US2423463A

US2423463A - Resistance network

Info

Publication number: US2423463A
Application number: US470413A
Authority: US
Inventors: James R Moore
Original assignee: Individual
Current assignee: Individual
Priority date: 1942-12-28
Filing date: 1942-12-28
Publication date: 1947-07-08
Anticipated expiration: 1964-07-08

Description

July 8, 1947.

J. R. MOORE 2,423,463

RESISTANCE NETWORK Filed Dec. 28, 1942 'vvvv s JAMES R.MOORE Patented July 8, 1947 RESISTANCE NETWORK James R. Moore, Rumson, N. J., assignor to the United States of America, as represented by the Secretary of War Application December 28, 1942, Serial No. 470,413

(Granted under the act of March 3, 1883, as

6 Claims.

The invention described herein may be manufactured and used by or for the Government for governmental purposes, without the payment to me of any royalty thereon.

My present invention has to do with resistance networks. More particularly, it relates to a device for adjusting electrical resistance whereby a voltage is varied in accordance with a predetermined non-linear mathematical curve.

It is the main object of my present invention to provid a device of the general character indicated wherein a variation of resistance and, therefore, a variation in voltage is made substantially smooth and continuous to closely approximate the exponential charging rate of a capacitance.

While not limited thereto, my present invention is admirably adapted to controlling the operation of a range-determining device.

In the accompanying specification I describe and in the annexed drawing I show an illustrative embodiment of the resistance network of the present invention.

In said drawing, the single figure is a schematic diagram of a resistance network assembled in accordance with .the principles of the present invention. I

Referring now more in detail to the present invention, with particular reference to the drawing illustrating a preferred embodiment thereof, the reference character R generally designates a group of series-connected resistors R1, R2, R3, R4, Rn. Associated with said resistors are contacts Re, Re, Rb, Re, Rd, Rim, and selectively engageable with said contacts is an adjustable arm 0.

The resistor R1 is connected to one terminal of a source of voltage E and the arm is connected, through a fixed high resistance Rs, to the other terminal of said source of voltage.

The value of each resistor R1, R2, R3, R4, Rn is such that the voltage drop across the total resistance of the combination of resistors respectively corresponding to each of the contacts Re, Re, Rb, Re, Rd, Rm, is an exponential function of the number of resistors in each such combinatlon.

Adjacent the group R of resistors, I provide a second group R" of series-connected resistors R'1, R2, R's, R'4, Rn and associated contacts R'o, R's, R's, R'c, R'd, R'm. The resistor R1 is connected to a second adjustable arm P selectively engageable with the contacts Ra, Ra, Rb, Re, Ed. Rm; and selectively engageable with any of the contacts R'o, R's, R'b, R'c, R's,

amended April 30, 1928; 370 O. G. 757) R'm is a third adjustable arm Q, the opposite end of which is connected with the adjustable arm 0. The value of each resistor R1, Rz, R'a, R4, R'n is such that the equivalent resistance and, therefore, the voltage drop across the parallel combination of selected resistors R'l, R'z, R's, R4, R'n and any selected resistor of the group R is an approximately linear function of the number of resistors of the group R. entering into the combination.

The output voltage of the network, designated in the drawing as E0, is between the contact R0 and the meeting point of the adjustable arms 0 and Q.

I shall now describe a specific procedure for determining the values of the various resistors above referred to.

The potential across a resistance-capacitance combination builds up in accordance with the formula:

where A and B are constants depending upon any selected resistance and capacitance for the circuit under consideration and T is time measured from the instant of application of the potential E.

Now the group R of resistors 15 divided into n sections such that 2 v AE(1 K E for integral values of it up to and including n; and V is the output voltage across a selected number of resistors of the group R, excluding the effect of the parallel group R, and k is said selected number of resistors.

From Ohms law,

and V =IS Where Sr is the value of the selected number of Solving for Sir, We find 3 The value of each resistor R1, R2, R3, R4, can be determined from the formula:

(7) R,, =S S,,- Substituting therein for Sr and sir-1, we have ree e ce and substituting still further, for

Fe m Fu and simplifying, we have Hts- )"Htse where k takes on values from to Thus, having selected values for A, B, and R for the group R, comprising 11 sections of resistors, we can immediately determine from Equation 9 the value of each of said resistors.

The procedure for calculating the values of the resistors R1, Rz, R's, R's, Rn, of the group R is as follows:

The group R consists of n sections, not necessarily the same number as included in the group R, having values such that the equivalent resistance across the parallel combination of RR and S'h is given as wher Sh is the total value of the first h resistors of the n res i stors of the group R, It varies from 0 to n and R. is the average value of the abovedefined Rr. Therefore, by applying the law of parallel circuits, we have Solving for Sn we obtain The value of each resistor Ri, R2, R's, Ri, Rn can be determined from the formula:

Eliminating I, we obtain as a final expression of the voltage output of the entire network,

( 0 (R( k l r) I shall now describe the mode of operation of the resistance network of the present invention. I will assume, as shown in the drawing, that the arms 0 and P respectively engage the contacts Re and Rb, the arm Q engages the contact It's and that it is desired to decrease the output voltage E0. First, the arm Q is moved through R'c toward R'o. The result is a progressive decrease in said output voltage. Assuming that the arm Q has reached the contact Ro and it is desired to further reduce the output, the arms 0 and P are moved toward the contact R0 in such a manner that the arm 0 is engaged with the contact Rb before the arm P is disengaged therefrom. This movement is continued until th arm P is disengaged. At this time the arm Q is moved so as to engage the contact Rm and the arm P is moved into engagement with the contact Ra. During all of these movements the arm 0 remains engaged with the contact Rb and no change occurs in the output voltage E0. Now the arm Q can be moved toward R'o as previously described in order to decrease the output voltage E0. The entire procedure outlined can be continued until the desired reduction in the output has been attained.

To increase the output voltage E0 all of the foregoing movements are reversed.

This completes the description of the present invention and it will be noted that I have provided a simple resistance network whereby a voltage drop can be varied substantially smoothly and continuously so as to closely approximate a nonlinear mathematical curve, such as the exponential curve of a charging capacitance.

Other objects and advantages of the present invention will readily occur to those skilled in the art to which the same relates.

I claim:

1. In a resistance network, a first group of resistors each having a value such that the total resistance of selected combinations thereof is a given non-linear function of the number of resistors comprising each such combination, and a second group of resistors each havin a value such that the equivalent resistance of a parallel combination of selected resistors of said second group and any selected resistor of said first group i an approximately linear function of the number of resistors of said second group entering into said parallel combination.

2. In a resistance network, a first group of resistors each having a value such that the total resistance of selected combinations thereof is an exponential function of the number of resistors comprising each such combination, and a second group of resistors each having a value such that the equivalent resistance of a parallel combination of selected resistors of said second group and any selected resistor of said first group is an approximately linear function of the number of resistors of said second group entering into said parallel combination.

3. In a resistance network, a first group of resistors each having a value such that the total resistance of selected combinations thereof is a given non-linear function of the number of resistors comprising each such combination, and a second group of resistors connected in series each of whose value is given by the expression Where E is the average value of the resistors of said first group, n is the number of resistor in saidsecond group, and h is the number of the resistor of said second group whose value is being determined.

4.111 a resistance network, a first group of resistors each having a value such that the total resistance of selected combinations thereof is an exponential function of the number of resistors comprising each such combination, and a second group of resistors connected in series each of whose value is given by the expression Rn (n-h)(nh+1) where R is the average value of the resistors of said first group, n is the number of resistors in said second group, and h is the number of the resistor of said second group whose value is being determined.

5. In a resistance network, a first group of series-connected resistors each of whose value is given by the expression where A, B, and Rs are constants of the network, 11 is the number of resistors in said first group, and k is the number of the resistor whose value is being determined, and a second group of resistors connected in series each of whose value is given by the expression Rn (n-h) (nh+1) where R is the average value of the resistors of said first group, n is the number of resistors in said second group, and h is the number of the resistor of said second being determined.

group whose value is 1,479,051

6 6. In a resistance network, a first group of series-connected resistors each of whose value is given by the expression k-l 1e where A, B, and Rs are constants of the network. n is the number of resistors in said first group, and la is the number of the resistor whose value is being determined, a second group of resistors connected in series each of whose value is given by the expression REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date Best Jan. 1, 1924 1,948,675 Rhodes Feb. 27, 1934