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Патент USA US2404387

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July 23, 1946.
1c. A. LOVE‘LL ET-AL ‘
Filed May 1, 1941
2 Sheets-Sheet 2
"112/ I
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l I.
Clarence A. Lovell and David B. Parkinson,
Maplewood, N. .L, and Bruce T. Weber, New
. York, N. Y., assignors .to Bell Telephone Labo
v . g
ratories, Incorporated, New York, N. Y., a cor
poration of New York
Application May 1, 1941, Serial No. 391,439
, ~ "4 Claims.
(c1. 235—61)
r This invention relates to electrical computing
the vacuum tubes, the impedance of the anode
cathode circuits of the vacuum tubes is balanced
against the resistance of the resistor 34, and both
clutches are disengaged. As the patentee is pri
systems, and particularly to systems including
comparison circuits associated with servo-motors.
The object of the invention is the solution of
an equation, or a system of simultaneous equa
. marily interested in measuring electrical power,
tions, in which the data are represented by elec~
which is inherently a positive quantity, he has
chosen the position of balance so that, in the
A feature of the invention is a system in which
absence of any signal voltage, the wiper of the
electric elements and mechanical motions are
potentiometer will be in one extreme position. If
combined to form representations of mathemat 10 a voltage e be applied to the input circuit, a vari
ical functions whose arguments are indicated by
able fraction K of this voltage will be selected
the mechanical motions.
by the potentiometer and supplied to the ampli
‘,‘Another feature of the invention is a compari
?er. This voltage is balanced against the volt
trical quantities.
'son circuit, associated with a servo-motor, which
continuously compares a plurality of input volt
age E in the control circuit to produce a devia
tion voltage 6e, thus
ages and supplies a voltage equal to the deviation
of the sum of the input voltages from zero to
control the servo-motor in reducing the devia
The shaft of the servo-motor is coupled by the
tion to any desired small value.
clutches to the brush of the potentiometer so that
-,_An important form of the invention is a de 20 its motion under the control of ac tends to set
vice which, when supplied with electrical volt
the wipers of the potentiometer to make 8e=0.
ages proportional to two sides of a triangle, will
set itself to indicate an angle of the triangle and
to produce a voltage proportional to the other
Inthis condition
25' The patented device thus can solve a linear
equation, having the right-hand member equal
Another form of the invention is a device
which, when supplied with voltages proportional
to zero, by varying one term, K, of the equation.
side of the triangle.
to the rectangular coordinates of a point, will set
In using a device of this character in accord
ance with the present invention where the input
'30 voltages may be positive or negative, the biasing
voltage preferably is adjusted so that the clutches
‘Other modi?cations, features and advantages
are in the released position in the middle of the
of the invention will be apparent from the fol
lowing description, and the drawings, in which
range, thus establishing a virtual zero value, and
Fig. l is a partly diagrammatioal elevation of
any deviation from this value will operate the
‘a system embodying the invention;
* -,
clutches to move the potentiometer wipers to re
Figs. 2A and 2B show a potentiometer card
duce this deviation to a small value, or zero.
itself to indicate the polar coordinates of‘ the
used in the system;
' ' ~
Fig. 3 is a geometrical ?gure illustrating one
application of the invention;
Fig. 4 diagrammatically and schematically 40
‘ shows an embodiment of the invention for solv
ing the equations involved in Fig. 3; and
v“Fig. 5 schematically shows a summing re
From one point of view, the present invention
may be considered as an extension and elabora
tion of the system disclosed in U. S. Patent
' The nature of the extensions made in the ?eld
of use of the patented device by the present in
vention may be expressed in a generalized for
v In the present invention, a single servo-motor
may be controlled by a deviation voltage having
the form
~ I
6e=§fi<® +1)
where 6/ is any argument in a form which may
be controlled by the shaft 01’ the servo-motor
2,003,913, June 4, 1935, E. C. Wente. While the
disclosure of this patent has been selected for
and b is any constant. The servo-motor will
the purpose of illustration, the invention is not 50 thus simultaneously solve any number of equa
limited to this speci?c device, but may be adapt
tions all having the same argument.
ed for use with many other forms of servo-mo
»A clearer understanding of the nature and
advantages of the ?rst extension in the ?eld of
- In .U. S. Patent
7 for
~ 4 some
use will be obtained from the following descrip
‘ininedvalue of biasing voltage on they grids of
tion, which isintencled only as an illustration of
the use of the invention and not as any limita
tion thereon.
conveniently be arranged so that the potentiom
eter is grounded by the leads 61, 68, though such
In Fig. 1, the motor I, differential gears 2, 3, 4,
magnetic clutches 5, 6, and control circuit 1, for
the purposes of discussion of the invention, may
be generally similar to the corresponding parts
in U. S. Patent 2,003,913. As the present device
may be operated on slowly varying voltages, the
a connection is not essential, and other connec
tions may be used if desired. The control volt
recti?ers may be omitted, and, if desired, a single
vacuum tube 10 used. The control voltages are
applied to the input circuit of the vacuum tube
‘Ill. The control electrode of .the vacuum tube 10
is biased by the source of voltage ‘H applied
through resistor 12. The resistor 13 corresponds
to the load resistor 34 disclosed in Patent 15
the potentiometer must be reversed.
2,003,913. Theclutch coils 5, 6, and associated
unilateral devices 14, ‘I5, operate in a similar
manner to the corresponding devices in United
age is supplied directly to the leads 65, 65 of
the potentiometer shown in Fig. 2B, but, owing
to the inversion of sign in the function, the po
larity of the voltage supplied to the lead 66 of
The potentiometer 9 may have a uniform
winding connected to leads l6, 11, or may have
a winding with resistance per unit length vary
ing in accordance with any desired function, or
varying in accordance with a set of values em
pirically determined. The leads ‘[8, 19 connect
ed to the wipers may supply the selected volt
ages to any desired circuit.
In, Fig. 3, the rectangular coordinates, x, y, o
States Patent 2,003,913.
Any desired standard
of a point T with respect to a point D have been
voltage, which may be zero, is applied to the in 20 determined in the form of voltages proportional
put of vacuum tube 10, and the bias voltage from
to the coordinates. The problem is to determine
the source ‘ll adjusted to make the anode-cathode
the angles of azimuth a and elevation e, and to
resistance of vacuum tube 10 equal to the resistor
produce a voltage proportional to the slant dis
13. The clutch coils 5, 5 are thus connected to
tance r from D to T. The line of zero azimuth
substantially eqm'potential points and are not op 25 may be assumed along the :2: axis. This is the
erated. If any other voltage be applied to the
type of problem frequently encountered in the
input of vacuum tube 79, this balance will be up
control of anti-aircraft artillery, though the in
set and the appropriate coil 5 or 6 will be ener
vention is not limited to this speci?c use.
gized. The shaft 8 is extended to carry the
Designating the hypotenuse of the ivy triangle
wipers of several potentiometers which are in 30 by h, the horizontal range, from simple trigo
sulated from the shaft, and from each other, il
nometry, we have
lustrated by the potentiometers 9, l0.
only two potentiometers are shown, it is apparent
that many more potentiometers may be operat
ed by the one shaft. These potentiometers may 35
have one or more wipers as desired.
Some of the
potentiometers may be directly concerned in con
trolling the voltages supplied to the control ‘cir
cuit 1, while other potentiometers may control
independent circuits in accordance with the mo 40
tion of the shaft 8 as set by the voltages supplied
to the control circuit 1.
.r==h cos a
' _'y=h sin a
:csin a=h COSaSina
2] 5111 12:12 sin2 a
> 1
'1: sin a—_1/ cos a=0
' y cos m='h sin 0: cos a
I1! COS 11:71. 0082 a i
From which
. 1 {(10)
1 In many cases, the, solution of geometrical
A; 1: cos d-l-y sin m=h ‘
problems involves the use of functions of the
In 'Fig. 4a source of ‘voltage 91 is connected
geometrical quantities concerned, such as the 45 across
the winding of a potentiometer 98 and the
trigonometrical functions of the angles con
_ wiper of potentiometer 98 is adjusted to select a
cerned. The potentiometer H! has a winding
voltage proportional to a: which is supplied
varying in resistance per unit length in accord
through an isolating repeater H of unit gain, to
ance with the sine function of an angle to il
lustrate this feature of the invention. The po 50 the lower diametrical point 65 of the potentiom
eter winding l2, of the type shown in Fig. 2B.
tentiometers may conveniently be of the known
Voltage is also supplied through the polarity re
form in which resistance wire is wound around
versing repeater l3 of unit gain to the upper di
a flat strip, which is subsequently formed into a
ametrical point 66 of the Winding l2. FOr clar
circle. The wire on the top edge of the strip
is bared, and the wiper arranged, When rotated; 65 ity of illustration, a single line isusedto desig
nate a circuit, the grounds shown on the various
to rub over the bare wires. The ?at strip is
repeaters signifying that one side of both the in
shaped to produce the desired variation of resist
put and the output circuits are grounded, thus
ance with movement of the wiper. Tolinsure
completing the return paths of the various cir
good contact at all positions between the wiper
cuits through the ground.
-; ‘
and the winding, the upper edge of the card 60
should be straight. Now, as shown in Fig. 2A,
plied to the repeater II, is positive, that the re
a normal sinusoidal function has a positive
'I l reverses or inverts the polarity to make
variation from 0 to 180 degrees, with a positive
it negative, and that the repeater I3 again in
maximum at 90 degrees, and a negative varia
tion from 180 to 360 degrees with a negative 65 verts or reverses the polarity. The voltage sup
plied to the point 65 will be proportional to —-:n,
maximum at 270 degrees' Such a card does not
and the voltage supplied to the point 66 will be
provide a‘ straight surface for the wiper, and will
proportional to +0.‘. As the resistance of the po
introduce 'suoh mechanical difficulties as to rein
tentiometer l2 varies per unit length in accord
der it impracticable. Preferably, the'potentiom
eter is made as shown in Fig. 2B, in which the 70 ance with a sinusoidal function, the :voltage
above ground ofthe winding of the potentiom~
wire may be wound on a single card of the shape
eter l2 will vary as a ‘sinusoidal function. i Iiaero
shown, or on two similar cards, each having the
shape of one half of the card shown in Fig. 2A
angle be at the point 61, and/ the wiper I4 ro-i
and the wiper is in contact with a straight sur
tates in a counter-clockwise direction, the spe
‘ face throughout ‘the revolution; ‘The circuit may 75 tential of the wiper 14 with respect to ground
will vary from zero to positive maximum to zero
with respect to ground will vary from zero to
negative maximum to zero to positive maximum
suitable networks may be used, depending upon
the frequency range to be repeated. Positive
voltage from the source 89 is supplied through re
sistors 83, 86 to the anodes of vacuum tubes 80,
8|. Negative voltage from the source 89 is sup
plied through resistors 85,88 to the control elec
trodes of repeaters 8|, 82. An intermediate tap
back to zero‘ and this is a variation which may
of, the source 89 is connected to connection 90
to negative maximum back to zero, and thisis
the variation of a positive sine. Iizero angle
be at the point 61 and the wiper l4 rotates in a
clockwise direction, the potential of the wiper M
b'ete'rmed a negative sine. If the polarities of
the potentials applied to the points 65, 68 be
reversed, the sign of the functional variation of
be grounded.
grid of the
tube 89
-, may
. be
10 and
self-biased in the usual manner‘by the cathode
the potential of the wiper l4 will‘also be re
‘ versed. If zero angle be at the point 88, and the
. For conveniencein securing a high gain, 'so
wiper l4 rotates in a clockwise direction, the po
as to provide a large amount of feedback, the
tential of the wiper H with respect to ground 15 vacuum tubes 80, 8|, 82 may be screen grid tubes,
vary as a positive sine, whereas, if the wiper
the screen grids being connected to suitable taps
l4 rotates in a counter-clockwise direction, the
of the source 89.
potential of the wiper I4 with respect to ground
a Negative voltage is supplied from the source
will vary as a negative 'sine. Also, reversing the
89 to the cathode of the vacuum tube 82, and
direction of the wiper l4 through 180 degrees will 20 positive voltage is supplied from the source 89
‘reverse the sign of the function. Thus, any odd
number of the following changes will reverse the
sign of the function, reverse the direction of ro
tation, reverse the polarities of the applied volt~
ages, vreverse the location of the zero angle, re
verse the direction of the wiper.
through resistor 92 to the anode of the vacuum
tube 82. By suitably proportioning the circuit
elements, the voltages applied to the cathode,
control grid and anode of the vacuum tube 82
maybe made of such value that the current ?ow
ing in the resistor 92 produces a voltage drop
equal to the positive voltage from the source 89.
Thus, in the absence of a signal voltage, the
anode of the vacuum tube 82, and the terminal
' ,If zero angle be at the point 61, and vthe wiper
I4 rotates counter-clockwise, as the potential of
the wiper M with respect to ground varies as a
positive sine, the potential of the wiper 22, which
leads the wiper M by 90 degrees, will vary from
positive maximum, to zero, to negative maximum
to zero to positive maximum and this is'the vari
ation of a positive cosine. If the direction of the
30 98 have the same potential as the wire 99 and no
potential is supplied to the output circuit. The
negative potential from the source 89 maintains
the anode-cathode current in the vacuum tube 82.
Assume that a signal voltage is applied to’ the
wiper 22 be reversed, so that the wiper 22 lags -
behind the wiper‘ [4 by 90'degrees, the poten
control grid of vacuum tube 80, so as to make
the control grid more negative. The control grid
of vacuum tube 8| will become more positive, thus
causing the control grid of vacuum tube 82 to
' tial of the wiper 22 with respect toground will
vary as what may be termed a negative cosine.
.Thus, if a cosine wiper leads a sine wiper by 90
become more negative, decreasing the anode
degrees, the cosine has the same sign as the sine; 40 cathode current of the vacuum tube 82 and the
whereas, if a'cosine wiper lags behind a sine
voltage drop in resistor 92 and causing the ter- wiper by 90 degrees, the cosine has the opposite
minal 93 to become more positive with respect to
. ‘sign to the sine.
the wire 90. The repeater thus reverses the
‘The wiper I4 is moved me counter-clockwise
polarity of the applied signal voltage.
direction from the point 61 from ground through 45 A large value of reverse feedback is supplied
the angle a, as yet undetermined, thus the volt
through resistor 94 from the anode of vacuum
" “age supplied by the wiper lgto the summing ref
tube 82 to the control grid of vacuum tube 80.
peater |5is proportional to
~ _
As is well known a reverse feedback of this type
. A source of voltage 99 is connected across the
reduces the apparent input impedance of the
winding of a potentiometer I80 and the wiper 50 vacuum tube 80, as viewed from the input cir
of the potentiometer I08 is adjusted to select a
cuit, to a very low value. Thus, a plurality of
voltage proportional to y which is supplied
input voltages, respectively connected from the
through the isolating repeater l6, and them
grounded wire 90 through individual resistors 95,
larity reversing repeater l‘! to the diametrical
96 to the signal grid of vacuum tube 88 will each
points of .the winding of the potentiometer l8 55 individually a?ect the vacuum tube 80 without
of the type shown in Fig. 2B. As :1; is to be mul
interaction, and the resultant effect will be the
tiplied by the negative cosine of a, and the neg
algebraic sum of the applied voltages.
ative cosine function is the same as a sine func
As a large value of feedback is used, the volt
tion displaced by 90 degrees, the wiper l9 is
age gain of the repeater is largely controlled by
mounted on the shaft 8, on which wiper I4 is also ' 60 the feedback loop. Thus, for each input, the
‘ mounted, at an angle of lag of 90 degrees com-_
voltage gain is proportional to the ratio of the
pared’to the Wiper I4; ‘The voltage from the
resistance of the resistor 94 to the resistance of
wiper |9 supplied to the summing repeater I5 is
the input resistor, such as 95 or 96. If these re
, then proportional to —1/ cos a. Thus the volt
sistances are equal, the voltage gain of the re
age supplied to the comparison circuit has the
the form 6e=m sin a-y cos or and this is an illus
tration of the ?rst extension. ' The summing re
, peater I5, which may be of the type shown in Fig.
5, is a thermionic repeater comprising three vac
peater is unity. 'l'hew'i?tggeférorn/the
e control
circuit , and causes the excitationtoof one
or the
other 0
e clutch magnets 5, 8 rotating the
shaft 8 to such an ‘angle a as will make the input
uum tubes80, 8|, 82. As this repeater may op
voltage, 86 to the control circuit ‘I equal to zero,
erate with low frequency or slowly varying volt 70 I that is, a: sin a-g cos 11:0. The position of the
; ages, the 'interstage networks, formed by re
wipers then indicates the angle a. As there is
, sistors 83, 84, 85 and resistors 88, 81, 88, may be
no theoretical limitation on the size of the mo
01' the type shown in United States Patent
tor | or gears 2, and the accuracy and sensitivity
of the control by the clutch magnets is not af
‘1,751,527, March v25, 1930, HrNyquist. Any other
corresponding to ‘the same angular value of sai
_fected by the power controlled, the drive may be
"made powerful enough to directly control some
function, means for obtaining the algebraic sum
‘device, such as an anti-aircraft gun, rotating the
‘ of said selected voltages means for comparing the
gun in azimuth to the angle indicated by the co
sum of said voltages with a standard voltage
ordinates a: and y. '
and a device actuated by the deviation of said
The wiper 2! is parallel to the wiper i4'and
algebraic sum from said standard voltage to
simultaneously adjust said selection points for
will thus supply a voltage 1/ sin a to the summing
repeater 62. The wiper 22 is 90 degrees from the
wiper l4 and will thus supply a‘voltage :0 cos (1,,
and, as wiper 22 is 180 degrees from wiper I9, 10
this voltage will be of opposite polarity, that is,
. the-voltage supplied to the summing repeater 62
will be +0: cos a. The ‘voltage produced in the
output of the repeater 62, say, across the re
sistor 23, will be proportional to
‘n: cos a+y sin a=h
successive angular values until said deviation is
reduced to zero and the position of the wipers in
dicates said angle.
, 2. In combination, a source of voltage varying
in magnitude with one side of a right triangle,
a ‘?rst potentiometer having a winding varying
in resistance per unit length with a complete
sinusoidal function and a ?rst wiper, a ?rst 'po-‘
larity reversing repeater, means for connecting
one pole of said source to the points in said wind
the horizontal range. If h wereneeded as a mo
. tion a second servo-motor could be used to gen
ing where said function passes through zero, and
---''0 cos e, and the sum of these voltages 6e, sup
function is a maximum, means for simultaneously
erate the desired motion by associating with the 20 the other pole of said source to one point where
said function is a maximum, and through said
motion a variable voltage to compare with the
repeater to the other point where said function
voltage h.
is a maximum, a second source of voltage varying
If the repeater 62 reverses the sign of the po
in magnitude with the other side of said triangle,
tential representing It, so that the sign of this
a second potentiometer having a winding Varying
potential is opposite to the sign of the potential 25 in
resistance per unit length with a complete
representing 0, then, when these potentials are
function and a second wiper, a‘second
applied to the device shown in Fig. 4, the po
polarity reversing repeater, means for connect
tential reversing repeater H, or l6, as required,
ing one pole of said second source to the points
may be omitted, so that the applied potentials
in the Winding of said second potentiometer
' will be of the same sign as a and y.
where said function passes through zero, and the
If we now apply the voltage h in place of a: to
other pole of said second source to one point in
a second system as shown in Fig. 4, and apply
the winding of said second potentiometer where
the voltage 11 in place of y, the wiper M will se
said function is a maximum and through said
lect a voltage proportional to h sin e, and the
second repeater to the other point where said
wiper l9 will select a voltage proportional to
plied to the control circuit 1, will cause the shaft
driving said wipers, said second wiper lagging 90
Thus, given :13, ‘y, and o, the two steps have
wiper contacting the winding of said ?rst poten-v
tiometer and a fourth wiper contacting the wind,
degrees behind said ?rst wiper, and means for
8 to rotate to indicate the angle 6. At the same
adding the voltages selected by said wipers and
time the wiper 2! will select a voltage propor
said driving means by the sum of
tional to 1) sin e, and the wiper 22 will select a
said voltages, whereby the displacement of said
voltage proportional to it cos. c, and the sum of
wipers indicates one angle of said triangle; V345,
these voltages will be a voltage in the output of
3. The combination of claim 2 ‘with a third
the ‘ampli?er 62 equal to it cos 5+1; Sin e, that is, r.
solved the equations
ing of said second potentiometer, said wipers
being driven by said driving means, said third
J (12)
wiper leading said ?rst wiper and said fourth .
wiper leading said second wiper by -90 degrees,
to produce the angles a and e physically and to
produce a voltage proportional to r. The two
systems may Work simultaneously to produce the
and means for adding the voltages selected by ‘4
w. said third and said fourth wipersto produce a
voltage proportional to the hypotenuse ofv said
?nal result.
As discussed above, the second servo-motor
may be powerful enough to directly elevate an
4. In a computer, a source of voltage propor
tional to one side of a right triangle, potentiomi
anti-aircraft gun to the angle 6. The voltage 1‘
may be supplied to some device which will indi
cate the appropriate fuse setting for this range. I
eter means for selecting from said source a voltage porportional to the sine of an angle of said
ber of equations by using more of the devices
braically adding said selected voltages and motor
triangle, a second source of voltage proportional
to another side of said triangle, other poten
By the use of two of the devices disclosed in
Fig. 4, a set of three equations having three un 605 =tiometer means for selecting from said second ‘
source a voltage proportional to the negative of
knowns has been solved. Evidently, this use of
the cosine of said angle, electrical means for alge
the invention may be extended to solve any num
What is claimed is:
1. In combination, resistance means to attenu
means controlled by the deviation of the sum of
said selected voltages from zero .to ‘adjust both
said selecting means to reduce said deviation to
ate a ?rst voltage in accordance with a sinusoidal
zero, whereby the displacement of saidmotor
function, wiper means to select an attenuated
voltage corresponding to an angular value of said
means indicates said angle.
function, resistance means to attenuate a second
voltage in accordance with a cosinusoidal func
tion, wiper means to select an attenuated voltage
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