, while the second input terminal of comparator 71 is connected to terminal .69, at which the maximum value of independent variable in the particular range is available.
  • Comparator 71 yields an output signal when the independent variable signal, X, is less than the maximum signal available over the range.
  • Comparator 70 yields an output signal when X is less than the minimum value of independent variable available in the range.
  • An AND gate 72 has a first and second input respectively connected to the first and second comparator output. This AND gate thus gives an output if the independent variable is less than the maximum and less than the minimum independent variable value available in the range.
  • a second AND gate, 73 has a first input connected via an inverter to the output of comparator 71 and via a further inverter to the output of comparator 70. AND gate 73 therefore yields an output when X is larger than the minimum and larger than the maximum value of independent variable of the range.
  • a first and second monostable multivibrator are respectively connected to the outputs of AND gate 72, the first AND gate, and AND gate 73, the second AND gate means.
  • the first monostable multivibrator yields a signal
  • the second monostable multivibrator yields a signal.
  • the signals are respectively applied to a switch means 50.
  • Switch means comprises a first coil connected from the output of the first monostable multivibrator to ground, and a second coil connected to the output of the second monostable multivibrator to ground.
  • a step switch, coarse step switch means are driven in either a first or second direction in dependence upon which of the multivibrators furnishes the output signal controlling the step switch.
  • the coarse step switch means in response to an output signal from the first monostable multivibrator, would move the pair of contacts 42, and thereby the pair of contacts 41, a step to .the left, whereby contacts 42 would be connected from contact 51 to contact 43.
  • this particular arrangement namely FIG. 4 in conjunction with blocks 47 and 50 of FIG. 6, serves to furnish first a coarse approximation and secondly a fine approximation signal.
  • the output at terminal 35 is the dependent variable signal which is related to the independent variable signal applied at terminal 37 by the function being approximated.
  • FIG. 5 A further embodiment of the present invention is shown in FIG. 5.
  • the circuit shown in FIG. 5 operates in such a manner that the initial point in the curve x,/y, and the slope between this point and a neighboring point x,,/y,, is detennined.
  • -Terminals 57 through and 53 through 56 respectively, again determine the coordinates, X, Y, of the difierent points of the curve.
  • terminal 54 contains the value of Y,, terminal 55 the value for Y;,, terminal 58 the value X,, and terminal 59 the value X
  • Terminals 55 and 54 are connected to the inputs of I second subtraction means 61, while terminals 58 and- 59 are connected via the movable contact arms to the input terminals of first subtraction means 63.
  • Third subtraction means 64 have a first input connected to terminal 37 and a second input connected to the contact arm which, as shown in the Figure, makes the connection to terminal 58.
  • the first, second, and third subtraction means have first, second and third subtraction outputs, all connected to'the inputs of a computer 62.
  • the computer forms the product of the output of the second and third subtraction means, and divides this product by the output of the first'subtraction means.
  • This the output signal of the computer is k i) txrxn
  • the above output signal of the computer is applied to one input of adder means 65 to whose other input is applied the contact arm making contact with terminal 54, that is the other input corresponds to Y
  • the output function of the adder thus is the desired value of dependent variable, namely:
  • FIG. 5 has the advantage that no fine approximation signal furnishing means must be present at all, that is all the resistors interconnected between the various coarse approximation terminals, may be omitted. Further, theembodiment of FIG. 5 has a much shorter response time since the only switching is between coarse approximation terminals while the remainder of the operation is carried out by computer, which of course is almost delay-free.
  • resistances interconnecting the various steps need not be linear resistances, but may vary in either a logarithmic or trigonometric fashion.
  • Function generator for approximating a predetermined function relating a dependent variable to an independent variable, comprising, in combination, an input terminal receiving an independent variable signal corresponding to a selected value of said independent variable; first signal furnishing means furnishing a plurality of first signals, each of thus said first signals corresponding to a determined value of said independent variable; second signal furnishing means furnishing a corresponding plurality of second signals, each of said second signals corresponding to a value of dependent variable related by said predetermined function to the value of independent variable associated with the corresponding one of said first signals; first scanning means scanning said first signal furnishing means and furnishing a plurality of scanned first signals; second scanning means connected to said first scanning means for simultaneous scanning therewith, said second scanning means scanning said second signal furnishing means and furnishing a plurality of scanned second signals, each related to the corresponding one of said scanned first signals by said determined function; and closed loop control means having a first input connected to said inputterminal, a feedback input connected to said first scanning means, and output control means responsive to the difference between said
  • first and second signal furnishing means comprise voltage furnishing means; and first and second resistance means, each having at least a first and second connecting terminal connected to said voltage furnishing means.
  • first and second scanning means respectively comprise first and second wiper means, mechanically intercoupled; and wherein said output control means comprise motor means moving said mechanically intercoupled first and second wiper means along said first and second resistance means.
  • said closed loop control means comprise comparator -means furnishing a comparator output signal in first wiper means to said feedback input of said com parator means.
  • said first and second signalfurnishing means comprise, respectively, a first and second plurality of series-connected resistance means, each of said plurality of series-connected resistance means having a plurality of connecting terminals; means applying predetermined voltages at selected ones of said connecting terminals of said first and second plurality of series-connected resistance means; wherein said first and second scanning means comprise, respectively, a first and second movable contact; wherein said closed loop control means comprise comparator means having a first input connected to said input terminal, a feedback input connected to said first movable contact, and a comparator output; and first switch means connected to said comparator output for moving said first and second movable contacts along said connecting terminals until the difference between the signal at said first input and said feedback inputis said predetermined difference.
  • said voltage furnishing means comprise a source of voltage having a first and second voltage furnishing terminal; a plurality of third resistance means connected in parallel with said source of voltage, each of said third resistance means having a movable arm; and means connecting each of said movable arms to a corresponding one of said connecting terminals.
  • each of said third resistance means is a low resistance.
  • first and second signal furnishing means respectively comprise first and second coarse approximation signal furnishing means furnishing respectively a plurality of first and second coarse approximation signals; further comprising first and second fine approximation signal furnishing means each having a first and second end terminal and intermediate terminals, and furnishing fine approximation signals at said intermediate terminals in correspondence to signals applied at said first and second end terminals; wherein said first and second scanning means respectively comprise first and second coarse scanning means applying, respectively, successive ones of said first and second coarse approximation signals to said end terminals of said first and second fine approximation signal furnishing means, and first and second fine scanning means respectively scanning said first and second fine approximation signal furnishing means; and wherein said closed loop control means comprise coarse closed loop control means moving said coarse approximation scanning means until said independent variable signal is within the range of said fine approximation signals furnished by said first fine'approximation signal furnishing means, and wherein said closed loop control means further comprise fine closed loop control means moving
  • said first and second coarse approximation signal furnishing means comprise means furnishing predetermined voltages at corresponding voltage terminals; wherein said first and second scanning means comprise, respectively, a first and second pair of mechanically intercoupled contacts, each of said pairs'of contacts being adapted to contact simultaneously sequential ones of said voltage terminals; wherein said first and second fine approximation signal furnishing means each comprises corresponding fine resistance means; and wherein said coarse closed loop control means comprise logic circuit means responsive to said independent variable signal and said signals at said first and second end terminal of said first fine approximation signal furnishing means, and furnishing a first logic signal signifying an independent variable signal exceeding the maximum one of said fine approximation signals, a second logic signal signifying an independent variable signal less than the minimum of said fine approximation signals; and coarse step switch means for moving said pairs of contacts in afirst or second direction in response to said first and second logic signal respectively.
  • said logic circuit means comprise first logic comparator means furnishing a first logic comparator output signal when said independent variable signal is less than the maximum one of said fine approximation signals;
  • second logic comparator means furnishing a second' logic comparator output signal when said independent variable signal is less than the minimum one of said fine approximation signals;
  • first AND gate means having a first input connected to the output of said first logic comparator means and a second input connected to the output of said second logic comparator means and a firstAND gate output;
  • -second AND gate means having a first input connected to the output of said first logic comparator means, a second input connected to the output of said second logic comparator means and a second AND gate output; inverter means connected between said first logic comparator output and said first input of said second AND gate; further inverter means connected between said second logic compara tor output and said second input of said second AND gate means; and first and second monostable multivibrator means respectively connected to said first and second AND gate outputs.
  • said fine closed loop control means comprise comparator means having a first input connected to said input terminal and a second input connected to said first fine scanning means, said comparator means furnishing a comparator output signal at a comparator output; and servo motor means connected to said comparator output and controlling said first and second fine approximation scanning means as a function of said comparator output signal.
  • said logic circuit means comprise means responsive to the scanning of said end terminals by said first fine scanning means and furnishing a first logic signal when said first scanning means scans said first end terminal and a second logic signal when said first scanning means scans said second end terminal.
  • said logic circuit means comprise circuits responsive to the scanning of said first and second end terminals by said first scanning means and furnishing said first and second logic signal in dependence upon the sign of said comparator output signal.
  • said first scanning means comprise means simultaneously scanning a first and second consecutive one of said first signals and furnishing an X, and X scanned signal in response thereto; wherein said second means when the value of independent variable corresponding to said independent variable signal has an I and third subtraction output signal at, respectively, a
  • first, second, and third subtraction output further comprising computer means connected to said first, second, and third subtraction outputs.
  • said computing means comprise division means dividing said second subtraction output signal by said first subtraction output signal thereby furnishing a division signal; and wherein said computing means further com prise multiplier means multiplying said division signal by said third subtraction output signal thereby furnishing a computer output signal.

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  • Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Software Systems (AREA)
  • Computer Hardware Design (AREA)
  • General Physics & Mathematics (AREA)
  • Adjustable Resistors (AREA)
  • Analogue/Digital Conversion (AREA)
  • Supply And Distribution Of Alternating Current (AREA)
  • Feedback Control In General (AREA)
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US00182982A 1970-09-24 1971-09-23 Function generator Expired - Lifetime US3708659A (en)

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DE2047087A DE2047087C3 (de) 1970-09-24 1970-09-24 Funktionsgenerator

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US (1) US3708659A (de)
CH (1) CH531755A (de)
DE (1) DE2047087C3 (de)
FR (1) FR2107929B1 (de)
GB (2) GB1371025A (de)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3900745A (en) * 1972-07-28 1975-08-19 Matsushita Electric Ind Co Ltd Waveform generator
US3923022A (en) * 1973-05-23 1975-12-02 Bosch Gmbh Robert Combustion engine ignition timing system
US4394743A (en) * 1980-12-18 1983-07-19 Bell Telephone Laboratories, Incorporated Tone generation method and apparatus using stored reference calibration coefficients

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2311277A1 (fr) * 1975-05-16 1976-12-10 Tech Automatisme Dispositif electrique de conversion d'une position en une tension

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3100839A (en) * 1959-09-02 1963-08-13 Technion Res & Dev Foundation General purpose compensated diode function generator
US3345505A (en) * 1960-10-24 1967-10-03 Gen Precision Systems Inc Function generator
US3358130A (en) * 1963-02-19 1967-12-12 Hitachi Ltd Function generator

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3100839A (en) * 1959-09-02 1963-08-13 Technion Res & Dev Foundation General purpose compensated diode function generator
US3102951A (en) * 1959-09-02 1963-09-03 Nathan Amos Electronic interpolating time sharing function generators
US3345505A (en) * 1960-10-24 1967-10-03 Gen Precision Systems Inc Function generator
US3358130A (en) * 1963-02-19 1967-12-12 Hitachi Ltd Function generator

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3900745A (en) * 1972-07-28 1975-08-19 Matsushita Electric Ind Co Ltd Waveform generator
US3923022A (en) * 1973-05-23 1975-12-02 Bosch Gmbh Robert Combustion engine ignition timing system
US4394743A (en) * 1980-12-18 1983-07-19 Bell Telephone Laboratories, Incorporated Tone generation method and apparatus using stored reference calibration coefficients

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GB1371025A (en) 1974-10-23
DE2047087A1 (de) 1972-03-30
FR2107929A1 (de) 1972-05-12
CH531755A (de) 1972-12-15
DE2047087B2 (de) 1978-05-11
DE2047087C3 (de) 1979-03-29
GB1362570A (en) 1974-08-07
FR2107929B1 (de) 1975-07-18

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