US2441387A

US2441387A - Electronic squaring circuit

Info

Publication number: US2441387A
Application number: US561021A
Authority: US
Inventors: France B Berger; William A Higinbotham
Original assignee: US SEC WAR
Current assignee: United States, WAR, Secretary of; US SEC WAR
Priority date: 1944-10-30
Filing date: 1944-10-30
Publication date: 1948-05-11
Anticipated expiration: 1965-05-11

Description

May 11, 1M8. F, BERGER E rm. 2,441,387

" smc'momc squmms cmcun' Filed Oct. 30,1944

PLATE CURRENT GRID VOLTAGE FIG.3. r.

TO CONDENSER 7|, AND mom: 13,

FIG.3.

INVENTOR.

v FRANCE 8. BERGER .BY WILLIAM A. HIGINBOTHAM Patented May 11, 1948 ELECTRONIC SQUARING CIRCUIT France B. Berger, Watertown, Mass, and William A. Higinbotham, Santa Fe., N. Mex., assignors, by mesne assignments, to the United States of America as represented by the Secretary of War.

Application October 30, 1944, Serial No. 561,021

3 Claims. (Cl. 25027) This invention relates to electrical means for producing an output voltage or current which is a given function of an input voltage or current,

and it relates more particularly to electrical Another object of the present invention is to have the output of this circuit respond practically simultaneously with any changes in the input, which is of particular value in connection with sweep circuits of cathode ray tubes.

Still anotherobject of the present invention is to provide a simple, yet highly accurate and reliable, circuit to achieve the above-mentioned objects. I

The above and other objects in view will appear more fully from the following detailed description, accompanying drawings and appended claims. r

Referring now to the drawing wherein:

Fig. 1 is a simplified diagram of one specific embodiment of the present invention;

Fig, 2 is a graph showing variation of plate current (i vs. grid voltage (e for each of the tubes shown in the diagram of Fig. 1, with the sum of the plate currents being represented by the dashed curve;

Fig. 3 represents a schematic diagram of an illustrative embodiment of the present invention for which Fig. l is the simplified Version thereof; and

Fig. 4 is a schematic diagram illustrating modified connections of Fig. 3.

It is to be understood that the circuit represented generally by Fig, 1 and more specifically by Fig. 3 may be referred to as a "squaring circuit.

Referring now to Fig. 1, the input signal to the 2 squaring circuit is'applied between terminal 5 and grounded terminal 6. The input may then be fed through biasing means 1 to control grid 8 of vacuum tube 9. At the same time, the input may be fed through a phase inverter In, the output being a voltage substantially the same as that applied to control grid 8 of vacuum tube 9 but being out of phase therewith. This voltage may then be fed through biasing means II to control grid l2 of vacuum tube l3. Voltages appearing on control grid 8 of vacuum tube 9 and control grid l2 of vacuum tube l3 are then substantially equal but of opposite polarity. Cathode'l5 of vacuum tube 9 and cathode [6 of vacuum tube l3 may be connected to ground, and anode ll of vacuum tube 9 and anode [8 of vacuum tube l3 may be connected together and thence through a common load impedance 2!! to a source of 3+ potential 2!. The cathodes and anodes of tubes 9 and I3 are thus connected in a common cathode-anode circuit. I

The general expression for plate current in a vacuum tube may be expressed as where a: is the voltage applied to the control grid, where a, b, c and d depend upon the particular characteristics of the vacuum tube. If the tubes are operated entirely within the negative grid voltage region, fourth and higher powers of this series may be neglected. The general expression for plate current in vacuum tube I3 may be expressed as aba:+cx d:r the change in sign of a: being due tothe fact that the voltage appearing at control grid l2 of vacuum tube 13 although similar to that applied to control grid 8 of vacuum tube 9, is of opposite polarity.

' The-plate currents for vacuum tube 9 and vacuum tube 13 will flow through common load impedance 20. By addition of the two expressions for plate current, and neglecting terms above the third power, it will be seen that the odd power terms cancel out, leaving the resultant expression 2a+2cx 2a being a constant which can be eliminated by suitable level-setting action and 20 being a proportionality factor which can be altered, if desired, by suitable amplification or attenunation. Since the voltage output in question is that produced by the flow of the plate currents of vacuum tubes 9 and I3 through load impedance 2B, the voltage output will vary as the term x thus providing the squaring feature of the present invention.

A graphical representation of the plate currents for vacuum tubes 9 and I3 is given in Fig, 2. The curve 7:13 may represent the mutual characteristic curve of vacuum tube 9, and is plotted in the normal sense where the origin of the curve is at the lower right-hand corner and, the plate current i increases with an increase of grid voltage re to the, right. The curve 21 similarly may represent; the plate current of? vacuum tube i3, and is drawn to the same ordinate scale as curve ip but with the abscissa in the opposite direction, that is to say plate current i increases as grid voltage e increases to the left,.the,0ri1- gin of this curve being at the. lower left-hand corner. The dashed curve shown. in Fig..2,.obtained by adding the ordinatesof? i and. ip and thus representing the resultant: plate current through load impedance 20, is very nearly that of a parabola; or in other words, varies as a squared function.

The characteristic curves shown in Fig. 2; are

merely representative of plate current vs. grid voltage curves, andmay, typify the operation of varioustypes of vacuum tubes... For ease of description, certain Voltageswhi'ch may. be realized in. actual operation. have been. indicated. directly on these curves. These/arev not. to. be construed as required voltages to. be applied to. the circuit, but merely represent valuesthat have been .found suitable in one illustrative embodiment. of the present invention (Fig. 3.). wherein 638 type vacuum' tubes are used. in. place, of; vacuum. tubes; 9 and: l3-of- Fig. l. The.-6B8. type tube was found to have particularly suitable characteristics for the purposes of. the present. invention, due. in large measure: to. the. high, second harmonic. dis.- tortion. produced by. tubes oh that type- CIther tubes having similar. characteristics. might-also beusedifor this purpose.

Referring nowto Fig-2,- it will. be. noted that the characteristic curves of plate current. vs. grid voltageintersect at pointZZ, whiohis hereinafter referred to as; the. crossover point This point will generally, because. of the symmetry of the figure, intersect the. rid voltage axis half. way between the origins of the two graphs. The crossover point repr-esents the value of grid voltage at which the resulting plate current flowing through load, impedance 2!! of Fig. 1 willbe at its. minimum. This therefore may represent the point at. which thesi'gnal input at terminal 5-of Fig. 1 is zero. If" then the signal applied to terminal 5' is, increased in;a.positive-direction; the plate current. ip of vacuum tube '9 will-increase, and at the same time, platecurrent zp of vacuum tubeltlwill. decrease. If, however, the. signal-applied-to terminal 5 is,.increased in' a negative direction, the plate currenti of" vacuum tube: l3 will: increase and at. thesame. time. plate current ip' or vacuum. tube. 9. will. decrease. As previously mentioned, the opposite acti'ons of vac.- uumtubes. El and. i3 are due to. the fact thatthe signals appearing; on. the control. grids of. these tubes: are. of opposite. polarity/ The resultant current flowing through: load impedance 2b. of Fig,- 1 is thB'SumOfip and i11 and isrepresented by the; dotted: curve of- Fig. 2 which; issubstantiallyparabolic in form.

Anychange inthe input signalionz terminal 5; from Y the. value I corresponding to the crossover point; will'prcduce a changeinthe voltage across load impedance: 20 proportionalatothe-square of 4 the change in the input signal. Thus the input signal applied to terminal 5 may be either negative-going or positive-going. It is preferable for the input signal to begin at a value corresponding to the crossover point, said point coinciding with minimum current flow through load impedance 2b and hence maximum voltage output.

Referring now to the embodiment shown in Fig. 3, vacuum tubes 3c and fil thereof correspond to vacuum tubes 9 and H of the simplified versionshown in Fig. 1.. The. particular tubes 39 and 3| may be pentodes offthe 638 type, it being understood, of course, that other tubes having similar characteristics may be used. Vacuum tube 32 acts as an amplifier and phase inverter. Vacuum tube also acts as an amplifier wherein the signalinput isapplied to cathode M, the outputat. anode 58 being of the same phase as the input. to. cathode 4|.

Tubes

32 and 33 to gether provide essentially the phase-inverting action required of the inverter l0 shown in Fig. l. The type of tubes which may be used here is not particularly critical, but may be of the medium-mu-yarietv'such as a 6SN'7, or of the high mu variety, such as the 6SL7. Inasmuch as these particular. tube. types. have. two triode elements in a-singl'e. envelope, theyare particularly suitableforuse inthepresent invention.

Whenthesignalinput is appliedto t'ermi'nalS' I a voltagawhich is developedacross grid leak.resister 35' connected to ground, is applied to con.- trol grid 36. of vacuumtube 32. One voltage output isdeveloped'across anode. load resistor. 5 l and is applied directly to. controllgrid 38" of vacuum tube 39, and a second outputis. developed'across variable: cathode load resistorv 41 and is. applied directly'to cathode 4-1 ofivacuum. tube 331. Variable cathode resistor 4Z.has one-sideconnectedlto cathodes All and 41 ofvacuumitubesfll-and, 33', and. the. other sideconnected to'a negative. voltage: bias source. 43,. the positive. side.v of the latter being connectedz to ground.

By means of variable resistance; 42,.the:volt.- age drop: across: load resistance iifl may be. adjustedin order to obtain thadesirediinitial voltage output at junction. 6|. This; variable. resistance may be. one of the. conventional type or maybe a pentodety-pevacuum tubehaving theadvantage of substantially constant. currentfi'ow-..

The potentialof control.- grid 44 of: vacuum tube 33- may be varied positively or negatively with respect to ground by means of potentiometer 45, the arm ofwhich is connected to-said grid. Oneside of potentiometer 45-is connected to the positive terminal'of biasingmeans' 46; the'negae tive terminal being connected to ground.v The other side of potentiometer 45'is connected to the negative' terminal: of; biasing means; 41, the positive terminal being: connected to ground. The thus-achieved variation of potentialion: control' grid 44 serves: in effect: relatively to; shift the characteristic curves of the: pentodes, thus embodiment shown in-Fig.- 3, is potential source 62.

The signals issuing from -anode 50 of vacuum tube 33 and anode31 of vacuum tube 32 are 180 out of phase with respect to each other. The signal issuing'from anode 31 may be fed directly to control. grid 38 of vacuum tube 30, and the signal issuing from;anode; 50'may be fed directly to control grid 53 of vacuum tube 3|. Due to the fact that the outputs at the anodes of vacuum tubes 32 .and 33 are coupled directly to vacuum tubes 30 andi3l, respectively, the latter are operated at a higher voltage level than

vacuum tubes

32 and 33. For this reason, in the embodiment shown,

cathodes

55 and 56 of vacuum tubes 30 and 3| are connected together and thence to a source of positive potential 61.

An advantage of the direct coupling between tubes 33 and 3|, and between 32 and 30, is that objectionable time constants are obviated thereby, thus enabling the circuit to respond almost instantaneously to changes in the original input on terminal 34.

Suppressor grids

65 and 66 of vacuum tubes 30 and 3| may be connected to their

respective cathodes

55 and 55.

Anodes

51 and 58 of vacuum tubes 30 and 3|, respectively, are also connected together and thence to a source of B potential 69 through load resistance 60. The plate currents of vacuum tubes 30 and 3| are combined in load resistance 60, the resultant current varying as the square of the input signal to terminal 34. However, the voltage drop across load resistance 5D varies negatively as the square of the input to terminal 34. The output of the foregoing squaring circuit may be taken directly from the

anodes

51 and 58 at junction 6|.

If

vacuum tubes

32 and 33 are either GSN'Is or 6SL7s and vacuum tubes 30 and 3| are 6B8s, the following voltages have been found to be quite suitable in the embodiment shown in Fig. 3. Voltage source 43, which provides negative bias for cathodes 49 and 4| of

vacuum tubes

32 and 33, respectively, may be approximately 150 volts. Positive potential source 62 may be approximately 200 volts, and positive potential source 39 may be approximately 350 volts, and positive potential source 61, which supplies bias for

cathodes

55 and 53, may be approximately 100 volts.

If 6B8s are used, the crossover'point (Fig. 2) will occur at a grid voltage of approximately -12 Volts. This means that when the signal input to the squaring circuit is zero, variable resistance 52 can be adjusted so that control grids 3B and 53 of vacuum tubes 30 and 3|, respectively, are about I2 volts below the potential of their

cathodes

55 and 56.

Under these conditions the resultant current (represented by the dashed curve of Fig. 2) will remain substantially parabolic for a signal input variation of about 16 volts.

The voltage output from junction point 6| of Fig. 3, which varies negatively as the square of the input voltage to terminal 34, therefore varies with respect to the relatively high D.-C. potential at junction point 6| by a factor proportional to the square of the signal input voltage. It may be desirable, however, to obtain a voltage which varies from ground potential by the aforesaid factor. This may be accomplished by the use of a relatively simple level-setting circuit, which is indicated by the dashed portion of Fig. 3. This circuit is usually referred to as a D.-C. restorer 'or clamping circui and is well knownin the art.

The D.-C. restorer or clamping circuit-may comprise condenser II, resistor 12; vacuum tube 13, and output terminals Hiand 15. For general operation, the time constant'determined by the values of condenser H and resistor 12 should be large as compared to the period-of the input voltage to terminal 34. The voltage output of the D.-C. restorer or clampingcircuit is taken from anode 16 of vacuum tube 13 and'varies negatively with respect to ground as the square of the voltage applied to terminal 34. p

Although the discussion of the basic operation of the circuit of Fig. 1 indicated that the variable input is applied to the grids of vacuum tubes 9 and I3, if desired, in other embodiments the input may be applied to the cathodes and the grids connected to ground as illustrated in Fig. 4. The connections in Fig. 4 are identical to those illustrated in Fig. 3, except that the cathodes 55 and 5B of the pentodes 30 and 3| are now connected to the plates of the

triodes

32 and 33 and the

control grids

38 and 53 are grounded through a biasing battery 61-11, the latter corresponding in its function to the biasing battery 61 in Fig. 3.

Although separate vacuum tubes have been shown in the drawings, it is to be understood that, if desired, their electrodes may be placed inside a single envelope as in a multi-purpose tube.

One specific application of the present invention is shown in copending application of Luis W. Alvarez, Serial No. 542,287, filed June 27, 1944, wherein it was desired to obtain a voltage that varied directly as the square of another voltage. Other applications of the invention may be made in electrical calculating or computing machines wherein representation of squared term functions are needed. These and other applications of the present invention will readily occur to those skilled in the art.

Having thus described the invention, what is hereby claimed as new and desired to be protected by Letters Patent is:

1. A squaring circuit including vacuum tube means having a plate circuit, a grid circuit and a cathode circuit, at least one of the latter two circuits including tWo separate electrode elements, means for applying substantially similar input signals of opposite polarity to said electrode elements, and a load impedance in the plate circuit, the output developed across said load impedance being substantially proportional to the square of the input.

2. A squaring circuit including vacuum tube means having two separate control grids and a common cathode-anode circuit, means for applying an input signal to one of said control grids, inversion means for producing a substantially similar signal to opposite polarity, means for applying said latter signal to the other one of said control grids, and a load impedanc in the cathode-anode circuit, the output developed across said load impedance being substantially proportional to the square of the input.

3. A squaring circuit including a pair of vac uum tubes each containing at least a cathode, an anode and a control grid, a common anodecathode circuit for said tubes, another vacuum tube containing a cathode, an anode and a control grid and having anode and cathode load impedances, means for applying an input signal to the control grid of said last-mentioned tube,

marshy developingz signafls: air oppositei polarity across said impedances, means for applyingthe signalzkieve'lopedfacnoss the 'anadeioa-da impedance t0ath-acontrohgridi of: one a ofzithe'itubes: of said first lmenti'onedz pain'of; tubes;- and means for: anplyifi'g the sig-nalildeveloped aaross =thecathode ldaw-impedance to thiicontrol": gridzof the other tube-of said paimofftubes; saidr g-ridiappliedsignalsmf opposite' polarity being-substantially:simi, lssiria-nd aslbadfiimpedance in th'e common anodecathod circuit of said first-mentioned" pair of tflb'es: the" outputbeing: de'velbped across said. last-mentioned "162x]. impedance and being substanti allyr:promrtionahtmthesqua'zze oiltheainnut signal.

FRANGE; B. BERGER.

A. I-IIGHV-BOTHAMI;

REEERENQES; CITED.

Theifollowing-zreferences:arewf record!in the file ofthis patent:

UNITED p STATEST PATENTS Number Name Date;- 7

12728 311 Taylor Sept: 1.7; 1.929 2,199,820 Gannett May 7; 19.40