SCIENTIFIC ABSTRACT MARKANOV, N.A. - MARKAROVA, T.A.
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CIA-RDP86-00513R001032410010-9
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S
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100
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Publication Date:
December 31, 1967
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SCIENTIFIC ABSTRACT
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HARKANOV, N. A.
FARKOOV, N. A. -- "Penoganchl (foamed gypsum-clay stucco binder?).*
Inst of Structures. Acad Sci Uzbek SSR. Tashkent, 1955- (Dissertation
for the Degree of Candidate of Technical Sciences.)
SO: Kmixhnava letopIALL, No. 4, Moscow, 1956
HARUKOV, N.A.. kand.tekhn.nauk
.W~ . ;: Testing and controlling properties of lightweight materials and
concrete mixes. Bet. I zhel.-bet. no.6:231-232 Je 158. (MIRA 11:6)
(Lightweight concrete)
KARKMV, N. A.
- -- - - -
Problem of IsTroving the properties of foam, Izv4I Uz.SSR.
Ser.tekh.nan no.1:45-50 160. (XIBA 13:6)
1. Sradneasiatakiy politekhnichoskiy instituto
(Foam)
MARKA 4, (brestskaya voblaset')
The joy of work. Rab. I sial. 34 nD.5:6-7 MY '58. (MIRA U:6)
(Drogichin District--Svine-Feeding and feeding stuffs)
MARKARIAN, M.
Ccntamination of water resources by radioactive materials
and sanitation problems in the water suppiy. Tr. from
the Russian. P. 131. VODNI HOSIODARSTVI. (Ustredni.
sprava vodniho hospodarstvi) Praha. No. 5, 1954.
SOURCE: East European Accessions List, (EEAL).
Library of Congress. Vol. '5 no. 12,
December 195%
MARKAROV A V. gornyy inzh.
Use of the 111-1.,75 boring unit for drilling h&Uv.
Ugoll 37 no.3-lz42-43 N 162. (MM 15:10)
1. Treat Tulshakhtoosusheniye.
(Rock drills) (Mine ventiliation)
G.
MWAUV SitftGUINUM Agents Jul/Aug 1946
Spraying appwatal
"Ixtinguishing Oil Fires by Means of Atomized
Water Spray," G. Markerov, 4 pp
"Mor Flot" No 7/8
Partly mathematical discuesiox-. Mentions that In
choosing spraying equipment it Is important to In-
vestigate not only the rate of flaw per secoad but
also the diameter of the area covered by the spray.
P~,, 16T,7
16T7
SI"OV.r -L
It t Sur- I,.- sw9 tems nt-. F L-11.
127 T). ')ill
"Litera- ra": T'.
7WA
41"i
40
Illy
ob
log
00
os *3
~44
--rt7r-,j-j j-v-%j-j_m $w too
u 0 AV r# to A 4 v a w of a n 14 a Ko 1 1* 1: 1 04
10, *1'0 0
000
,so
-90
see
TV . 1D# N&L,; XUA~, G.I.
Impale* moswurements In a ba3A amplifier* Vost*Lsn*uA6 9 nooll:95-98
1 154. (KIRA 8: 7)
(Ampliflors, Vacuuo-tabs)
AUTHORSz Krasillnikov, V.N., Makarov, G.I, SOV/54-58-3-5 /19
TITLE: Transient Processes in Linear Vibrators (Nestatsionarnyye pro-
tsessy v lineynykh vibratorakh)
PERIODICAM VeBtnik Leningradskogo universiteta. Seriya fiziki i khimii,
1958, Rr 3, pp 27 - 50 (USSR)
ABSTRACTs The present paper is a part of the dissertation written by TT,~
Krasil InikcFv. G.I., Makarov suggested the problem and helped cla a
number of quistions. The authors investigated transient processes
in thin serials '. Paragraph I deals with the problems arising in
the theory of thin aerials, Although the basic investigations on
the steady theory of thin aerials have been published already
soffie time ago (Refs 1,2) discussions arose in Soviet and Ameri-
can technical publications (Refs 4-8), dealing with the formula.-
tion of the integral equation for an aerial with a so-cqlled gap
The transient excitation of a thin cylindric aerial (� 2) as weil
as transient current waves in the aerial (� 3) were investigated
From the practical point of view 2 facts are of particular im-
portance in the investigation of transient processes in various
syitems: 1) the behaviour of the system during the initial mo-
Card 113 ments, especially the investigation of the first half waves of
Transient Processes in Linear Vibrators SOV/54-58-3-5/19
the signal, 2) the characteristic of the process as a whole and
the determination of the time after the lapse of which the sys-
tem becomes steady. Paragraph 3 gives the answer to the first
question. The current in the direct and in the once reflected
wave was found in the first approximation. Transient distortions
were found only in a small domain around the front. These tran.
sient phenomena which depend on the diameter of the serl-al musi
be considered in the examination of the signal front. As regardp
the second problem, it appears that from principal cons2derationp
repeatedly reflected waves must be investigated and the constant.
ly increasing transient process in the range of the front has ~.o
be considered, In the case of thin aerials the real transient
process can be assumed asymptotic. In the case of an arbitrari,y
thin aerial the transient distortions in the range of the trav-.-
ling wave front are completely absent. As the radius of the aerial
is insignificantly small, it can be assumed that the transient
characteristic impedances introduced in � 3 adopt their definite
values Z(z) from the very beginning. For this reason the .7oeffj
cient of reflection on stead as well as on transient c~ondition6
Card 2/3 differs only little from (-1~ and can be replaced by the steady
Transient Processes in Linear Vibrators SOV/54-58-3-5 P9
2i or.
formula K a 0. The interaction of the reflected waves witn thoR-
0
generator must be considered as well. This is possible if the
considerations are started from the simplest quasisteady case.
The summation of all travelling waves must yield the steady con-
ditions in the vibrator. According to the suggested method tran-
sient processes in thin serials can be thoroughly inveBtigated
also ofi-the occasion of more complicated cases. The analysis does
not become too voluminous if in the case of a sufficiently low
ratio two basic classes of transient processes in aeria2s which
are determined by the longitudinal and transverse dimensions are
investigated separately. The transient phenomena in the field of
the aerial (above all in the distant zone) can also easily be irk-
vestigat6d. Work on these calculations is under way. There are
7.figures and 22 references, 12 of which are Soviet.
SUBMITTED: March 5, 1958
Card 3/3
XMIMMIKOV. T.N.; KAKAROT, G.I.
Nonsteady processes In linear antenn a [wltb summr7 In Bn,-,Ilshj.
Irest,LM 13 noal6t27-30 '58. (MIRA 11:11)
(Antennas (Nlectronics))
F+
W! SO. 'a
It 'a Len .0. 110 1 z -0~ 'I,
a , . a .18~ I
d t-11
IV.
to A~
ru
0. sr am a 0. 0
1,32 z
ke %, Q
00
c
fail. goo
tvc 10, A
'a
5 SIM 9
202-5 2
L D 6~ A- I
HUI
TILIZAROV, B.V.; KRTLOV. G.N.; PAKAPDV. 0.1.
.Mm~
AsyrptotIc methods for the calculation of transients in low-frequency
-69 F 959. (KIRA 12:1)
filters. Radlotekbulka 14 no.2:63
(Radio filters)
69908
s/iog/60/005/04/023/028
1,0 0 0 E140/E435
AUTHORS: Krylov, G.N, and Makarovs G.
TITLE: Attenuation Functions of the Electroma~netic Fields
of a Vertical Dipole and a VeRicalAntenna 01i
PERIODICALt Radiotekhnika i elektronika, 196o, Vol 5, Nr 49
pp 684-688 (USSR)
ABSTRACTs Approximate expressions are obtained for calculating
the eleetvomagnetic field components of a vertical
dipole located at an arbitrary point in space and a
vertical antenna with radiation directed along the
surface of the earth. The results of numerical
calculations at a frequency of I Mcs:for earth
parameters c = 9, a = 5 X 1o-3 mho/m are presented
graphically. There are 4 figures and 4 references,
I of which is Soviet, 2 English and I English in Russian
translation.
ASSOCIATIONtFImicheakiy fakulltet Leningradakogo gosudaretvennogo
universitets im. A.A.Zhdanova (Physics Department,
Leningrad State University imen! A.A.Zhdanoyl Vr
SUBMITTED: May 18, 1959
Card 1/1
KRTWV, G.N.;,HAXMV, G.I.
Struature of the electromagnetic field of a vertical electric dipole
and a vertical antenna In space over flat earth. Test. IGU 15 no.16:
42-" 160, (MIRA 13:8)
(Xectromagmetic waves) (Antennas (Xectronice))
04
1';k41 'q 7~7j~,,,,T
ropagl.
r f
,,-PIRIODIC
~15 ~M
Y-J
4 v
an sLrdd..,T958o,.*,6
or 28
f.vlav
.;.,PropagAtio -"0 '-O_n iLs4t4ti6riary:; radio';':,
A- e.
attention-lell,b6i Dlyit.', v
1k9 e gt*em
'6: over,. a,, p anp
g 7, a
--Onto , p W,-,s i-]~dkbge e.
f i
--~~hi,~..dliplapemp
u At
k1i
rong,,,.Ibw:4 rf
4valid -oii*'.: 6i--,,-4 , 9-1.0 f
'a
',pro
Inro g e -.,o.ver e ;i
a
b. -Sl)pen:,.
.37!4~
.7~
Z
3TJ "3: '-f!',
ii;,Z
.1.
a i:W.
t6l.'4hibW -Lnore
y:. of, --propag4:4"
t1w, tozi
q,~;.par. --m r ace ne-,,.-
t~" T
iald
our e A
%vomponents'' of~-. .:Xnel-.
uency
-,Vdry-,.,go.o ,'or~ me um.-,
d d
6-f 006, 0 2
wv
L
igizi~ -lid-tii6x* -the! a,-. non, stitibn
I -A- .
-0-
ric"' d -F
-ai owa -Fv 4
r
..gatIoMbf k vqi.~ -.1. -1 - 4 -
'40
lime, dw-, -,,.t
qgehecu reqir.,~ %t
'nip aceme dl iii;~i
iDiw h you
LC
"Th'
-4rg=en e m,
t
-A,
-;~pb*homena. iati 6ii S.
t
i
bjkj--~,~O rit 'dip
A, -ver,
id
~ .? , -
at--,. a, tp 'Momlopneous -var"t t vity" cr an
Ak #eu,,7.
.04vac ance.-, 4 X-
ti i- awle,e
dimdo
as
.9 ti
-f; T SVC,
!P,( n-4
'MIN. iklb
Q
'Opt,;,
T-4
j,-
Ar
5
09/61/oo6/ob5/005/027
/1
Propagation of pulse -D201/D303
dh.--'height of dipole: s1r..= -ikr/2 -numer'ical distance),
.
he're
6
CUF lativ"e.complex- ecific*inductive capacitan-
p
M
M -0
' celdf the,.earth; 'yi(x) i s giVen-by
Odi
1+ 2 xe-0 e (2)
Sommerfeld
the
whichAs- f~ *in:- 1 the
e -pre s
attenuatimfufiction'..';J x
..
s.Lon.under the sign of .
I represente.the curreht spectrum in the di-
pole
cc
(f) OWN,'
"he'ent
-it.-would
theri re 'the spectrum of the'VeKtioal,:-component of
etr'ic fi
Ahe ele
dv and
e its integral with res pectL.,to the frequency
l
.
.
dive 9'.the' solutibnI or the non-;-stationar*y pro blem;for this oompo-
ar
0 d 3/1 2.~
8 09/61-006/605/005
/027.,
Tropagation:of pulse.~.: I /D303:
D 0
nent~
1jj
,:Vt
f a- -
-,.7 requency characteristics' -fn-ction'_'-.of.-attenu
-In, analyzing.' ,.:as:.., a.,,.,u
Laded b'- -dimensionless ps,3~pine.t 'h
er,-- c6ouw ere
Q? (4)
rot
"can
Istance, be' represent
r
splaoiement;; ourren. s ar' taken into AcooUntj-- .,as definidd%
d
i e
1.5 ndf4ir6 -wd for r6il- e0ils,'at
a'! than unity; Calcu'l ati ons, hivie"'J bin", at:,,'~for'~.ca-"
currents-reduciA e, b id,; of
lq~ladement h a)
~;4
A
S/109/61/006/005/005/027
Propagation,of pulse D201/D303
From the evaluation of integral of 3
propagation track (3) a
comparatively si4dpje expression
ipl A
UV (U) c7u--2'*
0% M a;" t (W) T da, (12)
J" 7
h.of Afoh-la.,shown in Fig. 2
can be obtainedv :the integration'pat
-A Pig. 2. The plane of complex
variable (u).
Fig. 2.
S/109/61/006/005/005/027
:Propagation of plee D201/-P303
and in which u is given by
MCO
(7)
anA T and %Xu) by
T 'O(U) ?JOT
7S V (9)
If the dipole is excited by a emit step pulse with either sine or
cosine oarrierp the stationary part of the field can be derived as
2W W (Vi-rer) (13)
and its non-stationary part describing transient p7ocessesq as
E2 W) tt(U ~O (14)
e
Umvtl~ 2n Vi6p (u) - a(4
Card 6/12
3/109Z61/006/005/005/027
Propagation of pulse D201/D303
Introducing into (12) and (14) change of variable P ?u/2,
Ldk 414
E, 01)
(e) ~=
u'(p) eip 2 (p)] dp. (15)
and
up 2 /(P)l dp, (16)
r
iare
obtained, whe34e
. U (P) -!P (VI --e - ip); f(p) + iTU (P);
+4)
BY applying the mithod of stationary phase Eqa. (15) and.(16) be-
come
JEI) (T) U (T)
;F (T) exp IF 4- fr + -C
Card 7/1~
S/109/61-/006/005/005/027
Propagation of pulse D201/D303
ES-01 -. .t7 F(T) exp -L It'r + PU (r) +
soon SUA
and I + * (c4, t,,v) 2zW-s-0 4w elldj~'l (19)
where- +
F 2 1+
(I + 2T) (1-+ YF+-2T)U 2 VI -+2T
(20)
It + 2ir + V1 -+2T).
(10
T T T Y'. -+-,c 2
+ Z02 S$r + jW01
T/ W.
the condition of applicability of (18) and (19) being
2 1. ('21
Card 8/12
S/109/61/006/005/005/027
Propagation of pulse ... D201/D303
if in (18) and (19) convection 'currents are neglectedt the two
equations are identical to those obtained by J.R. Wait (Ref. 1: O-P.
cit'.). In order to analyze the radiation field given by Eq. (18)
produced by the dipole excited by a unit step function, this equa-
tion is rewritten as
dh
AIa
A(~v T)i
2 7
A(Tp T) F(? T) tZ + ~u(yT)j exp T) T _/, where functions
2
P(YT) and u(YT) qLre determined by formulae (20)' and T are given
by Zqs. (5) and -(9) and
2
X (X) =
+ X + V1 + 2x
3;' 1f,the dipole is~excited with a HF sinusoidal or cosinusoidal step';-.:
-Card. 9/12
St'109/61/006/005/005/027
Propagation of puise D201/D303
input pulse, by beans of bpply'ing dimensionless variables of
-r, - (#9t', x - (8" + P
lw#ladh
---,5-fW()f8Or) IV (P,.X,'[,),
vf~' X, -c3) + w (p, X, (22)
is obtained. In it w (-\/a7) is the.sommerfeld attenuation functi-
ono c its argument; and
fcom
w X. irl) exp (X). + U (z) +
f (Y;.,) I 4P 2p TP
.2& (23)
+ IF W + V (P. x TO 24'-. 0 1 e0dz]j;
P +
V (P. X, TO
Card 10/12
Prop6gation of pulse ...
S/10 61/ 1006/005/005/027
D201YD303
2
:1 scr + iT, - % (x)
K(z) - (23)
)(F+-2. (I + V-1 + 2.)
is valid for the non-stationary part of the field for the conditi-on
49
of the function W (Eq. 23) describes the non-stationary cart of the
radiation field, the real part of the function V (Eq. 22 - the
total field when the dipole is excited by a current of-the shape
of
(t) 7 1. sin (o,,t - I ~t). (24)
Functions ImW and ImV.describe the non-stationary part and the comi~'I
plete field respectiVe-ly when the current in the dipole has the
shape given by
Card 11/12
It
F.,
N,
3/10 61/006/005/005/027
Propagation of puLpe D201X303
Graphs show that 'displacement currents introduce an attenuation of'
the amplitude of the non-stationary part of the field and that the
amplitude.of-transients depends on the current spectrum in the di-
pole.- From graph of ReV it is seen that transients may introduce
considerable distortion in the propagated signal. It is stated in
conclusion that the problem,of propagation of pulse signals ovet
the surface of the barth is also of practical interest, In that it
gives the picture of signal distortion and that the results obtain-
ed could be used to solve the problem of the inverse diffraction
problem and that from measurements of the delay time of the maximum
of the signal, having other data availablep one could determine
the conductivity of the propagation path. There are 6 figures and
5 references: 2 Soviiet-~bloc, and 3 non-Soviet-bloc. The references
to the-English-language publications read as follows: J.R. Wait,
Canad.*'J. Phys. 1956, 34, 27; J.R. Johler, J. Res. Nat. Bur. Stan-
dards. 1958, 60,)28)
ASSOCIATION: Leningradskiy gosudaretvennyy universitet im A.A. Zhda-
nova, Kafedra Radiofiziki (Leningrad State University
im !.A. Zhdanovq Department of Radiophysics)
SUBMITTED: March 24, 1961 Card 12/12
KOZINAV G.I.
Transien-ts in acoustic fields generated by a piston membrane of
arbitrary shape vith arbitrary surface *ibrations. Akust. zhur.
no.1:53-58 161. (MIPA 14:4)
1. Leningradskly gosudarstvennyy universitst.
(Sound)
9.;Ls-?t)
27589
8/108/61/016/010/002/006
D209/D306
AUTHORS: Yelizarov, B.V., and Makarov, G.J.
TITLE: Transients in delay lines with a great many sections
PERIODICAL: Radiotekhnika, v. 16, no. 10, 1961, 10 - 19
TEXT: This article was read in May 1960 at the Radio-Day All-Union
meeting of the Scientific and Technical Society of Radio Engineer-
ing and Electrical Communication im. A.S. Popov. The present ar-
ticle is a continuation of the work of the authors (Ref.l: B-V.
Yelizarov, G.N. Krylovo G.I. biakarov, Radiotekhnika, vol. 14, no.
2, 1959; Ref. 2: V.B. Yelizarov G.N. Krylov, G.I. Makarov, Radio-
tekhnika, vol. 149 no. 10, 1959~ on the use of asymptotic methods
for determining the transients in delay lines. The circuit conside-
red in this article consists of n symmetrical identical M-type sec-
tions Fig. 2 of a low-pass filter connected in series, loaded by
zL and excited from a voltage generator with internal resistance
zg. The properties of such a circuit are studied by deriving its
Card 1/9
27589
3/108/61/016/010/002/006
Transients in delay lines ... D209/D306
transfer coefficients K(X)
Z., L 2Z&Z, e--nir
K W Z2
, + Zb,2~
1
(ze + ZL) VC + V (I - q)
(ZW+-
Zi chng+ Sh ng
Ze (Zp
+ 74
. (2)
q =. (Z' - Z4) VC - e-2nj
(Z' +
where Z
z L' Z , g are functions of dimensionless complex fre-
c g
quency x p/w -
and w the cut-off filter frequency, g - being
O 0
the propagation constant. The stationary characteristio is found
considering T - sections only and Z = R
and Z L = R L' so that
g 9
RE
r. = zC (0) rL= zC (0)
(4)
Card 2/9
~2 58
8j
3/10 61~016/010/002/006
Transients in delay lines ... D209 D306
can be introduced. X(x) can then be represented as
'(' ; f, (x) - ch nk!~ + I + X, Sh ng. (18)
K(x) = /0 W
and the output voltage by
1 (19)
U (C) K (x) U,, (x) e" dx, -c = coo t,
S
cc
where Vin(x) - the generalized spectrum of input voltage. The de
termination of the root sign in K(x) is arbitrary since after the
transformation of ny perbolic functions fz(x) is represented by a
polynomial of the order 2n + 1. It can also be shown that f2(x)
has simple roots - and
if t Mx hence x ti (20)
1 = \0h+(, _ m2) X2' VM 2 _(1 - M2 ) t2
Card 3/9 1
Transients in delay lines ...
where m -+-,t. Also
t1 = sh g/2
(21)
so that YI +
thng - - rr
.,+ I +
9 Ar th Y Ln (22)
n
zq+ I+ x% 2n I+x2+
and finally from (22), (21) and (20)
Card 4/9
s = 0,1 ... n.
27589
S/108/61/016/010/002/006
D209/D306
1%23)
27589
B/108/61/016/010/002/Oo6
Transients in delay lines D209/D306
ieL,obtained. Taking the real and imaginary parts of Eq. (23), ex-
pressions of the type of
a = f 3(at 0); f4(at (24)
are obtained, from which a and P can be consecutively obtained.
Functions f and f are very complicatedo Their iterative expres-
3 .4
s~ons converge very quickly, however, , and are non critical with
r;spect to the initial approximation~pe;g* the evaluation of roots
for n = 50 using the fast com uter C B A (STRELA) takes only 3 mi-
nutes. Knowing the poles of KM and of Uin(X)l Uout(T) can be re-
presented as
V UZ64OWNS U:: (x,) e",
U. U.. (.0 +U 4. 2Re (25)
Jtl (X.) E 1; (X.)
j-n
or U. (T) = U W Y, M. e-Y cos ~;c + (26)
iZF 172 '.0
Card 5/9
27589
3/108/61/016/UlO/002/006
Transients in delay lines ... D209/D306
Ust(T) is the steady state solution for poles of U 41A (x) and all
other terms tend to zero for T ---# oD and determine the transients.
For convenience the constant factor U0 can be extracted and then
Uout(T) = U osul(T) with
lim Ul(T) = 1 (27)
T -11 OD
and only the graph of Ul(T) can be plotted. All calculations were
made by the authors after programming the "Strela" computer and
much numerical material has been compiled which because of the li-
mitei space could not be reproduced in the article.. Only U,(T) for
n = 5 is given in all figures and graphs. For larger n the reason-
ing remains the same but the transients become much lengthier. The
graph of Ul(T) is given for various i, if rg = rL = 1 with unit im-
pulse function at the input. The values of a at 08, M. and cf. for
Card 6/9
27589
S/108/61/U16/010/002/006
Transients in delay lines D209/D3U6
2 = 0 are given in-tabulated form. As may be seen the change in mu-
tual inductance strongly influences the delay and the shape of the
signal. If at the same time ;,c ~- 0 , the delay only varies v for ~c ~~ 0
both the delay and the signal shape are changed. From the point of
view of overshoots there exists a certain optimum value of ~t. This
value is R opt 0.25. Fig. 6 shows U (T) with input signal
0 'C 0 W#
for r. = r L 1; f2c = WC/Wo 0.5 (we 2 ) for various x, and _(2c
771L71=3
0. 2. Curve 1 - fie = 0. 2, 0; curve 2 - '_)c = 0 - 5, -t = 0 - 3; curve
3 -~Ic =0.5, e = 0; curve 4 -~'Ic = 0.5; ,=-0.3. Withafurther
in-rease in frequency the length of transients rapidly increases
an~ the effect of parameters begins to be felt. The characteristic
shape of output signal for frequencies near the cut-off is shown.
The envelope of the signal, while oscillating slowly tends to its
Card 7/9
Transients in delay lines ...
27589
S/108/61/016/010/002/006
D209/D306
steady state value and time taken depends on all parameters but
mainly forriC --*l. The derived exact expression (26) allow not on-
ly certain physical phenomena to be demonstrated but are also use-
ful as a means of checking the accuracy of approximate expressions
derived earlier by the authors (Refs: 1, 2; Op-cit.). The main term
of
2n dt - It (29)
2
describes the process more accurately than the expression obtained
earlier (Refa lp 2z Op.cit.) and is handier in calculations. The
case of a unit impulse input is then considered. There are 8 figu-
res, 3 tables and 4 Soviet-bloc references [Abstractor's note:
Ref. 4, although in Russian, is a translation from an English-lan-
guage publication].
SUBMITTED: February 11, 1960 (initially)
December 19, 1960 (after revision)
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AUTHORS: Gyunninenp E.M.p Zanadvorov, P.N., Kotik, I.P., and
Makarovp G.I.
TITLE: The effect of a complex shape periodic signal on a
free-running oscillator
YLTIODICAL: Radiotekhnikag v. 16# no. llp 1961, 59 - 44
TEXT: The pure theory of phasing of oscillators presents difficul-
ties which make the solutions of its problem practically impossible.
In the present articles the author considers the solution of this
problem in its numerical contextp by means of a fast electronic
computer. Such a problemp as opposed to the purely analytical onep
is stated to be comparatively eaByp but the quasilinear method of
analysis is applied for simplification and numerical substitution
of the equation of the osciilator, upon which acts the external for-
ce A(T). If x is the voltage at the gridp reduced to the amplitude
ItMof the steady state oscillations at the grid, w 0 and 6 the fre-
quency and attenuation of the oscillnting circuit, T W0t dimen-
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The effect of complex shape '.. D201YD304
sionless time; -Sg - average reduced slope of the valve.
and constants, then the fundamental equation may be represeRted
as
2
A X + X M%S'Ll are tg P xmj~ 41 + yA(T). (3)
0 YC dr
dT
Practical values are now assigned to the parameters of (5) thus:
-2 -3
0.8; MW0so = 1.12; 0.422; 10 and 10 0 ~ = 0.1 and
0.01 are.the values resulting from practical assessment of the val-
ve parameters and regime* The acting force has bee-n taken as having
the form of consecutive "distorted sinueoidal pu4es" A~T) with li-
near variation of amplitude and initial phase. This A(T had the
form of
0,08(r+3)-sin[,r(0,8+0,02-c)j, 0 0; U1(t) ' 0' t"
illustrated in Fi?,- 5. 1-1L the membrane is excited accordinr to 'j,' t)
s inWt , 1; 0, U (5) two waves occur with a )hast,, differe:k-,
2 2(t) ' 0' t