US3519931A

US3519931A - Scaling circuits for voltage dividers of the constant source impedance type

Info

Publication number: US3519931A
Application number: US546846A
Authority: US
Inventors: Frank R Bradley
Original assignee: Individual
Current assignee: Individual
Priority date: 1966-05-02
Filing date: 1966-05-02
Publication date: 1970-07-07
Anticipated expiration: 1987-07-07

Description

Juy 7, 1970 F. R. BRADLEY 3,519,93l

SCALING CIRCUITS FOR VOLTAGE DIVIDERS OF THE CONSTANT SOURCE IMPEDANCE TYPE med May 2. 196e 2 Sheets-Sheet 1 FIG.

INVENTOR FR'ANK R. BRADLEY ATTOR NEYS L e L T. 3 U E 3 N D July 7, F. R. BRADLEY SCALING CIRCUITS FOR VOLTAGE DIVIDERS OF THE CONSTANT SOURCE IMPEDANCE TYPE Filed May 2. 1966 2 Sheets-Sheet 2 FiG. 6

[30 NULL DET.

United States Patent O 3,519,931 SCALING CIRCUITS FOR VOLTAGE DIVIDERS OF THE CONSTANT SOURCE IMPEDANCE TYPE Frank R. Bradley, 9 Dash Place, Bronx, N.Y. 10463 Filed May 2, 1966, Ser. No. 546,846 Int. Cl. G01r 1 7/ 02 U.S. Cl. 324-98 16 Claims ABSTRACT OF THE DISCLOSURE Scaling circuits for voltage dividers of the constant source impedance type in which said circuits are formed 'by a plurality of resistors of substantially equal value which can be connected together in at least two permissible combinations in which each of said combinations each resistor has substantially the same amount of current owing therethrough.

This invention relates to scaling circuits for voltage dividers and more particularly to circuits for scaling the voltage output of voltage dividers of the constant source impedance type, and applications using such circuits with potentiometer devices.

There exists in the art a class of voltage dividers which are known as constant source impedance. These dividers have the properties of producing a linearly varying output voltage in accordance with the divider ratio setting Dividers of this type also have a constant source impedance, that is, the output impedance of the divider remains constant over the range of its voltage division ratios. Dividers of this type are discussed in greater detail in my copending applications Ser. Nos. 487,465 and 546,822 entitled: Impedance Measuring Bridge with Voltage Divider Providing Constant Source Impedance to Bridge, and Potentiometer Devices, and filed on Sept. 15, 1965, and May 2, 1966, respectively. My aforesaid copending application Ser. No. 487,465, filed Sept. 15, 1965, entitled Impedance Measuring Bridge with Voltage Divider Providing Constant Source Impedance to Bridge has now issued as Pat. No. 3,443,215 on May 6, 1969.

In the latter application, several embodiments of potentiometer devices using constant source impedance voltage dividers are disclosed. In these potentiometers, it is generally necessary and very useful to have the capability to scale the output voltage of the divider accurately, that is, to reduce or attenuate the divider output by a predetermined ratio or amount. This gives the potentiometer greater exibility for accurately measuring unknown voltages over a wider range by providing two or more full scale voltages.

In prior art potentiometers, scaling is accomplished either at the input to the voltage divider, that is between the source of main operating potential and the voltage divider, or by dividing down the divider output voltage with volt boxes. This latter technque has the advantage of drawing current through the divider. The former is complicated because the effective voltage source to the potentiometer includes the impedance of a dropping rheostat.

Constant source impedance dividers lend themselves particularly well to scaling. Because of the divider constant output impedance, circuits can be connected to the divider output to produce highly acurate scaling rather than at the divider input as in prior art devices. Volt box techniques continue to be applicable as before. Novel scaling circuits, not possibleV with prior art types of dividers, can be used with constant source dividers, these circuits being comparatively simple to construct ICC and being of the type which minimize the errors introduced by their components.

In accordance with the present invention scaling circuits are provided for voltage dividers of the constant source impedance type. Three s-uch circuits are described, the first of these :being the 'use of a set of n impedances, such as resistors, each of value R which are arranged in series and parallel combinations using the mean value resistor of the set as a reference standard for calibration of divider source resistance. The second circuit uses a set of resistors arranged in series and parallel combinations without the need for picking out the sets mean value resistor. The third circuit uses several sources of standard voltage connected in a predetermined manner to trim the divider source impedance to a desired match relative to a matched resistor set on a true voltage basis.

It is therefore an object of the present invention to provide scaling circuits for constant source impedance type voltage dividers.

A further object is to provide scaling circuits for constant source impedance voltage dividers used in potentiometer devices.

Another object is to provide scaling circuits for constant source impedance voltage dividers using sets of matched resistors.

An additional object of the present invention is to provide scaling circuits for conductance type voltage dividers using a set of matched resistors in combination with a predetermined number of sources of a standard reference voltage.

Other objects and advantages of the present invention will become more apparent upon reference to the following specification and annexed drawings in which:

FIG. 1 is a schematic diagram showing in generalized form the conductance type voltage divider utilized with the present invention;

FIG. 2 is a schematic diagram of one form of decimally coded constant source impedance divider;

FIG. 3 is a schematic diagram illustrating in general form a constant source impedance voltage divider used in a potentiometer;

.FIG. 4 is a schematic diagram of one type of scaling clrcuit;

FIG. 5 is a schematic diagram of a second type of scaling circuit;

FIG. 6 is a schematic diagram of another embodiment of scaling circuit; and

FIG. 7 is a schematic diagram of a potentiometer using the scaling circuits of the present invention.

FIG. 1 illustrates in general form the type of conductance (constant source impedance) voltage divider 5 used with the present invention` The divider is a three (four) terminal network and has a pair of

input terminals

1 and 2, the latter terminal 2 being common and serving as one of a pair of

output terminals

2 and 3. Divider 5 is constructed with one or more xed or variable impedances, such as resistors, therein which can be adjusted and/or interconnected by any suitable means (not shown in FIG. l) in a manner such that when the impedances of the divider are set by a switching arrangement to produce any particular voltage division ratio x between the input and output terminals, and a voltage e is applied to

input input terminals

1 and 2, the output voltage e0 across

output terminals

2 and 3 varies as a linear function of e given by:

Here, m is the slope of the straight line function and I: is the zero intercept on the abscissa of a cartesian coordinate (x-y) graph. Both m and x are determined by the components and connection of the divider. The intercept b is normally (but not necessarily) made equal to zero in potentiometer devices.

The divider 5 is also constructed so that the voltage e of Equation 1 has a xed source impedance r looking into

terminals

2 and 3 for any ratio setting x of the divider. The source impedance r of the divider is also determined by its design. Another way of describing the characteristics of the divider 5 is that when

input terminals

1 and 2 are shorted, the impedance measured between

output terminals

2 and 3 or

terminals

1 and 3 is constant and equal to r, independent of the ratio setting x. Many types of suitable dividers having these characteristics are currently in use including those commonly called conductance dividers.

FIG. 2 shows one type of constant source impedance divider constructed according to FIG. 1, and using a plurality of resistors for producing a decimally weighted output. The

divider input terminals

1 and 2 are connected across a source of input voltage ein. A separate, singlepole, double-throw switch 40 is provided for each resistor and the upper contact of each switch is connected to divider input terminal 1 while the lower contact is connected to input terminal 2. The center arm of each switch has a resistor connected thereto and one end of each of these resistors is connected to common summing point terminal 3. Depending upon the setting of its respective switch 40, an impedance is either connected in series between

terminals

1 and 2 or across

terminals

2 and 3 of the divider. It is understood that these switches may be multiply controlled by decade or other switching means such as a rotary switch type, for example, which connects any number of the resistors in the decade to either

terminal

1 or 2. Each decade of the divider preferably has its own switch. One switch 45 is shown in FIG. 2 symbolically for all of the switches operating adjacent a scale 46 which can be linearly calibrated in accordance with Equation 1. Preferably, each of the switches 40 is of the conventional break-before-make type so that one connection is broken when a resistor is being switched to avoid shorting out the power supply. In all of the embodiments of the invention described below, the controls, scale, and break-before-make switches are preferably used, although not specifically described. It also should be understood that while x, the division ratio of the divider, varies between zero and one, that the scale 46 can be calibrated differently, for example, a scale of from 0 to 1.1 to produce an x of from zero to one.

The divider of FIG. 2 illustratively is to produce one hundred and ten steps of one unit each. To do this, two decades 12-1 and 12-2 are used. The rst decade 12-1 includes 10 divider resistors of value R, designated R(1) through R( 10), one end of each of which is connected to the movable contact arm of a respective switch 40. The second decade 12-2 has ten resistors each of value 10R, designated 10R(1) through 10R(10), one end of each of which is also connected to a respective switch 40. The ratio of e0 to ein of the divider of FIG. 2 is:

were 0 SnlOO and n is the number of switch weightings for those switches 40 returned to the high side (up-position) terminal 1 of the divider. The weighting is shown adjacent each switch 40. It should be clear that each resistor of value R contributes a Weighting of l0 parts (.1) of the 110 .available while each resistor of value 10R contributes 1 part (.01). By selectively operating switches 40 the value of e0 can be selected in steps of ein/110. For example, where e0 is to be 87/110 of em, resistors R(1) through 11(8) and 10R(1) through 10R(7) each has its respective switch 40 connected to the high side terminal 1.

The number of output voltage steps available from a divider of the type shown in FIG. 2 can be increased by adding other decades of proportionately higher value re `s istors, or by adding other decades of the same or lower value resistors and introducing scaling resistors in the line to the summing point 3. The latter technique is conventional in the art. It should be understood that decimal, binary coded, or any type of coded inputs can be used.

FIG. 3 illustrates in generalized form a constant source impedance divider used in a potentiometer circuit. Here the value 1.1r/x of equivalent resistor 24 corresponds to the fractional portion of the divider switch Weightings which are up, while the value of equivalent resistor 25 corresponds to the fractional portion of the divider switch weightings which are down. Here again, x is the input division ratio setting of the divider While r is the constant value source impedance. This divider has its scale 46 (not shown) calibrated in a 0 to 1.1 range.

The voltage output of divider 5 is applied to one input of a null detector 30 whose other input is selectively applied by a switch 32 from a source of reference voltage of value es, such as a standard cell 33 for calibration, or from a source of voltage 34 of unknown value eX for measurement.

A Calibrating potentiometer 27 is connected across

divider output terminals

2 and 3. By setting switch 32 to apply eS to the null detector, and with divider 5 set to the exact value of e,s (a setting between 1.017 and 1.019), the slider of resistor 27 is adjusted to tap off a voltage to produce zero reading of null detector 30. An accurate measurement can then be made of ex, referenced to es, by applying eX to the detector and adjusting the division ratio of divider 5 to again produce a null. All of the foregoing action, nad other forms of potentiometers, are described in detail in the latter of my aforesaid application.

As should be apparent in FIG. 3, it would be desirable to be able to scale the voltage at terminal 3 `for accurately measuring ex over a greater range of voltages. In prior art potentiometers, additional dividers or volt boxes are used to scale the input voltage to the divider, or resistors are placed in series with the divider (constant input impedance). While these techniques can 4be used with potentiometers constructed with constant source impedance dividers, such as described in my aforesaid patent application, they do not take advantage of the constant source impedance r of the divider which enables scaling of superior accuracy to be achieved.

Considering one scaling circuit in accordance with the present invention, it is known that a matched set of n resistors of average value R, where n has factors a1, a2 ak, can be connected in a total of k series, parallel and series-parallel combinations to synthesize resistance values ranging from R/n (all resistors in parallel) to Rn (all resistors in series) Where the individual values of the combinations thus synthesized are correct relative to each other within an error which is less than the sum of the squares of the deviation of individual resistors from the arithmetic mean Value resistor RM. This error compensation and relative value prevails as long as theoretically equal current ows through each of the n resistors of the set and as long as leakage and dilferential lead resistance eifects are negligible. In the embodiments of scaling circuits described below, such a connection of the resistors in a set to satisfy these requirements is called a permissible combination. The error theory for the resistor sets is described in the National Bureau of Standards Circular 470 entitled Precision Resistors and Their Measure- `ment, issued Oct. 8, 1948, by the United States Government Printing Olce.

FIG. 4 shows a constant source impedance voltage divider 5 represented in schematic form =by the

equivalent resistors

24 and 25. An adjustable trimmer resistor 61 of value s is connected to the divider output terminal 3 in series with the source impedance r. An equivalent resistor 54 of value RT, which corresponds to the value of a set of n matched resistors arranged in apermissible combination, is connected between terminal 2 output of the divider 5 and the right-hand end of trimmer resistor 61.

In any set of matched resistors, the values of the individual resistors are not exactly the same. To accurately produce the scaling ratios in accordance with the circuit of FIG. 4 it is necessary to select the arithmetic mean value resistor RM of the set. This is done by measuring each resistor of the set or by choosing an appropriate permissible combination if one exists. For example, in a set of lz resistors where n is a perfect square, there exists a series-parallel combination whose resistance value is the mean value of the set.

The arithmetic mean value resistor RM is used to set the trimming resistor 61 to produce a known value resistance in series with the source resistance r so that s-|-r=RM. Techniques for intercomparing two equal resistors are well known.

Terminals

1 and 2 of divider 5 are shorted together during this adjustment. This provides an accurate voltage scaling circuit to produce a desired E across equivalentresistor 54.

Referring again to FIG. 4, the composite resistor 54 of value RT forms a voltage divider with the source impedance r and the trimmer resistor s whose combined total value is accurately known as RM. Thus, the output voltage E0 across composite resistor 54 is given as the output voltage of divider times To illustrate how the scaling is accomplished for the circuit of FIG. 4, consider a set of ten resistors each of value R, where R=RM, forming the composite perimissible value resistor RT. Within the conditions imposed by a permissible combination, the ten resistors can be arranged in the following four ways: (l) all in series; (2) all in parallel; (3) two chains of ve resistors in series, the two chains connected in parallel; and (4) ve pairs of parallel connected chains each of two resistors connected in series.

With a divider output voltage E appearing across

terminals

2 and 3 with the divider at a full scale setting, so that E equals the voltage of source for the four possible connections of the ten resistors set forth above, the following table can be constructed for values of RT and E0, where E0 is the voltage across RT:

Eo as fraction of Using the ten resistor set as an illustration consider that the voltage E of source 10 is exactly l1 volts and that the conductance divider 5 whose calibration is such that 0 l, is set to a full scale so that ll volts is produced at output terminal 3 when the divider is not loaded. When the auxiliary resistance S4(RT) is set to load divider 5 with either ten resistors in shunt or ten resistors in series the resultant output, which are then potentiometer full scales, will be either one volt or ten volts.

It should be understood that other sets of matched resistors with fewer or more resistors in the set and with resistance values higher or lower than R can be assembled to produce permissible combinations capable of achieving any desired scaling (attenuation) ratio.

FIG. 5 illustrates another embodiment of scaling circuit in which it is not necessary to select the mean resistor of a set. Here, consider a set of k closely matched resistors, 51-1, 51-2 51-k, whose total value Rser when connected in series is slightly in excess of r, the

source impedance of divider 5. Seven resistors 51 are illustratively shown in FIG. 5 and the conductance divider illustratively has a 1.1 full scale setting. An adjustable trimmer resistor 61 of value s is used and it is adjusted so that the value of r-l-s is equal to the value Rser of the series connection of the k resistors. The resistors 51 can be connected either in series or in parallel across

terminals

2 and 3 by a ganged switch 52 having sections 52-0 through 52-7, with section 52-0 being normally closed.

In FIG. 5, assuming a voltage e for source 10 and switch 52 connecting resistors 51 in series, the output voltage for the series connection is given as:

R ex Eo :ex=

se' Rss-M+S 2 where x is the division ratio of divider S, r is the divider source impedance and s is the resistance of trimmer '|S2Rser With switch 52 connecting the k resistors of the set in shunt across

terminals

2 and 3, the value of Rsh is SSH/k2 and with resistor 61 set so that r-f-szRsh, the divider output voltage for the shunt connection is given as:

Reer k2 Rael' T+S E051): :te

Since r+s=Rser, Eosh is rewritten as:

ex Eoserand Bosh is -1 xe= 1/50xe 1-1-49 Of course, a different number (k) of resistors can be used in the permissible combination to produce different scaling ratios.

FIG. 6 shows still another embodiment of the invention using a matched set of resistors arranged in a permissible combination together with a group of voltage sources with precisely known output voltages, such as a. number of standard cells. For example, consider a set of eight matched resistors, each of value R. These can be arranged in the following permissible combinations to produce RT equal to: (1) R/ 8-all resistors in parallel; (2) R/Z-two sets of four resistors connected in parallel with the two sets being in series; (3) ZR-four sets of two resistors connected in parallel with the four sets connected in series; and (4) SR-all eight resistors connected in series. The switching for producing RT is not shown in detail but it is conventional in the art.

The divider of FIG. 6 illustratively has a full scale setting of 1.1 and a source impedance r. A trimmer resistor 61 of value s is in series with divider output terminal 3 and RT. Trimmer 61 is adjusted so that r|-s=R. In the above four cases with the divider at full scale,

the output voltage E across RT in response to the voltage E across

terminals

2 and 3 is Value of RT: E0 at full scale (1) R/8 1/9E (2) R/2 3/9E (3) 2R 6/9E (4) SR 8/9E When, for example, 1/9E across RT is 1.1 volt with a divider full scale of 1.1, a standard cell 20-1 can be measured on this range in the detector by setting the divider to the standard cell voltage and adjusting the slider of a potentiometer 127 to produce a detector null by tapping off the correct amount of voltage. In this case RT is R/ 8. Adding two more standard cells 20-2 and 20-3 in series with the first, by a switch 23 and changing RT to R/Z, makes 3/9E, or 3.3 volts possible across RT at divider full scale. The remaining full scale values produced by RT equal to 2R and SR are 6.6 and 8.8 volts respectively with great precision.

Any difference between the null detector output with one or three standard cells in the circuit, can be compensated for by adjusting the trimming potentiometer 61 to slightly change the source resistance of the divider. Rheostat 61 is adjusted for detector null at the precise theoretical divider setting established by intercomparison of the three standard cells. Assuming a matched set of cells this will be close to the same divider setting as that for measuring one cell and error will result only from local linearity errors in least signicant section of divider. Note that adjustment of 61 interacts with 127, but not vice versa, hence several passes may be necessary. Rheostat 61 is adjusted until the intercomparison of the three standard cells is accomplished with the desired accuracy.

Another possible scaling scheme using the circuit of FIG. 6 is to make the divider source impedance equal to 4R. Using the eight resistor matched set, the following output voltages are produced across RT:

Value of RT: E0 (i) R/s 1/33E (2) R/2 1/9E (3) 2R 1/3E (4) SR 2/3E Here, if the 1/3E output is scaled to 1.1 volts for measuring one standard cell, the 2/3E ouput can be used to intercompare two matched standard cells connected in series while the divider source impedance 4R is adjusted |'by trimmer 61. Now, the 1/33E full scale voltage is 1/11 volts and the 1/9E is .366666 volts.

FIG. 7 shows a potentiometer device using the constant source impedance divider and either of the scaling embodiments of FIGS. 4 or 5. Here, potentiometer 127 has its ends connected across divider output terminals 2 fand 3 and its slider connected to one input of the null detector 30 whose other input is either es or ex. The scaling circuit is shown illustratively as ten resistors 51-1 through 51-10 which can be connected either all in series or all in parallel by the switches 52-0 through 52-10 as in FIG. 6.

The set of resistors arranged in any permissible combination will see the impedance looking back into the divider 5, where r is the divider source empedance, p is the lixed resistance between the end yterminals of potentiometer 127 and, s the lresistance of trimmer 61.

When scaling is accomplished as in the embodiment of FIG. 4, each resistor 51 has a value R and trimmer 61 is adjusted and p selected so that the value of Equation 2 is equal to RM. Where scaling is accomplished as in FIG. 5, the value of all ten resistors connected in series Rser is slightly greater than r and trimmer 61 is adjusted and p selected so that the value of Equation 2 is equal to Rser. The scaling ratios described before hold for both cases. The switching to achieve other permissible combinations with the ten resistors. is not shown.

While preferred embodiments of the invention have been described above, it will be understood that these are illustrative only, and the invention is limited solely by the appended claims.

What is claimed is:

1. The combination comprising a variable voltage divider for operation from a source of voltage, said voltage divider having input terminals for connection to said source of voltage, output terminals, and a plurality of impedance means, said voltage divider including switching means connected to said impedance means for linearly varying the voltage division ratio of the divider by changing the connected relationships of the impedance means of said divider to produce a correspondingly varying output voltage at the divider output terminals and a substantially constant output impedance of a known value at said output terminals irrespective of the connected relationships of the divider impedance means, and scaling circuit means having a pair of input terminals connected to the output terminals of said voltage divider to receive the voltage divider output voltage thereon and to further modify the divider output voltage, said scaling circuit means including a set of resistor means with each resistor means of the set being of substantially equal value, and means for selectively connecting selected resistor means of the set in at least ytwo diiferent permissible combinations each of which permissible combinations produces substantially equal current tlow through each of the resistor means connected in a respective one of said permissible combinations.

2. The combination of claim 1 further comprising switching means connected to said set of resistor means for selecting diiferent permissible combinations of the resistor means in the set.

3. The combination of claim 1 wherein the voltage divider impedance means are resistors and further comprising first resistance means connected to an ou-tput terminal of said voltage divider and to an input terminal of said scaling circuit means and having a value such that the sum of the resistance of the iirst resistance means and the known value output resistance of the voltage divider is equal substantially to the resistance value of the arithmetic mean value resistor of the set of resistors of said scaling circuit means.

4. The combination of claim 1 wherein the voltage divider impedance means are resistors and further comprising first resistance means connected to an output terminal of said divider and to an input terminal of said scaling circuit means and having a value such that the sum of the resistance of the first resistance means and the known value output resistance of the voltage divider is equal substantially to the resistance value of the resistors in the set of resistors of said scaling circuit means connected in a permissible combination.

5. The combination of claim 1 wherein the voltage divider impedance means are resistors and further comprising iirst resistance means connected to an output terminal of said divider and to an input terminal of said scaling circuit means and having a value such that the sum of the resistance of the first resistance means and the .-lcnown value output resistance of the voltage divider is equal substantially to the resistance value of one of the resistors in the set of resistors of said scaling circuit means.

6. The combination of claim 1 in a potentiometer device Vfor accurately measuring a voltage of an unknown value further comprising null detector means, means applying the output voltage of the voltage divider which has been scaled by the scaling circuit means to one input of said null detector means, a standard reference voltage source and a source of unknown voltage, means for selectively connecting said standard reference voltage source and said source of unknown voltage to another input of said null detector, and means for interconnecting said resistor means of the set of said scaling circuit means in a said permissible combination to select the voltage division ratio of the scaling circuit to determine the voltage applied to said one input of said null detector.

7. The combination of claim 6 wherein the voltage divider impedance means are resistors and further comprising yfirst resistance means connected to an output terminal of said voltage divider and to an input terminal of said scaling circuit means and having a value such that the sum of the resistance of the first resistance means and the known value output resistance of the voltage divider is equal substantially to the resistance value of the arithmetic mean value resistor of the set of resistors of said scaling circuit means.

8. The combination of claim 6 wherein the voltage divider impedance means are resistors and further comprising first resistance means connected to an output terminal of said voltage divider and to an input terminal of said scaling circuit means and having a value such that the sum of the resistance of the rst resistance means and the known value output resistance of the voltage `divider is equal substantially to the resistance value of the resistors in the set of resistors of the scaling circuit means connected in a permissible combination.

9. The combination of claim 6 wherein the voltage divider impedance means are resistors and further comprising first resistance means connected to an output terminal of said divider and to an input terminal of said scaling circuit means and having a value such that the sum of the resistance of the first resistance means and the known value output resistance of the voltage divider is equal substantially to the resistance value of one of the resistors in the set of resistors of said scaling circuit means.

10. The combination of claim 6 further comprising a plurality of standard reference voltage sources, and means for selectively connecting any number of said plurality of sources in series to produce a voltage in a range corresponding to the voltage output of the voltage divider as modified by said means at the different voltage `division ratio settings of said voltage divider.

11. The combination of claim 1 wherein the voltage divider impedance means are resistors and the output resistance of the voltage divider is equal to a multiple of the resistance value of one of the resistors of the set.

12. The combination of claim 4 wherein said last named permissible combination comprises the resistors of the set all being connected in series.

13. The combination of claim 4 wherein said last named permissible combination comprises the resistors of the set all being connected in parallel.

14. The combination of claim 1 further comprising a potentiometer having its ends connected across the output terminals of said voltage divider, first resistance means, and means connecting the iirst resistance means in series between an output terminal of said voltage divider and an input terminal of said scaling circuit means and the series combination of said first resistance means and said scaling circuit means in parallel across said potentiometer, the output yvoltage of the volt-age divider which has been scaled by said scaling circuit means appearing at the slider of said potentiometer.

15. The combination of claim 14 wherein the resistance value of the network formed by the output resistance of the divider (r), the resistance across said potentiometer (p), and the resistance of said first resistance means (p), given by References Cited UNITED STATES PATENTS 2,784,369 3/1957 Fenemore et al.

2,803,799 8/1957 Siegel et al. 324-98 XR 2,894,197 7/1959 Berry.

3,305,769 2/1967 Julie 323-74 3,319,162 5/1967 Sattinger et al 324-57 3,320,526 5/1967 Julie 324-57 3,377,555 4/1968 Lewis 324-63 FOREIGN PATENTS 863,591 3/1961 Great Britain.

GERARD R. STRECKER, Primary Examiner U.S. C1. X.R. 323-; 324-63