DEP0033907DA - Electrical computing device - Google Patents

Description

Put © Si T Q Γ; ν; ::: Π '

Hazeltine Corporation, 'Washington D _n C ₄ , (United States of

North America)

Electrical computing device

The invention relates to an electrical computing device for solving equations with known and unknown parameters. Many relationships can be expressed by such equations in which the known parameters are one or more contain independent variables, some of which can be assigned constant values in a special case, with the unknown parameter is the dependent variable.

üa group of known computing devices, to which the relay machines, the punch card machines ,, as well as the mechanical u * - \ d. Electric adding and multiplying machines belong, works with fixed arithmetic units and in many cases requires a very extensive pre-setting in order to carry out more complicated arithmetic operations. As a result, such machines are usually rather complicated and their handling is rather cumbersome ¹ , but they have the advantage of a high 'calculation accuracy',

Another group of known computing devices working with continuously varying mechanical or electrical Grossen, this group gehörA-44 _»y .sowipAein device _s in which a primary winding to which a corresponding one vector voltage, with on a rotor are arranged two secondary windings is coupled , wherein the rotor is moved so that the coupling between the primary winding

and the two secondary windings in accordance with the sine _s BEZW the cosine of the angle of direction of the vector changes, so that the voltages induced in the two secondary windings voltages representing the image projected onto the axis of a rectangular coordinate system components of the vector. This type of computing device is superior to that of the first group in terms of its handling and the speed at which the computing operations are carried out; however, its accuracy does not always meet the requirements “In order to be able to solve a certain computing task with these devices, it is necessary to find a size which continuously follows the independent variables occurring in the task without an impermissible time delay. A wide variety of mechanical, electrical and electromechanical means have already been proposed for this purpose and for the purpose of displaying the calculation result, but it has not yet been possible to find a completely satisfactory solution. Therefore, each of the known computing devices can only be used to solve a very limited number of tasks, and for this reason it is usually mechanically or electrically permanently connected to the source of the independent variables occurring in the tasks mentioned the nature of the mechanical or electrical organs used in the computing device results in a limited usability of the computing devices, which work with constantly changing quantities, for solving the most frequently occurring mathematical or algebraic tasks,

The aim of the invention is to create a computing device which is free from the limitations and other disadvantages mentioned of the devices mentioned and which is generally suitable for solving equations whose solution is based on the usual

based on mathematical relationships.

In the computing device according to the invention, two voltages are generated, which are in one of the form of the equation to be solved change the corresponding dependence on the time, at the point in time at which one of these tensions its a known variable of the equation to be solved is reached from the value given at this point in time Instantaneous value of the other voltage is a voltage representing the unknown variable of the equation to be solved derived and this is displayed.

The invention is explained in more detail with reference to the exemplary embodiments shown in the drawings. 1, 3, 4, 6, Ö, 10, 12 and 14 are circuit diagrams of various embodiments of the computing device _{according to the invention, while FIGS. 0} 2 ₉ 5, 7 / ^{l ;!} H> 13 and 15 show diagrams illustrating the operation of these devices,

1 is the circuit diagram of a computing device for solving known ^{equations containing 1} and unknown parameters, which is particularly suitable for raising a number to a power which can be greater or less than one. The computing device contains a number of energy-storing networks which, when excited, each deliver a time-dependent voltage, the known and unknown parameters being represented by those values which these voltages assume at certain points in time,

One of these networks is the reference circuit H _5, which contains an adjustable resistor R '"and a parallel-connected, likewise adjustable capacitor C. This network supplies a voltage that is exponentially variable as a function of time, the value of which is a known parameter at a certain point in time .

The network is fed with the voltage E 'supplied by the adjustable battery 12. The battery is connected to the outer control grid of a tetrode 13 connected. The anode of this tube is connected to the voltage source + B while its cathode is connected to the network 11.

The computing device also contains a second network 15, which consists of an adjustable resistor R ″ and one to it parallel-connected, also adjustable capacitor C "and when it is energized, a function of the Time also supplies an exponentially variable voltage. This network is powered by the adjustable battery supplied voltage E / '. The battery is connected to the outer control grid of a pentode 17, whose Anode is connected to the voltage source + B, while its cathode is connected to the network 15.

The excitation of the networks 11 and 15 is controlled by the pulse generator IS . This represents a multivibrator consisting of the discharge tubes 19 and 20. The anodes of the tubes 19 and 20 are connected to the voltage source +3 via resistors 22 and 23, while their control grids are connected to a voltage source + B * via resistors 24 and 25, the control grid of each of these tubes being connected to the anode of the other tube via a capacitor 27, 20. The anode of the tube 20 is connected through a capacitor 29 to a grounded resistor 30 and to the inner control grid of the tubes 13 and 17,

Furthermore, the computing device contains means controlled by the voltage of the reference circuit 11 for evaluating the through the Network 15 supplied voltage at predetermined times and for generating a voltage which an unknown Represents parameters, these means consist of one to the

Reference circuit 11 connected comparison circuit 31, as well as a ripple generator 32 , whose input circuit is connected to the comparison circuit 31 and whose output circuit is connected to the input circuit of a selection circuit 33, the input circuit of this selection circuit is connected to the network 15.

The comparison circuit 31 contains a discharge tube 35 with a working resistor 36 connected to its cathode. The voltage E ^ supplied by the adjustable battery 34 is applied to the control grid of this tube. The cathode of the tube 35 is connected via a resistor 37 to the anode of a diode 3 $, the cathode of which is connected to the reference circuit 11 41 connected,

The ^ node of the tube 41 of the relaxation generator 32 is over
one winding of transformer 42 is connected to voltage source + B. Another winding of the transformer 42 is connected with its one pole to the control grid of the tube 41 and with its other pole via a resistor 43 to a bias voltage source -C. The resistor 43 is also connected
connected to an open delay network 44, if the
Output voltage of the comparison circuit 31 should not be high enough, between the capacitor 39 and the
A pulse amplifier can be inserted into the anode of the tube 41.

The selection circuit 33 contains four diodes 47, 40, 49 and 50, which form a rectifier bridge * which is a pair of diagonal output terminals of this bridge circuit
between the network 15 and a grounded resistor 52
connected, while the other pair of diagonal output terminals of the bridge circuit via a voltage source 53 to

a third winding 45 of the transformer is connected.

A tube voltmeter 54 is provided in order to utilize the voltage EX '* which is produced at the resistor 5J> (polygamy represents the unknown parameter). This includes a discharge tube 55j whose control grid with the resistor 52 v, he "bundon and is located in the cathode circuit, a capacitor 56 whose voltage EX" are read on a voltmeter V kannc The capacitance of the capacitor 56 and the resistors of the ^above pannungsmessers-V is dimensioned so large that the voltmeter has a sufficiently large time constant «

The mode of operation of the computing device according to J? Ig. 1 is based on the curves in ^ i g. 2 explains, ^ he curve A represents the negative pulses supplied by the pulse generator 18. These pulses appear in regular periods of time; the beginning ■> of the first pulse occurs at time t-,. These negative impulses pass from the resistor 30 to the inner _{control grid of the tubes 13 and 17 and their size E a} is sufficient to block the said tubes regardless of the level of the voltages supplied to the outer control grid of the tubes, and even then when the voltages resulting on the networks 11 and 15 are very small. Before the start of each of these negative pulses does the inner control grid of the tubes 13 and 17 receive a positive pulse from the pulse generator IB _? scd that Gwch the tubes - 13 and 17 a discharge current flows. As a result, the capacitor C of the network 11 is _{charged to the voltage E 1} ″ of the battery 12 and continues to maintain this voltage due to the known fact that the cathode of the tube 13 in the circuit shown faithfully follows the voltage of the control grid of the tube. At the point in time t-,, in v; elohen the tube 13 is disconnected from the network 11 by its blocking, the capacitor C begins to move across the resistor

R 'to discharge exponentially, as shown by curve B of FIG.

In the meantime, the tube 35, which is also connected as a cathode follower, generates a voltage EX at its working resistor 36 which is equal to the voltage supplied to the control grid of this tube by the battery 34. As a result, a appears at the diode 3 $ and at the resistor 37 connected in series with it . Voltage, which corresponds to the difference between the voltage on network 11 and that on working resistor 36. As soon as the voltage on the network 11 falls below the voltage E ^ appearing on the load resistor 36, the diode 3 $ becomes permeable and generates a negative voltage pulse on the resistor 37. This reaches the pulse generator 32 via the capacitor 39 at time t ~, as is shown by curve C in FIG. The leading edge of this pulse appearing at time t ₂ causes a short pulse to be generated in pulse generator 32 is thrown back. This pulse duration is selected by appropriate dimensioning of the network 44 so that the selection circuit at the time t _? and in the immediately following time on network I5 the voltage from this network decreases "

The pulse generated by the pulse generator 32, shown by curve D in FIG. 2, comes from the winding 45 of the transformer 42 to the selection circuit 320 This pulse makes the rectifier bridge 47, 4 #, 49, 50 against the bias voltage resulting from the voltage source 53 permeable, so that the during the duration of this pulse on Network 15 effective voltage now also at resistor 52

seems. The voltage on the network 15 is controlled by the tube 17 in the same way as the voltage on the network 11 is controlled by the tube 13 and it therefore corresponds to the voltage ET 'of the battery 16 at the point in time tp at which the tube 17 is blocked , the profile of the voltage on the network 15 shows the curve F of Figure 2. As a result of the t ₀ at the time when onset of discharge of the capacitor C "'via the resistor R"' the voltage at the network 15 falls to the time t 'to the worth Eg '. JYes the electoral district 33 made effective at this moment by the voltage EX appearing on the network 11

the

the voltage appearing at the resistor 52 of the selection circuit also has the magnitude EX /, the tube voltmeter 54
also works as a cathode follower, so that its capacitor 56 is also charged to the voltage E ^ '
Fig, 2 shown.

The ^Ji rt and according to the use of the arrangement
Fig, 1 for carrying out arithmetic operations is based on a mathematical analysis of the operation explained in this arrangement,

The reduction of the voltage on the network 11 from the 'value E,' at time t-, to the value E ^ at time tg, as well as the
Decreasing the voltage at the network 15 from the value of E / 'at time t * to the value EX / ^ - ^ ^m eitpimkt t ₂ is the following formulas in front of:

^HC (1)

^t 2 " ^t l

■ R "C"
EX /.= E £ "e (2)

The time constants of networks 11 and 15 are in the following

gender relationship with each other:

A common solution for equations [I) ₉ (2) and (3)

results from the relationship:
η

(4)

■ ff ^f \ ^W 2

As a result, it is used to solve an equation of the form

y = χ ¹¹ (5)

only necessary to adjust the batteries 12 and 16 so that the voltages E / and E / 'equal the unit of a suitable one Tension scale will be. Then equation (4) is simplified to the form:

ψ = (Ep ⁿ (6)

where the voltage Eg 'represents the parameter y and the voltage Ep represents the parameter χ of equation (5) «,

If, for example, assuming that Ef = E '' = 1, χ - Ορβ and η = 2.1 are set, the time constant of network 11 is set in relation to the time constant of network 15 by setting the resistors R ', R accordingly ", of the capacitors C, C" are dimensioned so that the ratio η between the two time constants is the same in order to satisfy equation (3) £ = E / '= 1, the voltage becomes Ep = 0.6. The voltage E ″ now read on the voltmeter V is O ₉ Jl + volt and this is the value of the dependent variable y in equation (5).

If the parameter χ of the equation (5) is greater than one, the device according to Fig can be ₀ 1 used in a way that is chosen for the voltage E ^ 'in Equation (4), a suitable rfert ₈ This equation can also fol-

to be written gender:

(7)

I ^

if one now sets E £ 'o = (E ^) ⁿ , one obtains the form for equation (7):

2 "2 '°'

For example, it is assumed that in equation (5)

χ Ff 5 and η - 2.1 let _s At E £ = 10 volts, E "= 1O ² * ¹ = 126 volts and the voltmeter V gives the voltage EX" = y to 29.5 volts. This operation could be done also be expressed so that the voltage e, "from their ^H nfangswert of 126 volts in the same ^ eit to the value y = EX /« = 29.5 volts drops, in which the voltage e 'from its initial value of 10 volts to χ = E ₂ = 5 volts drops,

With appropriate care in the design of the apparatus of Fig rake _T "1 can be the desired solution of an equation with each normally desirable accuracy obtained. For example, you can see the scale for indicating the voltage of the batteries 12, 16 and 34 correct so _f that takes into account the fact that the voltages across the resistors R 'R''and 36 t at the time, some of the voltages E ₁ 'E ₁ "resp. EX can deviate "A further correction of the scale indicating the voltage of the battery 34 can be useful in view of the small deviations in the difference between the voltage at the network 11 and at the resistor 36 required to bring about the permeability of the diode 30" the scale of the voltmeter V can be corrected to take account of the small voltage drop across rectifiers 47> 43, 49 and 50, as well as the small voltage caused by the discharge of capacitor 56 between successive arithmetic operations.

differentiated to take into account. Under certain circumstances, careful neutralization of the inductive reactances in the branches of the back circuit forming the selection circuit 33 can also be advantageous. The accuracy of the calculation can be increased by choosing the time constant of the networks 11 and 15 so that the point in time t _? , in which the solution of the problem is determined, falls in the time span in which the discharge curve of the capacitors C and C "is still steep. The calculation is more accurate, the higher the voltages E, * Ej" and EX should be chosen because an increase in these voltages reduces the importance of the inevitable voltage drops in the circuits of the arithmetic unit A In the above example of solving an equation of the form of equation (5), the value of χ and therefore also the value of y is less than one and this would also be the case if the exponent η were less than one. "Venn the value of χ and y are larger than one in the equation (5), so it is at a given value of η price, a computing device shown in Figure ₃ ^ 3 to be used rt. This device complies largely with the device according ^ ig, 1 match, and the matching parts are designated with the same öezugszeichen as shown in FIG. I ₀

The computing device according to FIG. 3 differs from that according to FIG. 1 fundamentally in that the Selection circuit 33 from a network 1 $ extracted voltage EX "is set arbitrarily, preferably made equal to one and represents an independent variable, so that one thus has the voltage E ^ 'to which the network 11 is initially charged must be set so that the predetermined value of Eg "'is obtained. Accordingly, the device contains an adjustable

Voltage source 16 ', which supplies the required voltage ET'. This ^ü pannungsquelle consists of a battery with the voltage E, which is connected via a resistor 63 to the input circuit of the excitation tube 17th The voltage E "can be read from the voltmeter 54" connected to the input circuit of the exciter tube «

The voltage EX 'is supplied by the adjustable battery 64, which is connected to a control device 66 for controlling the voltage E, "the voltage source 16 ¹ ". The control device contains two series-connected resistors 67 and 6B, which the output voltage of the selection circuit 33 is supplied. Are these resistances so large _? that the capacitor 69 connected in parallel with them can only discharge slowly through them. A tap of the resistor 67 is connected to the control grid of a discharge tube 71, the anode of which is connected to the voltage source 16 * 'and the cathode of which is connected to the connection point of the resistors 67 and 6Ö. The cathode of a discharge tube 72 is also connected to this connection point whose control grid is connected to the battery 64.

When the calculator is switched on, the voltage Eg 'of the battery 64 appears at the load resistor 63 of the tube 72. As long as there is no discharge in the tube 71, there is no voltage drop across the resistor 63 and the exciter tube 17 receives a high voltage E ₀ at the capacitor 69 a voltage which is greater than the voltage EX 'at the resistor 66, so that a current flows through the resistor 67, which generates a positive bias voltage at the control grid of the tube 71 and causes a discharge in this tube » The resulting voltage drop across resistor 63 increases until the voltage E £ 'so far

has fallen so that the output voltage of the selection circuit 33 is equal to the voltage EX 'as desired,

To explain the operation of the arithmetic unit when solving an equation of the form of equation (5) is Reference is made in turn to the curves in FIG. The batteries 34 and 64 are set so that the through the curve B voltage EX shown and the voltage EX 'shown by curve F becomes one. Then it is simplified Equation (4) for:

Ef - (E £) ⁿ (9)

Here, the voltage E £ 'represents the parameter y and the voltage E' represents the parameter χ of the equation (5). If, for example χ = 1.6 and η - 2.1, the time constant of the networks 11 and 15 is set so that the ratio η of their time constants have the mate 2.1. The battery 12 is then set so that the voltage E £ = 1.6. The one on the tension meter 54 ', the voltage EX' corresponding to the magnitude of the dependent variable y of equation (5) is obtained then to 2.7 "The curve G in FIG. 2 in this case represents the voltage across the capacitor 69"

If one selects the voltages EX, EX, E, '', EX 'accordingly and sets the quantity η in equation (4) equal to one, . ' 'Inside equations of the most varied of forms' are solved, for example if the ratio η = 1 and also the Voltage E / is set equal to one in the arrangement according to FIG. 1, equation (4) is simplified to:

SX / = E £ 'EX /. (10)

This equation corresponds to the equation

ζ = xy (11)

However, if both χ and y are greater than one, EX is advantageously set to one instead of E £ and in this case

one uses rather the arrangement according to FIG. 3. If E ^ '= * ä 1 is set, the equation (4) can lead to an equation as follows Shape to be reshaped:

* = f (12)

To solve such an equation one also uses the arrangement according to FIG. 3, if y is less than one, or but one writes equation (4) as follows:

B - iä ₅ / <E £ / E £ ') (13)

^E l
y ₌ _ _x _ £ _unc | _z _ ε is set, one obtains

IJi ff <~ <~

again aie equation (12),

Fig. 4 shows the circuit diagram of a particularly suitable for solving equations of the type of equation (10) The battery 12 ", the voltage of which is higher than any of the various parameters to be solved The voltages representing the equation is connected to the anode of the tube 13 'which excites the network 11', the control grid of which is connected to the output circuit of the pulse generator 10 ' is. The pulses from this generator are shown by curve H in FIG. The capacitor C "of the network 11 ' is already charged to a suitable initial voltage E "before the beginning time t of the first pulse of the pulse generator been. At time t this capacitor begins to discharge through resistor R "'. The exponential curve This discharge shows the curve J of FIG. "5" The network 11 'is connected to a comparison circuit 31 "

connected to Fig.l, which is similar to the comparison circuit 31 /, with the difference that the point of the diode 3 $ the resistor 37 'and the place of the resistor 37 which Di6% 33' takes, as soon as the voltage on the network 11 'at time t-, falls below the voltage E-T 'of the battery 34, results on

Resistor 37 'is a positive pulse represented by the curve K-, which reaches the input circuit of the relaxation generator 75 via the capacitor 39 and the shunt resistor 33.

The tilt generator 75 contains two discharge tubes 76 and 77, which have a common cathode resistance 7 $. The anode of the tube 76 is connected to a voltage source + B via an operating resistor 79 and to the control grid of the tube 77 via a capacitor. This control grid receives such a bias voltage from the voltage source + B 'via the resistor 32 that it normally keeps the tube 77 in its permeable state. The "node of the tube 77 is connected directly to the voltage source + B. As soon as a positive pulse is fed to the input circuit of the relaxation generator from the comparison circuit 31 'at time t, the tube 76' becomes permeable and the anode of the tube 77 results a negative pulse represented by the curve L, which is fed via the capacitor $ 4 to a resistor 63 connected to one input circuit of the exciter tube 17. Another input circuit of the exciter tube 17 is connected to a battery 16 which supplies the voltage E / C of the network 15 ", which was charged to the voltage E ^" via the exciter tube 17, begins to discharge at time t-. The exponential course of this discharge is shown by curve M in FIG.

As soon as the voltage on network 15 ″ at time t ^ to the value Ei of a second comparison circuit 31 controlling Battery 64 falls, a negative pulse shown by curve N of FIG. 5 is generated in this comparison current circuit, which causes the pulse generator 32 ζμΓ generation of a short pulse represented by the curve P. This impulse

reaches selection circuit 33 »

Meanwhile, the pulse generator 1Ö ', respectively connected' tube OEO 'at the time of the .batterie 16 t' einai.negativen pulse and thus this tube was blocked so that the _t from the battery l6 '"until then through the tube 86 to the voltage Eg " ¹ charged capacitor C '''of the network Ö7 is now discharged through the resistor R" / of the network, the exponential course of this discharge shows the curve Q, at the time tp the selection circuit 33 activated at this time conducts the instantaneous voltage EX''' at the capacitor C "to the tube voltmeter 54, the voltage of which consequently has the course shown by the curve R"

The manner in which the arithmetic unit according to FIG. 4 is used to carry out arithmetic operations results from the following mathematical analysis of the 'mode of action, from the curves J, M and Q of Fig. 5 results:

'E _n "- 1

^J l

) / R'C

(H) (15)

Jjp - ill <5 (L \ XU /

Equation (Ιό) can be evaluated by inserting into it the value of t-obtained from equations (14) and (15). Equation (14) gives:

[e "K ^c "
t: = iog-1-2- (ι?)

and from equation (15) '

t ₂ -

- log _c

^E i

R-C '

or:

E '"
ο

R "C

_ ^E 2

O ₁ .

"C"

R "C

R'C

(20)

Substituting equation (20) into equation (16) is obtained

man:

E '"C"

R "C"

R "C

^E 2

B'C

R ^ ^ C ^

^E 2

(21)

(22)

"E""
ο

E _n

As a result:

E '

E;

= E ¹

R "C"

R'C

(24)

if R "-C" - R'C and R'C / R '"C'" = η, one obtains:

^b 2 ^{= h} o

(25)

'If in this equation Ε,''/ E " -%, EX " = EX''and

E "'= E," is set, one obtains the equation (4). If one sets n = l,

so equation (25) is given the form:

■ £ ,,, ₌ ^,., Il Z2_

2 .o _E " _E 'ο 1

and if you have E "'(= E' = E 'ο oil

(26)

= 1 sets, one obtains

- 13-

Ji ₂ = E ^ E ;, \ <Ί)

ie, _{8 takes} the form of equation (II). So if you want to multiply 5 by S, do you put E £ '= 5 _? E ^ ~ 8, E '' = E £ = 10, E ^ "r = 100 and gets:

^E 2 " ^{= 1ϋϋ} Ϊ0 ~~ ϊ ~ ΐϋ" ⁴ ° ⁽²⁰ ^

In other words, the voltage E '"falls from' ICQ to 40 volts in the period in which the voltage E '' falls from 10 to 5 volts and then the voltage E, 'from 10 to B volts.

At the in ^ ig. ^A shown 6 usführungsform the inventive computing device is the of the resistance R 'and the capacitor C composite network 11''', the voltage E of a battery 12 controlled excitation tube 13 '' is supplied via a by the pulse generator 18th The control pulse of the pulse generator 1 $ 'also acts on the ripple generator 32' and the short pulse generated here under the action of this control pulse reaches the adjustable delay circuit BS, which consists of the strip S9 provided with windings 96 and 96 ', the changes its dimensions under the action of the magnetic field of the windings. At the ends . Energy-absorbing retaining members 90 are provided on the strip. The output circuit of the relaxation generator 32 "" is connected to the winding 96 which can be moved along the strip S9, while the winding 96 'is connected to the input circuit of an impulse generator 97 of a known type.

In ^ igo7, the curve S represents the negative pulses supplied by the pulse generator IB ″ ₀ At time t, the leading edge of the first of this pulse in the tilt generator 32 ″ causes the short pulse represented by curve T, which is fed to the delay circuit SS and initiates this | .reis at time tp, which is determined by the position of the

Winding 96 on the strip 39 is conditional. The curve U represents this delayed and in its shape by the pulse shaper 97 corrected impulse.

In the meantime, the voltage at the capacitor G ″ of the network 11 'represented by the curve V has increased from the value E' at the time t to the value El determined by the battery 34 at the time t-, as a result of the blocking of the exciter tube 13 ″ at the time t, The network 11 'and the battery 34 are connected to a comparison circuit 31, so that at time t 1, the latter delivers a control pulse represented by curve W, which in the ripple generator 75 triggers a pulse represented by curve X.

The pulse represented by curve X blocks at time t-, the exciter tube 17? via which the battery l6 has charged the capacitor ύ ″ of the network 15 to the voltage Ej ″, so that this capacitor is now discharged via the resistance R ″ of the network, as curve Y shows. At the time tg, the delayed pulse represented by the curve U activates the selection circuit 33 connected to the network 15, so that it transfers the voltage EX 'given to the network 15 at that moment to the tube voltmeter

the 54 forwards what tension as a result / through the curve

Z has the course shown.

If at time t-, the comparison circuit 31 has not caused any disturbance in the voltage curve on network 11 '*, the voltage on this network decreases to the value E ^ up to the point in time tp. So in this case is the tension at the network 11 'at the point in time t, equal to E,' and at the point in time t2 equal to E ', while on the network 15 they are at the same points in time

2
E-f '"and E". As a result, equation (4) holds for

these four voltages, provided that the networks U ''

and 15 the same Zeitk-onstante, have i Equation (4) simplifies to di:

E ₁ "EJ i2

If the voltages E, "and EX remain unchanged during a series of arithmetic operations, the equation (29) can be written as follows:

EX '= - (30)

¹ E ^

In this case, the voltage Ej "* can be determined by suitable setting of the battery 16. The voltage EX can be completely neglected in the arrangement in FIG ; r-. Equation (l) similar equation with predetermined value of E 'and EX, or by the fact that the possibility of a disturbance of the voltage curve in the network 11' is switched off by the comparison circuit 31. If the mentioned time span is determined by calculation _? It can happen that the voltage EX appears at a point in time at which the steepness of the discharge curve V of the capacitor C "is relatively small, so that the determination of the exact instantaneous value of this voltage would not be possible." The freely selected voltage E ^ is always greater than the voltage E ^ and must remain constant during successive arithmetic operations because it influences the size of the time span t ... - t ^. In the arrangement according to FIG. 6, the size of the time span t-tp is determined by the pulse U, the delay of which compared to the pulse T appearing at time t ^{depends on the setting of the wrapping 96 on the strip f "· 1} = under the influence The selection circuit 33 responds to this pulse U at that point in time t ^ at which the voltage on the network 11 'reaches the value EX, without this value being changed

would have a tax effect itself,

If with the arrangement according to FIG. 6 an equation of the form

y = * (3D

is to be solved, the variables EX 'and ET of equation (30) can be used for the parameters yu, ad x of equation (31). If the value of E- / ^/ and EX in equations (29) and (30) is chosen so that the constant becomes one ', then the arrangement according to FIG. 6 came to determine the reciprocal value y of the parameter x of the equation ( 31) can be used.

5 shows an embodiment of the computing device according to the invention which is particularly suitable for performing additions and subtractions. Here all the variables occurring in the arithmetic operation are represented by one of the variables proportional to the voltage to earth. The pulse generator IB controls a ripple generator 91 which generates a voltage represented by the curve AA in FIG. 9 and having a linear, sawtooth profile. The lie-current circuit 92, which is connected to the ripple generator via the capacitor 93 and consists of the resistor 94 and the diode 95 connected in parallel with a grounded anode, ensures that the voltage surge shown by curve Aü starts at time t starting from the zero value. This ^above pannungsstoss reached at the time t, the l6 by the voltage source specific fourth-S, '' on which the comparison circuit 31 "to Kippgeaerator 7 5 to

caused in the generation of a pulse by which / a second ripple generator 91 'a linear, sawtooth-shaped voltage surge shown by the curve BB of FIG. 9 is generated. A resistor 94 "and the diode 95" connected in parallel with it are connected to the relaxation generator 91 "via the capacitor 93"

grounded anode existing control circuit 92 "connected, which ensures that the voltage surge BB at the time t-, starting from the zero value, begins. The output circuit of the control circuit is connected to the moving contact of a changeover switch IO3 connected, while the output circuit of the control circuit 92 "is connected to the moving contact of a changeover switch IO4 is.

Since the movable contact of the changeover switches IO3 and IO4 is in contact with the fixed contact of the changeover switch , the tilt generator 91 'is connected via the control circuit 92' to a selection circuit 33, the output circuit of which is connected to the tube voltmeter 54, while the tilt generator 91 is connected to a control circuit 92 is connected to a comparison circuit 31 _; which is controlled by a voltage source with the voltage E ^ ₀ As soon as the voltage AA reaches the value EX, the comparison circuit 31 generates a pulse, which causes the pulse generator 32 to generate a pulse that actuates the selection circuit 33, whereupon this the instantaneous voltage Eo "" of the tilt generator 91 ″ forwards to the tube voltmeter 54.

If the relaxation generators 91 and 91 'are set so that the voltages generated by them increase to the same extent, then the voltage of both relaxation generators changes during the period t ·, -to by the same amount, this can can be expressed mathematically as follows:

ψ - Ej - E £ (32)

The voltage values included in equation (32) can be the parameters of the equation

ζ = x - y (33)

represent, so that with the arrangement according to Fig. ₃ Ö in the aforementioned position of the switch 103 and IO4 subtractions can be carried out "

To carry out additions, the changeover switches 103 and 1U4 are switched over, so that their movable contacts with

their fixed contacts a come into contact. Here the

in

Voltage of the sweep generator 91 '/ comparing circuit 31''' with the voltage Eo 'of ^u pannungsquelle 64 "compared to the time to determine tp. At this point in time, at which the instantaneous voltage of the ripple generator 91 'is equal to the voltage EX', the comparison circuit 31 "generates a pulse which causes the ripple generator 32" to generate a pulse that actuates the selection circuit 33 ". This circuit then leads the instantaneous voltage EX of the relaxation generator 91 to the tube voltmeter 54 ″.

Since, in the arrangement just described, the dependent variable is the voltage E ^ of the relaxation generator 91, can the equation (32) can be written as follows:

E ^ = E {+ Eg '(34)

The voltages appearing in this equation can be the parameters in the equation

ζ - χ + y (35)

represent.

Linear functions of the kind, as they are in the relaxation generators of the arrangement according to * ^r ig. 3 can also be used to multiply a number by a factor that can be greater or less than one. An arrangement suitable for this is shown in FIG. 10 and its mode of operation results from the curves in FIG _. 11 "The pulse generator lä generated at time t in.dem with the control circuit 92 connected to a sawtooth sweep generator 91 going voltage CC and in the 'related relaxation oscillator 91' to the control circuit 92 a steeper rising sawtooth voltage DD. As soon as the voltage of the relaxation generator 91 at time t, the voltage Ej "of the voltage source 34

is sufficient, the comparison circuit 31 causes the ripple generator 32 to generate a selection circuit 33 actuating Pulse, whereupon it forwards the instantaneous voltage E-T 'of the relaxation generator 91' to the tube voltmeter 54.

The voltage generated in the relaxation generator 91 and in its control circuit can be given by the equation

E '= k't (36)

are expressed while the voltage generated in the relaxation generator 91 'and in its control circuit 92 "of the equation

E "= k" t = jCV (32)

k "
corresponds, The quantities E ", rr— and E 'can be the parameters of the equation

χ «a y (3S)

represent. An arrangement of this kind can therefore be used, for example, to replace the parameter y with any suitable Constants a, z »B. multiply by ten. So if one uses such an arrangement for solving an equation of the Type of equation (10) is used and the range of change of the voltage E 'in this equation is such that the voltage EX always remains very small, this voltage can be used with any constant when using the arrangement according to FIG.

will

for example multiplied by ten /. The resulting voltage is then sent to the computing device as a voltage E ^ the next higher order of magnitude to perform the arithmetic operation expressed by equation (11), Das on the arithmetic unit The product ζ read must then be divided by the constants used, for example by ten, in order to obtain the get correct solution.

The arrangement according to Fig, 10 has dßn _f advantage that the accuracy in the procedure of the location of the point in time t, with respect to the curves CC, and DD is independent. A white

Another advantage of this arrangement is that the arrangement, due to the linear course of the voltage of the ripple generators 91 and 91 'for multiplying or dividing with
large numbers can be used. Since the amplitude of this voltage only increases with time, the size of the measurable voltages is only limited by the duration of the sawtooth-shaped voltage surges,

Fig. 12 illustrates an arrangement in which one of the
Comparative variables, in particular the voltage generated by the reference circuit, changes as a function of time in accordance with the equation to be solved. The operation of this device is illustrated by the curves in FIG. 13. The capacitor C of the network 11 composed of this capacitor and the resistor R 'is charged by the voltage source 12 via the exciter tube 13 to the voltage E'
with a Üegelstromkreis 92 connected to ripple generator 91 for generating a sawtooth-shaped voltage surge
GG and leads, on the other hand, by blocking the tube 13, the discharge of the capacitor C through the resistor R ', as shown by the curve FF. As soon as the voltage of the capacitor C at time t-, to the value E / corresponding to the voltage of the voltage source 34, the comparison circuit 31 causes the ripple generator 32 to operate the selection circuit 33, which then sets the instantaneous voltage ET 'of the ripple generator 91 and its Control circuit forwards to the tube voltmeter 54.

Assume that with the arrangement an equation of the form

- _X
y = ae ^ΰ . (39)

should be resolved. The voltage on network 11 is determined

according to the equation
t_

PT '

E'- Ε; e ^RG (40)

and the voltage generated by the relaxation generator 91 and its control circuit 92 results in:

E "= k" t (41)

Plugging equation (4I) into equation (40) gives:

E '= E ^ e ^{Λ iL v} (42)

The quantities E ', Ej, E' 'and (k "R'C) in equation (42) can represent the parameters y, a, and b of equation (39).

When inserting "specific values of the dependent variable χ and the dependent variable y into the Equation (42) takes this form:

E £ - EJ e ^{k HC} . (43)

This equation can be transformed into:

B £ '

e ^k " ^R ' ^C ' - ^ (44)

E ^
1

and in:

E.T E '

¹ p

Γ7ΤΤ ^log e ^ T (45) ■

If the voltage source 34 of the arrangement according to FIG

is set so that its voltage is E-T = I, equation (45) is given the form:

E £ '= C log _e EJ (46) where

= k K υ (47) vvif the circle constants of circles 11 and 91 are chosen so

that C = I, then the voltage ET ^- * represents the natural one

The logarithm of the voltage E '. If one sets the constant C = log- ^ Q in equation (46), then becomes

E £ '= (log _b e) (log _e E ^) - log ^ (4Ö)

where b is some corresponding base, such as base 10 of the common logarithm. By reversing the position of the network 11 and the relaxation generator 91, 92 in relation to the comparison circuit 31 and the selection circuit 32 , the voltage E | ' can be made the dependent variable and the voltage E 'the independent variable such that equation (48) has the form

E ^ = antilog _b E £ '(49)

assumes, The arrangement according to ^ ig. 12 can therefore be used to find logarithms and antilogarithms Basis can be used.

The arrangement according to FIG. 14 is in particular for solving equations of the form:

y = sin U + 0) (50)

-or of the form:

-1
x = 9 + sin y (51)

In this arrangement, the pulse generator is connected to a ripple generator 91 which generates sawtooth-shaped voltage surges connected to a Hegel current circuit 92 associated therewith, the output circuit of which is connected to a phase control device 109 The device IO9 contains two batteries 110 and 111 connected in series, whose connection point to the cathode of the Control circuit 92 associated diode 95 is connected. A voltage divider is connected to the free poles of the two oil batteries 112 connected, the ochiebekontakt with the fixed contact T of a changeover switch 103 and with the fixed contact AT of a Switch 104 is connected. The moving contact of the

Switch 103 is connected to the input circuit of the comparison circuit 31 ', while the movable contact of the switch 104 is connected to the input circuit of a selection circuit 33.

The pulse generator Iß is also connected to a ringing sine wave oscillator 105 which contains a discharge tube 106, the anode of which is connected to the voltage source + B is connected, while its cathode via a composed of the capacitor 107 and the coil 10ß parallel resonance circuit is grounded. A coil 102 adjustably coupled to the coil 10β can either be via the fixed contact T. of the changeover switch 104 with the selection circuit 33 or via the fixed contact AT of the changeover switch 103 with the comparison circuit 31 'are connected,

The mode of operation of the arrangement according to FIG. 15 is explained on the basis of the curves according to FIG. The one through the curve HH shown pulses of the pulse generator Iß cause the ripple generator 91 to generate the shown by the curve JJ, sawtooth-shaped voltage, which runs through the control circuit 92 and the phase control device 109 " A voltage E is added to this voltage in the phase control device, the magnitude and polarity of which is determined by the voltage divider 112 can be regulated. As a result, the size of the switching contacts T and AT supplied voltage between those Limits vary which are determined by the dashed curves accompanying curve JJ.

The pulses of the pulse generator Iß are also supplied to the oscillator 105 and the discharge tube 106 is through the Trailing edge of each of these pulses blocked. The resulting sudden interruption of the discharge current in the Tube triggers oscillation circuit 107, 10ß to oscillate,

their frequency

_fe _l_ (52)

where L is the inductance of the coil 10 $ and C is the capacitance of the capacitor 1Ü7. These vibrations, which the Curve LL represents, are fed to the coil 102 with an amplitude dependent on the degree of coupling between the coils 103 and 102 and then get to the fixed contacts T and AT of changeover switches IO4 and 103 "

When solving an equation of the form of equation (50), the toggle switches are placed in their drawn position, in which they close their contacts T, the phase control device 109 with the comparison circuit 31 ″ and the Coil 102 is connected to the selection circuit 33.

As soon as the output voltage of the phase control device IO9 at time t-, equal to E. or at time t ·, + _ θ equal Ε.Γ + E, the ripple generator 32 generates the short pulse shown by the curve KK. This impulse causes the ^ selection circuit 33 for 'forwarding the voltage E ^ resulting at the coil 102 at this moment to the tube voltmeter 54. Since every sinusoidal oscillation of the oscillator 105 begins at time t, the one in the selection circuit is in any one Time t applied voltage:

E ₂ = E ₃ sin 2nft (53)

The time t depends on when the sawtooth voltage appearing at the contact T of the changeover switch 103 is fourth E, achieved; it is thus determined by the equation;

E ₁ = Kt ₁ IE ₀ ■ (54)

where K denotes the slope of the rising branch of curve JJ. To G so the time _run d of this equation, t to:

¹¹ I - ^ - ^{2 (55)}

i / Venn this value of t, is used in the equation (53), one obtains the forwarded to the vacuum tube voltmeter voltage to:

2πί (Ε - + E)

E ₉ = Ε, sin ^ - - (56)

* ■ * K

If one sets E- = 1 and 2πΓ / κ = '1 ρ- - ^ · in this equation the equation is given the form:

E ₂ = sin (E ₁ + E ₀ ) (57)

If one sets E ₂ - y _s E, = 1 and E = Q here, one obtains':

y = sin (x + 0) (53)

_{Dj..e voltage E 2} measured in this way with the tube volt meter 54 is represented by the curve MM.

When the changeover switches IO3 and 104 are switched to their contact AT, the ripple generator 97 is connected to the selection circuit 33 and the coil 102 is connected to the comparison circuit 31 '. The comparison circuit now actuates the selection circuit in that one The moment at which the voltage on the coil equals E-, and the selection circuit is carried out in this The voltage resulting at the voltage divider 112 at the moment to the tube voltmeter 54 to »In this case results from the Equation (53) the one. Time t-, at which E, = to:

U ^sin V ^E 3

Inserting this equation into equation (54) j one obtains:

^E l ^β 2if ^sin ^ V ^E 3 ± ^E o ⁽⁶⁰⁾

If one sets Κ / 2πί = 1 E, = 1, E, = χ, E = y and E = O, he »

j ± 2 °

this equation holds the form:

-"1
χ = 0 _ + sin y - (6l)

The above examples show that the invention

according to computing device is suitable for solving all common equations, whereby it is characterized by the fact that there is no has mechanically moving parts, is light in weight, takes up little space and works very quickly.

Claims (1)

Claims; I ₅ Electrical computing device for 'solving' Bg equations with known and unknown variables, characterized in that at least two voltages are generated, which change in a dependence on time corresponding to the form of the equation to be solved, whereby at that point in time in which one of these voltages reaches its value corresponding to a known variable of the equation to be solved, from the instantaneous value of the other voltage given at this point in time a voltage representing the unknown variable of the equation to be solved is derived and this is displayed, 2, computing device according to claim 1, characterized in that the change in at least one of the time-dependent 'variable voltages is linear, 3 “Computing device according to claim 1, characterized in that the change is at least one · £ ** £ & -? the time-dependent variable Stress is exponential, 4 «A computing apparatus according to claim 1, characterized in that the change _s of the time-changing voltage is at least logarithmic. 5e computing device according to claim 1, characterized in that the change is at least one of the time-dependent changes Stresses according to a trigonometric function « 6 ». Computing device according to one or more of the preceding claims, characterized in that at least one of the time-dependent variable voltages are supplied by a network, which consists of a capacitor and a there is a resistor connected in parallel » 7. Computing device according to one or more of the preceding Claims; ^ characterized in that at least one of the time-dependent variable voltages from a relaxation generator is delivered, B ₁ computing device according to one or more of the preceding claims, characterized in that at least one of the time-dependent variable voltages is supplied by a sine wave oscillator ₀ 9, computing device according to one or more of the preceding Claims, characterized in that one is known the equation to be solved Variable / corresponding instantaneous value of a time-dependent variable voltage by comparing these Voltage is determined with the voltage of an adjustable voltage source, 10, computing device according to one or more of the preceding claims, characterized in that the change at least two time-dependent variable voltages are triggered at the same time, 11, computing device s claimed in one or more of claims 1-9, that a first time-dependent variable voltage in the point of time in which it reaches its a known variables of the corresponding equations to be solved ^w ert, triggers the modification of a second time-dependent variable voltage ,, 12, computing device according to claim 10, characterized in that the change of the time-changing voltages ert from a predetermined ^ (ET, E / "*) extends and by means of one of the voltages in the timing when .in which j $ ie its a known The value {'S, ^) corresponding to the variable of the equation to be solved is reached, the value given at this point in time, corresponding to the unknown variable of the equation to be solved /^f?rj.bJ:n.ckwert (E ^') of the others Voltage is determined (Fig, I, 10, 12, 13 »Computing device according to claim 10, characterized in that the change in the one time-dependent voltage starts from a predetermined value (E £) and this voltage at the point in time at which it corresponds to its" i: ". Ner known variable of the equation to be solved ^ ert (EX) is reached, the comparison of the given at this time ^K ugenblickswertes another time-dependent variable voltage with an other known variables of the illustrative equation to be solved adjustable voltage (Ei ') causes, such comparison to the automatic adjustment of the output value of said other time-dependent variable voltage on the value (E £ ') corresponding to the unknown variable of the equation to be solved. (Fig. 3) 14, computing device according to claim 11, characterized in that three time-dependent variable ^ voltages are generated and the time-dependent change of the first and second voltages begins simultaneously while that of the third voltage begins is triggered by the first voltage as soon as it corresponds to a known variable of the equation to be solved Value (E ^ ") reached, with this third voltage at the point in time in which it is one of another known variable Ivert (EX) corresponding to the equation to be solved is reached, the determination of the at this point in time given, the unknown variable of the equation representing instantaneous value iEp '* ") of the second voltage, (Fig. 4) 15 »Computing device according to claim 11, characterized in that the determination of the unknown variable of the to The instantaneous value (E, ") corresponding to the solving equation of the time-dependent variable representing this variable Voltage caused by a simultaneous initiation of the change in a known variable of the equation, time-dependent variable voltage generated pulse (T) takes place with adjustable delay (Fig "6), 16. Computing device according to claim 11, characterized in that the time-dependent variable voltage triggering the change in the second time-dependent variable voltage at the point in time at which it reaches its value (EX) corresponding to another known variable of the equation to be solved, the determination of the in given this point in time, the unknown variable of the equation representing visual value (Eo ') of the second time-dependent variable voltage brings about (Fig, O) ₀ 17 ". Computing device according to claim 11, characterized in that the second time-dependent variable voltage at the point in time at which it reaches its value (EX ') corresponding to another known variable of the equation to be solved, the determination of the unknown given at this point in time The instantaneous value (Eo) of the first time-dependent variable voltage, which is represented by the equation, brings about (FIG. ₀ O) ₀ 1Ö, computing device according to claims 16 and 17, characterized in that the two vary as a function of time Voltage sources generating voltages are mutually interchangeable with a comparison circuit and one controlled by it Selection circuit are connected (Fig. Ö).