ELECTRICITY - VACUUM-TUBE OSCILLATORS

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• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80-00809A000600230932-2
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 14
• Document Creation Date: December 22, 2016
• Document Release Date: July 18, 2011
• Sequence Number: 932
• Publication Date: June 30, 1949
• Content Type: REPORT

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COUNTRY USsi
SUBJECT Electricity
HOW
PUBLISHED Monthly psriodi!:al
WHERE
PUBLISHED Leningrad
DATE
PUBLISHED Apr 1945
LANGUAGE
SOURCE
Zhuroal Tekhnichoc _Yiziki, T;,1 `11
64749 Translatir,,, rea,jeeted.
Phye-Tech That
Por'kiy State Unim
Submitted 7 01toher i947
/igurea are appended
By a method :f abridged equation, t study is msdv of o vac-tun-
tube oscillator itb ei".,matic cathode-bias rircal t. For Lhn dis-
continuous linear characteristics of the tube an exrr,aslon Is four.-
for the amplitude of self-ereitatlon and an exi?1aneLton Is 17'ver, of
the necessary eonditiona for self-modulation of self-exeltatior. It
In demonstrated that a "soft" formation of self-modulatton t-.ken
place.
The results obtained were quite satisfactorily proved by
experiment. Photograph, wire taken of prase traces on r van der
Poi Plane by means of a cathode ome1llograph, which proved the
Usoet" formation of self-modulation.
ASS(Jl~%4?
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CEPS 1R.4 -1. , it e INCY
INF hr?,?`.r1ON EP. .;i
FOREIGN DOCUI.'. i_c. OR RADI BROADCASTS
DATE OF
INFORMATION' 1947
?'.EPCRT
0NO.
DATE DIST. ?o : un I' 9
NO. OF PAGES 14
SUPPLEMENT TO
REPORT NO.
THIS 15 UNEVALUATED INFORMATION
The phmnomenon of eels-modulation and its particular form, intermittent
oscillation (The phen menon ;,f self-modulation was discovered by Armstrong 0
and, independently, by Rzhevktn g-. The first explanation of intermittent gan-
erstiahtf- We at^;pldst form of self-modulati3n -- vas S.-en by Tvedenakiy and
Rzherkin Other worke E - 72 have also beau devoted to intormittent
generation and self-aodulaticn.) was observed in oertaln z'eiations bbtween
the parameters i-. vacurm-.ub^ oscillator with automatic cath,d e-bias circuit
-I -
CLASSIFICATION v117~
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or grid circuits. In the farmer case c ^gntive grid bias, varying auto-
matically with variation jr oscillator rhythm, is obtained on account of the
emission current of an electronic tube 'Figures 1 and 2); In the latter, on
account of grid currents flowing through a grid leak. Such automatic-bias
circuits are used in an overvaelming majority of vacuum-tube oscillator
systems to develop the necessary grid bias without using special batteries
and to improve oscillator stability.
The phenomenon of self-modulation takes place when the operations carried
out are unstable without automatic bias and the capacity of an automatic-bias
circuit exceeds a certain critical amount. This means that a vacuum-tube
oscillator, instead of "normal" quasi-sinusoidal self-excitation, produces
self-excitation modulated according to amplitude (the form of self-modulation
and. its period are determined by the parametere of the vacuum-tube oscil-
lator). As the capacity of an automatio-bias circuit increases, the self-
modulation of self-excitation increases in depth and is gradually converted
into intermittent oscillation expressed by periodic cessations of high-
frequency ..auillations.
This article studies a self-excited vaonum-tube oscillator with automatic
cathode-bias oirouit, by assuming that such an oscillator approximates a
linear oscillatory coneervat' system and by using so-called abridged
,equations.
0. Abridged cations
Let as examine a vacuum-tune oscillator with automatic cathode-bias
circuit (Figure 1). The processes in such an oscillator are determined bs
the following system of differential equations (see notaticoe in Figure 1)
whore I,- is the natural frequency of the oscillatory circuit; and the
dimeoslon ess dependent variables x, y, z are defined as follows:
Ldt+Rr=v-M
Vq= v.- - v.
+
f
+2
-c
a
k
a
y
Y- ax, l=-0&' V9~az
1
(3)
(a is some unit of voltage).
het us assume that the anode and grid currents of the electronic tube
do not depend on the anode voltage Yq., but are simple and derivative
fanotions of the grid voltage vg :
Zq-id (1/4), 29-i9 (vsq).
Then, when 4,( la , the system of equations (1) is reduced to a system
of the following dimensionless form:
dX =Y-KYfy(Z)
'Q af
all, 1*
47
CORFIDMIAL
"ONF1DENTIAL
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f(Z)= L a ( z), y (zi- = a- "Ey-i 91 (ctz)
tl== co, 9C. S
Zv7
are reduced to the dimensionless form of electronic tube characteristics
( S and5g must denote the sharpness of the cheracteiletice for anode and
grid currents, respectively, at any fizei 1,oint, for instance, in the linear
parts of the characteristic3);
RC '9 - _2L
?,Cwo Rky- Y .Ad 1- 5/k (7)
*(The parameter which can be written (i=R1C , is nothing but the ratio
of the time constants of the automatic-b+.as c r uit Rk Ck and the oscillatory
oiroult .)
R
**(If the electronic vaouam- oscillator is a tetrode or pentode, the screen
current ig will also flow t. ;ugh the witomatic-bias circuit. Than, assuming
proportionality between the anode and screen o rents, yr obtain 9~-(S+$ R4,
where S(9) is the sharpness of the ecreer. current characL~erTatic.)
If the nonlinear system under discussion approzimatee the coy irvative
a!stsm, fairly entiefactory results can be obtained by the van der Pol method;
that is, by substituting for the former system of differential equations a
simple nonlinear system of so-called abridged equations Lu - 11'.
To pass from the system of equations (4) to the abridged system we shall
assume that the positive parameter ,u is small and that the quantities oc,p, y
and / are of the order of unity so that when e-4(4a,144 Y, -e zndLu q
then toward zero. 9 Q
When (tt. = O, the solution of system (4) (now linear and conservative) is
X-Vcoc (2-+ P) V_-V.;infr-- ~)z ' - L (8)
where V 9p are arbitrary constants.
In equation system (4) (when �) let us substitute V , U and 4P for
a, and z in accordance with (8). Substituting (8) in (4) and solving for
Lj'rh, , we' obtain a non-autonomous system defining V, U, q~ as
e ow r9 g functions of time V (their rates of variatit, are of the order
of the small parameter ? ). The abridged equation system is ontainad by
eliminating the right-hand ter-me in 'r and by dizcarding terms in Ott higher
than the first power. Obviously, it will now be written in the form
dV -d ,'_pV{-l+off, V)) (9)
410 2. (
Wrffi -61- 1 & u V) i
-3-
COlt? ID IA,.
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(The right-hand terms of the first equac+can in (9) have an obvious physical
significance. The first term, ? Y , reflects the attenuation of oscillation
because ofbscUlating current losses; the second reflects the increase in
oscillation amplitude because of the presence of an electronic tube, and feed-
back; the last reflects the decrease in amplitude because of grid circuit losses
canoed by grid circuit reaction to the oscillating circuit.)
t
20 _Rk C*
(12)
For further analysis of equations (9;, let us approximate the
"
characteristics of the anode and grid currents of the tube by means of the
discontinuous linear functions following:
,
RC
y= LL'L
The "shorter" equation for _ Y gives 9 M a constant, that is)
the correction for frequency of t e order /4 equals zero.
If the oscillating current is in the anode circuit (Figure 2), the
same abridged equations are obtained for V, the amplitude of the variable
component, and for U, the constant component of the grid voltage bet with
?(UV) r "f(U4
is "slow" time and ??~~~~// 'B
~,( ,Y,~a; f~rV'I'vos
f19(t',V) -= f (1l+V )s%n1fd '
is-S(vy--vg?)I (Vy-V7?), if -51 "Y 1 (V5)
(irigure 3), where the unitary function, as usual, Is
(z)- 0 when z< 6,
tIwhen z>&
as the unit of voltage, we shall obtain
f(a)-(a+))l (z "-i), f,(z)'z.1 (4
=P(i r?l,(i,,)J
(/ to-- U-I Vir1((z)S
4 T,
l)9!-+- Vsen 81)
- ii .
COIIF MUAL
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U,~r
y, 32= _`!
Where p, - . L
by the ftt.ctIonc
6, :re dett .ir.et in accords"-a with y,r~ y~1
0 wh..r V,Il(ri)7(18)
0. Si nBular Po11?te
Let as examine the following phase semiplene of abridged equation
system (9)'?
o / there ie a _single (for each combination of the parameters
pt, )r,q) sib?luar point (U, V) outside the axis V- 0 -- a point corre-
sponding to periodical (unm.odulated) self-excitations. In the given soalo, V
Is the amplitude of self-excitation and IJ Is the constant enmponent of
voltage in the autorlatio-bias current. This po.3t is defined as the point
of Intersection of the following two curves: the R-carre
R(v, u)= ar'-; (~1)-y~'i 0 (20)
Q(V _t/_TV-r1(?z, 0. tr (21)
(The reason for there being but one singular point is that along Cie
Q-ourve, the parameter Q. of the R-curve is a monotonically Increasing
function of V.)
Figure 4 gives the family of R-ourvee (parameters of the family CC
for YY 20; other Y's have aralogous families. The larger Is (as com-
pared with of ), the nearer the R-curves In the region V,>-/ become a
straight line Vr = -/ . It shtuld be noted that in the region V, p,, ) and the form of the limiting cycle is
nearly ellipsoidal, then self -moduletion 1s -tlm.oet sinusoidal with frequency:
(28)
(gyp
Furthermore, as may easily be demonstrated, the infinitely remote parts
of the pease semiplaue (U, V) are absolutely unstable: all phase traces enter
some finite area near the origin of the coordinates. Hence, when 8>00 is this
area there is known to be at least one stable limiting cycle. By means of
graphic integration of differential equations (16) for particular values of the
parameters cc, )r, 9. , it is possible to show that: (1) wean -k> and
the singular point (U, V) is stable, there are no limiting cyc Les in he phase
semiplane; and that (2) when f < and the singular point (U, V) is unstable,
there is one and only one limiting cycle in the phase semiplane and it is stable,
Thus, under any initial conditions, "normal" unmodulated s'slf-excitations
are set up in the vacuum-tube oscillator under consideration, if a process of
yL self-excitation is carried out. which Is stable without automatic bias (singular
f 9i3 point (U, V) lying outside the L-area.) or when conditions (27) are' satisfied,
.4 but Ck> (Ck)c_tccei ? When conditions (27) are fulfilled and Ck>(Ck)ariticdl
to the oscillator, under any initial conditions, solf-excit,atian n -Aninted
9ocording to amplitude is establtrhsd When ~k (C') :r:i;oal the result Is
continuous transition c.f the unmodulataZ self-exc"atRlcn process to a self-
modulated process (when C k increases) and bacl. (when Ck decreases); tl,e extent.
of the self-mo.lilation of self excitation is a continuous function of C/, and
can be made as rmall as desired. by selecting the corresponding capacity o'f Ck
A sufficiently close to (Gk) 60' itiCa1.
Such a process of developing self-modulation can be called soft (by analogy
with the soft process of the development of self-excitation in a vacuum-tube
oscillator) and to distinguished in Its escential form from mthe hard process of
the developmect of self-modulation discovered by Yevtanov U in the coca of a
vacuum-tube oscillator with a grid leak, and experimentally corroborated by the
author.
With increase in r (after transition through P. ), the dimensions of
the limiting cycle In the phase seaplane increase and its form differs always
core and more from the ellipseida) and the lower part of the limiting cycle
approaches more and more closely to the U-axis ( V-= Q). In other words, when
the capacity Ck of the automatic-bias circuit increases, the result is a
smooth transition from sinusoidal self-modulation, with modulation a3 small as
desired, to Intermittentosci)latlon which is exprsased I.. periodically dis-
continuous high-frequency self-excitations and occurs when CL > tCk~crit.*a
(when 8- too ). 'C
CONIMA1
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To illustrate the chsracte of the '"?'.Furcat1on" when ~l fp and the
transition of quasi-sinusaidni svif-modul'Ir.i.~;n in intermittent oscillation 'with
Increase in 4 , Figurer o, "; 8 and dive part of the phase pictures of
the vacuum-tube oscillator uuader discussion, plotted from the results of graphic
integration of equations (:~y) for of= 4; '/i10r q=IO ; and ~- q, 6, 15,
+e0 ("bifurcated" value the parameter ii for given O(,Y7 t7 is equal to
(30.- S,0) . Figure 10 gives the curves showing the dependenc6 ofi the 7-
amplitude of high-frequency self-excitations on the "slow" time 7~6RZrI
plotted in accordance with the corresponding limiting cycles in Figurbe % to 9.
It is interesting to note that in the case under consideration the transition
from quasi-sinusoidal self-'modulation to intermittent oscil;.ation occurs when
ks, 7:. ) r; N a/
E. Extent of Parameters
CO)IFID. 1IAL
A graphic representation of the process established in a vacuum-t;'ae
oscillator may be given by its parameters by expanding the oscillator parameters
in various regions. The vacuum-tube oscillator in question has four essential
positive parameters:
Y
oc-- q-(S+S(g1 Rj , q G and y LIS '
( 4-' not is Is taken as a third parameter, since the latter depends not only
on Gk but also on /2k ), where Me ,,R~G is the imaginary Induction co-
efficient M required for the self-exoitatidh of an oscillator,' 25r? l-
L' L for an oscillating circuit in's grid circuit and L' = Lg for can
oscillating circuit In an anode circuit.
9 Z sal-Y ,-1V
For a given Y the surface of-/ divides the area where self-excitation
Is absent (Figure 11, area I) from the area of "normal" unmodul.ated self-
excitation (area II); the surface . 1 0e (a, . that Is,
divides area II and area III, the area of the self-modulation of self-excitation.
In Figuf%$11, cross sections of plane o(=sl and surface = CO ,
for lie 20 are given for the planes q- oonst (qmm 5, 6, 8-
, 10,
For example, in this Illustration the erode section of area III Is orooshatehed
by the plane q=10. Cross sections of these surfaces for other Y's are
Identical with that shown in the illustration on the left-hand boundary of area
III and differ ly on the right-hand boundary corresponding to processes with
grid a rrents. does not depend on r when and when self-
excitation Is p uced without grid currents; that is, when ac ' - ~~) (30)
In Figure 11, points(its, j. are denoted by circles. The larger )! Is, the
nearer thevrors eictIen ~,f the right-hand boundary of area III is to the
straight line c(-as(q).
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The results obtained were checked on an oscillator, in connection with the
plan of Figure 1, with a 6Zh7 CZh * J ?7 tube as an oscillator. In a very satis-
fying way its ;hai'acteristice approximated the discontingous linear fun tions
in the form (13) with +'-c fall-,w1rrr nrre.meteri: 3=Z 1.9V, ,`"O,s ? 5jG'c
0,x0 -A, L,?= -/OV($oV' q,~2,rdVepd V) ~220 Y) The remaining parameters were
as foTlowa L-97 aB, 500 pF 5755V !weffi84Jl/?'%ec.., t=6 ?"43
and )''65. Back-food i','.uction bl varied vitbiz~ the interval from 0 to 4 mH.
The measurements cited were completely corroborated non only qualitatively
but ,quantitatively, within 10 to 15 percent of the calculated results of the
theo'y`?stated above, for processes in a vacuum-tabs oscillator with automatic
cathode-bias circuit, both for amplitude of beif-excitation without self-
modulation and for critical capacity. A similar quantitative verification of
~ptr.~Q:l)?
theoretical results occurred with greater circuit attenuations (when
The "soft" process of the self-modulation phenomenon vap demonstrated by
a series of photographs cf phase traces on the complex piano (U, 7), taken by
means of a cathode osoillograph, which showed the genesis of a limiting cycle
corresponding to "normal" unmodulated self-excitation when C1, passed through
the critical value (Cocritical
In contrast with the worh of Bendikov and Oorelik fff, 2hotugr..pas were
taken not only of singular taints and limiting cycles, but albo of phase traces
which approximate them asymptotically. For this purpose voltage was supplied
to one pair of defleotiog plates from an automatic-bias circuit, and to the
ether was applied a voltage proportional to the "amplitude of self-ezoitation"
7; the latter was supplied from a diode detector conneoted with the oscillating
circuit through 1 "buffer" cascade with initial resistance approximately 10/x.
To get the phase traces, corresponding with the treusient processes, it vas
necessary repeatedly to fix the very cam., initial conditions in the oscillator.
For this work a relay was used which short-circuited (about 15 times per second)
the automatic-bias o1rouit.
Figures 12, 13, 14 and 15 (photographs, not reproduce] were obtained for
the following values: M = 1.q ?,hl'o=&2.); Rk-8k.Q.( -a0); and onpaoitanoee
CA.. O.oS6f,F - (Figure 12), 0.090~F (Figure 13),0!092 F(Figure 14),
and 0,095,-F (Figure 15). In this case (Ck46tOial-0091 ,KP (calculation by
formula (29) gives (Ck~cr,Y,cal~0.0%~F~ In the first two photographs the
oapantty of the automatic-bias circuit was lose teen the critical capacity and
the phase traces entered the stable focus (U, 7), corresponding to the steady-
state proceei of unmodulated self-excitation. It can be rm_dily seen how, vhenCk
a proaohesll )e rtt,c,,/ , the spaeigg of the spiral grove smaller ar,d coils on
(U, 7) and how, from the focus (u, 7) a stable limiting cycle makes ate
appearance (Figure 14).
Thus, a fully verified a&reument between the results of theory and experi-
ment ehcwe that the "eaall parameter" m,?thod, the method of abridged equttiona,
gives not only a qualitative but a quite satisfactory quantitative description
of the processes of a -acuam-tube oe..lilator vita automatic cathode-bias circuit
(even with oscillating circuit attenuation k rr 0./ )-
In conclusion, I consider it my dut_ to express my deep gratitude to
Academician A. A. Andronov for his valuable advice and assistance.
ftr
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Andronov, A. A., Ehaykin, S. S., Theory of Oeoillations, Ch. 1, OMTI, 1937
4. Bnkop, H., Z9 f. Techn. Phys., 441, 1924
5. Gorelik, G., Susovkin, P., Sekerekaya, Ye., "Teohn. Radio 1 31. Toka,"
629, 1932
Yertyanov, S. I., Eleotracommuoioation, no 9, 66, 1940; No 11, 33, 1940
7, Barkhsueen and Bose, Nigh-Frequency Technics and Elea troac oustics, 60, 37,
Bzhevk.+.n, S. N., Radio Technics, No 8, 1918
Rahevkin, S. A., Vvedenakiy, B. A., TIT6P, 11, 67, 1921
BTBLI0G1'APR!
1. Armstrong, E., Proc. IRE, 3, No 3, Sep 1915
Bulgakov, 3.V., Apy1. Math. and Mach., 71, 396, 1942; a, 313, 1946
Bogolyubov, B., Some Statistical Methods in Mathematical Phyaioa, Isd.
AN SSSB, 1945
12. Bautin, N. N., zi rr, 8, 759, 1938
13. Bendr1kov, G. A., Gorelik, G. S., ZhTF, V, 620, 1935
Appended figures follow)
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-l.4
d-4 *y -w; Y' 10,'f -C
Figure 7
Figure 8
'
i
?`
+
; -
?~,
?
f
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-l8
01--V Y-20; P-+to
Figure 9
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