US2854622A

US2854622A - Circuits for producing non-linear voltages

Info

Publication number: US2854622A
Application number: US662397A
Authority: US
Inventors: Homer G Boyle
Original assignee: Avco Manufacturing Corp
Current assignee: Avco Manufacturing Corp
Priority date: 1957-05-29
Filing date: 1957-05-29
Publication date: 1958-09-30
Anticipated expiration: 1975-09-30

Description

P 1958 H. G. BOYLE 2,854,622

CIRCUITS FOR PRODUCING NON-LINEAR VOLTAGES Filed May 29, 1957 INVENTOR. HOMER s. BOYLE. a! M. pe 1W7? G 2 ATTOR EYS.

United States Patent CIRCUITS FOR PRODUCING NON-LINEAR VOLTAGES Homer G. Boyle, Dayton, Ohio, assignor to Avco Manufacturing Corporation, Cincinnati, Ohio, a corporation of Delaware Application May 29, 1957, Serial No. 662,397

17 Claims. (Cl. 323-74) This invention relates to a variable impedance network and, more particularly, to a voltage divider network employing linear resistance elements for deriving non-linear functions.

In many applications it is necessary to convert the linear rotation of a shaft into a non-linear, electrical function. When the non-linear function is complex, it has been the general practice to wind an electrical impedance element on a form shaped in such a manner that the required function is produced; or the rotation of the shaft may be converted by mechanical means into a non-linear motion by means of cams, etc. In many cases a special card is required. All of these methods entail individual winding, calibration and tailoring, which are extremely time-consuming and expensive. On the other hand, there are available on the market linear and first-order variable impedances which can be duplicated in production quantities with very high accuracy, and it would be very advantageous to use impedances of this type to produce the required results.

It is, therefore, an object of the invention to provide a non-linear, variable impedance device constructed entirely of linear elements.

Another object of this invention is the provision of a short-circuited, linear potentiometer for producing nonlinear impedances.

Still another object of this invention is the provision of at least two short-circuited, linear potentiometers, each having a grounded tap and connected in parallel for producing non-linear, complex impedances.

Another object of this invention is to provide an impedance network comprising single or plural potentiometers composed of linear elements driven from a single shaft and capable of producing complex functions.

For a more complete understanding of the nature and objects of this invention, reference should be had to the following detailed description and to the accompanying drawing in which the single figure represents a preferred form of my invention.

Briefly stated, the invention comprises a first potentiometer connected in series with at least one short-circuited potentiometer, the movable tap of which is connected to ground. With this arrangement, and by proper selection of the values of the resistances in the network, each of which is linear, almost any complex curve can be duplicated.

Referring to the drawing, a first linear potentiometer 1, having variable resistance values of R and R above and below the movable tap 2, respectively, is connected at one end to a source of reference potential 3 and at the other end to a short-circuited dual potentiometer comprising first and second parallel branches, bothvshortcircuited by the line 4. Depending on the complexity of the curve to be duplicated, any number of branches may be used. For example, if the curve is basically a parabola, then only one branch is required. If the curve is more complex, two or more branches may be used. The

Patented Sept. 30, 1958 two branches shown are merely a convenient number for illustrating the invention.

The first branch comprises a potentiometer 5 having variable resistance values R and R above and below the tap 6, respectively, and a series-connected resistor 7 having a fixed resistance value R Similarly, the second branch comprises a potentiometer 8 having variable resistance values R and R on each side of the movable potentiometer tap 9, as indicated, and a series-connected resistor 10 having a fixed resistance value R While I have shown only one fixed resistor in each branch, it is to be understood that the resistors 7 and 10 may be variable. It is also to be understood that the resistors 7 and 10 may be positioned on the opposite side of the

resistors

5 and 8 to reverse the slope of the resultant curves and, also that additional fixed or variable resistors may be inserted in each branch.

The

taps

2, 6 and 9 are mechanically coupled to a shaft 11 from which all are simultaneously driven. The shaft 11 may be driven by a reference element in a servo system, or it may be the input to a computer or other type of system,not shown. The

taps

6 and 9 are both electrically connected to ground or other point of reference potential by means of a lead 12. The output is taken from the terminals 13 connected between the tap 2 and ground.

If we consider the dual potentiometer with the second branch disconnected, and with the resistor 7 having a resistance value R equal to zero, movement of the tap 6 along the resistor 5 will produce a resultant of two reciprocal linear curves, a solution which is a symmetrical parabola. By proper selection of elements 5 and 7 of the first branch, the resultant voltage at the tap 2 may have similar or vastly dissimilar slopes to the sides of the parabola. If an output is derived with identical elements in the first branch, that is, R +R =R the resultant will be a lambda function, and this may be used, for example, as an error voltage for the servo control of mechanical driven tuning cavities or lines.

By a proper selection of values for the potentiometer 1 and the elements in each branch, logarithmic or asymptotic functions may be obtained in both branches and, with all the branches connected and the

potentiometer taps

2, 6 and 9 arranged for movement in unison or in opposition, higher order effects may be obtained.

Where n number of branches are employed, the impedance R of the network between the terminals 13 will be represented as follows:

where Cu'i' RDn+ RE and, therefore:

not contain sharp breaks or steps, a practical solution of a complete potentiometer card problem can be resolved by plotting about ten points with approximately thirtydegree distribution. These points are derived quickly by simple calculations, using standard, commercial, close tolerance, ganged potentiometers connected as shown, and the desired functions can be produced as accurately as with the expensive, custom-wound and calibrated card. The solution of almost any curve can be accomplished quickly and accurately by manual or machine calculations.

It may now be seen that from a very simple arrangement of entirely linear elements, I am able to produce impedances which vary in accordance with very complex and high-order functions. It is clear that certain modifications and variations will be apparent to those skilled in the art, and it is my intention, therefore, that my invention be limited only by the prior art and the annexed claims.

What I claim is:

l. A variable impedance network comprising: at least first and second parallel connected impedance elements, each provided with a movable tap and the ends of each element being connected to a point of reference potenial; and means for simultaneously varying the position of said taps on said impedances at a linear rate, whereby the overall impedance of said network between said point and said taps will vary at a non-linear rate.

2. The invention as defined in claim 1, wherein said impedance elements are linear elements.

3. The invention as defined in claim 2, wherein said linear elements are resistors.

4. A variable impedance device comprising: at least first and second parallel connected impedance elements, each having a first movable tap and the ends of each element being connected to a point of reference potential; a third impedance element connected to said point; said third impedance element having a second movable tap; and means for simultaneously varying the position of all said movable taps on said elements at a linear rate, whereby the value of impedance between said first and second taps varies in accordance with a predetermined nonlinear function.

5. The invention as defined in claim 4, wherein each of said impedance elements is a linear resistance element.

6. A variable voltage device comprising a source of reference potential connected across a variable impedance network, said variable impedance network comprising: a first impedance having a movable tap and a second impedance having a movable tap, one end of said first impedance being connected to one side of said source, the other end of said first impedance being connected to both ends of said second impedance, the tap of said second impedance being connected to the other side of said source; and means for moving said taps on said impedances at a linear rate, whereby a non-linear output between said taps is produced.

7. The invention as defined in claim 6, wherein said impedances are linear.

8. A variable voltage device comprising: a first impedance branch having first and second series-connected resistors, said first resistor having a first movable tap; a second branch connected in parallel with said first branch and having third and fourth series-connected resistors, said third resistor having a second movable tap, both ends of said branches being connected to a fifth resistor having a third movable tap; a source of potential connected across said fifth resistor and the junction of said first and second taps; and means for simultaneously moving said taps at a linear rate, whereby the voltage between the junction of said first and second taps and said third tap will vary at a non-linear rate.

9. A variable impedance device comprising: 12 parallel connected branches, where n equals any whole number, both ends of each of said branches being connected to a point of reference potential; each of said branches comprising a resistor provided with a movable tap; means for electrically interconnecting each of said taps; and means for simultaneously varying the position of said taps on said resistors at a linear rate.

10. The invention as defined in claim 9 wherein a voltage source is connected between said point of reference potential and said taps, and wherein n equals 1.

11. A system for converting the linear rotation of a shaft into a non-linear voltage comprising: a first resistor having a first movable tap coupled to said shaft; a variable impcdance having at least a first branch, each branch comprising a second resistor having a second movable tap coupled to said shaft; means connecting both ends of said second resistor to one end of said first resistor; a source of potential connected between the other end of said first resistor and said second movable tap; and means for deriving a resultant voltage output from between said second movable tap and said first movable tap.

12. The invention as defined in claim 1], wherein each of said resistors is a linear element.

13. A variable impedance device comprising: 11 parallel connected branches, where n equals any whole number, both ends of each of said branches being connected to a point of reference potential; each of said branches comprising first and second series-connected resistors; each of said first resistors being provided with a movable tap; all of said movable taps being electrically interconnected; and means for simultaneously varying the position of each of said taps at a linear rate.

14. The invention as defined in claim 13, wherein said impedance is designed in accordance with the equation:

where R equals the total impedance measured between said point of reference potential and said movable taps; and R R and R are equal, respectively, to the impedance of each branch between said point of reference potential and said tap measured independently of all other branches.

15. The invention as defined in claim 13, where each of said resistors is a linear element.

16. The invention as defined in claim 12, and another resistor series-connected with said variable impedance device, said resistor having a movable output tap.

17. The invention as defined in claim 16, wherein said other resistor and said variable impedance device are designed in accordance with the following equation:

References Cited in the file of this patent UNITED STATES PATENTS Nielsen et al. Dec. 9, 1952 Brancato et al. Mar. 17, 1953