ELECTRICAL REPRESENTATION OF FUNCTIONS IN USSR

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80-00809A000600400644-2
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 10
• Document Creation Date: December 22, 2016
• Document Release Date: August 25, 2011
• Sequence Number: 644
• Publication Date: August 10, 1951
• Content Type: REPORT

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CLASSIFICATION CONFIDENTIAL
CENTRAL INTELLIGENCE AGENCY REPORT
INFORMATION FROM
FOREIGN DOCUMENTS OR RADIO BROADCASTS CD NO.
COUNTRY USSR
SUBJECT Scientific - Electricity instruments
HOW
PUBLISHED Monthly periodical
WHERE
PUBLISHED ? Moscow
DATE
PUBLISHED Nov 1950
LANGUAGE Russian
THIS DOCUMENT CONTAINS INFORMATION A!HECTING THE NATIONAL DEFENSE
or THE UNITED STATES WITHIN THE REAMING OF ESPIONAGE ACT SO
U. S. C.. 35 AND SE. AS AMENDED. ITS TRANSMISSION OR THE R[Y[LATION IN ANY
TO AN
PRONISRITED. IS PR O?
U.AUTHQ HI[ITEDC ST TLAW. REPRODUCTION OF THIS FOR M ,,RIZLD
ELECTRICAL REPRESENTATION OF FUNCTIONS IN USSR
F. V. Mayorov, Dr Tech Sci
Submitted 8 Jun 1950
Inst Er4p sion mechanics and
Calculating Tec ques
_?1cad"5ci"USSR?
fFigures are appended]
Soviet Editor's Note
The US periodical, Review of Scientific Instruments, Vol XXI, No 1, Janu-
ary 1950, p 77, contained an article The Principle and Design of a Universal
Generator of Functions With Potentiometers" by A. Korn. In this article, Korn
presented a "new" type of functional device with potentiometers, which was
actually proposed and developed in the USSR by F. V. Mayorov in 1946. In 1947,
Mayorov reported on his invention in the Department of Technical Sciences of
the Academy of Sciences USSR, and the report was published in Izvestiya Otdeleniye
Tekhnicheskikh Nauk Akademii Nauk SSSR, No 11, 1947. Mayorov's invention cov-
ered not only functional devices for one independent variable, but also devices
for electrical representation of two a..d three independent variables not cov-
ered in the article published in the Review of Scientific Instruments. Thus,
Korn's article is not original and repeats work done in the USSR years ago.
Mayorov's article, in which he describes his invention, follows.
Need for Electrical Representation in. Regulation
The electrical representation of some given function in the form of an elec-
tric voltage is frequently required in instruments for automatic regulation and
also in electric computers. For example, in artillery fire-control'instruments,
one must deal with ballistic functions describing the motion of the shell. The
control of mechanisms according to any given law also requires that a functional
dependency be introduced into the regulating device. There are'the so-called
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CLASSIFICATION COIF IDENTIAL
DATE OF
INFORMATION 1950
DATE DIST. 10 Aug 1951
NO. OF PAGES 10
SUPPLEMENT TO
REPORT NO.
THIS IS UNEVALUATED INFORMATION
50X1-HUM
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functional potentiometers, with which a representation of functions of one in-
dependent variable can be obtained,. However, such potentiometers are useful
only for the representation of any one function of one independent variable and
moreover for a limited class of these. The production of the potentiometers
with shaped mandrels used up to this time is expensive and their accuracy is
none too high. In 1946, the author proposed and developed a new method for
representation of functions using electrical profiling (curve-fitting) of a
potentiometer by means of forced distribution of electric voltage along the
potentiometer according to a given law (Certificate of Authorship No 72856
awarded on 19 April 1947). This method of electrical representation of func-
tions covers a broad class of both monotonically and nonmonotonically varying
functions and sign-variable functions,
A very important characteristic of the new method is that the law govern-
ing the change of voltage can be set arbitrarily lysforothexsameepoten-
tiometer, which is especially important for integrating where the integrand is established according to any required law. Moreover,
the new method is useful not only for the representation of functions of one
variable but also for functions of several independent variables. In addition,
this method provides much higher accuracy in the operation of the device, i.e.,
of the order of hundreths of a percent. The substance of the new method is
that the resistance of a linear potentiometer is divided into a number of sec-
tions which are shunted by auxiliary resistors with the purpose of forced dis-
tribution of voltage according to a given law. The value and number of the
resistors are determined by the given law of voltage variation and the accuracy
required.
A potentiometer circuit with shunting resistors is shown in Figure 1. The
voltage taken off between point 1 (the beginning) and the sliding contact of
the potentiometer changes according to the law
U=Uof(,x), (1)
where f(x) is the given function; x is the relative displacement of the slid-
ing contact of the potentiometer (proportional to the independent variable);
and Uo is the voltage applied to the potentiometer. Here the linear potentio-
meter with a continuous winding along its length is divided into a number of
-
sections, the resistances of which we designate al, e2,,... , an. These sec-
tions are shunted by the resistances b1, b2, , b. In addition, the additional
resistances ro and rn4l are connected in series with the potentiometer to set
on the potentiometer the values of the resistances corresponding to the initial
and final values of the function. With the help of the shunting resistbl,
b2,..., bn, the voltage distribution along the length of the linear potentiometer
is varied to correspond with the given functional law. Actually, the resistance
of any kth section of the functional potentiometer together with the shunting
resistance is
c-k f-bk
The resistance of the functional potentiometer from the beginning (point 1)
to the end of the kth section is
.t' k = 57 -Kfb (3)
~t=> K
The voltages distributed along the length of the potentiometer are propor-
tional to the resistances
Uo R
o
where Ro is the total resistance of the entire functional potentiometer together
with the additional and shunting resistances, i.e.,
CON F VPINT 3glr;'.,
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If the voltage distribution along the length of the potentiometer must be
defined by formula (1), it is obvious that the values of the resistances ro, rl,
r2, , rn, rn+1 must be,-
/
ro = R"rf rX
R,
/q = f f (x,) - rx,, d-7,
pp
.gyp, ..1, , . , --n
where the sections are shunted. Here we assumeathat the resistance Ro+corre-
that f(xmax) - 1 Therefore, in they calculation of the resistances ro, rl, r2,
- iii _tit
t
therein the relative Values
u
e
of the function f(x),
rn of the functional potentiometer and substituting them in (2), we obtain the
uired in order that the voltage
values of shunting resistances bl, b2,. ? req
the length of the potentiometer according to the given func-
l
a
ong
he
l
ote
omete
lawn +
p
?~i
-
tona
the dependency f(x) will be linear within one section with the required degree
__a +L... ..ti..,..+i.lg nnint.a nn the
of accuracy. 'rnu5? U". 1-1- ~~~_---- -
potentiometer can be determined by a linear approximation of the curve f(x) by
ree of accuracyo
d de
i
g
re
straight-line segments This will give the requ
the voltage taken from the potentiometer will have some relative error because
the interval between xl and x2,. Consequently, the curve or the function y
f(x) has a linear approximation in this interval (Figure 2).
The relative error of the linear approximation can he determined directly
- Uz X -- xo s -V (7)
Go 6/11 U x/ G
where Uo is the voltage applied to the potentiometer and U1 and U2 are the po-
-_ _ -_+1
+c
t .list noes Yl and
n
a
x2 from the beginning of the potentiometer (in relative units.
Thus, the voltage U taken from the potentiometer will vary continuously
(the approximation error).
Potentiometers for Nonmonotonically Varying and Sign-Variable Functions
n
--
l..... -+ -------
cording o a give
--
tween the supply source terminals and the shunting points xo, x1,-.., Xn of the
rminals
b
th t
f
o
e
rom
linear potentiometer (Figure 3), The sections are shunted
of the supply source, so that the additional resistances bl, b2 1_' bn may be
--.
f the c
source _
o
pp y
COIIy1LLCrGLL ao oaauu~aa.p
By varyi.,g the value of these additional resistances, we can arbitrarily change
-
_
the
tentiometer
ng
f
po
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eat
Figure 4a shows the representation of the nonmonotonically varying function
given in Figure 4b. The voltages proportional to the ordinates b0, boll b02, and
br,3 are given by the corresponding additional resistances while the shunting resist-
ances bl, b2, and b3 serve fvi, electrical profiling (curve-fitting) of the linear
potentiometer in the interval between h0 and b01, then b01 and b02, etc. If we
are given a sign-variable function (Figure 5), the middle sections of the potentio-
meter are connected together as equipotantial and at these points the voltage
taken from the potentiometer is zero, since the point 0 serves as the beginning
of the reading The additional resistances h0i bl, and b2 are used to obtain the
required voltages at the points where they are connected,
The value of the additional resistance for any section of the potentiometer
where Uk, Uk-1? and Uk+l are the voltages corresponding to the points xk, xk-13
and xk+l where the additional resistances are connected and ak and ak+l are the
resistances of the sections of the linear potentiometer between the points xk-1,
xk and xk, xk+l If bk turns out to be negative when calculated, it means that
an additional resistance should be connected to the other terminal (minus) of
the supply source,
Representation of Functions of Two Variables (Electric Conoid)
Many functions with which we must deal in computers cannot be expressed
analytically and are given in the form of experimental tables or graphs, for
example, ballistic functions.. Up to this time, mechanical devices, the so-called
conoids, have been used for representation of functions of two variables, since
there have been no electrical methods of representing functions of two variables
in the form of continuously varying voltages.
The author has proposed a method of representing functions in the form of
an electric voltage using a functional potentiometer with variable shunting
resistances. In this method, the principle of approximation of the given func-
tion by straight-line segments is used.
Suppose we are given a function U of two independent variables x and y.
We represent this function (Figure 6) in the form of an electric voltage U
taken from a linear potentiometer Px, the sliding contact of which is displaced
in proportion to the value of the independent variable x. The sections of the
linear potentiometer Px are shunted by variable functional resistances bl, b2,
,,,, bn. The sliding contacts of these resistances rotate on a common shaft,
the angle of deflection of which is proportional to the variable y. Two addi-
tional functional resistances ro and rn+l, the sliding contacts of which also
rotate on the y shaft, are connected in series with the potentiometer Px. They
are used to set the initial and final values of the function.
To determine the shunting points xo, xl, x2,--0, xn, we make a number of
graphs of the function U for some given values-yo yl, y2,.,,.,, Yn which cover
the range from y yo to Y = Yn, i.e., graphs of the functions
1 4 ) p = t ' (X' yo ~'
(x,
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Then we approximate each curve of (9) by straight-line segments in a manner
that their approximation error does not exceed the assigned value. In approx-
imating these curves, we select those values of the shunting points xo, xl,=a?,
xn which satisfy the acsigne(i accuracy of approximation for all curves of (9).
From the conditions of the problem, the additional resistance ro when the
sliding contact of the potentiometer Px i.. at point xo must be (for any value
r= f xa'y) iPo,
where R. is the total given resistance of the functional potentiometer.
When the sliding contact of Px is at the poi.nts xl, X2-.,, xn, the resist-
ances rl, r2, - . , r0 evict be:
Z-1 rx
=,o - , (X,,, y) Ro ?
Since we know the resistances r0, rl, r2,... , r from formula (2), we can
determine the value of the :hunting r~si::`ances For values of x between xo and
xl, x3 and x2, x2 and x , etc , the values of the function U = f(x,y) will be
determined with a certaun error, which will depend on the number of sections (the
approximation error).
Representation of Functions of Three Independent variables
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{ (A, Y, z) (12)
of three independent variables x, y, and z cannot be represented by means of a
mechanical conoid, since the conoid is a surface in a three-dimensional space.
However, we can suggest an electrical method for representing the function (12)
in the form of a voltage U dep-ndent on tree variables:,
We take the potentiometer Px {Figure 7), the sliding contact of which is
displaced proportional to x? We assume that the additional and shunting restst-
ances ro, bl, b2, ?.., bn, rn+l of this potentiometer represent some functions
of the two remaining variables y and. z. We select the shunting points xo, xl,
x2)?,,,,1 xn of the potentiometer Py, in such a way that the error in the determina-
tion of U = f(x,y,z), where y and are some discrete values of the parameters
y and z, does not exceed the assigned value S. As we did in the case of a func-
tion of two variables, we made a number cf graphs of the function U of the variable
x for various discrete values y and z which cover the entire range of variation
of the parameters y and z. '.,ea, the curves
IT _ f(t,J,z)? (13)
On the graphs of the curves (13), we select those values of xo, x1,o ?,
x between which the sections of the curves (13) can be approximated by straight
n,
lines with a sufficient degree ct accuracy. We now determine the values of the
resistances for the separate sections of the functional potentiometer which will
reproduce the function (12).
OOMFWWENT A .
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Obviously, for x = xo, the additional resistance ro should be:
ro= P.of(xo,y,z)
for any values assigned to y and. z.
In the same way, the resistances rl, r2,:?., rn of the functional poten-
tiometer must be?
S' ?f, z)J~
~=1 y, )-7,
/q = lro Lr fix,,, y, z) -f (x?-~, q z) 1 (15)
n
C/. L
'_11 4-1
where R0 is the total resistance of the functional potentiometer, which remains
constant..
The functional resistances ro, h1, b2,...., bn and rntl are functions only
of the two variables y and z and can be represented in be form of an "electrical
conoid," In the circuit shown in Figure 7, the values of the resistances r o,
bl,??^, bn rn+1 are developed (with the help of tracking system consisting of
servomotors SD, SD2, etc, and electronic null amplifiers EUo, EU2, etc) propor-
tional to the values of the volt.age:s taken from the functional potentiometers
Py0, P 1, P , P n+l' which are the electrical representation of the functions
of tvoyvari lesyy and z For this purpose, the sliding contacts of the linear
potentiometers PyO, Pyl,...., Pyn, Pyn+l are displaced through the shaft of the
variable y, while the sliding contacts of all the shunting resistances Rz ? RZ2,
R73, etc are displaced through the shaft of the variable z. Thus, we obtain
a variation of the resistances ro, b1, b2,,,..., bn, rn+1 as a function of y and
za The number of sections of the potentiometer Px and of potentiometers P0,
Pyl,.., , Pyn, Pyn+l depends on the form of the given function and the accuacy
required in its representation. Ordinarily, in practice it is sufficient to
have five or six sections in each potentiometer, which provides comparatively
high accuracy. The approximation errors of both potentiometer P. and potentio-
meters Py0, Fyl,,- basically determine the error of such a ievice as a whole.
The devices described make it possible to represent a very broad class of
functions having tabular, graphical, or analytical expressions.: The restric-
tions on the class of functions which can he represented by these methods are
imposed basically by the physical properties of the elements (potentiometers
and functional resistances):
Design of Functional Devices
The device developed by the author for obtaining any functional dependencies
consists of a linear potentiometer, the sections of which are shunted by variable
resistance boxes The potentiometer (Figure 8) consists of a closed aluminum
ring 1 with a diameter of 130-150 mm covered with insulating varnish on which is
wound (with the help of a special winding machine) about 8,000 turns of thin
enameled constantan wire 0.05 mm in diameter, After it is wound, the ri?3 is
pressed into a bextolite housing, The enamel is removed from the face surface
of the ring and I .e sliding contact 3 of the potentiometer moves along the con-
tact b,.d thus formed
The sliding contact is displaced along the circumference of the ring on
the shaft 4 with the help of a Vernier worm mechanism 5. A rough scale is in-
stalled on the shaft 4 and a fine-reading worm scale on the shaft 6, so that the
total number of scale divisions is 10,000. The brushes 1-18 (with silver con-
tacts) are installed rigidly along the edges of the c.4cact bed of the potentio-
meter. Thest are used to connect the shunting resist-ices to the potentiometer
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9ecti.ons They touch the potentiometer turns and divide it into 40 sections
(only 18 of these are shown in Figure 8). The brushes are installed along the
edge of the contact bed so that the sliding contact of the potentiometer can
move freely along the contact surface.
Decade boxes connected to the brushes 1-18 with a multistrand cable were
used as shunting resistances. The number of shunting resistances required is
determined by the accuracy required of the functional device, For this purpose,
a linear approximation of the given function is made and the m"^ber of sections
required is determined, The values of the shunting resistances found from cal-
culation are set up with the resistance boxes, This calculation is not diffi-
cult and can be made in 15 or 20 minutes. Tables of the values of shunting re-
sistances can be drawn up beforehand for well-known functions.
For the most frequently used analytical or tabular functions, special sets
of resistance coils are used instead of resistance boxes, These are connected
to the potentiometer brushes by means of pluggable connectors, Tests of an
experimental potentiometer, made by the author according to the "sine" law,
showed that with 3l taps on the potentiometer, the maximum error for sin x was
0,01-0003 %, i-e,, the valuer of the function were obtained in the form of an
electric voltage with an accuracy tof fouthe r places,. This a of about 25,000 11 9nces with the shunting resistances was 10,000 n . This potentiometer was
usci by the author to introduce integrands into an integrating device.
The author has also developed potentiometers with controlled wire spacing
and shunting resistances for computers where the functional law of voltage dis-
tribution does not have to change.. These potentiometers are machine-wound
linearly with a variable instead of a constant spacing, i.e., the density of
the potentiometer turns varies according to a given design. The type of spac-
ing is established in the machine by a shaped eccentric. The use of nonlinear
winding permits us to reduce considerably the number of potentiometer sections
with shunting resistances. Figure 9 shows a diagram of a circular sine poten-
tiometer made from 0 to 3600, which has only two shunting resistances (for the
values x = 70? and x- 83?) from 0 to 90?. The winding from 0 to 70? is made
according to the sine law (as is that from 70 to 83?).
Testing of the circular sine potentiometer with a ring diameter of 80 mm
and a resistance of the entire ring of 12,67211 showed that its accuracy was
002-0.3% if the potentiometer taps were set fairly accurately. The method of
shunting resistances proposed has been used. extensively by the author for cor-
recting production tolerances in linear potentiometers. Because of production
conditions, he maximum possible accuracy in potentiometer production is 0.2-
0.3%. Shunting resistances enable us to increase this to 0.02-0.03%.
Correction of a loaded potentiometer with the help of shunting resistances
is also possible in potentiometric computii, circuits. The loaded potentiometer
is electrically profiled. according to the required functional law in dependence
on the value of the load resistance.
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Figure 1., A Potentiometer With Shunting
Resistances
Figure 2, Determination of the
Approximation Error
for y-= const
Figure 3. A Potentiometer With an Additional
Resistance
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Representation of a Nonmonotonic-
ally Varying Function
Figure 5, Representation of a Sign-
Variable Function
Figure 6o Representation of a Function of
Two Variables
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Figure 7 Representation of a Function of Three Variables
Figure 8. Potentiometer Construc-
tion
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Figure 9. A Sine Potentiometer With
Two Nonlinear Winding and
Shunting Resistances
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