A NEW ELECTRICAL APPARATUS FOR HARMONIC ANALYSIS AND SYNTHESIS

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000100080006-7
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 16
• Document Creation Date: December 22, 2016
• Document Release Date: May 30, 2012
• Sequence Number: 6
• Publication Date: August 21, 1950
• Content Type: REPORT

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~~ ~~ T?kh~l~l~o~~dkh Nau~,
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~c No No 3, 19l6
(OHF IDEIU tAL
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50X1 -HUM
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/30 : CIA-RDP82-00039R000100080006-7
(ONFI DENTIAL
SZV. RKa~ N~uK,S3.SR,,Q1' 'rc.kh NauK, No 3, Iq`Fd
P. 39., Gov
Xu. Q. Toletav
The probloma of harmonio to 1yaia are not new. Nevertheleaa, however they
have beet none of their importance and a fast reliable and, at tho same time,
Auffioiently a~oourate method for finding the ooetfioiente of a Fourier aeries
hao otili not been found, inepite of many i:ntennive aearoheo.
Mothode that involve aotual oomp tationc and numerical analysiQ require a
great aIAA1rflt of work and time far tasting and therofore prove to be but slightly
convenient in those oasea where large-naale invoet~.gatione are necessary; that
ia, where a large number of Duryea are resolved into Fourier serien with many
harmonios. Ecletin types of meohanioc1 harmonic analyzers that posoesa more
or leas widespread application (Mader, Coradi, NenriCI , etc) -- although they
of serious dofects, whole prasonoe often prevents their une.
f acUttate oon siderably the work of harmonic analysis -- suffer from a number
qualities of the person oncrating the apparatus.
In working with these apparatuses one must draw a graphical representation
of the ourve to be analyzed, as many times as a harmonic must be found, This
work itself requires a~1fficient experience and errors depend upon the personal
In order to make the results more accurate, it is neoesaary to repeat lev-
oral times the drawing of the curve and to oaloulate the average value of the
coefficients found.
Such a method of operation does not even give high accuracy. This is ex-
plained by the fact that a graphioo-mechanioal method is employed here, and the
accuracy of any graphical calculation is aiway$ limited by the accuracy of con-
gtruotion of the graphs.
Moreover, none off' these apparatuses permit one to conduct synthesis; that
is, to obtain the ' auinmed' curve oorreeponding to given ooefficienta of a har-
monic series. Such a problem, however, is often enoountered by reaearchera and
require as muoh work as does analysis fdr its solution.
In thie artiole the author proposes a new apparatus based on principles
other than those of previous analyzers. This apparatus permits one to conduct
1
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C `" 1
+af'
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50X1 -HUM
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(OHFIDENT
ou a
diralAtl~r dram the vaLuea of th0 ~rvo' ordinate n ~ivor~ in ttbV1'
M
ao
a
nalysis ui~ed flr the
~aalifioationa arc not x?~
form In opoxaticna w~.th it, high re and of Pdotor~
ouxa is indepondont of the poraon 0poxat1ng the appsxstaa
~,,cl ~~~ i can in principle be made a? that it always
~
~nad taahsiioal~Cthe appara ~a_ ~
Tho a Food off' apoxatign on it
iven demo of aoouaraoY)
giveQ reauta with a g ho ed that thie apps.
at on other anal7eere 3 thin it is p
o;~Qeoda aonaiderablY h Q.aoale
a eoiall7 in thoao cases whore oompu-
rat~~e oars f~r~d a,pp1ioatic~- ?p 1?otro~ne'trY of
oratory of oleotro-modeling
tationa are larg
~a~,uir?d~ The 1a
?
the power Znatit exeouting the ?irat practise/
ate~ Academy of ~oienco u99R~ i n And
e which p?,tenta rind in the oo~~ree
oonatruotion of such an apparatu
design and
o~ onehalf and and w!.th an accuracy
8 harmonica or a o~Irv? being analY
- hoar 1
'tip to 1~ o? maximum. In the ? po?a ~6 ?r~" mme thin apparatus one can find with
iaallY in a
djnatoa (ov?rY 10?) of a total curve, i? trio curve is gi~ren analYt
f harmanias~ done not ?xaRed l8.
Foi:irier eories Wtoeo number a
oonstruotion part of the apparatus
A. Ti. Qo?lin worked out the
pP(l1ulTUS DtIRThO flAR1OI4IC A~IALYSTS
2. SCit1}11 0? OPERATION 0TU1 A
coefficients of the Fourier soriee
a status is int?nded t ~ find the
Thc pp
Lion f(x) moat be expanded; that ion to fird the aoaf
?into which a given f~ano series;
ie 0: 1, 2, 3...) of the ? Ollowing ~,oionts Ak and ~ (whore k
n -~-- 2x--~j,oon
f(x) -: Ao ..{-- Alsi x A2ein +
ti li?r~ which is represented
in detail of the apparatus is the P
The ma
te: All fides a'e appended in the anne
tioally tn Fire 1 ~o
schema
erminsle 4N) is connected to an alt?r-~
soil of transformer '? (t
The primary lied to the
The voltage of the aeaondary coil is supp
ne,ting-current airau~.t?
potentiometer.
-t
~' Y p of
E mo coil on~~/1~uppl
v1.ng the ,glide P on the potentiometer coil the
voltage U to the voltage divider CD.
why. oh perrnits one to a stabli eh on CD a given
potentiometer AB is graduate,
to a potentiometer peals
art of V2 c~ireatlY aooording a curve
P
s the number of ordinates into which
The number of tipiiers eq,ual
a number of portions ie divided.
graduated into
(O$FDET t
Declassified in Part - Sanitized Copy Approved for Release 2012/05/30 : CIA-RDP82-00039R000100080006-7
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/30 : CIA-RDP82-00039R000100080006-7
CONFiDET;AL
As an oxampl.o, an apparatus ie deaoribed below whioh oa1ou1atAe with 36
ordinates and 1 hsrmonioa. An apps' t a oan, in prinoiple, be o~-nstruoted
for any number o1' ordinates and hermonioa.
The apparatus doribed requires 36 mutipliere.
Lot us daaume that the multiplier rspresmntod in Ficuxe 1 oorrooponda to
the n-th ordinate. In thin ease the voltagQ divider cD muet have outputs ae-
leoted in suoh a way thato 1) a part of the voltage appliAd to OD, which
(part) equals
uln - =Lbw/~n(1Qa)a/ (b)
cote between point 0 end 1 (Figure 1); 2) a port equal to
aote between points 0 and 2;,...m) a part equal to
Un = U~/sin (m.iOn)?/ (o)
acts between pointy 0 and m.
Aa is seen from the formulae, only a fraotional part of the voltage U~
must act between point 0 and any other output, since the abpolute value of the
acne of any argument is always either zero or lees than unity.
This fact makes it possible to realize a divider in the form of an ordinary
reeiatance with tapa without employing more complex means.
The ntnmber 10, which enters everywhere ac a factor in the argument, poaeeaaea
the following derivations the whole period of the curve analyzed, which is ae-
eumed to equal 360?, is broken iap in this oaae in 36 ordinates of equal parts
which (parts) are apaoed from one another, in degrees, by the amount %O/36 =100;
onnsequently, the number of degrees from the origin to the n--th ordinate will
be 10n.
The number of taps of the divider must equal the number of terms of the
aeries -- in thin oaae L.
If, besides a sine expansion, we alao assume a cosine expenaion, then the
divider must poasesa additional tapa beeidea the Indicated taps. The voltagee
between these tapa and the null point moat equal reepeotivelyt
?OtiF1DECdl'IAL
Declassified in Part - Sanitized Copy Approved for Release 2012/05/30 : CIA-RDP82-00039R000100080006-7
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/30 : CIA-RDP82-00039R000100080006-7
Thug in order to expand a certain function into d Fourier aeries aontain-
in~ 18 harmonioa and having its terms mado up of both sixes and oosinea, eaoh
dtvtdor mmot be provided with % taps, however he aotua 1 number of divider
topa is condiderablY 1eso, ainoe many valued of /sin(n'1On)?/ and /aca(m'3.On)?/
ooinoido. For this reason tho nwmbezr of taps does not exceed 10.
Aotualiy, oinoe in and n arc whole numbers, tho produot mn also oar be only
whole pocitivn numbers; therefore the ar umentg of all pines and oosinee will
always be 1tip1oa of 10.
It in easy to aeo that the absolute valwoa of the oinoe nand ooaines will
rit be repeated onl f ,then mzs vary of
When mn eq'ualo 10, we
/sin (10.10) 0/ - = /einl00?/ = /ein30?/ = /sin (8' 10 )0/,
/einUO0/ - /3in700/,
/ainl2O0/ :- ' /cin600/, eta.
I is
Thnthe mead,mum number of tape on the divider dividing the voltage into
us
quantities proportional to the absolute values of tho sines of anglea, whioh
(values) are multiplec of 10, I'e /~j //i/f/fl/( (/ /,7
The resiatanoe between the nu11 point and the respootive tape must be pro-
portional to the following values:
R01 /einloo/ = 0.174 R06 P .
/
R02 /en20?/ 0.342
R03 /ein30?/ :.. 0.500 R08 /sin 0?/ = 0.9$5
/sin9O?/ =1.000
Roy /ain40?/ ==o0 )643 R~ E
.~
In order to divide the voltage U into parts proportional to /oos(10xnn)'/,
CD
it is neaeseary to have between the null point of the divider and thetespeotive
tape resistances that are proportional to:
d A 4f01 = 0X66
/ein50?/ -` 0.766
A completely similar dependence can be obtained for the cosines.
(ONFJDE11TIAL
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CONFIDENTIAL
/ooo9o?/ 0.000
Pbom a oomparieon of' this table (with the preoedin~ one (t), it i~ ovi-
dent that i
that ie, in order to form division y ooainoe ono oan tae the eam? tape ae thoao
used for division by einoa.
Lot ue oonaider now how to dntermine the oooffioiento of a Fourier aerieo.
Lnt un aeaume that we noad to determine thn ooe!f ioiont for the K-th harmonio
of tho ciao.
Ae :Le known from tho theory of Fourier seriea:
whero ie the period of the funotion f(x).
The relation (1) can be approximately deedribed in the form:
or in computation with cbgrees, instead of radians:
In our oaae the total period is divided up into 36 equal parta3 therefore
thua'P' ..E = $'.4x, and formula (2a) tran aforms into:
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(ONFIn Ei1ii
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