GENERATION OF DECIMETER AND CENTIMETER WAVES

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000200090009-2
• Release Decision: RIPPUB
• Original Classification: R
• Document Page Count: 195
• Document Creation Date: December 22, 2016
• Document Release Date: April 9, 2012
• Sequence Number: 9
• Publication Date: July 18, 1952
• Content Type: REPORT

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of the scientific radio.'physics seminar which his conducted in
my laboratory from 192 to 1913, and of a number of theses worked
on and completed there during the 19391916 period.
Exposition of the data is of a predominantly concentrated
nature Sometimes this requires the repitition of certain things;
it affords the opportunity to conduct the narrative in
however,
with the development of basic physical ideas, and not in con
step
junction with various modifications or particular types of devices.
'tate initial acquaintance with the basic ideas, all of
To f ac ila.
the non essential material which can be outlined on the first
reading of the book has been set forth in fine print. In reviewing
and proofreading the manuscript I have received valuable assistance
senior scientific associates of the NIIM? SC~1 radiophysics
from the
laboratory, candidates of phrsicommathematical sciences, V. L.
Patrushev and G, M. Gershteyn, to whom t am deeply grateful. It
is up to readers to pass upon the effectiveness of s Lyle and
adequacy of this book, whose comments and desires will be greatly
received.
V. Kalinin
(-.- ; - 1 ! _ f 4, ' -
SGU 5dr~ ~V 4 )
Saratov~ Radio-physics laboratory NITM~'
March 1918
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INTRODUCTION
In speaking of raclowaves of the deolme' r and oentjmeter
Wavelengths the term "microwave1? a,s frequently used. However,
despite its compactness, it is hardly convenient to
use this term-.
inoiogy, which is not fully descriptive. In this book we shall use
the expression 11microradiowavesn, only for the sake of brevit
y, with-
out any pretense toward having found an exact definition
By,microradiowaves we shall denote electromagnetic wave, having
wavelengths of 1 meter to l millimeter, corresponding to frequencjes
from 3.10$ to 3o1011 cycles, The microradiowave
region is located
between t meter wavelen the of ?
g , purely electrical properties, and
the intermediate wavelengths, with strongly pronounced optical
characteristics.
The microradiowave technique is based on electrical methods
of generation and radiation of oscillations. Their ' '
peculiar uopticity??
manifests itself, mainly, in the lower portion of the bandwidth which
is of interest to us in directional antennae arrays, in measuring
methods, and, especially in specific applications of these waves,
In its geometrical dimensions the generatirig, receiving and measuring
apparatus of the microradiowave band is usually comparable to the
wavelength, or in some instances, exceeds the latter. This results,
as is well known ~ 1' 2 } in the fact
, that the usual analytic processes
are of little use in this field, and is especially pronounced
in the
study.of specific naicroradiowave oscillatory and common'
a.catjons
systems
But the most important property of the physic and technique
1'Jr M1~ Hf~ jl'14Y lr~ J1hi+~l i hrt t, Z ~ f M1>~ i S ~l 1 ~(t ~ IU~'(~"q i ,, } }7 ,1~"~~ ^ G~~a ~ i 4~ifr~~ ~~ 7 ~i ~ii
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ed by
high frequencies is ln1J1
N~c~n~.festation of electroziic ~,ner~.a
damensa.ons of electron tubes
of the usual methods of explaining phenoniena
leads to the 5erapping n electrron tubes. The rapid and intensive do-
e place th'~.
'ow av~ field in recent years is actual~.y
velozXnent of the micrnra~. , t'The
~' n of the electron transit time e, ,~;~ec~t.
due to the uta.l~.za do
electronic limitation, but only a
total transit time is not an 1
tional methods of tackling the problem~i
li~.tation of the trada.
icroradiowave physics and tec~~niglles
The present day state of m
i5 based on the f ol1.0wing ~.mportant facts: (a) accumulation,
ormou5 amoulnt of expervnental and
beginning with 1920, of an en
ectronic generators" generators
retical data in the field of 1?el
theo
f utilization of the electron trans~.t
operating on the pr. ~.nc~ ~.ple o
devices, magnetrons, various velocity~
time effecto re.tardxna field
modulated devices, etc.);
' Mato systems, well adapted
to (b) the the creation of h9.gh-quala.ty o.~ci
ements of u~.tra~high frequency technice5.
. ,
tics which has facilitated
(c) the develoent off' electron op , development of efficient methods of coupling the electron beam to
the oscillatory systems.
In turning to the prablem of microradiowave generation it
,
osel corine:d to the problems
is necessary' to note that it i5 most cl ~'
i~
of. T'electrona.cs of :ultra h~.g~h . frequencies. The subs~;nce of the
.~ '
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Outilization of &Lectron inertia in the
of rnicr ~~waves a.s the
' s electxona.c ~,nstrumen. The attempt
functa.on~.n~ of the vara,au
y
~,ertialess e~.eatxan~:c relay to very
to apply tk~:e principle of an ~ ?
the m;ninum ,ecbnolog10lly feasible
I`y
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o a basic study o~ the electron transit
:1,attex ~aoils dpwm bxa.efly t
n tim phanomenat, the e1ectrOMva0uurn instrrum~nts? In the
? -1a1 radio the intereloctrada electron
frequency band a,E conventa.b~ 9
? o~ l0"~ seconds, and Qlectxoriic de"-
transit tirtie is an the order
? nextia in view o:~ which the controlled
va. ce s ~unc ta. an almost ~ with . ~
n base in accordance with the control
al
electron currents vary i p s Jn excellent example' of this is the classic
electrode valta~,ge ?
reed-back oscillator. 't'he 180-degree phase difference between the
plate and grid voltager, produced as a result of suitable conned
~
:Feedback winding, ensures action of the tube as a
tion o? the
sistance relative to the plate circuit. How-?
dynamic negative re
ever, as the uency increases, the phenomenon off' electron
,~re~,
inertia, which marLa. .restn f in that the election transit time
~ itself
between the ;rid and the plate becomes appreciable as compared
with the period of oscillation, results in the violation o
normal phase relationships within an electron tube oscillator.
A desire to circumvent this limitation still remaining within
the lir of classical oscillator systems, has led to the
>r~ts o
emergence o er of special electron tube designs, in whic1of a nwne
it has been attempted to neutralize the effect
by vary. ous means, ~ '.
of electron inertia smaller interelectrode spacings, choice of
special electrode shape and material, etc.). Efforts in this
d anced tie conventional radio~tec1~nical methods direction have advanced
amplification to frequencies iee on the order
of wave generation and
8.5 c,ertimeters), However,
of 2000-300 megacycles
it is not the overcoming of the effect o2 electron inertia, but
resent da
its ,~.ntella.pent utilization which has determined present day
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up of more or less general theory is confirmed by the existence
of properties common to all generators and characteristic relation-.
ships. One of the widely known and important relationships, which,
in one form or the other, holds for all of the generators of e1ecM
tropic oscillations, is the "Barkhausen' s equation",
where 7 is the wavelength and Vp is the applied constant accelerat-
ing potential. A relationship of this Form, first derived by- Bark-.
hausern, Kurtz and Zilitinkevich, should be understood not as a
condition of continuous dependence between .? and V, but only as
a
a connection between these quantities, which characterize the
optimum conditions for starting o,f electronic oecillation within a
given device. The last observation is significant, since the only
element which determines the frequency of electronic oscillations
is the oscillatory circuit. Assumption of the presence of inherent
frequencies of electron flow determined by certain "non-circuit"
effects (for example, "fluctuation of electrons according to
Barkhausen and Kurtz), is, in the final analysis, completely un-
reasonable for the usual conditions of operation of electronic
oscillation devices (electron flow in high vacuum).
Thus, the natural and unified scheme underlying any generator
of electronic oscillations boils down to two basic elements;
-
-~~,..
'f~l,r4"1"r it, a .. u:tN,,.,. .r. ~,.,., ~.r .. ,,?r ~~w ,R' r? ~._ ,., ..., ., .~ .~. 1 ~.. s.-, '. ",n,
,r .tr{a ,y !.11.' ,~' V ,~ .p p a .. ~4 ty' I i cqy+ ~ irV 7t. N ~ ,I ,. tr, G r , x /R~iq ? p~p - vjw t.. , ,.,,~ is v~l rs:, ~l ;q~rwia 3.. lq 1 ~ ,,.', ' ,'h.,~.,,.: ;,,. 4H,. rya, 1, it y' .. , ~ a ql, .~i~q'.{ ' ,.p a
,, , ~~' f ?r r~' ~ ~ ~,'~:. '(~ 4. ~ ! ?P , ~ R ~ ~ ~~,' .ear .I 5. ^~ t.J,1. ~~ .7 -~ 1, r"r?,1,7.~ ~tRr?9 ~~^'~? ~~ ~U`l~ +';!r S: F)n.lt
fiY~ I~..{~ ~;,, ~ ir~d n ~ ~ ,p l{~q i. 'q'~, .~.d~, L i ;'+~1,. 't ~.~r R~~, a +{rf r. $? ! 'i ,p, %.. ~~,~.r {~~~~~~~i~~Y ~1~~,a i~~.'r11~~r .7,y; ,y.~4yVa wrA1. ~n,v~~ p.,~9~I~` ;~~y~~?~,? ,~i firt~};
n"~rdtl,4nt.; I~ .,^4 ~"` ~ , c tl? t. i~ ~1 d d ~.',
!v. ~ A~ f,'. a I~, v ,~1'.JI., r,,, T ~r,lt, d r ,u J} ~+Y ~S pp b. '~ ~, V ~ } M ~~ qk t'. 4ir1<
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'Y~ F '~~,+'" l.li., The effectiveness
o2 circuits of this type is emphasized by their high figures of
merit, which, 'according to holster, have Q's on the 'order of 1000,
~~~, ~ ~1r ; ~ ~ ~ - h? ~ ~ ,~~ P ~~~"' p~ (i'~~~~~?~"~fJk~~~~,~~~r '~~dt' r ~~Ik~d"~"'~'i #~v~ti~' ~~~''~ ~5(~~~f'ya~~',+~F,'~ ~~ ~I~~
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and meaauxements, Q's o1 approximately 200.
Figure i.6
In the range of sub meter waves, t'spheroidalt" circuits of
this type were introduced by Hollmann , who developed several
C d' ficationsf permitting very convenient tube mounting and
~.rCUit m0~,
a simple oscillator construction. The bell-shaped Cups of Kolster's
circuit were replaced by Hohmann with the perfect hemispheres Dk
('Figure 1.6), The oscillator circuit here consists of an axial
cylinder R' a R?1 having a diameter d, upon which are mounted the
hemispheres S' and 3' ', terminated by the flanges F' and Ft , of
outer diameter D. The flange spacing a may be varied by moving
f
the hemispheres along the axial cylinder. When the system of Fig-
ure l.6 is oscillating, a voltage loop appears on the flanges, and
a current loop in the middle of the cylinder. To divide the con-
stant potentials applied to the hemispheres, an anode and grid of
a tube are connected to the flanges, and the axis cylinder is split
in half by a capacitor formed by plates F and F' . The purpose
elements of the system is clear from Figure 1.6.
of the remaining
Figures 1.7 and 1,8 show the constructional details of one-tube
generators having spherical circuits: the first one with the
RCS-831. tube operating on a wavelength of l.S meters, and, the second
one with an acorn tube9 operating on a wavelength of about ,80 cen
timeters.
In treating the spherical circuit as a lumped-constant
circuit, Hollmann had arrived at the following formula for computing
,
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I,s
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waves evidenced themselves in the folllowingt reduction of the
natural circuit wavelength for the same geometrical dimensions,
increase in the dissipated circuit power, and improvement in the
.
stability of generated oscillations. Figure l.1S gives the idea of
the electrode structure of a maietron with the internal spherical
circuit, designed by L. Dudnik , and Figure 1.16 shows the drawing
the entire magnetron tube with dimensions shown in millimeters.
of
Some of this magnetron data is given in Table 1. 1
A lumped constant oscillatory circuit has recently been re-
('?) ~ basic sample is furnished
vived in its several original farms
by a circuit consisting of the usual variable condenser with an in~
ance consisting of a metallic strap fastened to a ceramic ring,
duct
which is mounted coaxially with the rotor of the condenser (Figure
stator of the condenser is connected to one end of the
1.17). The
strap, and the metallic contact fastened to the rotor slides along
taneously with the increase in capacity, the length of the strip
within the circuit increases. With this design, as the capacity is
varied from 12 to 8~ micromicrofarads, the inductance changes from
.OJJ to e099 microhenries, which makes it possible to cover the
frequency band of 5 to L.Ga megacycles. In order to. avoid any re-
sonance phenomena due to the part of the strip behind the contact,
it can be connected to the rotor of the condenser. Such conned
ton is employed in another c?ircuit design shown in Figure 1.18.
There the capacity is varied by means of an eccentric head, which
serves as the rotor of the condenser. This model covers a consider-
ably greater frequency band, from hO0 to 1600 megacycles.
N 1xa..}7 x ~,h,.~.h u C ..a,.?am~u.l ,f ,~L4~hr.irt~,J~ fuA`~fi~k H^t.L
d ,vpit, .ti~,r ry^, ,r .y, ~. ~ry, as , it, nai^h.w A ?J; d d~. ,.1 t, ir, ,+~+ ^r^^, r:~,a is ~; 4,,.1 :f,..,, ,w~8r'S.r r, ru - ^r,: i o,. r4+af: 1
{y p I~ );.r ;y!.F!lR^ .~7"j.~. I~'i4,t ~~ T, ~'i7, (^r ,?- d,~I~.d fd A~i in ~, ~(~1'i ~, ~,.,. r~ ~~ Ih.54)e^Ifkr ! !.... , V, m,,,~I,m,l'I,t,,, I~.A;~~ .!%Y:Ili. iY.^ ~, p ~ .,~',?^,I 1
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cam:.;: .;~ ,~ ~:u>
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 1.3 OSCULATE SYSTEMS WITH DISTRIDU'TFD GONS~ NTS
Figure 1.17 Fire 1,18
Osciilating systems with distributed constants in the micro
radiowave field are represented. by twin conductor and coaxial lines
or by coils, the dimensions of which are comparable with the wave
lengths (intratube grid circuits). One of the most characteristic
parameters of a line is its characteristic impedance, given by
formulas;
Figure 1.20
Th.e probe'm of the natural frequency of a line has many solu-'
s s line of ckiaracteristic impedance ,O ,with a
Lions. For a no to
c amplex input
the natural
impedance .Za and terminated resistively or capacitively,
,0w 60 log (b/a)
I
resonant frequency is determined from the relationships
n jeu_vpy? .vn,+hr+'~'rl, nv~~ fr+p~
~~?x~jj7gIf~fff`y~t`~~K?ry{ar~~r11I%,''
'",3'r'1 r' e..'tP ~ 15v ~"~"i'f~uPi r?"~~iY?'~,.;~, ~ .. ?G r,~,,,~ r. , ~y'Iq ,.?P t .y7 `~~$. i.. E'k'7,!'.5 ~ ~'~~`l~ '?'r`oH ~ ~ ~!+ ~+irv $~ ! ,; f ?4 J.Sn::,rM , h:~: ;q?ri1? I I II~1~'r ~,. 'Y h t ! E r z i d i b{Y~r ~'''~~~ ~Id J~ 1r 9 t,{ r r~ S`~>{. b .~ t, v ?r l i1'GI rf r s y r ;,
1V~l~dJ.i~1:.7i~lilcdih.,t11f ,
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fy,
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When studying such paraxneters as the resonant impedance and
;figure a e , we cannot assume a no-loss sine, as is
~' merit of a ~,axa
done in solving the pp roblein of natural frequencies with sufficient
~.ving th
practicial accuracy. It is necessary to take into account the actual
resistance of a line, which per unit length of a pure copper line
is given by the following formula:
for a twin-conductor line, and by formula
R1 :? 41?6Y h/ f( + ) io' ohms/centimeter (1.22)
a b
for a coaxial line.
Here f is the frequency in cycles, and the values of a and
same as given by Figure 1.21.x. If the conductors of a
b are the
line are closely spaced, Rl increases and can be de-
twa,n~c onductor
value obtained from the formula (1,21)
termine d by multiplying the
by the 'proxa. o 'mity coefficient's, which depends on the relationship
b/a, and is determined from the graph of Figure 1.2S.
uniform resonant line, which is equivalent to a parallel
circuit and has a lame input impedance, can be short-circuited
and thus Kaye a length equal to an odd number of
at the output
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In bath cases, and on the basis of the transmission
line
vo1ta.ge and current equations, the resonant in eda
p nce of the trans.
mission lyre js given by the formula;
Here n is the number of quarter wavelengths of
the line,
G is the velocity of light (Centimeters/second)
. Taking into account
the values of the unit and characteristic impedances, we arrive at
the following formulas of Z for the coaxial
(1.2k) and twin-conduces
for (1,25) lines;
The factors F and G depend on the ratio a /b and are
determined from the graphs of Figure 1.26.
As is expected from
formulas ('1,2,x) and (1.25) the resonant
impedance of the lines is
proportional to the diameter of the outer conductor or
the conductor
spacing, and, to what is especially significant the square root of
the frequency, We note that at the same time, for circuits with
lumped constants, the resonant imed~ ,
p race decreases with frequency,
which eircurcistanca emphasa,zes the... advantage of transmission lines,.
Formulas (1,2)
and (1.25) show that the resonant impedance of
trans-
mission lies _nay .r_each_.v_er
Analogously, the magnitude
of the figure of merit Q determined by the
_ .,usual. methodcan
be de-
termined
. by the forrriula, ~ 5
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the calculated values due to unaccounted radiation and other
than
losses; however, in this case we deal with values of Q. common to
quartz crystal oscillators. These circumstances deter~fine the
p?ss lity of employing coaxial lineas as stabilizing devices at
ul tra~.biho.gh frequencies, the basus of which was laid in the meter
wave M
region
I:~ in meter~Wave band devices, it is possible to distinguit
a special stabilizing system along with the basic oscillatory cir-
cult then in the sub-meter-wave band such a stabilizing system
coincides both structurally and electrically with the basic oscilla-
tory circuit. The employment of resonant lines in this case becomes
e .
specially convenient and affords an opportunity for comparatively
simple and at the same time mechanically sound generator design.
Even the supports can be made in the :Form. of 'tmetallic insulatorstt,
i.e., of quarter-'w'ave lines having an almost infinite impedance at
the resonant frequency. Due to its considerable charging capacity'
1Ltote enemy stored by the line (C1, U )/2 nd ght be considerably
C ,
neater than that of a lumped constant circuit of the same frequency.
g (10)
was made use of by Rohde and Schwarz in the
This c~.retzms~nce
design of the original spark generator, and ubSequeflt1y'3 numerous
.? investigators epm toYed resonant lines as a circuit element or even
as the component of the thermionic systems.
most successful application is that of the coaxial and not of a
F
.
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~~. ~ FM19"', ~ - t fu,!!:h>'I~1~ . L, ~/lr.~ k ~rrl~`:S~ p~~r r.1?a'?lrrl`~~, !,? ~ ~.. ~~;~d`) (~ . 1.R,t ~I~ .:p~~, la~~ Sk~~r~I' flh y~r i, ..,.. Fth ~~.{, ~.d1. aR4M1rr 1 !y~.S1,M`tl, ~~ k~~?Na,:fiw
al4t~, uaf ~.. ;{ sl .rl ~1;411r V+ft, ~u;d) ?.~`
=f,l'4~rr ~1 ~,it,5$',ai 31 ari J?p ,3' i ~r ,etF(,,"7rrt,~ rh;7A r~rl i~yt~ I.. ~S?~;~{,,r '~~~ 1,~ 4 1 ,?, ~ ! u: ~ c aAp7~~ia
, rllr ~~4:r,r,rne rrilV 2rrFr~{asr i+,i
~,u~; tr 1' a., ~iv 3,~/rnC ,fi r~,l v~r94!t;t~.'yy;, vy~wy,{!letd +
Yl
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. Figure 1.140
(c) A cylindrical cavity open at one end may serve as a re-'
sonatar anda filter for pertinent frequencies. Thus, with the aid
of the 36E3A type vacuum tube, operating on a second harmonic, it is
possible to obtain waves of 9-10 centimeters, if a generator
operating on its fundamental frequency is placed inside a waveguide
tuned for t 91O centimeters (6.37.6 centimeters in diameter), ;as
iS shown on Figures 1.11 a and b.
(d) Tighter coupling between the oscillatory system and the
electron stream can be obtained by designs providing for intratube
grids only for the purpose of setting up electric fields in the
path of the electron stream. One oC the examples of such a design
Katsmants tube (26), inside of which and along the
is furnished by
path of the electron stream there are located two pairs of grids
terminated by Ferro-chromium rings, by means of which contact is
effected with the walls of rectangular endovibrators, wherein, in
the appropriate opening, a tube is inserted (Figure i.12). Such a
combination of the endovibrator acid a tube affords the possibility
of speedy replacers nt of the latter without interruption of the
operation of the entire device,
klystronst
Iron stream is coupled directly to the endovibrator and the latter
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Finally, the introduction in the microradiowave practice
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fFSrWIy'~Snl+r F",~J,,rsr~Y~~k~~Y1~i f"s'~?u~N;
.vF igtr' 'rvp j%t~ ''~~. 7~..iy."+Vy~t'iti . Ir7~. y?,l '`~u i ...,,..~ur rX,~(Ir~~t'`-~t1'V; aYi~''v
~~. ~~ i~ iJ~.Y~;tn M. ~~.~P~~~. ~
' ~~~
~
~~~
velocityMmoduiated amplifier, shown schematically in Fi rya 1.L7.
the
In j,/ultra-high frequency signal to be ariipli.fied is applied to a
rid which controls a narrow beam of eleetronsp This electron
beam passes through a gap within a bicylindrical endovibrator where
there takes place the interaction of the beam with the high frequency
electric field., with this arrangement the tube is frequently simply
mounted inside the circuit, and, therefore, may be easily replaced.
The oscillatory circuit itself permits simple tuning for a given fre-
quency independently of the tube s
The design advantages of such a system of circuit and tube
coupling are obvious, in view of which a number of theoretical and
experimental attempts have been made to apply it to the energizing
r
of double as well as single circuit klystrons, which, however,
did not receive adequate develo ment in view of the simultaneous
progress in tube and "circuit's technolog~r, which resulted in the
development of certain "combinati on't systems, to be dealt with in
the concluding paragraph of this chapter,
1. NEWEST I" COMEINATI N" OS CILLA TONY SYSTEMS
_..,,,.,.....
Our review of oscillatory systems employed in the micro
radiowave field should be supplemented by a discussion on the more
interesting designs evolved during recent years, which frequently
embody the elements of all of the basic types of oscillatory systems;
lumped-constant circuits, long lines, and cavity resonators, all at
the same time,
(a) In the US literature there,is frequently used the tern
"tan' circuit which stands for `a circuit similar to a resonant con-
.
u
..
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centric ltfee Ofe of the exaanples of this is furnished by an
interesting design of a stable ultrahigh frequency oscillator by
Peterson (32) who employed such a "tank circuit"' in conjunction with
,
a special 316A type of tube, which operates on the cgnventional feed..
back principle. The external appearance of this generator and a
schematic circuit cutaway view are shown in Figures 1.1,8 and 1.L9.
As can be seen from these drawings, this circuit is similar to that
of a bi cylindri cal. en dovibrator. Its inner c onduc for is in the form
of a rod with a plunger, thus resulting in certain capacity with
reference to the wall of the outer. cylinder. 'i'he scheme of circuit
mounting and load connections (R'L) is shown in Figure 1.0. For
the outside "tank" diameter of about 10 centimeters (L inches) its
capacity was equal to 130 micromicrofarads, and inductance to about
.018 microhenries. In operating on a frequency of 100 megacycles
( M 3 meters) the Q of the circuit 'was about 2O0.
(b) A different example of the use of the term "'tank circuit"'
Is furnished by the work of. Linder (33), who made a magnetron anode
appear as a line shorts-circuited on one end, labeling it, however,
as the "tank circuit anode".
The anode of Linder's magnetron represents merely an incom-
pletely split cylinder, and. it can be fashioned in the form of a
strip of copper with a drilled cylindrical opening and a slit parallel
to the cylinder's axis (Figure i. i) A load is connected to the
frt
split cylinder ends. In order to generate wavelengths i 8-?9 cen-
+iw
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,prwedfdtJ~
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equivalent circuit
of Lecher system
Aanode
Figure 1.S1
time power output obtained from a magnetron with a small anode and
small laminated circuit did not exceed 2.~ watts at the same free
quency.
(c) A "cylindrical circuit" (7) formed by two coaxially slit
cylinders revolving one inside the other, as shown in Figure l.~2,
which illustrates the method of tuning (position a corresponds to
the maximum frequency and position b corresponds 'to the minimum
frequency). Large resonant impedance is.. obtained .at the inner sur-
face of the outer cylinder, at which point the appropriate tube elec-
trodes are to be connected. Figure 1S3a illustrates the method of
mounting of the 6FLj? acorn type tube. Appropriate cuts are made in
the outer and inner cylinders, and the tube is mounted upon the outer
cylinder in such a way that the grid terminals are taken out over
Figure i.
Figure 1.3
cylinder cut ("icapacitive connection). The presence of the tube
limits somewhat the possibility of rotation of the inner cylinder,
yhh{al ?~ Fur? a
3r
'YRf dK PN`x7 AU FdI .~91,~1~ t) .d ?ApAA9hky's,+'Y N:+!
t
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 I~r~~~~nAll~~f~~,~~A~~~'t~'~!'~i~5'i~~~a/~f!,'7i~+?}irrir..l Ilyc,~k ,l(,~ llv,lMr~,rtrJf ,vl~1 tl1N'~t1~19ryl~:, i?~~\k Sr, /n ,A,',tii~: Y'~ ,.d l,r;`1{~r ~i re ~t1~~1.1 ~1!'?!Il1} I,rl f>'p:, ,ua ~,}~
~J I, t?,'yr15. ~.ii7~N fN. 7W; +ys r~1~74:~.v~~""b w(1,.,!?}'?I vt N~ey~t'~rll SiJI (nfl:, 7?~~It.v,;u?'~di{r"'?119 N~.. ~.y~." ~~:.
I rP1h ~~r `~ry~'I"
,
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Oscillatory power output
Tabu 2+1
100 100 100
20 20.
20 20
100 100
14
100 3I!.
20
100 314
20Q 100
200 12
20
20
100
114.
38
360
sur 1us and parasitic capaci tes and
In order to decrease the p .
ent lead-in construction is employed
inductances,. an entirely differ
the rahigh frequency tobes'. Instead of the conventional
fox ult?
latinum or molybdenum lead-in wires
ti leHsu with tp1a to s'i where the p
. ?, ter ara11e1 to each other within the
extend almost f or a centime p
e. ca acities there are utilized
lass itself, thus forming considerabl P
D~p~~~E~ UL 0
ijavelength
Linear dimensions
Electrode potentials
Jumplif ication factor
Interelectx~ode capacities
Lead-in inductances
Impedance of the circuit
plate current
Curvature of the characteristic
Electron transit time
Input impedance
Cathode emission density
Power dissipation density
}1(ryP d ~5..y. ~?? 1. "': "I I'hr "~qWr~1, .1' i'9f ? 'U,~, ,t gi~ie+ ', Y,pa4 `4 11A J.u rl7C ipP rh FV i~~W, V+Ir1~( ! fi ~.I ;
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J,PLIh7 ~~,M
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lead'.ins through "eyes" sealed directly into the glass bottom of a
tube and located, whenever possible, perpendicularly to the lead"ins.
In recent years use has been made o: the so-called disc"shaped lead
ins which provide for the convenient mounting of tubes with concenw
trio lines coupled with the improvement in the electrode heat dissipaM
Lion ('tligllthousett tube, refer below).
Let us look over a number of tube designs and oscillator cir".'
cults, which characterize present day progress in the field of ultra-
high frequency application of the feedback principle.
To begin with, many various miniature tube designs were em-'
pToyed in the submeter waveband (approximately, for ,,X up to 2-'30
centimeters). These tubes are represented by a number of makes of
the t'extremely close clearance" tubes, geometrically similar to the
conventional types, with analagous lead-ins, and also by several
types of acorn tubes distinguished for their original lead-in con-'
nections. The latter are very short (Figure 2.1) and are located
in the equatorial plane, which is the plane along which are welded
the top and bottom portions of the tube. To this series belong the
95, 98 and 6F1I. type triodes and the 9 4 type pentode. An idea of
their parameters is furnished by Table 2.2.
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Figure 2.2
The power of the oscillations obtained with miniature tubes
does not exceed tenths of a watts From the standpoint of power'
considerably better ~esultS are obtained with various special os~
e, r
callator tubes (miniature tubes and acorn tubes were developed
.
mainly f or appltion to receiving apparatus). The prototype of
~- ca
a whole series s of rather successful models was the 3164} tube C8],
later samew~lat improved by Tsvetovskiy and Dzhibelli C9a? In this
of the electrodes on thick straight outlet leads
type the fastening
which pass directly through the glass base of the tube (Figure 2.3)
The anode is a tantalum cylinder equipped
calls for attention.
which radiate and conduct heat away. The grid
with three plates
consists of tungsten wires located along the generatrices of the
to two wide rings on each side. The power
cylinder and fused
ratings and effi~. c'ency coefficient obtained with this tube are
illustrated in Figure ?guxe 2.L, from which it may be seen that this
i.
tube develops more than watts ref oscillating power at a wave`
length of about 50 centimetersth an efficiency of the order of
+ ~M~`, d6~h;~gyy~C J~q !,~ 'M1 ~~ R i n,'Kt{{n,~~~ ~i I ant 4 i~l,5h~~k~1 ~ 4~h i tIF ~
p
ti ~! ~ l
a
~
~
~ ~?
r
t ,
~ ,
, ? D i , r R n 4 r ti +
rr '" kb f
i
I kr d it"~' al v+.anir.l A ,a 9.tL~ uit'd +t ~~,i'~r~~~k%~ '~r~ ~'.~t'4Y?C ~S'~~di~?Iit'd~1k+'ru iL iu?w ;ti4~1?,~'RJ1 ~'aU~Vh ~~n,~~i i A1y ~~'art~N Ul.V
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 f!'sit~~;{Vry,
?'j .r Q
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lA percent. By using a hih-quality oscillator system it s
possible to increase the efficiency and the stability of the os?
cillations of an oscillator which operates with a tube of this
type, The Barrow tttubett generator (See Chapter 1, Section 2,
Figure 1.28), developed for, a range of 11.00 to pLo centimeters,
serves as an example of a rather successful design of a laboratory
oscillator such as this, The upper portion of the oscillator is
a screening metal cylinder into which three concentric tuning
lines are introduced; two of them tune the filament circuit and
the third is the basic circuit included between the anode and the
grid. All of the lines are tuned by pistons which move along them
and are fixed at any position desired. The oscillating power is
taken off by means oaT a coaxial line attached to the plate-grid
circuit at some optimum point near the tuning piston. The oper-
ation of this generator with a 3164. tube is characterized by
the following figures:
Frequency (megacycles) 700 500 300
wavelength (centimeters) 43 60 l00
Power (watts) 2 6 8
Efficiency (Percent) 20 2S
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Figure 2.3
The plate dissipation of a tube of the type described may
be increased by adding to it a 'book-case structure" [10] (Figure
2,5): a number of parallel tantalum plates, from 4 to 12 in
number, are located on a common holder and have semi-circular
notches located one above the other, in which the grad and cathode
are situated. The overall structure of the electrodes acquires a
somewhat asymmetrical character, The gd (Figure 2.6) is formed
of a number of loops of very fine ( = I.~ millirrneters) tungsten
qua re whose ends are welded to heat-dissipating plates which have
the form of a book cover which is placed on its back on the lead-in
of the grid. . .
The operating conditions of ultra-high.~freauency tubes are
.considerably improved if their electrode arrangement is equipped
with dual lead out ra res; the plate and grid are fastened on thick
parallel molybdenhn wires which pass throughout the entire tube
(Figure 2.7). The very short 'leads of the heated filament are made
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 G~'1~i+ 11! f i l'.I rk r Pr NY :J 1 1 l S ~i~t tr~l 1 ~ifYi R(~'18JY~
~J~+ fm Ya 9 1.1 111 11 1 I~ i 111h 4114177ly,+N~~ IY
14~ ri 11Vf i'I h r ~~ 1 ~,~ ~iy"111 '7,a IrJ la Y rlyiyl, 1~Fy1sr hi1o~
n~lrti) rS q
I~.,;i~~ a ;h`~3I~~?,~te1 a}
and as I'ar as passible from the plate and grid leads
an one side
The palates oI such tubes may consist of a piece of graphite E8]
ttbookcasett design E101 , The construction of 'the grid
or have a
d cxibed above. For the saa>>e electrode
s
?
to tha e
:Ls jdenta.cal
tubes with dual leads make it possible to increase
mens.t.ans r
the frequency by approximately 1. 2i.)4. times. Typical and natural
I
for them is their inclusian in the center of a halfwave Lecher
Art example of the make-UP oi' air oscillator with such a
system.
tLwos M dedtt tube is illustrated by Figure 2,8, where the tube is
~.
included in the middle of a "box-t,ype Lechertt,
3
a
0
Figure 2.)1
7f4
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Ne
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 ~~ Declassified
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C3) C4a C ~
C~a
Samuel tube with ,. th limit
16.0 1870 0.01 wave long
twawsided leads (368-A)
Figure 2.9 illustr).tes the same data graphically.
important trend in the development of the
Al~r,~~haher, no less 1
. with negative grid uses as the basis of
ul?trawh~gh"f requency tube
flit arrangement of electrodes. This makes
design of the tube a
a substantially larger mutual trans-
it possible to obtain
to 12 milliamperes volt) and to achieve a more
Con-ductance (up to 10
' n g the electrodes. The first tubes of
convenient mode of secure. ~,
this type were developed by Soviet designers cllJ and made it
waves as short as 16 centimeters in length.
possible to obtain
h'ch made it passible to obtain such short
The expexa.mental 't'ubes w a.
cathode in the form of a flat box which is covered
waves have a
within by an Alundumized tungsten ..spiral
with oxide and heat from
(Figure . d is made in the farm of parallel tungsten
2,10). The ~ xy
ore. of the metal disk G. The anode A
wires stretched,..a.n the apext .
index which passes into a truncated cone
is in the -form of a cyl
inside which there is located a copper ;bushing which has goad..
.
`
thermal contact with the base of the truncated cone, which in 'turn
yV,lgtt'7.,hP"~1TY Y ~ M ~ ~i ~~ ~~ i4;y ~/ ~~ a ruf{ `Vnwl lAr i unf 4 ~u 1 y r ~~ ~~,
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faces the grid. The distances between the electrodes are measured
in tenths of a millimeter (Q.2 wa. ~ mt11.meters) .
The design of these tubes makes it possible to combine them
conveniently with coaxial oscillating systems so that the oscillator
proves to consist of three circuits connected to the tube (Figure
2,11 ; the plate-grid circuit (1), the grid-cathode circuit (2),
and the cathode-heater circuit (3). AU of these are tuned by
means of capacitance bridges, which, with sufficient blocking
capacity (200-300 micromicrofarads), provide a separation of the
constant voltages fed to the tube. The length of the generated
wave depends mainly on the tuning of the plate-grid circuit, and
the
the tuning of/other oscillating systems, in making very little
change in the wave-length, affects chiefly the amplitude of the
oscillations obtained. Changing the parameters of the system
(principally U) also leads to a change in the power as well as the
a
RL Wt -! 1Z l~ 44'h' .
Figure 2.7
.,. "p.f~. iyF
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1 ~~9 ~~9tsr. ,
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Mae 2,8
'theL tubes been d- ?' have beudescribed.
the A ~~n
the - ~2SLu.,~tiS ob rained d tit V experimental p
sad 'le below describes ~P
,
DTs-21 15.8 190 Th
17.0 15o 69
20.0 134 62
18.0 130 )4o
19.E 120 32
22.8 u.o 25
51
DTs-21 18?3 71.t6
20.0 138 46.8
22.1 13)4 1~6e2
2J-.L 120 ~.8
25.8 110 3903
10.0
18
114.
1800
7.0
18
7)-1.
2700
7.
18
11E
2700
10.0 20 10 2000
10.0 20 10 2000
10.0 20 10 2000
(1
1 11.0 1$
1 11.0 ?G
1 10.5 20
1 10.0 lP
1 10.0 18
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I ?nilliamperes
~J
Table 2.i.i.
S milll?-
/__ Z s
ampere s1 of {,
 Declassified in Part - Sanitized Copy Approved for Release 2012/04/09 : CIA-RDP82-00039R000200090009-2
design of the so-called Itlighthouse" tubes, which are externally
reminiscent of a lighthouse tower. The arrangement of the cathode,
grid, and plate is essentially identical to the one described.
The electrode leads are made through metal disks to which glass
cylinders are soldered (Figure 2.13). This design of the leads
makes it convenient to include "lighthouse" tubes in the coaxial
circuits of which we have seen an example in Chapter I (Figure
1.58). Below are given the data for two "lighthouse" tubes
receiving and oscillating (Table 2.5)
"Lighthouse" Tube Data
i
Vk 1K ; psc1
2C.0 Tube 6.3 v. 0,75 a. 500 v, 25 ma. 6.5 watts 0.075 watts 1100 meg.
GL-3022 Tube 6.3 v. 2.0 a. 1000 v. 150 ma. 125 watts 50 watts 600 meg.
decimeter spectrum. This fact insures for oscillator circuits with
a negative grid a broad application in oases where it is necessary
The few examples which have been considered show that, thanks
to the application of specially designed tubes, the ordinary oscil-
lator circuit with negative grid may provide an opportunity to ob-
tain oscillation over the entire band of decimeter waves. Their
basic design and application advantages are preserved, although the
power of 'the oscillations falls rapidly with a shortening of the
wave-length, as low as fractions of a watt in the lower range of the
to have a source of stable oscillations of small.
portable, well modulated, and simple to control..
A~ei".~'W,~~C'.u?'tfM~;M1~^;1'.'e~ls7ft E,.~'`~~;"1?~~~^{~7'~h~5"1!W A'itf~;~
"
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? r. 1 k! r~ UJt ~ ~ 1 ~"i"~r 4~r~r ~ ~i' I'~ ~~ r f~ i j ~ 1 1 ~h~ 41ir~i~ rJ 'J h ~ J`+~i ~'t~~
'
~
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i fy
r}. ti
~V i? f'r A~' i~rrrr~ MpFiS1i k ~ , hY'i ~+ 4n~F'f a"ar ( t yw; li
+a i u r 1" t t! 2" f,
i 4i P' 1! rh it } a i1' ti ~ ~ r a er
n Part - Sanitized Coov Aooroved for Release 2012/04/09 CIA-RDP82-00039R000200090009-2
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exceeds the saturation potential. A result of the action of the
alternating electric field is the period changing of the velocities
of the electrons in the stream, which leads, for finite transit
tamesa to an interruption of the static nature of the current and
the formation in it of dense spots which are periodically changing
in time and space; in these densifications the instantaneous values
of the current may exceed considerably the saturation current of
the electron emitter which feeds the system. The utilization of
such periodically occurring densifications in the electron stream
in conjunction with a weli-designed oscillating system is one of
the basic processes in devices for generating microwaves
Figure 2.12
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r
h'cL
ea4A
t:,
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However these facts have been understood for only a comes
,
parative].y short time, and the retarding field circuit has been
used since 1919-1920. It is characterized by the fact that a high positive potential 'a1. is fed to the triode grid (Figure 2.1L) while tpositive .ve potential ~.
at a zero or even negative potential. Th.e occurrence
the plate is
o:f very h -frequency oscillations in this circuit has been ex-
plained ~. by b~h .
~.;a,rlchausen and Kurz [ 1] and by Zili'tinkevi c2 ] by the
nagt of the electrons around the positive grid. They ob-
tamed ~.ta~tionl wavelengths ofup to 30 centimeters with ordinary tubes.
-
The poss.bl ~la. ..ty Of generating such ..short waves with a. simple
~.
of a^oa' ects dedicated to the investi-
circuit has provoked a, number p
eta~din afield s ,
gatian of processes. in th circuit as well as to
e r ~
its applicat~on. From simple delibera'tioris based on the concept
.
o arkhausen 'and' Zil.tinkevich Lound that
?
of "el,ectron ag~tat1ortst B
`?. ,
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the wave generated in the retarc1ing; 4ield circuit depends only on
the geometrical dimensions of the tube and the otentials applied
to it. For a flat electrode design where Ug is the grid potential
in volts, Ua is the anode potential in volts, d is the distance
between cathode and grid in centimeters, and d is the distance
a
between the grid and plate in centimeters,
~.
C\ ul1
~"
t).Fccl-y ~pt-tdqc
w i-;-('\ --r errs o--
Figure 2.1L.
In the case where U 0 formula (2.L) becomes
a
which is fulfled' mare or less satisfactorily in all cases where the..
From this the "Barkhausen relationsh ip'1 is obtained
(2,b
l
~,': T~..r.:,. w... ~,, :'~..y ".?IY. A -:.. .....: ,~ s,,,r"' e , ~. ., y,:. ,. Y.i,. ,::~'t'. I ., U t1 f, ?. :: ., .~,,,::. 5 ,, , ',; :.::.. ;
.. ~. .... :. ",: .:
x ,., ,,u..~ do .~ ~, s ,. .,. :.. , ,,, ,, . I , r : ,a ;..,,. ,...,, :, ~., r. S,?
.
:~?,, _, ..:.,.~
,~,
i;J'51 ,(i
({I
h 1~tw0.~AV!q
}~ffy'6
a1. v3,~nYli~li~>T,
OOo
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4? P+ + .iip6i +? r"r~p.'Fii ' '~i'pC'..?rM } rffl +.a"?r 6 y.l. l9}..,."C?4 ~ ,~,I ~ I4'n I Q.'C'7V:'~N a vr~dB', ,r v+ 4,Z1%" i ''4,c^ a v
rP~{+.~` ~~~;.r.~~k'.pl l~.,!r1',~U''^ I?I. ~,I.y~F~~'i%;`7 ~i~,{.~gSy~~, ~f~v,Y~~.y., ~2~ v!t'~, ,VM,dy'I "}.~~~ ,11Iy.P?w~9~~,("~.~'.f~?;~a n~`~'}~~;,l ~;l ~6I,~'.~~i+.K..41.~V~gy{~r~h~rq ~yv r~l au~+a+~14?vlM ry~pe r.,ip,
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of a dynamically controlled
sc;1.i1&'G~.Qns a,re excited by means
a
electron e'~rearn
. a eneral power nature to an
cansiderata.ons of . g detail4
echanism elec r
,been woxke out in sufficient
m :wh~.ch had.,
l~OSt fruitful, however, were those theoretical. deliberations
hcnomenan, applying
account both aspect of the p
which took into 4-ti inema.tic
a tenco of the xe~arc~n~-Meld
In the first years of the cxi$
of the great cQmplaxity .
p) observations were made
circuit (192Q 193
of it and of the comp:l~'Le1S~
the hanomena wha,ch bake place in ~t
~'
he theox~,~ of ttelcctron a.g:~tat2ons ?
logical inconsistency of t nts of
r~.verse poa.
a the develapment of extremely
'phis gave vent ' ~
lain with vara.aus degrees of
flew, each of which a,ttemp'ted. to exp ? , take
racesscs wh~.c,h
and in part 'did explain ..w the p
prec:i~sion
1 mental facts which are obw
~~lace in the circuit and the exper in~
these theories are now of only historical
seablea Many of the
taken of two schools of thought.
terest, Notice n~-Y be ~~ nema,tics of
se point of departure was the ki
lcinemat~-c `~hear, whoa ' .. ld
the circuit and wr~ich attempted
electrans't in the retarc~c.ng f a.e
to create a sufficiently graphic concept of the mechana.ca oft the
os which the repreSen~at~-ves of this
cillaLions, to accampl.= ~sh
howl often had recourse mechanical models which illustrated
to sc thought which may be
13] and another school of thous ,
their theoxJ ~ '
called the eneral phYsica.l
+ owerlt school, proceeding from more g
tp
certain quantitate resuJ.ts by
considerations and lead the
' or less independently of
somewhat more formal means, more
, rcui'~.
concrete details of the operating mechanics of the ci
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If we attempt to sunznarize the enormous quariti'by o1 experi"
mental projects devoted to the xea^da.ng-ie~.d circuit [iL'.]a we
may establish the Following fundamental experimental 1aets:
(a) Electron oscillations are rather easily obtained in
the Paz d -f' eld circuit, with the majority of triodes of
re ~.n~, z
syrametra.cal design. Due to high grad potential and large grad
currents tubes with a high-power grid and a pure tungsten cathode
operate with considerably more stability and make it possible to
obtain shorter waves (a wave-length as low as 6 centimeters with
tubes of the P- type).
The power of these oscillations and their coefficient
of efficiency are very small. Thus, for example, in the operation
of specially constructed tubes (30 centimeters) about l~ or
watts power is obtained with an efficiency of about 3/l~ percent.
Such low efficiency is caused by the enormous losses in the grid
current circuit and also by the poor design of Itorcjnary't tubes
with respect to the marriage of the electron stream to the os-
cillating system. Application of a system of grid-plate elec-
trodes in the form of half-wave or quarter-wave segments of
coaxial lines or hollow resonators (the ttresotanktt with retard-
ing field) somewhat increased the effectiveness and stability
of the oscillations in the retarding-field circuit, without
relieving it, naturally, of the basic source of losses -- the
grid currents
(c) Even with a fixed oscillating circuit, the intensity
of the oscillations depends in a considerable degree, and to a
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1 by
lesser degree the wave length, on the parameters of the circuit
conditions of the tube, i,e, on the potential on the grid and
the plate and the emission current.
(d) The basic elements which determine the frequency
of oscillations generated in the retarding-field circuit are
the oscillating systems which are directly connected to the
tube's electrodes or which are formed by the electrodes them
selves. As an example, mention may be made of the "grid spirals"
which determine the oscillating frequency in the case of one of
the most often used retarding-field circuit arrangements. Such
self-exciting oscillating circuits are always present in ordinary
tubes and manifest themselves as a rule with no regard to the
external 'tcontrolledtt oscillating circuits which are connected to
the tube, As a result of this extremely complex and erratic
"operating diagrams" (the function of the intensity of the os-
cillations and. their wave length with respect to the parameters
of the tube circuit and the tuning of the external circuit) are
often. obtained.
(e) if it is possible, by virtue of the multiplicity of
possible oscillating conditions, to obtain different wave lengths
with the'same tube, then the function of
with respect to Ug
reproduces Barkhausen's condition rather closely -- with respect
to currents -- but with values of the constant in formula (2.6)
which are sometimes different. The F3arkhausen constant most
often observed with a given tube corresponds to an excitation of
the first order. The successive, smaller values of the constant
t e'+Iyyyr iyFnly~{t M~r'1~A.i~'l~x~,Fa pp~~'f~1. !V'. i1 x. a}~tk i'd~ tig~~ityn~"e {I.,',,, (, tt ~whi~1~~~~~~yt `1 ~.:}~~~+,?4kQt?7 IJr{, ItIh~V %Yd i`~~ tlr t~t~l',4art~S lp ViN4.j~^vy~~ t ttw~;~~.1V; ~;..!G
~1,IF ~Y?}7'i.~}~ury.F,h,.,t.Y k~1}~~7+,.r ,', ~A1f!k({i7nYl rnCy~,~~;Y.~ t14"r~`S`:~F~r"'~. 1~'G 4Yv0i~rlY,~dd ~,~~~f1 u~~~~4 rtYi~,~~11f+1 ,yc~a+1 ~t r;ii ;i7p. UtY lv.l~;~~r}}d 4h tt;ptPfp3f
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correspond to the excitation of ~tdwarf~~ waves, which are chase'
terized by a arna11 intensity of the oscillations and a lower
efficiency, but which occur more easily under favorable conditions.
(f) With determinate values of Ug, Ua, and 'ern (where lem
' the emission current) one or several maxima of intensity are
for each generated wave 7'- , `re aggregate of these
obtained
' ma creates an operating diagram which is characteristic of
maxi.
the retard.ing~field circuit and consists of a number of discrete
excitation regions whose optima according to principle with
respect to variation of all three of the parameters of the tube
circuit which have been mentioned, U , Ua, and Ism.
(7 Ar\ock:
i--:: -r kc'
Figure 2.15 Figure 2.16
A continuous variation of the wave length when any of
these parameters is changed is observed only within the limits of
one excitation region, and proves to be comparatively small with a
faxed circuit. If then a change in the tuning of the oscillating
system. is made simultaneously with a change in one or several
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+u,ti f~~Ve ~ha Fp ~ Iaa~G"a'M ~I{ 9~`,II ~~4~ ~a,
ararn ters oi' the lamp circuit, then changes in wave length, may be
ed over a, wide frequency band located within the limits
accomplish
of the sarnc excitation range. Thus a ticontinuous spectrum of
electron oscillationsis obtained. through the use of an aperiodic
tube 1 i ] . .
(h) In the case of the excitation of extremely short waves
infra"tube circuits which possess inherent frequencies usually serve
as the resonance systems, for example, the grid leads.
(i) Oscillations similar to the electron oscillations in
the Itnorrnal retarding-field circuit, and conforming, to a first
approximation, to the Barkhausen condition, also occur in systems
with considerably distorted symmetry and in two-electrode systems,
if an opportunity is created for the electrons to pass through a
closed trajectory. As an example we may cite the one-sided tubes
with semi-cylindrical plate and grid in the form of an open guard
encompassing the plate, which were used back in 1928-1929 in Kohl's
projects (Figure 2.15), and with which it was possibie'to obtain
extremely short waves (as small as 4.5 centimeters in length), due
evidently to the excitation of the grid guard. Oscillations have
also been observed in ttgridl and ttfilamenttl diodes [17, 18, 19],
and have been explained by the fact that a part of the electrons
accelerated by the field of the positive element of the system,
which element possesses a certain degree of penetrability, passes
through it due to inertia, into the reverse field, is retarded,
and returns backward. Ii'igures 2.16 and 2.17 represent such systems
with the possible trajectories of the electrons represented sche-
matically.
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In simple diodes with a continuous metallic anode the
electrons may be caused to move along closed paths by means of a
?c a.eld apA plied to the system parallel to jts axis. Thus
gncta.
was created, a circuit which has received
the magnetron circuit
~ ~~ the field of ma,cro-waves, but which under
,~men. ~ a,
widespread develo
some cone,tn.ons, for example under conditions of electron oscil~
lat f first order, does not differ in principle from the
~.on., of the f
circuit of the retarding field.
Figure 2.17
?) In the case of operation of a tube tidth retarcU.ng
(J
field, rather clearly evidenced phenomena. of coupling are ob~?
served in the external tuned system (change in the frequency
with tuning of the external circuit simul-
of the oscillations
taneously with a change in their aptitude and trajectory,
characteristic of tightly coupled oscillating systems). The
latter have given a number of authors reasons for representing
the retarding;field system as the aggregate of the infra-tube
-
electron mechanism, which possesses a certain inherent frequency,
and the outer a rystem, which is coupled rather tightly to it.
-
86
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However, as Will be shown later it is extremely inexpedient to con
ceive of an electron-osciliation rnechanism which is not dependant
on any 'circuit" systems, in consequence of which the observed phew
nomenon are due to some intrawtube oscillating system or to the
reactive properties of the stream of electrons itself; the proper.
ties occur upon the interaction of the electrons with rapidly
varying electric fields,
Such an explanation is also partially confirmed by the fact
that the coupling phenomena described are considerably less vividly
expressed in the magnetron than in the retarding..tube field
, by
virtue of the sample electrical design of 'the magnetron,
Historically, the obtaining of ultra-high frequency oscil-
lations through the use of the magnetron oscillator was reached
as a result of investigation of the behavior of the retarding
field oscillator in a magnetic field, It was discovered that by
placing the tube in a magnetic field oriented parallel to the axis
of the electrodes or at a slight angle to it, it was possible to
facilitate considerably the excitation of oscillations, With
sufficiently large values of the intensity of the magnetic field,
close to the "criticaltt values, it proved passible to obtain ex-
tremely high-frequency oscillations, even in a diode [20] . In so
doing the oscillating system is enclosed between the anode and the
cathode (Figure 2.18.). The oscillations obtained in such a circuit
are due in origin to the combined action of the electric and
magnetic fields, which determine the , motion of the electrons
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p''I
through eio aed Lra jr ctoriG S inside the anode-cathor,e space, The
trajectory of the electron in this .LnterMeicctrode ;I)aCC is closed when the maprietic field attains 'the criticai value ~Il
(2.7)
where ra is the radius of the anode in centimeters and ~a is the
anode potential in volts,
-2--fp1nTr
J ' ?:*i.aw_____M__,_____1*_nuo_4_________?___?VW~
L '~~w~r~ww_+_
Figure 2,18
Due 't( axial symmetry of the entire system the process
is r1e l;ermineCi mainly by the radial motion of the electrons, which
occurs in analogous fashion to their rriotion in retarding-field
circui.?t. The wave length of the oscillations obtained in the
magnetron depends on the intensity o the applied magnetic field
lie, charring in inverse proportion to the latter,
2.8)
Here Co is the so-called ' C)kabe constantu, which has a
calculated value of o,65o, In pracice the observer/ values of
8
~r
iV~~~~4 k R
F
LiirC"~iu( Y"t,'J!11r~Pi+til'f~'e p,ri}Jil yr }.i4Vf, am,e,lt,1 y1.
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'bhis con tari.t range approXl,na'k,ely from 7,000 to 16,000. Re'
is equivalent to the ~arkhauuen :formula
~.~ ~a~or~sha.p (~~~ }
a4~?~~6+"~115Y:Y~t~7.P.F1 +14AA6V.Si~I!
Oscillations a{' this type, desig nabed as 11clectron os-
ciLl_ations" of the ?'irst order, are cornpiete.iy analogous to the
oscillations in the retard:Lngwfe'i Ci. circuit.
, Ra.
F \ c - \ e t " t \ . n
/"' , - - N1ce4 I
Figure 2e.20
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They are oharacterized by sma1i intensity and a low efficiency
factor, which does not exceed ten percent, in spite of the fact
that losses due to grid current are not present in the magnetron,
In this type of osci ia atiorl, however, very short undamped electro-
magnetic waves have been obtained. Mere mention should be made of
the above-noted. work of Rice, and also of the work of Clinton and
Williarns [21] arid Richter [22],
The magnetron tube and the Tice setup are represented
in Figures 2,19 and 2.20,' This tube is a simple diode with a
solid anode made up so that the anode and the filament serve as
a section of a uric with distributed constants, through which
the oscillating; power is fed off' into a radiating dipole, The
tube is located between the poles of a constant magnet and is
cooled with water, The nature of its operation may be evaluated
by means of the following data;
Plate diameter
Cathode filament current
Emission current
Anode voltage
Irrberlsity of the magnetic field
Wave ~J..ength
Oscillating power.
Efficiency
7.5 millimeters
32,5 amperes
115 milliamperes
3050 volts
3300 oersteds
?1j..2-L.,8 centimeters
10 watts
3 percent
Clinton and Williams [21] went still farther, and ob-
tamed waves of 1.1 centimeters in length with tubes which had a
dual-segment anode and an internal. "framet1 circuit.
one of their. tubes are as ;follows;
The data for
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.
1
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Length of the Frame attached to. the segments L millimeters
va~.ts
870
Plate voltage Magnetic fa.el.d
11,000 oersteds
Plate diiarneter
It is diff'?CU.lt to judge with sufficient' precision the
power of the oac:l. 'l lations obtained, since it is unquestionably
below a miLLiwatt.
Richter, using an asymmetrically located filament in a
IIhalf'.sectiona]-'t tube (2.21) achieved a reciuction in operation
radius and obtained waves to L.9 millimeters in length.
Figure 2.21
The difficulties arising from the generation of such
short waves, are clear from the fact that the electric fields
used in these tubes reach gradients of the order of lo5 volts/
centimeter, by virtue of which the disturbing phenomenon of
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high?field emission from the cold surface of the metal begins to
be of cons~quericee R:i,chter tubes, and their operating conditions
are described by the data in Table 2,6 (page 61)0
The conditions of electron oscillations of the ;Cirst
order are observed in magnetrons wLtii solid anodes, as well as
those with sectional anodes. However, for magnetrons with
sectional anodes other oscillating conditions are characteristic
"electron oscillations of higher orders", It is customary to
designate the ratio of the period of the oscillations to the time
of return of the electron along its trajectory as the nth order of
oscillation, By oscillations of higher orders we usually u.ncler-
stand oscillations characterized by values of n from 2 to 10.
Electron oscillations with values of n 10 become, in essence,
so-called 'dynatronl1 oscillations, which owe their occurrence to
the statically falling-ofd' characteristic in the inter-segmental
circuit and are not associated in any respect with the transit
time of the electrons, Most interesting and typical for sec-
tional magnetrons in the region of the shortest waves in the
condition under which electron oscillations of the higher orders
are produced. 'T'heir excitation takes place at magnetic-field
intensities which differ considerably from the critical values,
and are due to the interaction of the rotating electron cloud
inside the magnetron with the changing fields between the seg-
ments of the anode, While the oscillations. of the first order
are governed mainly by the radial components of the motion of the
electrons, the leading role in the oscillations of higher orders
belongs to the tangential componentstl
?A9
Unyfnfaf,r 'J~+, V~., ~#4k9~'~~
fy~G~
n~
N (~
d44~~i9'Z
~J
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wl"lt
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.:emu
2.5 2.5 io 0.2 8 1300 lc1oo 2000 3,2 e.75 11.6%
1.5 1.S 6 0.15 ~.8 21e0 10100 370 3 0.15 3%
1 1 5 0.12 2.8 3600 10000 2300 0.?~ 2.5-14-2 2.8%
1 i .5 0.12 2.1~. Mao 10100 2800 o.s
~..2?1O-a 1.9?1fl-3
l 0.32 ~.5 0.12 1.5 10400 15000 2000 1.1.~ ?lo-5
o?4 0.22 2 0.1 0.75 13800 10300 1900 2.~ 3.106 6.5?ia-?
0.35 0.21 1.5 0,:.. 0.L9 20000 9800 X000 0.6 2.5?3t3?7 1.1fl-7
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1a Operating radius Length of = Lecher Filament --
~ Ua Ia Oscillating ~, ~ ff~. ' -
-
Te_._ o mlllii e Uer s mi l; m power
_e te~'S System, mm diameter mm. Centimeters ~
7
Oersteds volts 1
..., ma.. watts c? any
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trans the asciiiata.ng system is usually
In sccta-anal, mane
~~? m111en'~s (Figure 2.22a) in the case of the
connected to opposa.~e see,
two gaups of segments whose elements are
two_segmentube, or to
' r ~e 2.22b), Thus the densa,a.ca'ba,ans ob~
in o,lterna're order (~":~~u~
d almic control of the ?tangsntial electrari
ta~inecl by virtue oyn
ctrjC fa:e7.d whjCh alternates 2p times or
stream enooun~er an ele
we sklould+ understand the number a1: pairs
each rotation. By A
~a.th relative1.;l small angular velocities
slots (or seglnenbs).
of the rotatin( electron space charge and a large number of
r
.,
.l~. , .~ of generating asca.ll~t~.ons of e~titrenlely
se~,rmen~Ls, the passiba. Y '' s realiZed in conSeque11Ce of this. At the same
high frequencies a.
$SG~r~ to note that the electron oscillations
ta.m.e it is also nec.e ~
orders possess considerably higher effic~.encies
of the h.i,he~ ~
t' ons of the first order; their wave-length con-
than the os1lla~.
forms rather closely to the. relationship X23].
Figure 2.22
U (2.10).
The COristELnt 0 is approximately equal to 1000.
CrH
4 ,
X I~LI ~.t f Ali
t k )
~ .f II
z!f. 11 }
i i 161 I fy ~ ~i ~ a~ tlr
I I v
s'yhv il1j~~7~dk ilfq Ir ~~ Ifs yk VJ ~ ~ i4r ~~,J
11:~J~~t~~~r}l f(ttt
1 r~ }
n u hf i 1+,t Lf'
II~~! j Ito yfl ) n ~~i~ d ~~ ail4~it k I~~ 9 "j
GF~- k~~7k6^If 'a6i~fi~{i k o~iq 11trul lI~I
,I a J
t
~} Ij
~~~ itl I II~~ ~~1 YIr j'(iI ~114t~1~~~~
i r' 1 ~~ 1 ~I ~jrp~h.
~P~~i1 rl ~jj~~f'~l kilj~flu~ItiJl~ l(-?
}rft \a)li1irft r: i~ea!;C:Jj yt9,}II~
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~1~t1
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Table 2.7 which corresponds to certaa.n Rwxe tubes, is
given to show the characteristics of oscillations of higher orders
and for comparison of them with oscillations of the first order
[ 2L ].
Increasing the number of segments of the magnetron makes
it possible to obtain very short waves under less severe condi-
tions of operation. At the same time the oscillating system may
be represented by the segments themselves, as shown in Figure
2.23, where the wavelength is fixed and determined by twice the
length ABCB, Anode segmentation of this type was used by Lirider
in the two segment '~tank'I anode of his magnetron, and by Gunton
and i3erline [25] and by Kuz'min [26] in multisegment magnetrons
A more complicated, but also more synunetrical oscillating system
is formed if the segments consist of two groups, each of which
is connected with its supporting ring, as may be seen from
Figure 2.2L. [25, 26, 27]e In this case the wave-length is de-
termined by the oscillating system connected to rings A and Be
` ` cj r e\+6
WiW MUWArt,WWWM w.+~.r?Y.Wi.MMiXMi1M1AVNlKp,M~
it
aKMAMUwM4iG!/ANJYMR/~{ it li A y r;ll' n t~btk ~itt'~yW lU , (rrrx{r??'! 4~a1y r~ slti~lnu A u;,
S~4r} In i y~y''f#' ~Ir idVrl~ ~ ~ k~&n+t~1~,~i ~1~~ ^~ I , i(~r~ {"~W (` a ~~^~'C?~~ 14 {HkG1 r r 195 ,Vr.?4 fl,~r ml 4~ K ~W'P ~ ~ {f ?~G"'r
ttU`(r{
f r'f+'t~PEst ,:4, 14~,rti~Q ,t i~{r~r p3~'I ty~r'4{~ 1i,,.j}i{p,l ~~q('IP~~'d ,rl,l~~+~1'01k?G~~ft~{7k
I
w L'
I
p,i
J ,.
t r r, 1.{ ~ t 4 , i rv u,
~ ~n t}Iai~ir~ISUdyA i rlu, ~i C?,,i.~r~~Yfa,}Fr, ~ ua, 91}'4~~ I w~r~ri, iL. !.
xr t r~,~rrr,i,`~ ry d11a,~17~'iurtl'I~r>V 1~ ~y, 9a?~!,(h>,~~'u , Nt~w l , ,,@('tf;r~jr fr ,`~~rS @trt4~, ~;~ V,JR`~~~`?VU y
tl ~1, ): r?~r'hU , rc.. ~ f; ,V~~,I'I ~rt l,,,;,.;
~d l~Y? 1. W;,dt. Yt~,~ Y~41 ~y,.. ti7~ ,.,5, ,~~+ .,ti>$d xrr Antn ~t ~.~:',ti vad9 wICP+v'r~Cfrt?ri;ll ~. !r nv?y,~,9F~ rY?i`+tii "Ir VN.lff~,i t,~r~. 1; hl ~'Ir~`~~fr~1"~~a~~tl :'~O.t~~ ,~. ~~ nE~te~`Y1~r~;oliy llY r,' Cll", .;J,i14 ,rla-la+i:"~,:it
tiS p I+u ~. rti {: i-' ~ y,,l. !. Y,t.r r!; ~ Pi Flt l.ytf it l t1u o,~f..~ ~ } fd ! r}'~ltr. 4," a ~nL ?rw,b~~,;rt: 119, 4~a^vl - ~, r r ~i, t { , r ,I~ 1. I x~r a..:l~: ~ r`~1 !f+: re it 1 1 ~o-l~, ~.~i,.;r!~4 Y{t ~r 4~1S,~rriult 7u ~.r.!:qrrBpJ {1 ri5Fifrih+t}{'11iv:",~it"`1l ~~"+r( IJ~I ~4, bc~ t, 4~'~Qy~4.rw ~~ ,, ~yl ~d~.. ~'.: ~"~.. ik~ i4i}Y;'~{ . ~'~ ~J~ Y(r ~~. iit'J ~t rv7:~~~lyrryr;~' l~III' ~"i3Y;ir'ii
f. SI.Y ,f}r Yr, r1} h t ~ m ~ t~~'~` +(V7C~~ 'y1 jt~+,~~~Y rrb~ja~.r t r~''r1?Y? ~~r: I d i .~(a ~d t~u~, r,J ~V~~1+~~ 5~y1, l I e::
~ud+il1SllGrihrv,er~~r~,~'k+tl,Yrrhl~l~..:.,a~~~,~4~.~'~iJo~;.rtryl~rr't~~;~IG~ra~~x~f~?al'~n~r'1~~~nniil~!I~rEt"r?~~~!;r,~;t>1i1~~?~:,~r~1~~a?7r~~~~"her,,,~~l~SF~I.~GG~}c.~:.blaru )EJ.~~:,,r:!,~l.~ir,X1AU.E1'~?h~lt
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Declassified
 ?
Independent Uarlables
0.1
0.5
0.8
1.0
1.2
1.5
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Table 3.3
^1tlELE OF THE FUNCTIONS I MID g
'unction f
anct? an g
Independent Variables Function f Function
-
0
0.00993
0.2122s
o.)25G$
0.5308
0.60872
006237
0
0.010
0.289
0.98
2~o3e
b.c8c
12.190
:. F
1.8
2.0
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0.62tt19 l+0.36
0.60268 98.01
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All of the formulas which have been given for determining the
wave-1engbh have a common structure, which may be expressed by the
Barkhausen relationship
?..\r:-cO -r St
(3,27)
according to which the length of the generated wave, for a given geo-
metrical structure of the eleetrodds which determine the constant, is
related by a continuous function to the accelerating potential applied.
to the circuit.
B. Radial Electron Processes in the Ma jnetron
The periodicity of motion of an electron in the retarding-field
circuit is caused by the combination of successive effects of the ac-
celerating and retarding fields. In the magnetron a similar effect
is obtained by the joint simultaneous action of the electric and
magnetic fields on the electron. In the usual form the magnetron is
an axially symmetrical system consisting of a cathode and a cylind-
rical anode which is continuous or broken up by longitudinal slots into
some, usually even, number of segments. Magnetrons with a flat electrode
construction have been used by only a few authors [L].
(Fig. 3.8)
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The magnetic field is usually directed parallel to the cathode
or at a slight angle to it, Assturiing that H is parallel to the filament
and associating a system of cylindrical coordinates r',9, and z (Fig.
3.8) with the diode, it is possible according to Hull E~J to formulate
the following equations for the motion of an electron leaving a point
at a distance ro (radius of the cathode) with an initial velocity
equal to zero; )z+
, r E H r
'(r (3,28)
P
By virtue of the coirplete axial symmetry of the system and the
homogeneous radiation of electrons in all directions by the filament
the chief interest lies in the radial component of motion of the elec-
tron. Integration of the equations of (3.28) in the assumption that the
electron leaves the filament with zero velocity leads to the following
expression for the radial velocity of the electron
V2 = T), (3.29)
Here Vr a.s the potential relative to the cathode at point r.
The curvature of the trajectories of the electrons caused by the
magnetic field becomes so large at a certain value of intensity of
the latter, Hk, that the trajectory is confined to the inter-
electrode
space which is enclosed by the inner surface of the anode (Fig. 3,9).
It is obvious that as a condition of this the radial velocity must be
equal to zero when the electron reaches the anode;
) VrV Gig Ar
The corresponding value of intensity of the magnetic field H k
bears the designation of critical value and may be obtained from ex-
pression (3.29). If we neglect the member
/r, which is entirely
possible in the case where ro( r, then the expression for H k will
have
the form
'r y , _
rR (3.30)
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or ;i.n 1~'7Ct)jC,.1 un:i.ts
H
1"11
4.Y 47
Q-Cvol~)
(3.31)
c I l~
(I'is.. 3.9)
the trajec. ,torY described during this by the electron (Fig. 3.9)
is sim.iar to a cardio:i.d, lies in a plane perpend1cui.~1.r to the ay.a.s
of the system and is described bI the equation
5 1 n
The arigL~ar velocity of motion of he electron along; this
trajeCtOTY 15
ca-e_ Ike
at-zM
0
3.32)
(3.33)
~~.nd remains practically constant, charitin; only in. the ininiediate
vicinity Of the cathode.
Thus at any moment the velocity of the electron is made up of
a radial and a tangential component. The role of these components is
determined by the corresponding; mode of operation of the magnetron.
The following basic modes of electron oscillations of the magnetron are
distinguished .e. oscillations in which the leading role i played
by the a.neri t' of the electrons) : (a) electron Oscillations of the
.a
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,r
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:fa,rose periOd LCi ~'Y to the racl .ai cori:poneft of no
' u., ~ order wh
s anti b) electron oscil"j.ations o1 bigb.er orders,
ta,Qn oi th eiec'l,r?Of,
k,
in whose proceSS of occur"r"ence and mai,nterr nce the tan ential CCm-
ponent tbr e1ectr0fs p1:y .n important :r.o1e . This, off: course,
off' '; s ~~
and scherrlatac d:i.fi;'erer.ice - the etaiis will lie dis-
~,s the e:~~.~te~ntar 'y,
c;ustic'd iate1' on.
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In the case of electron oscillations of the first order the
he eriodLcity of revolution of an electron
situation is defined by t p
' represented in ~~~-g. 3.9. the pex~.od
about its cardia:~da~. trajectory, ,. be taken to be twice the time of transit of
of the os c~.lla'~ons may
cathode to the anode, which for critical con-
Y
the e1e ctron from the
ditions is equal to
a ~
A r r~ 1
d v
:licity f that ro-O or r = o~ (which.
Assw'r,ing for purposes o p
of flat electrodes), Okabe found that the
corresponds to the case
elds in both cases the single expression
transit time y i-
(3.35)
Hence, the period of revolution of an electron along the caar-
dioidal trajectory is 2'T h
(3.36)
The periodicity of motion of an electron is determined in this
the same angular frequencYH.
case by
~~.,~,he first order, observable in magnetrons,
Oscillations
conditio
ntl of the number of segments, occur under
y~~depende y
- ~or
the critical, and have a wave length of
i (SO ~. Cc,
C h~ ~Cr5~d~ ~l
were O0 is the so-called "Okabe constant".
(3.37)
the formula H=Hk also includes, in this manner,
In :formula (3.37)
a function of geometrical. factors. Actually
.~ to~Q (3.33)
t " ~ ~' field,
which la.kewl 'se leads, just as in the case of the aretarda.ng-
nshi const. This is one of the
circuit, to the Barkhausen relatio p a
most important evidences of the analogy between phenomena in the re-
fording-field circuit and electron oscillations of the first order in
the magnetron.
1.4
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The Okabe constant Co , theoretically equal to 10,60, proves
on the basis of acperimental data to be equal to an average of 13,000,
although rather considerable deviations from this value are observed
on both sides (from 7,000 to 16,000). The nature of the wave-length
function obtained under critical conditions of oscillation, then, with
respect to the intensity of the magnetic field, which may be determined
by formula (3.37), is confirmed rather well in practice.
the analogy between the magnetron and the retarding-field
Using
circuit, it may be shown rather simply that the so-called Okabe con-
stant represents a value which, like the Barkhausen constant, is a
of the tube. The curve of the variation of the
function of the geometry
radial component of velocity of the electron when it moves from the
cathode to the anode under critical conditions, as represented for
example in Fig. 3.10, exhibits a maximum at a certain distance rm
f?am the cathode, and then goes to zero at the anode. The quantity
r1 r1Lay be found from the formula
(3.39)
(Fig. 3.10)
Turning our attention away from the presence of a magnetic field,
we may ascribe the variation in radial velocity of the electron which
we have been considering to the action of some equivalent electric
field eld whose potential Vre at every point r may be determined from the
relationship [6] (~'
which under critical cpnditons reduces to
Vre(rj2)r . (3.)41)
re
(3J~o)
Hence putting ro /r on the basis of formula (3.29), we obtain
1
'I re ' T t/r '' M
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rem'
this e quiva1ent potential will have the raxiniuar, value
Vre v Ct - ) .~ C ~ V (3 .L2)
Here; we substitute Z i'Ur inra Tor the sake of brevity. The value
1n I? .s a purely ~eoruetrital party eter oi' the tube. The
course ()i' the curve oi' Cc1uiva1e:nt potential Vx,e i.s represc.nbed with
a dotlted line in Fi ;. 3 lO, iron whi.cb it rriay be seen that this curve
may he app'roxinzate3d rather closely by two straisstht lines. 'thus, we
replace the ruaF;netron with ~~.ri equivalent i'la.t system with retarCiifl
i'ielcl, whose grid is located at the point rnt ha~a the potential
f oiiowing relationships :
=-
~ u~
:1ation.ship (3.22) roust be applied to the periodic "agitation" of the
electrons in this equivalent systemi, on the basis of these relationships
it is possible to express the wavelength by means oi' ~fly one of the
Comparing these expressions to each other, we i'in.d. a, con-
nection between the Okabe constant Ooa~~d the geometry oi' the tube
(3
The limit value of the Okabe constant at ro - 0 proves in
accordance with this formula to be equal to 13,LL(), i.e. is in con-
siderably better agreement with experimental data than was the case
with Okabe' S calculation's. Thus, for example, i'ar the concrete case
where ra
?
At, the point a which may be determined 'rom equation (3.39),
nl
Then both the Okabe r'el4 tionshiI) (3.37) and the Barkhausen re-
~ilY:ho.M
centimeters and ro .= 0.00 centimeters, the following
ified in Part - Sanitized Co
tir~Y;r6~fi~ .~
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e Ga:~uculGtit:~ar1 17~etYiad , CO , 6~~.; rrl}
data are ob~taa.nec~ by t~l
o.h~l era;
" given re at' the rna.~r~e~:x?ara un,dc~^ car~,~.~.t?.ons
"~k~e oornpar~. aan sawc~r~ he
c1.ex^ ~~_th the
111a' the i?rt or
of clccIran asc :tster~ce of
extended, W1th.1ra t1-1( ~j~uits a the ex..
C1.:C' t,U.;l.t 'f i lcly ~,~. s a ~., C
os first to concla.tior~s sa~~aewY1t a~.~"~`crexl
c~.~.:La.t~.ans o'the .order, s not
_ ~ . scs w~c~ r~~Gly put k~~kH~~, where k ~'z^ozr~ ?tY~c cx.a.ticc..1.? in ~k,~aca e ca `, , ~, the ~v~.].ucs rm,
~ SG. tO It, Then the exprCSSi1S f o
equal to unity but c1a
ti:l:l. ass ~.~rne a. ;; ornE~tirh G~,t different a: a rrn ; ~ rcL V~x,e, and ~rcru w' (3.L;)
v_ m r *f
In r/rp ~.~
C -
: a
r~.
\-\ - _
\1eM -~.
d"
L
:k' these cxpx'ea-ons, just ~,s that
~~Y>.e region of application o has bec.;n
~" cla.nr~..:~ cix~cuwhich has of the whole of the ec~1~.;i.v,l.c:nt ~.etar _
ai
described, to conda.t:i.ons clan; to the cx'idescribed, is na.tura~.1?y ..m.:~.. ~ed
j,e, ,b-;c~tx"an. osc~.l~.ak,a.ona of the first
?us~, to those wh.icl~ car.~respand to ~. ~~1 a rat~.an the role of the radial cozcparient o,
ardeary . Taking into car~.s? ~dc
the ~:ineraa,t]_c process here described,
rnation. of the electrons in the as ,~., ' al"
order may be cha.racter:l.7,ecl a.~.~ x ada.
oscill.at~.ans of the first
ascillatians.
Processes in the Ma~;n-ron
Co Tangential.
--------------------
of n.etic field, increa.sirL~ s passes
when the intensity K ai the ma g
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tlarou&'h the crLtical vaJ.tM, tl-i n all e;Lectrons emitted by the 'iiament
are i'orced to return from some cylindrical surface whose radius i
inversely proportional to I-f In consequence ol: the fact that the
radial velocities of the electrons are equal to zero, there i.s formed
in bh.e reion of this return surface a kind o? notating "virtual
cathode" (the tangy,:entia1 velocity is not equal to zero). Looking
upon the )J QCeSS obtal.ned in the course oi' this as a simple picture
oI' t?:radual contraction of the dull card.io:Lds, with preservation of the
eri.tlar velocity and periodicity detern fined by the duantity(Q)i.I,
prove; to be of no assistance o For the, electrons which pass i,rrto the
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cathode a situation is seated whickl is
auto regions a~ the v~xtual
u in Section 3.1. We shad apply this
xeminis cent a~ the cane taken p .. tkl
case as a whole to the cvrreG~panc.ng cor~d~.ta.ons a.n flat systex~s.
~
en the electricie1d at a distance from
cylindrical coordinates, th ,
'farm and there are it may be assumed to a
the ca,t;h.ocle is almost una. ~ hick
the ~uidixlg line along which the circle w
first approximation that ~
in and which always r..aincides with the
farms the cardioid is rail ~
electric field, is transformed here ~.nto a
equipote1taal line of the the arcs of the cycloid re ,t . Depending on
circle of radius r on which
c
? ~ the vaz~a.ous values, it is paseiblc to obtain ases
the rc;lataonshapa of th
e taken up in Sectiari 3.1, B. Fig. 3.11 rc-
which correspond to thos
of the electron: it moves along a cycloid the
presents the trajectory
.~ b ~ The linear velocity of displacement
height of whose arc a~ ~.~ ?~
he rolling circle along the guiding lane a5 equal
of the center oft V
Gee * -?. The following cases, represented
and the angular velocity C'
to
in Fig. 3.11, are possible:.
in
Cb) b
1-)
b<
b=o
V
=2.
(c
)
e
c~
:
(Fag. 3.11)
UI
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For the casa of a very small b or , we may take as a first
approximation;
=- n c =--; 3.146
i.e. we may obtain relationships ana1ognus to the case of homogeneous
fields. However, an order that rotation along the guiding lane be
aecorr>plished with constant velocity it follows from the relationships
of (3.L6) that the int~rrsity of the electric field must increase
linearly with distance.
which, under conditions of the usual logarithmic distribution of
(3.147)
potential and in the absence of a space charge between the ylz.ndrical
electrodes, cannot take place. If the path of the curve of intensity
of the electric field required by equation (3.147) (curve b in Fig.
3.12) plotted together with the actual variation in intensity (curve
a in Five 3.12), it turns out that only at the one point c does the
quantity F satisfy the relationship of (3.17). Only at this distance
from the axis is it possible, it would seem, i'or there to be stable
motion along one of the trajectories shown in Fig. 3.11. Actually,
however, this not the case. The crux of the matter is that we can
do nothing in this case with the original hypotheses as to the complete
absence of a space charge (consideration of the motion of a lone elec-
tron) and are forced to admit the existence of some space charge which
manifests itself to a first approximation in a change in the path of
potential and field intensity between the electrodes. Let us assume
for simplicity that the density of the space charge is constant in the
entire space between the electrodes. Then, proceeding from Gausst
theorem, it is not difficult to show that the intensity of the elec--
tric field at any point r will be expressed as
Vr 3.g
?E=: ,) ,
s
1.,
i:.
vt, h ~~.~~,,. ......; i1 i i..,.ll I .Y ,,. ii Y ..,..,, ~.~4r,~{,I. ~, ~ G~YL ?V`11r .~Pr JJ lb;?,W I,T ~.t~:+~r, i~M ~.l~-. J'~i:,.. ~1: C,~ .; ~,tl l ~ II. -.~I~,i~ Y
I ...6.i I. ~ .f; ,r {.d, "!~f r{Y,a+, ,~ ~til!~~ dl., ~ lr.J q.1.1 ~x~ f =d: "Nr 11t, {Z1~i-,? ~,.
yy
! 1 1.1 ~+?.I. i ~~~ ,:~ ! .. ~.
Cr l.. Wi.t ?~.,r. ,). , ;~ ?~a~'~,. ,. t,p. ~~~a ?.?n.1 .,1,. ,.r .~,~? t. ....z i v.~ i ~? ~
~~ N i','~! ~ ,` .. ,, ~e~{, f v~~C~; ~R~~t ~X~!.,~~ ~ i ~~ / t'J,x~ Sri 7. i..iu.. ..~.,?.~ 1 .N .~~d B+;~ Y, 7 ~,.tf ti J(l
y~, ,..,. n? ~ !!k ,1, +; ~. ,...~ +i ,l ... .~~. ws,?, II. ~Y?~..'~^G~.:~.d{.k r~ll~. ft~n 2rNl~ ik ~i^pl s~+~1~f ir.r ~:nr~ 1... rOI~fTi V~.~ e. ~, m?~irra~ .ir.., :7 tii ..~} :`fi~';iS,,.
s~ ,~~u~.l~~r i,,~, 1C?t ~x.2,~~~,.~"~hY.L,~..~..l~l~Y~~...~.~,~,~G...e.~~.la~~1~~~~,r1,~,..7~.,Cc~u~,~~.r~I~rC civYlr.M:?u~wAuY~.6.lri,4f4~...ki~d tdti~~~.ai~n. r"V~~..,i,~n !)4~.,v _.,.~., ri ._..,,. ~.. ......,! ~,,,~~ .,. ~~....~.
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(Fig. 3.12)
i.e. that E varies proportionally to r, as is required in accordance
with formula (3.Li.7). In this case we may speak of a constant angular
velccLty at various distances r from the axis, i.e. of the rotation
regate of electrons as a whole (See Chapter viii). Thus
of the entire agga
another periodicity arises which is associated now only with the
tangential component of motion of the electron. It is determined by the
angular frequency of rotation along the guiding circle, which frequency
angular
may be e~ resseds taking into consideration the relationships of
~
(3.1.6) and (3.18), as
E _v
k- ... ?,,,?.- (3.1.Y1 )
r kr
The wavelength which corresponds to this angular frequency,
thet,\~is
-
XCW\' '-:-- (3.o)
A glance at formula (3.50) instantly reveals an essentially
different dependency of X on H than there was for oscillations of
the first order from the Okabe relationship. Naturally, such a
titangential" electron mechanism is of interest only with respect to
magnetrons with sectional anodes. The number of segments m, or what is
~
used more frequency, the number of pairs of segments p= , will
play an essential role here.
51
15?
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(F1,,. 3.13)
matter of fact, thG oscillating process, determined by only
As a the one quantity may take plsco or Ly when b=Q. If then bO the
phenomenon is characterized by two angular frequencies: , the fre-
quency of revolution along the guiding line, and, the frequency of
H
the rolling circle. If the guiding circle is made up of
revolution of
an integral number of arcs of the
must be between and? some multiple relationship.
cyclo'
It then there It may be found from the following deliberations. Let the oscillating
system connected to the anode segments have an inherent frequency of 6i?
Then we designate as the order of frequency n the ratio of the fre-Y
quency ? which eterndnes the oscila.ations of the first order, to
d
the given frequency (-Q)
On the other hand, however, this matter is related in practice
number of anode segments, since with the customary wiring of
to th.e
ascillating system adjacent segments are always connected to
the
opposite circuit leads. Therefore, in order to maintain the fre-
s of the "tangential" electron mechanism which we
quency Cep by m9.
ussii it is necessary that the angular frequency of rotation
are 'sc ~
d 1
of the mechana.smCQ)be synchronized with the frequency of the circuit.
condition of such synchronization is the relationship
The
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.""m
(3.2)
? segmen'ts or pairs off' slots). From
Where p i$ the number of paa.xs o
(3,2) it ollaws that upon exc~.tatton
ta~or~sha.ps off ' (3.~1) and ~~
the xela ,
in a 2p_eegment mr~gentron ~,hpre must
~ cilla,tians a~ the n-th order a.
? os which
ueY~c:~es wh
'relationship between the basic'req
accux the following
ze the tangential electron mechanism
C~laraCter (3.~3)
rip
All lied
'berations given above may be properly app
of the deli, stem
at a distance r from the axis of the sy,
to an electron which, be;ing
has ' of the "tangential" mechanism and
been included in the aperat1an
'ecto of the type represented in Fig?
has begun to d,escrs.bed a tray '
3.13. This figure represents the case where n = 1, p = La and cants
'e maintenance of the oscillations stems
sequently `~~? In this case
.fl
enters into the region of the inter-
from the fact that the cycla~.d
segmental alternatielectric field at a place where at the given
axdin~ effect, i?e? the electron
moment the field exercises a ret
off to the field. apposite the
in these slots gives its energy
other hand, it moves off into the tube,
ttaccelera:ting" slots, an the
i.e. passes through a zone whose field. is weal(erp It is interesting
ntal s stems osaillatians may take place
to note that in multi?seg~ne y
the product np is equal to or greater than
even when n(l, if only th of
in ua,dri-segmental magnetrons oscillatioxls
1. Thus, for example, q
~~ observed with n [7~, which leads for p=2 to
e, "half order" are
may be illustrated by Fig. 3.1~.
the condition This case y
(Fig, 3.1)1)
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2
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Taking into considerst~.an equatiOn (3 .~0) , a f ormula may be
'tion of syxichroon (3.~2) for the wave
obtained from the conga. '
c~.llat1ons which are sustained by the
length of the circuit oa
entialtt mechanism 94 w
Pv- (3.)
This formula coa.nca.cle s with the i' ormula of ~o sthumus (see Chap.
confirmed repeatedly by experimentations
ii), which. has been
erfect concept of a certain ideal-
Thus, a verb' coarse and ~ . '
r sm leads in this case, too, to results
iced election-kinematic mech~a.r~i
i y
bearing on reality and are sa'tisfactorl
which have an indisputable
confirmed in experiments,
t be obtained. from investigation of the
More, however, canno
h sically accurate, although appxoxi-
kinematics of the electron. k p y
mate, and acceptable picture of the process may be arrived at only
consideration the aggregate of electr'ons'
by taking into
cess in Terms of the plectron A ~e ate
section 3.3 ? Tie ;elation of the ~ ro
If electrons leave the cathode in a homogeneous stream and
riodic rr>.ota.ons in the inter-electrode spaces,
accomplish identical pe lied
that the sum of all variable potentials app
it is then natural
t
tha
the electrodes roust be equal to zero, and consequentlf,
~ t
o
t
o
l ntionS cannot be observed' However, experiments testify
___
i
is
bas
Any system which consists of uniformly (on the, the contrary Y
i r' n cnnvice of comp.Letely re-
retarding field or the magnetron -- i'. c ~v~
ri
01 L1i .LL)
e
's moving electrons -- the circuit of th
r f7n'ln~ analyse
ultra.-high frequency oscillations. Ih.is is
practically applicable
e
m
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evidence of the presence in the aggregate of electrons of so
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"callectiv&' periodicity which lies in the periodic changes intro-
duced into the aggregate off' electrons under certain conditions of
the mutual effect of the constant and variable potentials applied
to the electrodes. The mechanism of this "collective periodicity"
may be represented in simplest terms as a "sorting out" mechanism.
The essence of this idea is in the following: due to the presence of
an alternating electric field created by the oscillating circuit
connected to the electrodes the electrons which leave the cathode at
moments corresponding to different phases o:~ the alternating voltage
behave differently, and form two basic groups -- "in-phase" and
"out-of-phase" electrons. As "in-phase" electrons we may designate
those the result in terms of power of whose individual periodic motion
is a giving off of kinetic energy to the alternating electric field
and. correspondingly a decrease in the amplitude of their motion.
"Out-of-phase" electrons behave exactly opposite: they land in the
alternating fields under such phase conditions as to take energy from
the latter and increase their own velocity and correspondingly the
amplitude of their individual periodic motion. If the effects in terms
of energy of these groups were to be absolutely identical, we would
again be unable to observe oscillations in the external conductors.
Operation of the "sorting-out" mechanism must also derive from the
decreasing by various methods, in order to maintain oscillations,
of the numbers of the group of "out-of'-phase" electrons or their effect
in terrlrs of energy by comparison with the "in-phase" group. Let us
illustrate these general considerations with a few examples.
a) The Retardirr -Field Circuit
Let us consider the motion of electrons in a tube, beginning with
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ANODE Q-
&rd9
3heoce K
TwwYM...~
(Fig. 3 ,1 )
The electrons l an 4i which we have considered are characteristic
hich the electron stream which has passed the
of the two gaups into w
ccoxdance with the above-designatec~ termin-
? ~ '1 In
grio is "soy ted out . .~ a
ology eleCtxan l is I'' n phase", electron II is "out of phase", and
~
the essence of the operation of the "sortif" mechanism (i.e. of the
mutual action a the constant and alternating fields and the phase
of of the election's departm' e from the cathode) consists of the fact
that electron lT -tleaves the game I' half a period after le aving the
cathode, in consequence of whi..ch a periodically changing current
-grid space. Its appearance is illustrated in
is createcl in the anode ~ p
of electrons toward the anode is occurring at airy'
.+~'].g. 3.16. Motion
but the move away from the anode only in the cross
moment of Mane, y
hatched portions of the space-time graph represented in Fig. 3.16.
'.d-anode electron current is decreased at that
Consequently, the gr7
time by a r?agni tude equal to the current created by the electrons
returning from the anode.
in r of the electron stream, and at the same
This periodic changing
nt maintains and controls th.e oscillations in
time of the anode curie ,
the external circuit. The mechanism described has been called by
Mioll.er [8] "anode classification".
It may be shown that the period of change of the electron stream
,
the eriod of oscillating; motion of an electron,
may also be unequal to p
r
Ui?
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ANODE &ri'a, y
CL+h c e K
(Fig. 3 .l )
The electrons I an I which we have considered are characteristic
of the two groups into which the electron stream which has passed the
grid is ttsorted out". In accordance with the above-c1.esignated termin-
ology electron I is "in phase", electron II is "out of phasett, and
the essence of the operation of the 11sorting" mechanism (i.e. of the
mutual action of the constant and alternating fields and the phase
of the electron's departure from the cathode) consists of the fact
that electron II "leaves the game" half a period after leavi.ng the
cathode, in consequence of wha..ch a periodically changing current
is created in the anode-grid space. Its appearance is illustrated in
Fig. 3.16. Notion of electrons toward the anode is occurring at any
moment of time, but they move away from the anode only in the cross-
hatched portions of the space-time graph represented in Fig. 3.16.
Consequently, the grid-anode electron current is decreased at that
time by a magnitude equal to the current created by the electrons
returning from the anode.
This periodic changing of the electron stream, and at the same
time of the anode current, maintains and controls the oscillations in
the external circuit. The mechanism described has been called by
Moller [8] "anode classification".
It may be shown that the period of change of the electron stream
may also be unequal to the period of oscillating motion of an electron,
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that there i some multiple relationship between these Values.
provided
the circuit connected to the electrodes have a period of
~n fact, le
oscillation T three times less than the period of ''electron agitation"
(Fig . 3.17). Then electron I, having left the cathode at the
moment of the maximum negative alternatan; potential on the grid., will
pass it in 3/L.T, and 3/LT later will reach the anode, which at that
.
the same phase as the grid at the moment the electron left
time is an
the cathodes Thus there is superimposed on the motion of this electron
a retardation caused by the negative half-wave voltage on the grid at
the moment of the electron's departure froiri the cathode, and a similar
retardation to the negative half wave voltage on the retardation due ~ anode wfl
the electron is approaching it. By virtue of this the electron will
be forced to turn back from the anode. Electrons III, V, VIII, etc.,
will behave in a manner similar to electron I.
(Fig. 3.16)
A
U
I
C a:\ h o~
(Fig. 3.17)
5f
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The motion of electrons II, IV, VI, etc?, which leave the cathode
at moments o positive half wwave voltage on the grid, is accoillplished
in such a way that they also approach the anode at a time when there is
a positive half -Wave on it and are absorbed by it, leaving the picture;
they are "sorted out".
BY similar deliberations we may arrive at the conclusion that
the electron stream will vary with a period equal to the period of
the alternating potential on the electrons not only in the case re
pre -
sented by Fig. 3.17, but also in all cases where the period of the
alternating ternating voltage, T, is related to the period of electron oscil-
lations, dt , by a simple repetitive relationship
T;.t't
This explains the frequently observed maintenance of oscil-
lations whose frequency is higher than the frequency of the ''electron
oscillations proper".
In all instances we follow the path of the first electron, for
example, it may be observed that the amplitude of its oscillations
about the grid gradually decreases, and in the limiting case, if it is
not caught beforehand by the grid, it should stop on it. At the same
time electron IL, if it did not land on the anode at the end of its
first passagea but were to reach the surface of zero potential, would
return and increase the amplitude of its oscillations about the grid
with each passaged t111is situation is possible, however, only in the
case where there is a negative potential on the anode and the return
surface is located somewhere between the electrodes. Then the classi-
fication of electrons may take place by a method somewhat different
from the one described. Electrons I and II are the representatives of
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of the two groups -- in phases' and 'tout o1' phase" ' which have the
most considerable change in the amplitude of their oscillations. Gen
f
erally, then, the change in amplitude o oscillations S(Fig. 3.18)
is a function of the moment of departure of an electron from the cathode,
which is illustrated by Fig. 3.18. Let uu' be the return surface, aa'
the anode, and gg' the grid. The sinusoids on aa' and gg' represent
changes in potential on the anode and grid, and the sinusoid on uu' the
course of as a function of tame. Electrons of ~ of group T, for which
r~ ,K
is negative, return somewhat earlier than electrons of the second group,
for which is positive. The representatives of both these groups
X
begin their second oscillation with an altered phase difference. Due
to this alternation an oscillation of the density of the electron
stream with respect to time is obtained.
fe;hu,r v~ SL4 Y ce
1
Uri'cL y
(h.f{'ode. ~
(Fig. 3.18)
Such 4rocess oi' classification has been called "phase classi-
. fication" by Svloller [8] . For sufficiently large applitudes of the
"phase"
alternating potential, i.e. sufficiently large values of , "phase"
classification may change over into "anode" classification, as evi-
denced by the electron current observed in many case 'n the anode
circuit accompanies the oscillations even with negative anode potentials.
It is clear that the sooner the "out-of-phaset' electrons are re-
moved from the field of action and the fewer of them there are by corn-
para.son with I'in-phaset! electrons, the higher will be the efficiency of
160
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this process. The removal of ttout_of uphasett electrons from the reM
tarding-field circuit takes place by means of absorption of them by
the anode or grid.
b) The Magnetron
Returning to the process of oscillations in the riiagnetron, we
may also evoke the idea of t' classification' to explain the occurence
of organized oscillations. This is partacuJ arty easy to do with re-
Spect to oscillations o1 the ?irst order, whose close analogy with
oscillations in the retarding-field circuit has already been noted
above. They occur, as is known, near critical cond.itions, which
corresponds to a return surface lying in the direct vicinity of the
anode. Since the transit time of an electron from the cathode to the
anode (the grid of an equivalent tube with retarding field may be
supposed to be located at the cathode itself) is equal to a half-
period of oscillations, it is then obvious that an electron which has
used for this transit a half-period, which corresponds to a positive
half-wave of potential on the anode and a negative one on the cathode,
will land on the anode, and with it also a group of others which are
close to it with respect to departure phase. At the same time an
electron, the half-period of whose flight is characterised by opposite
half-waves of voltage (negative on the anode and positive on the cathode),
will not reach the anode, since the radius of curvature of its trajectory
will decrease. With respect to the alternating field between electrodes
this electron is a representative of the "in-phase" group, since it
gives off its energy to the field, diminishing its velocity and. the
radius of curvature of its trajectory. If an in-phase electron
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c-1
w*s
+'\) sft c)t
I din ?hce
~haGe 5Mv\P
Fire 3.19
LU
a.
Figure 3.20
Side pla'~.c~
Figure 3.21
Figure 3.2~
v
b,
c~.-~~, ads
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11
 '
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dc~ tQr u~~.th decreas~.n~; velc~ca.'t;~ a,nd
~scx'a.bes a 1'ew loofas Qf its tr~,~ec Y ,
? ~t - r rava.rr~~ ex~aericlecj all a.ts a.na.ta.al enez ,
ra.da.us Qf curva.ture, a. ~,~ ~ etel
t~ d hava.nE' bcgurl,, after alnoat c.om~~)l Y
undcrsrQ "phase sh~.~t an
-
the ~ ~natian ~:'a.elds cl?+s,rrE in'tQ an ~~out
~~ fs to rr,ove in p~~a~.,e with 'thc ~,t,ltex
~.n,:. y
r ~~ible beha,v~.Qx' of da.e~'''ent electrons a.s
o1'Wphase" electron. the po~a
a flat ma.grxctz'Qfl i.s x'cpre$er~ted I'Qr
repx'esented In Fi3,19, where
s ~JCJ."M
~$un+ed that tYc mai n.et a.C field is Qr.e11'teCl z,,plic:t.t~~, It ?5 a.~
1
. d the electron
cr~da.cL?.lar' to the c~r11r1, ?1,ithOLrt an alternta.nr~ fiel .^ex . Li
p
:E'con t s.nt a.Trla.tu~~e(cup
will rl?QVe 3.lOn~' a cyclaidal. curve o
~ ~?? ,f i.eld there rnaJ occur the C~,ses repre
the presence of an alter n~+,~,a .n but
an
;h shows absor~7ta.0r1 of the field's enerY
sE;r~teci by curve x~, y wha.c
reVQ1L1'tia~la on the anode, and. by curve
e:J.ectY'on la.ndinafter several "
r the above described behavior of an ?inMpbast
11.9 wh~~.cYi i11u;,trU.r,aS .. ,~ ' k~i~~se" state. The
a Tthe transi'tian to the out~.o:~.p
electran when it t;.akes
,. ~ ~? electrons ;:raz~~i the ~-nter~.electrode space
desire to remove OLIt?0~"ph~.,ae - , , ? ~ at some
_,s the arran'e111ent az the Tria~netrara. s i~
more rapidly cause
to the da.rectian off' the r~.~.neta_c
~,.~. (u,u.ally several degrees)
a.Tlgle
.,. , ~ r the establisl~rnent; an both sides
~~ Lin es of :Circe (~{i~. .~.2U)9 ()I of ex~nposl,non tk;ese a bib.
Field.1 ,~
~g~'o-t'~1e anode off' So-called side plates, sup ,
. ion of a 1oTZ~?,itucti.nal ele ctx a.c f~,Clr
sitive potential zar the treat
to on af the
l
ec .
e , erir1ient shows that proper se
(~'i~~;. 3.21) . ~.ctuall~~r, ~
an the magnetic f'a-eJ.d a~~d tlac :Ca.l.arrrc.nt or
angle between the airecta-on of
role in the
l
ti
of the vo:l.tage on. the
Oscillating pr. ()Cess.
a
.
a, 's a very essE:n
side plates p1~Y
This
seen t'ror'a 'ig. 3.22 wh.ICh gives the
rr1a.J be
~:netrOni with. solid anode as a function
of a ma.r,
curve of
05 ciliating; power
of the angle
c7C.
the s:me value as a
and from Figo
3.23
which represents change of
tunct?a.an of the p et exit ia1 on to side plates.
E3
MIAI.
~fs1
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, ~ here aS t0 the meCh~,~51n Of regu~.at~.on of
The ConCe
~J+a given ' the simplest e~.rrctxan generators is, o
the rr>,ata.on of e),GCtrans in
? ? 've in chaxacteX". A f'ew authors have tried,
course, pug^~ly ~,uala.~a~~
to the retnrdin~-field circuit, to introduce
es'peca.ally with respect
. ~ ' s off' this mechana.,sm of "classif icata.an" ;
various numerical characterista.c,
the electron' s departure frara the cathode,
for exazr~plc, the phase of 't
e trough the grid, the displaceiYaent veloca. Y
the phase of its passag
The pith of the matter, however, c onsa.sts
of the return surface, etc. tt .~ .~tt
atin., the predominance of the action of in p
in all cases in demonstr ~ of
this
,t 11a.se't ones, i.e. in showing by vast . , of
electrons over out..of p
rata.ans of a given device as an oscillator.
the possablit~~ of ope
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,.terature Ouade LaJlzaterIII
KaJ-in?n Dec -leter arid Centimeter slaves, 1939.
1. V. I.
~ M 1923
'Tb w;
2. S. I. Z~.la.t~.zl)~eva.ch. T~ P, No 18, 222, 1923 No 19, 16617 ,
Scheibe. Ann? d.. Phys. 73, 1921, L ' 78.
A
a.
A. Icatsman. i1ektrosvya& , Na 2, 39, 1939.
L~ ? Yu.
A. L Null. Phys. Rev. XVIII, 1921, 31.
Vasserlnan. TA1~, ch,..fiz? X. 103, 19.6.
6. V. I. Kcl17.n7.1 and I. 1 e
7. N. . U. Ye. Nialyarov? ZhTF, x, lS, 19L0, 1297w130a.
F. Alekseyev and
PIRL, 32, i94b., 136-139
1829 2?1207 o ENT, T,~ ~~ , 1930, 2933O6. ANT
g, H. C,, i~)oller. Jdd.T, 34, ~
1930, lol1-119.
165
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r ,rflar:i.1y at` impart ancc~ in asts.la-
The tdcaxk wi.t,h di.ades is p
r 7inC~ It dis~~inct'I.y Coni'i.xms th~
la.sha.ng the, pra.r~ca.ples .~,nvalve~~
e a .
s~,a,ti.sticaliY
t?ve xesnc i_fl
possibilY" of ~moduclng a, negr~
means of the inertia of the elactrons,
xegu1F1ted electron stream by
that have been ~ dis-
cussed theore~r,a_cal aon,7~.aerabans do
b axiaus authazs to trio
CL7,ssed above have been applied y v
with a ne gati~t a grid are usual-1Y
operat~,on in U. H. F w Triodes
nt of the diode, for which ~}1e s amP con
cansid.e~?e~. as the equ:~. va ]. e internal
met,Y, the Woduc tiara of a complex
clusi,ons are obtained , na vol~
of the phas e shift be tw e en current and
resistance on ac count ,. ~ of the elecw
from the introductsan of the inertia o
~~age that result S ~
i I is not the result of a s a p
trans. The phase shift simple ~~~ than ic-
the transit
stream behin~) the voltage by
al lags of the electron
d.i.s placement current, the rela,ta.on~
angle ~ o Since there IS a
on a f airy-Y complicated character:
ship between 9 and ~ takes
)n a ? ;iG T 4 CC) ;4W (4e2
equivalent tube
w._-------a
Figure 4,13
equivalent loaf
50X1-HUM
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9-2
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3 ~ ~ (~ ~" ~~ 7C , ~ i.nver-1,$ L reaches tha va~,ues ~ s
s should be observed. Theoret~,ca~.lY,
a~an of the internal ~sist snce it s act 3ve and ~activa camzxo nents may be
the re~.at~.onship betweQn
that shown above for the aiade 4 ~aWever,
considered ara7.ag0u8 to
a feedback circuit, we must deal as a
when a triode is operated in
rule with very small transit angles, but in any case with v
Thanks to this, It is possible to simplify very considerably the
by theoretical methods and thus
rather cumbersome expressa,Qns obtained.
oxims,te computational Formulae. Rc""
to arrive at a number of app'
the classic equ~.valent circuit, as an os-
presenting the 'tr~~e in
trom0t0ive force Ug and internal resin Lance
w ~ ~llator ath eleG
ca.
Rls where R1 anc3 must be taken as complex quantities:
'. (4?23)
r1:
i~
t I M
,F&--
1a
i.o
(tD
Figure 4.16.
12
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the equ~.~ra~.ent tube circuit t~eS an
In cannectlan w ~.th this, ~,
n in Figure 4.13, w:fth the qu~ant
the ratl.~excomp~.icatcd form show
ti fafr~,Y complicated funet~.ans of the
/i\ ties x~.~ x~, and being
of the s e f unatia ns is S haven tn the
tr one it ang 1e G Q The course
Figure 4.14 xe'e cents the
hs of Figl~es 4.]4, 4~~ 4.15 and 4.16.
gr ap
1.00
t9
0,8
0.4
0,2
iMIM W W W M'N~RM~M~~o+~T./Mn' W~'~~'~M+w..^
~
~ 10 12
z 4 b
Figure 4.15
R is the internal
i
and xi RiO~
ves of the ratios ri/RiO where 0
cur
0, A otk~. th es e q~,ntit i es, as may
resistance of the tube at
seen The tube
increases. very r apidlY became very small a$
,
idlY with increasing f.requencY,
resistance falls rap which is graphic-.
in F j g8 4 ?15 ? This c~xcum-
the curve
ally i~.~.ias'trated by the tube in
stance manifests itself in the increasing lo$S caused by
one of the i pr n,cipa~. reasons for the
the oscillation circuit, and is on VHF.
of ascil].ator tube s as we pass to
rapid fall in the of fa.ciencY tram
am lifi cation factor w nth ~,ncre as ing
The Chang e in the complex p
in Fa.gUra 4.16, which represent.
le B is sh awn by the graphs
sit ang
and ~ ( p being the static amplif 3. cation
the curves ~ o JA
of
inertia
As is cle ar from the drawing, the
factor far CJ~ 0).
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the e1eCtxana weakens the contxolli action of the grc1 arid re''
ducea the amplff ication f actc2' of the tube.
1.0
0.~
o,6
0,4
opt
..o.~
_1.0
0 z 4 6 8 10 12 14Q
Figure 4.16
Chard parameter of the tube also assumes the form of a
complex expression: the
transconductancg of the plate current eharac-teristic as a function of the grid voltage, in consequence of the phase
shift, caused by the electron inertia between grid voltage and plate
with the basic equation of the triode, the
current. In accordance
be represented in the form Ri, which,
tranaconductance S m~'
when
and R are complex quantities takes the form
S
(4.24)
Declassified
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1.1
i,0
op9
0c8
007
2
\Z-
2
12
16
0246101216 1E 20 22 .24 26
Transit angle 9, in radians
If S is represented in the farm
(4,25)
of this ca mp1 ex
then the modulus S and the phase angle
quantity may be represented in dependence on the transit angle
by the curves in Figure 4,17, on which
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a lo e of the tube char aster is tip
.~,.~.. tae s p
are given, With ~ ~ '
0
for
OF THE THEORY OF CONDUCTIVIrY
4 03 THE pREST C ONDxTION
OF ELEOTR UN TUBES
number of imre st ~ at ions, mast of them
A very cansi~ arable overloaded with their mathematics ~. apparatus, have been devoted to
e theoxy, based on considexat~.on o an
the development of vacuum-tub that
and talcii~, a account those phenomen s
equivalent cl.rcuit, ~ :. , The work of
the transit angles are apprec1t ~e.
take place why
r been ma,naf est~-n~ ter~encies to
Llewellyn and his school has land
mplax of equations ag would cover, as
the construction of such a ~ al .~
ta.onships between the princip q
diversely as passible, the
d the sir suit eler~ nts connected
Cities that characteri se the tube an
ith it. In x 11 flOJ ~ d then Llewellyn and
recent years LleweYn
w
of equa.valent tube six cua.ts which
Paterson have given a the ory
spite of s certain unwieldiness. They
is fairly well arga,ni.Zed in of
went time there are two tendencies
point out that up th the ~
either' to study what goes an in'
treatment of v acuum~tube phen offsns
side the tube as a cex'tain canducw
?
' de the tube, and thus coming to treat
or regaarding
tion with interelectrode capacitances, ,
tanCe in comb~.na the usual. analysis
tingle element of a circuit, to apply
the tube as a other resistances, in~
circuits to it, together with the
of electric
ork, Llewellyn and Peterson claim
ductances, etc. In their latest w
The mathematical part of the
have combined both thesd methods
to
problem is solved by them with reference to the WoCeases that occur
in the electron stians in such a.
streams. 'Shay put their final qu,
le manipulation in applyi~ them
farm as to assure `relatively, limp
to e uivalent circuits. Starting out from extreraslY :simple geametxic-
q
~~a l J t
~.i ! ?~~I ply y
~ 1~j`jgqsjkl t tt~'r,? ti9 ~r i nn~r4rlSiy?t.{ :A'rV`ar ,'i'F kia rEdl('q'
??,1s4r t ,p~, .:mr 3o uke 7rr,r.1~~'~6`,'rP, . 'd' I:,N~~~p ~, ka i~,r.A'w a~JP 4i. QIG 1'~~41`F- ~I,~q'f,Y.Q jay '~;Yt
~ai r1dBu
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'Ii
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al picture of a diode with par a1iel plane electrodes a and b and
..
an electxofl stream flawing p~ penda. cularly to them, the auth cr s
~
ta: total current, curret conductivity and
operate with the d a
electron velacxty on the pl~te a b then, as surns.ng electron ve1ocitY
valued at all points of the interalectx'oce space, rew
to be singa, e
pr es ent ing these quantities in the form of sums of direct and al-
and carrying out an analysis on a principle
ter nxting components,
nal.agaudescribed .~d in the foregoing section, they obtain
a '~hftt de,,
two groups of equations one for direct current and a second. for al-
t ex Hat ing cur a. r rat The s e e quations ar e written in the f oiowing
, .
f orxn,
a The group of equations for direct current
= (t- t /t)
CVO ? v~
~ =Ci-/3) i
c_ :) 1p (t)-i4 (4q26)
the distance in centime t ers betty een planes a end b, is the trans it
far this distance, va anal vb are the electron-?
time of the electrons
v locities on the s e plat yes respectively, in centimeters second, and
Here
is d ensity in amperes per square cen~'1 .rfter. The time
the cursent
it will require, to transverse the distance x, the time , wn~c;ll
~
;~ ( 1zr a SIn le electron moviT) through the lnterel.ectrod.e .pac ,
'to and the "space charge factor" require some exp]Lana1ion:
M ~
. 4 4
may be found from the relation
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100
0,9
0.8
0,'7
0.6
0.5
0.4
0.3
0,2
0.1
/_" F~MIiMwM.M~MNONM~nMMNMWwwWM+AMMVNM~1.Mi1~M~.."W~~~rWw~MM~MM+MM~M~~
- 1.00
0.1 0,2 0.3 0e4 0Q5 0,6 07 0.8 0~9
Figure 401E
On comparing this expression with the second equation given
is a value that approaches t as
26 it may be noted that t o
; 0 The vanishing of the space_charge factor thus cerrespors
to the ideal case of the movement of a single electron between the
electrodes. In e are always dealingin a vacuum tube, wi.th
practice '
electrons and a factor different from zero. The
a great number of
the value of in such a way that it varies
authors determine
from -- 0, under the conditions of the absence of any space charge,
~ -
to ~- 1, wYuen the electron stream reaches saturation (or speaking
~ . .
constitutes all of the electrons impinging on electrode
more precisely,
a) and is expressed by a certain maximum current value
,
lata.onship between , Tm, and may be written as
~
(4.28)
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lm. The re_
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C2
9
(v& 4 Vba 3 = Z ft,
z
U
3
(4.29)
(where UDa and UDb are the direct?current potentials of planes a
and b ) , which leads ultimately to the Child equation The space
charge, as is clear from the foregoing, is thus taken into account
by introducing the factor , which is connected with the other
quantities indicated by the equations and characterizes the increase
in transit time due to the action of the space charge.
(b) The correspoi..ing group of equations for the alternating
current is as follows:
Ub - Ua : A*I +' B*qa + C Ewa
% : D*I + E*qa + F#wa (430)
wb = G*I * H~iga + I~~wa
The graph of the space charge factor in re1t1on to the
ratio of the currents i /I is presented in Figure 4,180 From the
expressions (4.2E) and (4.26) we can obtain
Here U is the alternating-current potential in volts, I is
the alternating current in amperes, q the conduction current in
amperes, and w the alternating-current velocity in centimeters/sec.-
and. The indices a and b refer to the planes a and b. The coef-
ficients A.*o o...I* are expressed according to Table 4.3. Tables
4.2 and 4.3 presented below contain a review of all formulae and
give expressions for the coefficients both in the general form and
for the limiting cases] = 0 or
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Table 4,2
F UND ANENT AL EQUAT D NS OF VACUUM TUB IN& THE
NUWR IC AL V ALUES .
ra 3b ,
Equations of Direct Current
of energy...?1??..????I?aeoS??I?p?.?1?.??IS
alqu4lti.on
-----------
x)aterm~.rta~ of spacecharge factor?.?.e....??..??.."ate 3(1 -
Determination o
Distance?. .??.?????????.?????.??.??.??...????1
Current densitY.??.?.?....?
-- - - - 'D/ (9/4);(1 -f)2
V1
Limiting current density......... ? .. ?. ? ? ? ? . ?Im
r
Equations of Alternating Current
General equations
Ub ? Ua A*I -+ B ^ q~ + C a
qb .- D*I E qa F wa,
wb ; G*I 4. H*qa 4' I a?
10"
x2.
The diode may serve as the first example to illustrate the
application of these equations. Let there be no electrons between
planes a and by Then = 0, q = 0, and from equation (4.30) we have
a
U ~. U A*I, from which the role of A*, as a certain impedance,
b a
Taking the expression A# for the case = 0 (Table
becomes plain. x
? and by comparing this with
4.), then A - ~ (va-~?B)j
L`
4vb)/2 #o we get
i l`1 f~M ty1 i ?j; 4n th 7~ !. id i~ ~~~ ~ ~ i~~~ ~ { '('~~pR~tti 71r ~i, r"3~iPit f1 '~ ~i (u4 1 I )11
i;{,~ i,14 7~~ +fl l~"i!~ i~-. ~~.~ qi :,~ irk! X~ iy rf 6=J a ~thrAili w 5 ! I~ 4~
)p T.'Lli~~`~15~ an~,w119~(ra?! ly~l R. i~~'i I :i j Yi Ii~IJ ~"~d~?~4v ~! rvf {~ ~~l~V l~~~i~l1~j{{~ I,Ml~~ii~ Pi'i~y~.
~{a
~~~r~ ~'' ;1 xtv~yd,~l~u,a'~?, y, i,I~ r `; ~~ P t~~y~a,y :1i? a,yl~ 4,~ ur ~ ~ fp, I
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~yty{~YBk~,
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VALUES OF THE COEFFICTFNTS IN THE FQUAT10NS OF
ALTERNATING CURRENT
i.e., it plays the role of the usual capacity reactance,
Table 4,3
and. since, in the seem of units adopted by Liewallyn and Peterson,
X ~C cap City in farads per square centimeter of surface, then
f _ _, _cv 3~
r ""n
-V~P-~~ (Va}ub)p~
~? n n
\ _\i )-%
-4
E [vb Cv + Vb
n
(V+Vb)
azZ
z
.~2 6g .
Lb)1 -- \/0j1PQ)
?D* w a-?;--I.
Values of the coefficients far the limiting cases
a Fulls ace charge (l); (b) No space charge (= 0)
P
(P_a -v P(~) :
B
()('-) -
vb
_7 r Va~Vb\"I e Y
". i
cp-,c) _vj
, -,
4
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F :: fr' (\?\)e
(2-
~. 0
_
FeSymbols Used in the Formulae of These Tables;
4
Q~
S
e
? bCve( ~ ~Q).v0.PJ
\VA~` e _
J1t/~"~fyJ ww - jrw"M~1_ t 4 1 r
/ 40
Let us nc~4 consider a second example, in which plane a is
the cathode, and the conditions for the sce charge corresporr to
saturation, i.e., for 1. Then by virtue of the absence of the
alternating current component on the cathode and the fact that elec-
tr an vel aci ty on plane a is Q, the first of the equations in (4.30)
is written again as f ollcw s;
U -U
b a
But the expression far' k must now take account of the fact
that 1. By performing an operation analogous to that in the
preceding example, we may obtain an expression for as the imped-'
ence, in the following form
r
r
(& +
4lj (4.31)
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By writing r 2( + Ib2"3 gyp, and remembering that this
a a
quantity is inversely proportional to the transconductance of the
diode characteristic, if UUa we may express Z as
E
At exceedingly high frequencies, this impedance approaches
the value ?cYo = , i.e. the value of the "static"
capacity of to resistance. At very high frequencies the diode
becomes equivalent to a simple condenser, the properties of which
are not altered by the presence of electrons, as was remarked in
the preceding section. A stuffy of formula (4.32) leads to the con-
clusion that at transit angles corresponding to
Q 2Xn +c/2 _ 7c/2 (i+4n) (n- 1, 2, 3....,.), (4.33)
maxima are obtained for the negative active resistance of the di-
ode
r ?i2
434)
Consideration of the case "partial space charge", when C
< t; < i, leads to a sometihat more complicated expression for
impedance A* :
4 (1-c
' b + RCoS& -- (4.35)
2
Coc -
The quantity rQ may be defined here as
(4.32)
(4.36)
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009-2
2
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It folic~ws from equation (4.35) that the impedance of a
diode consists in the general case of three consecutively connected
resistances: active and xeactive, which vary in dependence on G
Fi re 4,14) and are represented by the f irst two terms of f ormula
(4.35)r tggether with that of the simple capacity defined by the
third term of this far'mul.a. This capacity represents a static ':capa~
city which is somewhat varied by the existence of a space charge,
At very high frequencies, k~ may be expressed as
(4.37)
It is clear from this that as approaches infinity, the
impedance of a diode for any space-charge condition whatsoever
approaches the ordinary capacity reactance,
3
(2) 2 (3)
_?7 V_
x F-~--- x2--~" x
J J
q s
s J 2
Jq = J1 - J2
Figure 4019
The general equations we have presented, of which we have
just demonstrated the application to the already wellwknc~an pro
perties of diodes, enable us to set up rational circuit equivalents
for multi-electrode tubes as well, Such tubes have the form of a
series of successive diodes with plane parallel electrodes, as de-'
acted in F' ure 4.19 for a tetrode. Here the conditions between
p ~
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the electrons on passing through grid 1 are already subject to the
The conditions in region (2) are not sa simple. The fact is that
the cathode and the control grid L are analagous to those in the
been consk1ering. Between the control grid 1 and the
diode we have
situation is already somewhat different on account
screen grid 2 the
conditions that differ from those in the first diode.
of boundary
Roughly the same is true bet~aeen the s?Preen grid and the anode 3.
This series of diodes has its elements connected by the corresPond
ing boundary conditions characterized. by effective potentials.
These effective potenttals are naturally different from the actual
potentials of the wires in the grids. The grid current is repre-
sented as the difference between the total current to the right of
the c orre spa .>rng grid and that to the left of it (Figure 4.ia).
na
The diode equations are directly apl.)l.icable to interval (1).
action of the altprna,.tng field in the first diode e Equations (4.30),
~.
enable us to calculate the initial current and velocity in
hay ev er,
these coincide dth their final values in space (1),
space (2), since
'd 1 is negative. If it is positive and carries a certain
then the number of electrons entering region (2) is less
current,
than that of those leaving region (i) ? If a certain part q of
the alt., ernatiflg component of the conduction current q enters region
then the share (1 .p( )q characterizes the grid current. Thus,
(2),
each interval (1), (2), (3), etc is characterized by its on current
, I I , The application of the equations of Table 4.2 gives
,
,
I
1
2
3
i
the following expressions for these currents
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13 .. (U3 ' U2)y33
Ul)y23 U113
I4 : (U4 M U3) y (U3 " U2) y34 " (U2 " u1) y24 U1yl4
(4.33)
etc, where the quantities y11, y22,.., represent conductances and
yield the equations;
yll =." i y22 = 1 i 133 W
l
A .Ao
y12 - ' . (~'1>s G~a*02a~)
' A12* Y '~
D ~* 2B3* G2033~ )
_ (2
23
3
Y13 ::
A~ ~~A2~,~A3s< 2
r-r , etc.
A3
(D1*
E2+ G1*F2#) +
+03*(U1* ~1 H2* .. G1#I2*) . _ ~2B3,tD2*(D1* 1B2* 4
+ G14~G2*) '-" 033~G2*(Dl* t B2+ G1 02~, '(
(4,39)
The formulae (4,3) allow any region on Figure 419, for
example the third one, on Figure 419, to be re,pre sent ed by the equ:t'-
valent circuit of Figure 4.20. Here this region is represented by a
circuit into which and out of which, the current 13 flaws, The con-
ductance y33 is fed by two sources of current from Bch of the pre'-
ceding regions. One source gives the current Ib - (U2 " U1)y23,
while the other gives Ic
U1y13, where the quantities y23 and y13
are "mutual conductances" corresponding to the regions or to the
slaarpness of their respective characteristics. The sum of all the
currents arriving at point U2 is equal to 13 I p Ib 'S Ic in ac~
a
cordance with equations (4,14), The equivalent circuit for the en?
:18O
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tire electron stream of the tetrode in Figure 4.19 may be repreM
sented in Figure 1.21. The sources of direct current here play
a role analagous to that of M
Ug ? the oscillation in the old
equivalent circuit for the vacuum tube in Figure 4.13. The curM
rents here are expressed through the equivalent grid potentials.
Whatever connection may be known between the actual grid pc]ten
tials and their equivalents calculated by formulae (4.39), the
conductances may, so to speak, be "reduced to the terminals" of
the tube, i.e. correspond to the relations between the actual
currents flowing in the tube and the actual voltages applied.
As an example of the more detailed application of the general
equations, the tetrode cir cult s of Figure 4.19 are an alyzed, with
a full space charge present in region (1) and its practical absence
from the following intervals, Such conditions, as the reader has
vvv~
D Y11
(U2 ~. U1.y23
I I
I
I U1y12 I Uy13
11
~l
y22 2 y33
(vvv
I 1U :3'j I
Figure 4,21
Third Region
Figure 4.20
1;81
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0 yS 2
13
~Q2) ~ v2P
1
2
Sa Qi-) :I-1jP- 5
P3]
It is also of interest to bear in mind the limiting values,
' h fre uencies, of the quantities entering
at very low and very h:tig q
into these exireseian (Table 4.4)
Quantities
Low frequencies:
High frequencies
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12 _ A1~" (v~+ v2)
t:l.rel corres~aand to thaw of apexat~.ar~w
already been xerm?nded, pan Y
The exPra s s ions for conductance are simplified in this ways and
give the fallowing equations:
~, ; 472 ? ; 433 " Ayll " A1,~ A2 3
'~~A
'~ u
412 w 1 ? 1 2
y23
Y
y13:
~` ~ ~1~~2~~3~z?~A1~~,3~~
and y are xticul8X'14 interesting
The conduc?~ances 412 13
scanductance of the characteristics of
here ; they define the tx an
n their depehdonce on the control-grid
the respective currents i
be expressed somewhat more in detail:
voltage They may
nt r 2Pll, (2
Y
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The quantity 2P/A, which in essence represents the
sharpness is particularly interesting in this case. For > q
it is a complex quantity, and its behavior in relationship to the
transit angle is described, as we have already shown, by the curves
of Figure 4.17. A detailed analysl.s of the equations (4.41) leads
us to the conclusion that the influence of transit time reduces
down to causing variation in the phase angle of the transconduc~
Lance, w it hoot exerting much of an influence on the value of the
modulus (of. Figure 4.17).
Where the transit angles are large in all regions of the
stream, equations (4.11) reduce to the follow.irg set:
\J2
M
Qt( ~ 0 e
JUb
(4.42)
The course of the variation in the modulus value y13 is
a little different from that of Figure 4.17 and is sheen in Fig-
ure 4.22, from which it will be seen that the transconductance of
the corresponding characteristic approaches zero as the transit
angle increases.
To adapt this analysis to the conditions in actual tubes,
we must take account of the fact that there also exist certain
angles of flight and space-charge factors between the equivalent
planes of the grids and the grids themselves, even though they.
are very small. For this reason we may introduce the concept of
U
_NUD ~i8z
z,
-
2
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1,0
0.8
0.6
004
Opt
L() 12 14 16 20 9
Transit angle
Figure 4.,22
lent planes and the grids the m?
ductances between the equ~-va
the con essi.ons. The
that may correspond to the expo'
selves, with values
? mplicated the general
existence of these conduc ces somewhat co tan n in Figure
filch here takes the form sh~
equivalent tube circuit, w in the first
tetrode, with a space charge only
x, . 23 (for the same enerator of
e ; negative on grid 1, the g
region; if the volt ag
1 and G is elimiited) .
curr0zlt between
etc are here the electrostatic
The capacities c22' 023 cape ~ with the
cting surfaces that coincide w
cities between the c ondu es s are the
surd' aces of the electrodes The capaciti Og and C m wires, which in
lec?tr on stream and the gx' ~d
capacities between the e lification
nd C condition the static amp
their relation to 022 a 33
factor of the gr id s in que soon.
of Tables 4,2 and 4.3 may be ap-
The general xelationships elec~
od to systems with any number o?f
lied by an analagous meth
p electron stxeams
? with statically controlled
trades ? For tubes comp atianal formulae, which
this method yields rather convenient at different
are also the most general far' the various raters
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Figure 4.23
4.4 THE DIELECTRIC PB,NEABILITY OF THE ELECTRON INTE2VkLS
transit angles.
The authors of the w ork under discussion, Llewellyn and
Peterson, also point out the possibility of applying the general
equations to velocity-modulated devices as wells i.e. to systems
having dynamic control of the electron stream. The physical opM
erating conditions for the electron stream in such devices are,
however, so peculiar that the method of equivalent circuits can
hardly lay claim to being broad and general enough to take in the
treatment of devices with dynamic control, taking into account
the specific nature of their electronic mechanism. Katsman
has very correctly remarked that it is possible to employ confi-
dently the theory being cons llered as long as the individual elec-
trans or groups of electrons do not overtake each other, i. e. as
long as phase focusing does not commence in the electron stream,
for once it does, the above-postulated single-valued velocity far
all points of the interelectr ode space is at an end s
It has been noted above that the capacity of the electron
interval is less than the "cold" capacity of the electrodes on
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electrons, esu1ting in the variation
accaUnt of the pxeseraca a~
bilit ~-~ which becames less than ?ity -~
a~ dielectric permea y ~
~.ccardin~ ~~
and consequent reduction of capacity to Benham
t of the d ie].e ctr is pern~a abila,`ty, which
and Muller l,er /J, the value is defined as the ratio of the operating e].ectrade capacity C
to the "call" e caPachy C -- depends an the transit electrode ].
t through the interelectrode spaCeo At
of the electraras
0, and a full space charge, the interelectrade capacity
+' value. The course of the vaxi~
reaches 64 per. cent of its ++cold
tr is ermeability of the gap as increases is
atian of the dielec p .roaches
shown in Fi~,~re 1~,21~., from which it titili be seen that E apP
ncreases. For insignfficant values of
unity as the transit angle ' ~
bilit of the electrof gap depends also on
v r~ielectric perinea y
a
e s ace charge. The dielectric perrrieability or?
the density of th p
space canta char~~es, mc:r be expressed .-,d /13/ as:
~.n~.ng free
G~ is
here N is the number of electrons per centimeter and
~a
the angular frequency of oscillation.
of ~~ , which shows the deviation from
Thus, the valuc
of the dielectric permeability, is equal to
unity of the value
~c
of the time spent by the electron in the in-
The influence
3.s not reflected in the se formulae , To
texelectrode gap, hcwever ,
take this factor into account as 4 ell, Benner has given the
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f ormula
In this case N is the number of those electrons in 1 cubic
centimeter of the interelectrode space which re main there during
IA
the time t' ? Benham /l] gives a formula somewhat d i,fferent from
the foregoing:
where the function f() may be exprr~ssed in the follo~ing manner :
of the electron stream (for instance, current density and electron
Figure 424
In consequence of the periodic variation in certain parameters tix
permeability of that space may vary periodically in time, and with
it the capacity of the intereleetrode gap may also vary. Since
velocity) that occurs in the interelectrode space, the dielectric
a
ant erelectr ode capacity usually forms apart of circuit capacity,
this should involve modulation of the parameter and, under certain
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-2
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? Iy*A)(
max Groin Max M1h
conditions, parametric excitation of oscillations in the circuit
connected to the electron gap. If the minimum and maxiruar~ values
of N can be calculated for any specific case, gad also of
together with them, then the coefficient of modulation of the
pararneter can be found by definition, since
and expressed by the values characterizing .the properties of the
electron gap, for example by the current density, the applied di-
rect current voltage, the geometric dimensions., etc. When this has
been done, the results of the theory of rametric excitation of
oscillations, developed in the works of academecians N. D. Papal-
eks' and L, T. Mandelshtam and their students, can be applied to
the system being considered a
Unforturtately, he ever, the question of the determination
of the dielectric permeability of the electron gap cannot be con-
sidered to have been sufficiently clarif:ted either from the the-
oretical or experimental sides
The experimental work performed by various authors is evi-
dence that in most cases -- specifically in those cases where we
are definitely dealing with a pure electron gap, uninfluenced by
an possible ions of the residual gas _- the dielectric p~rmeabiU.ty
is less than unity, and depends on:
ternating current voltage applied to the gap; (b) electron concen-
tration; and (c) the time spent by the electrons in the gap.
VCStigations in the meter-wave field have shown tat the variation
in dielectric e:r'meability with variation infrequency and the other
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paramete:,r}of the systera is of resonant chEiraeter. This phenomenon
mrw be connected with the peculiar "anomalous dispersion" of the
electron gap and the existence in it of its awn natural. frequencies.
All of this sho s that there is still a certain degree of uncertainty
ty in the application of the ideas connected with the dielectric
permeability of the electron gap to the interpretation of the mech-
an ism of the operation of ultra-high frequency generators. Only
when applied to gaps with very small transit angles may we hope to
obtain results that are close enough by using the simple formula
~~~- if the mechanism by which the gap functions is
4 ell enough known and is simple enough to make it possible to cal-.
culate the variation in N, and together with it the capacity. The
attempt of V. P. Gulyayev '15J to apply the theory of parametric
excitation to the klystron generator has been fairly successful,
and we shall consider it in the balance of this chapter.
Gulyayev takes the two-circuit kiystron scheme of Figure
square. centimeter of cathode; vo 2eu0 is the velocity ac-
D.
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4.25 and assumes that the electrons fly from the cathode and
modulator through equal time intervals, and. that the forces of mutual
repulsion between the electrons may be disregarded. He obtains the
f olloa ing expre ssion for the number of ele ctr ons in 1 cubic centi-
meter of the output zone (the electric field of the second resonator);
where
No is the number of ele ctrons emitted per second per
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quired by the electron in the zone of ac cel,er ation;
is the coefficient of Woltage modulation", and s Is the distance
between the centers of the two resonators of the klystron.
searing in mind that the c~zrrent density in the electron
beam io ? Noe, the d le ctr is per rneability may be expressed s
EHtH
'Y\CA2' g)aU f ?YgL)S '\ (4.49)
o\ V0(1 y*\
Whence, by f orraula (4.47), the coefficient of capacity
modulation (assuming that + < 1). is obtained as the expression.
Figure 4.25
(4,50)
U25+r CCtYf` + 4')
The modulation frequency of the parameter in this case is
equal to the oscillation frequency, and the condition for excita-
tion is obtained. in the form
R
I io_23
190-
(4.51)
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if ip is expressed in amperes, and U in volts, Since i U /Uc,
o 1
the initial value of the potential on the modulator U10 at which
oscillation can be maintained may be expressed, from this equation,
as fo11ows t
U10 > 3.16.1O 12 U L~ R
10 ios L
(4.52)
The condition for the excitation of oscil1ation5 and the
other conclusions obtained for the klystron by Gulyayev, corresM
pond satisfactorily to the experimental data and to the ether
theories.
The application of the theory of p,rametric excitation to
the various types of ultra-high frequency generators is of great
interest and will probably lead. to, in a fairly simple way, fun-
damental results 4 One of the principal factors that is responsible
for the physically grounded applicability of this theory is the
reliable calculation of the die le ctr is permeability of the elec'
tron gap with varying space charge, which at the present time is
hardly possible for the magnetron or even for the retarding-field
circuit (ttreflex klystrontt).
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BIBLTOGRkPHX FOR CHAPTER 1V
1. W. Benham, Phil. Mag., March 1928, p. 641; February 1931, 457.
2. F. Llewellyn, FIRE 21, 1532, i93; 22, 947, 1934; 23, 112, 1935.
3. C. Bakker and G. De Vries, Physica, 1, 1045, 1934; II, 683, 1935?
4. G. Grtberg, Techn, Phys, USSR, III, 65, 1936.
5. Yu. Katsman, jektrc (Electrical Communication), No 7,
47, 1940?
6, J. Mhier, Hochf requenz & El., 41,156, 1933; 43, 195, 1934; 46,
145, 1935.
7. S. Ramo, PIRE, 27, 5g4, 1939.
8. F. Llewellyn and A. Bowen, BSTJ (Bell System Technical Journal)
18, 20, 1939
9. F. B. Levellin (F. B. L1ewe11yn) In rtsia,,o,-lectronov (The Ins-
ertia of Electrons), GTI, 1936.
10. J. S ahanek, Phys. ZS, 33, 693, 1932.
11, F. Llewellyn anal L. Peterson, FIRE, 32, 144, 1944.
12. Yu. A. Katsman, Lam d].y ul tr vysok.ikh chastot (Ultra-High
Frequency Tubes), Doctoral dissertation, 1945.
13. \. N. Shchukin, Ras rostrane? nye ra.d,~,,, ovoln (The Propagation of
Radio Waves) . Svyaz' izdat, 1940?
14. S. Benner, tnno d, Phys., 3, 993, 1929
15. V. Gulyayev, ZhTF, SCI, 101, 19410
-192r
hwR,~
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