RADIO ENGINEERING

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP81-01043R002000090003-3
• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 121
• Document Creation Date: December 27, 2016
• Document Release Date: May 22, 2013
• Sequence Number: 3
• Publication Date: January 1, 1955
• Content Type: REPORT

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(RADIOTECIZIQUE)
VOL. 10, NO. 12,1955
pp. 3-80
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L.
Table of Contents
Pulse Spark Excitation of Oscillations in the Microwave Band,
by I.V.Ivanov
The Reaction of Square Pulses with Random Duration and
Separation on a Line Detector, by V.I.Tikhonov 14
The Transitory Characteristics of a Compound Pulse System made
up of Nonuniform Sections, by S.N.Krize 22
An Analysis of Intermediate-Frequency Amplifiers in Semiconductor
Triodes, by Ye.Ya.Pumper, Ye.M.Petrov 29
High-Frequency Broad-Band Transformers, by S.G.Kalikhman 47
Calculation of an Ionic Voltage Stabilizer, by G.S.Veksler 61
A Method for Increasing the Accuracy of Frequency Analyzers
with an Electron-Beam Indicator, by N.F.Vollerner 73
The Effect of Capacitance of a Space Charge and Nonlinearity of
a Tube Characteristic on the Frequency of a Self-
Oscillator, by G.T.Shitikov 78
Calculation of the Amplitude Characteristics of Limiters, by
Ya.Z.Tsypkin 104
Page
1
List of Articles which Appeared in ?Radio Engineering" Journal
in 1955
New Books
110
117
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S
PULE SPARK EXCITATION OF OSCILLATIOUS IN THE MICRCWAVE BAND
by
I.V.Ivanov
The report describes the method for spark excitation of
oscillations in cavity resonators. The energy level of the
fundamental oscillation is given. The design of the resona-
tor is described, giving to the charge HF pulses of an ex-
ponential form whose duration is of the order of 0.1 A sec
in the 8 - 13 cm band: The pulse output power of the reso-
nator reaches 10 watts.
In connection with scanning by new methOds for generating microwaves, interest
has lately been revived in the Hertzian spark method for exciting oscillations in
the SHF band.
G.Anders (Bib1.1) describes an oscillator whose basic member is a Hertz doublet
in the video alteration inspired by P.N.Iebedev (Bib1.2). In the Anders oscillator,
the dipole is placed in a cylindrical circular cavity. The dipole radiation excites
the entire spectrum of the cavity oscillations, and the energy of one of the oscilla-
tions of this spectrum is filtered out and emitted further on. The shortcoming of
this method is that the oscillator works on the principle of extracting, from a
continuous spectrum, a narrow strip of the dipole oscillations, whose width is de-
termined by a quality factor of the cavity. There is no oscillating interaction of
the dipole and cavity, so that the fundamental energy of the dipole emission is
wasted on equal excitation of all the other oscillations of the cavity spectrum.
Besides, the power which the oscillator puts into the load has an insignificantly
small value.
' Oscillators, working on a similar principle of extracting a narrow strip from
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4
a continuous spectrum of narrow pulse current, are described by Davis and others
(Bib1.3 and i4). As in Anders case, there is little utilization of the energy en-
tering the oscillator from the modulator.
The problem of the given operation consists in increasing the degree of util-
ized energy from the modulator in a system, consisting of a cavity resonator with a
Hertz vibrator placed inside it. Speculation on the possibility of resonant in-
teraction between these two members led to the result that, when there is a coinci-
dence of the dipole and cavity resonant frequency, it is already impossible to
consider them separately. The dipole proportions become in this case comparable to
the resonator proportions, so that the dipole, together with the resonator, forms a
certain complicated topology of the conducting surfaces, a resonator of a new firm.
If in such a resonator, it is possible to charge the component conductors at various
voltages, then static electric fields arise in the system with corresponding reserves
of energy. When the charged conductors are brought into the resonant circuit,
currents and alternating electromagnetic fields are created, bringing into the closed
system the character of standing waves. In the capacity of a closing key, a spark
discharge can be used, whose operation time is much less than the period of the cav-
ity oscillations. Such a discharge arises between the charged conductors of the
resonator when the voltage drop between them is large enough for disruption.
-As is well known (cf. for example the works in Bib1.5 and 6), the development
of a spark discharge in air at atmospheric pressure has a streamer character. Dur-
ing this, in the process of forming the discharge, two stages can be observed. In
the first stage, a spread of the initial avalanche and streamers crosses the spark '
. gap between the electrodes. In the final stage, the stage of forming the main
dis-
charge, the electrodes are well overlapped by a conducting bridge, by which the
, pulse of the current crosses with a speed of the order of 1010 cm/sec, completing
the disruption of the gap. For gaps of 1 nut width, the formation time for the main
discharge has an order of 10-11 sec. So short a duration for the closing process
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Cl
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??????
?
guarantees the possibility of using the spark as a low-inertia key for the entire
microwave range. The explained calculations allow us to develop the Hertzian method
for exciting oscillations usable in electromagnetic cavity resonators.
As an resonant system, in our opinion the most convenient for spark excita-
tion in actual operation is a coaxial cylindrical cavity, a diagram of which is given
in Fig.l. The cavity is made up of two
concentric cylinders (1) and (2) and end
planes (3). The central conductor (1), be-
cause of the fact that its direct current
has no contact with the outer cylinder of
the end planes and enters through an open-
ing in one of the ends. Between the
disk (4), in contact with the central rod
of the oscillator and one of the end sur-
Fig.1
faces (3), there is a clearance (5), form-
ing a capacitor of fairly large capacitance. Between the points of the rod (6), in
contact with the outer conductor, and the end surface of the inner conductor there is
a spark gap (7). In this diagram, the following designations are used: 8 - coaxial
two-wire circuit of the sonde, 9 - sonde, connected with the charge, 10 - HF outlet
plug.
The inner conductor of the resonator is connected with the modulator, giving
pulses of 1 p? sec duration and 3 - 5 kv amplitude. An artificial line is used as
.modulator, which is charged by a high-voltage rectifier and connected across a thyra-
tron to the characteristic impedance. As a consequence of the characteristic imped-
ance of the line, the spark gap of the resonator is closed. During the firing of
the thyratron, the central conductor of the resonator is charged to the disruptive
potential of the spark gap Uo; during this time, energy is stored in the coaxial
part of the resonator
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Co U20.
we =
2
where Co is the distributed capacitance of the coaxial part of the oscillator.
While the disruption occurs, the spaik gap is closed and the artificial line
discharges into the characteristic impedmice. The square pulse of the current, flow-
ing through the spark channel, guarantees constant closing conditions for the last
oscillation of the cavity. The resonator, closed at one end by the spark channel
and at the other end by the fairly large capacitance of the central conductor en-
trance, on account of the stored energy Wo accomplishes the damped oscillation.
The fundamental oscillation - an oscillation of the Lecher type with a wave-
length of x = 2L, where L is the length of the resonator, and all the odd harmonics
with x 2 L(n1,2,3...)
2n + 1
ential means by comparison with the
cillations of the waveguide types H
- is excited, as will be shown below, by prefer-
even Lecher harmonics (x = ---) and with all os-,
and E. Preference excitation of odd harmonics is
related to the fact that the configuration of the electric fields of the odd harmon-,
ics is contained in the structure of the initial field of the resonator, so that the
initial field can be analyzed in terms of the fields of the odd harmonics. Such an
analysis, making it possible to determine the share of the initial energy entering
'into the fundamental oscillation (the first odd harmonic) can be nearly completed on:
'the following supposition: We will suppose that the configuration of the initial
'field in the resonator is equivalent to the field in a cylindrical capacitor. Ac-
tually a longitudinal component field extends to the limits of the cavity, and con-
:sequently there is room for a certain deviation from the field of a cylindrical Ca-
pacitor. After mirror-reflecting the charges, forming the field of the inner cavityi
relative to the two end planes, developing the fields, and repeating such operation
an infinite number of times, we obtain such a periodically spaced structure of the ,
field that:
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E,0
for
-2L> 1 And w7C21R2 >>
2
M2
1 1712
The second term represents the resistance introduced into the circuit by the
triode of the given cascade, and the third term is the resistance introduced into
the circuit by the input resistance of the succeeding triode. The voltage is
and,
4
Ei=
Urr
r2 D2
4
tni
U , m
CiRowt
R21
R:1.
The amplification factor of the cascade, in voltage, will be equal to
I R31
mints P
?
U, 1 2
R r? (w1..1 ? ?
t ? )
w-1
( 2 )
The amplification curve has the form of a resonance curve.
The condition of balance in the circuit Of the collector is written as follows:
M2o
R
2 2
M2P
=-- r
R
correspondingly, in the circuit of the emitter
2 32 2
in2 P ? int P
-t-
R in 1 R
(3)
The equations are not compatible, i.e., in a single circuit it is impossible
to attain complete matching. We will derive the approximate condition of complete
matching at least for the case where the resistances introduced into the circuit by
32
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11;
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?
S.
the shunt Riu and Rout are much greater than the characteristic resistance of the
circuit.
Then;
M2
Row t
fl ;n ?
(5)
The voltage amplification factor, in the presence of resonance and of matching
across the input (emitter) or output (collector) circuit, takes the forms, respec-
tively,
or
R21 yR in nsleP
K
ot 2 R Rout ,7.( Ps
le )Romr
Rowt
4.?
1 R?-y-R?, P
K?r= 2 -1?-1-1-. t /
( P2mL
R" V
R --/
(6)
(7)
2 2 2 2
'le T m21 t
In the case of almost complete matching, when '?r1 or >> xi
Rout Rin
the amplification factors in the presence of balance across the input or output cir-
cuits coincide and have the form
1 1 ifkottt K
K ? =
"K 411( 2 Rn V Rout 2 r R,? 0P,
. where a is the current amplification factor of the triode.
(8)
Qxx
;:e will express the voltage amplification factor by the ratio: . y,
wla Qwork (i) la
? where Q, = is the quality factor of the no-load condition, and Qwork =
XeC
. r1 ri
is the work quality factor..
We will first consider the case of matching across the emitter circuit. From
the expression,for the work Q-factor of the circuit and from eqs.(1) and (4) we
have
33
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??
n 3e1/Bin
liTC v.?1C.
(9)
Substituting this expression in the condition of matching across the emitter
circuit, we find
1
Atic..1/41-1121q(
P '2Qw,k Qxx)
(10)
Ana1ogousl7, in the presence of matching across the collector circuit, we have
A,4
w
to
ii
L
Ob. ?
? I
I I
_
0 ?, ?? 13 la
I 4. work
Fig.3
MiK YRout
2pQw ork,
mom 11
P 2 Q work Q xx
From eos.(6), (7), and (8) we will
determine voltage amplification factors
Koe and Kok in the presence of matching
across the emitter circuit or across the
collector circuit through the values of y:
? ? 0
('3)
at Y 1 Kok = Koe KoP-
It follows from eq. (13) that the value Kop has the meaning of a limiting ampli-
fication, which can be attained for the given triodes as y
Matching across the emitter and across the collector leads to the same amplifi-
cation at the same values of Y. The dependence of the amplification on y is shown
in Fig.3. The growth of Y to four or five does not lead to a significant increase
in amplification. For the selected value of Y the-amplification does not depend on
the frequency within the limits of accuracy of the inequality (1).
34 STAT
?1'
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Using the expression for the generalized deLuning all applicable to the given
case, we will obtain an expression linking Q;Icx with the intermediate frequency and
the pass band P:
Q..=
Tit/.
(14)
From this it follows that a decrease in fo permits scaling Qxx, while keeping y,
c( 1P and P constant.
The difference between calculating the amplification of a cascade with a single
'circuit in a semiconductor triode and calculating the amplification of an electron
tube consists of the following:
l) The values of Y are selected to match the curve in Fig.3 within the limits
2) The choice of an intermediate frequency is made while disregarding eq.(14);
3) The work .11-factor;
?
/0 a ,
Qviork'r T, -1,
4) Qxx =Y :work;
5) The cut-in factors are chosen in the presence of matching across the emit-
ter agreeing with eqs.(9) and (10) and of matching across the collector
agreeing with eqs.(11) and (12);
6) The amplification factor at matching across the emitter and collector are
determined by ea.(13).
3. km lifier with a Band Filter
A diagram of amplification with a band filter is sham in Fig./. As before,
the semiconductor triode is replaced by an active quadripole. The resistance Rn-
Li
is the input resistance of the succeeding triode, while ml = and m2 = are
1
the cut-in factors from the collector and emitter end, respectively.
35
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Pa
Splitting the network along the lines 2 - 2 and 3 - 3 and applying successive
ly
the theory of the equivalent generator, we arrive at the equivalent network in Fig.5.
Having used the basic formulas of the quadripole and having
SO C7 R20 u t .2 cF,P2.
>> 1 And ' m >>1
m4 4
1 M2
we obtain, the following values for the' parameters of the network in Fig.4:
ml2 2
h m?, p?2
r --t- r, =--
R but if in
(15)
where ri and r2 are the characteristic resistances of the first and second circuits
p2 = Ll p2 =
1 Ci 2 L2 . The value El is equal to
C2
U in I 112
E1
(1) CIR out R11
(16)
For a network with a partial' cut-in, the voltage amplification factor of the
Fig.4
a) Quadripole, replacing the semiconductor
triode
cascade as a whole will have the following value:
where
?
where
M
? mtm2
[UP MJ? rirl, (1 (1 iy C,R Out
Fig.5
(17)
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WS Lt
Qw.os tot/L.2
== ; Qw?rk,
r,
The amplification factor in the presence of resonance has a maximum with the
values mi and 11120 corresponding to matching condifions, which can be written in the
following manner:
1) for the emitter circuit
tions
where
2 2 2 kirl
773 2 P2 w0
? r2 +
Rirt
r, +
' R out
2) for the collector circuit
2 2
NII Pi (4- AP ,
-= rI 1
1 -1- 22 ?
R out . m2 ? 2
r2+
40
rx in
(18)
(19)
In the given case, complete matching is possible, which results in two condi-
Qxxl
2
11 = 12 = 7. 1=
1 ? P1P2
Qrx1 . Qx0
11=
Qwofki =--- Qwark K And Pi =-- Qvuok,2
--
n = _woL_2
r- , 4.41 xx2 ,
..1 == on LI
TI
Qwork a =
(20)
Here K is the coupling coefficient.
0 1
For circuits with the same parameters, we have r1 = r2 = r and 9xxl = 9xx2 =
= Q. From eq. (20), it thus :follows that
Qum* 1 == Qv/ark 2 '="- Qwork
13 132 = 13
37
(21)
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where P is the coupling factor.
At complete balance, not only is maximum amplification attained but also the
work Q-factors become equal for contours with the same parameters.
The second matching condition for the case of identical circuits leads to an
expression connecting Y and 04
since
10
6
4
0
02
04 0,6
Fig.6
a8
2
(22)
At complete matching, the choice.alO
determines the value of Y. When 2
we correspondingly have 0 < (3 < 1.
From eq.(22) whose graph is given in
Fig.6, it follows that, at full matching,
it is difficult to express 0 > 0.7 - 0.8
= 4 already at 13 = 0.707 and Y = 6 at 6 = 0.82.
< y < cc
From the expressions for the work Q-factor the switching-in factors can be
found:
mi= -I 1 r R.?, (r )
(23)
-1)
Having substituted the expressions for the cut-in factors of eq.(23) in eq.(17)
under conditions of resonance and using eq.(22), we get the following expression for,
1' the voltage amplification at complete balance and with identical.circuits of the
r filter:
, 1
KU=- 2 R11 R
1 R2I-VRin p=Kopp=Kopill?T ?
.ovt 2 (24)
The magnitude Kop coincides with eq.(8). It has the meaning of a limiting co-
efficient for the voltage amplification at complete matching and when y m?
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The calculation of cascades with a band filter differs from the conventional
calculation of vacuum-tube amplifiers, studied specifically by V.I.Siferov (Dib1.2),
by the following characteristics:
1) The values of the coupling factor 0 and the ratio of the Q-factors Y =
Qxx
are selected according to the curves in Figs.3 and 6;
QworR
2) The intermediate frequency 1'0 is selected while disregarding eq. (14);
3) From the generalized detuning, the intermediate frequency and the given pass
band are determined
le
YWCA-- p
1
4) Q.MX "WOrk;
5) The cut-in factors mi and m2 are found according to eq.(23);
6) The amplification factor at complete matching is determined in agreement
with eq. (21.).
h. Band Filter with Parallel and Series Circuits
A diagram of such an amplifier is shown in Fig.7. D7- means of successive ap-
plication ol the t3q-ivalent generator theory, this leads to Lhe diagram in Fig., we
,120 1 out 1,2
'
have, for ?, 1,
A
mi
^ 2
?
M p ,
r x.r ,
0,Ar
E = ? C 04 1111 ?
Such a cascade has as a voltage amplification factor of
? Ku =---
0
where
R21
M131?
CiR [0; ? M2 Zi (Z, R
39
(25)
(26)
(27)
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1 ?1. Z
u) L Cl/ 2
The matching conditions for the collector circuit of the schematic in Fig.7 is
expressed in the following manner:
n n
in' pi
Roo
4AP
- 1 . n
r2+ Ain
(28)
An analysis demonstrates that the maximum power in the emitter circuit is ob?
tained under the condition of an optimum link:
(29)
The given system in the general case is incompatible with ml and the coupling
2 2
r 6) o 111
factor K. When r1 '4 and r2 :114.., the condition of eq. (29) coincides with
p
out
Fig.7
a) Quadripole, Replacing the Semiconductor
Triode
Fig.8
,matching across the collector. In this case complete matching takes place, whose
condition is expressed by
2 2
MI PI
1ffifC
002 M2
R R;?
(30)
14.0. STAT
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We will determine the voltage amplification
factor with balance across the col-
d the congruence .condition (28):
lector circuit, using eq.(27) during resonance an
At optimum coupling we get from eq. (27) for the condition of resonance and from
eq. (29)
?
At Y1 1
We will then
Y2
define the
we get Kok = Koe KoPs
general conditions which permit determining the coup-
account that Qworkl = Qwork2 = Qwork, Ci C2,
Li L2, ri r2 and Qx..0. 9xx2. At bal.,
ance across the collector, eq.(28) will
yield, as in the case of the band filter,
ling factor = KQworhY
taking into
From eq.(33) it follows that (3 1.
In the opposite case the condition of con-
gruence breaks off.
For the case of optimum coupling, af-
ter dividing both parts of eq.(29) byt)oL
and verifying that Qworkl = ?
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An increase in Yi to 4, 5) or 6 does not lead to a significant increase in am,-
plification.
The dependence of the amplitude on Y2, in the
tor and of optimum coupling, has the same form.
likewise does not result in a significant increase
Having assumed the ratio of Koe and Kok according to
same relationship of Q-factors, it is possible to compare
tude during balance across the collector with the case of
t ,
.s
case of balance
across the collec-
An increase in Y2 to 4, 5, or 6
in amplification.
eqs.(31) and (32), at the
the amplification magni -
optimum coupling
Koc. + (7, - 2)
KOK
(35)
The case of optimum coupling thus leads to a slightly larger amplification.
Koe
When y1 = 4, we have = 1.06.
\ok
We will next consider
series and parallel circuits
former cases, the amplifier should guarantee the wanted pass band P with frequency
distortions cri in the cascade and an adjacent-channel selectivity Se.
1. For calculating such an amplifier:
a) We select a capacitance C1 equal to 200 - 400
Q-factors Yl;
b) We determine the coupling factor 0 [with matching across the collector cor-
responding to eq.(33); at optimum coupling 13 = 1];
c) We select an intermediate frequency and a Q-factor at
Yla 1
tions derived from the expression qxx = 1'0 It is
late the generalized detunin6al according to the
Siforov "Radio Receiving Systems," p.11/1, Fig.82.
2. From the capacitance C1 and the intermediate frequency we compute Li and pl.
Qxxl
3. We calculate Qwork =
When y1-
we have
Koe
Kok
a general schematic for calculating an amplifier with
under the conditiono- f 0_
-vrorkl
- 1.
= Qwork2 = Quork. As in
corresponding to the
no-load condi-
possible to calcu-
the book by V.I.
curve plotted in
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4. We determine the coupling factor K =1 0
4'work
5. From the expression for the work Q,-factor we determine the cut-in factor
mine
n121 = woCiR (wo
out (-)
xrk Qxal )
6. Given Y2, we determine r2 from the equation
rn"
R12 ;?
?
7. Starting with the equality of the work Q-factors of both circuits, we deter-
Pst == Pi
ri? -1- flin
nz; pi
r -1- '
1
Roo
C. Induction of the second circuit I =
2
o ol
9. Capacitance of the second circuit C2 =
woP2
10. The limiting voltage amplification of the cascade:
1VR out
Ko p = Rin a.
0
U. The cascade voltage amplification with matching acros the collector is
found according to
12. The cascade voltage amplification' at optimum coupling is in agreement with
eq. (31).
eq.(32).
2Nwork
13. We determine a2 =
fo
14. We determine the value of the adjacent-channel selectivity:
ao
0
Si,
1
(36)
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This formula for the hookup in question is justified by the fact that its am-
plification curve coincides in form with the amplification curve in the resonance
zone for the usual band filter.
5. Comparison and Numerical Rating of the Circuits in Question
From eqs.(13), (24), (31)/
hookups in question, it follows that, at Y , they are all characterized by the
the amplification Kop
the case of y - co leads
value imperceptibly small
the input and output re-
and (32) for the amplification factor of the three
same amplification which is equal to the limiting value of
eq.(). Such a
to reducing the
with respect to
sistances of the triodes. In this case, the limiting power, which can be segregated
into the outer load from the triode output circuit, is transmitted to the triode in-
put resistance. The quantity Kop is determined exclusively by the triode parameters.
For a home-made triode with point contacts, introduced into the circuit from a
ohm; 1111 =
result is physically understandable, since
characteristic
losses of the circuits to a
the losses introduced into the circuits by
master point in the base,
= 300 ohms; Rin = 232 ohms; Rout ' 15,500 ohm (Bib1.3). Then according to eq.(8),
Kop = 12.2. For the last value of y, the amplification has a lower value. The am-
According to ens.(24)
the following data is
possible: R21 = 6
plification values depending on y are plotted in Fig. 9.
and (13) an amplifier with a band filter with two identical circuits during complete
balance, and an amplifier with a single circuit, balanced across the emitter or col-
when the Q-factors of Y have an
ilector, are characterized by identical ami)lification
identical relationship. The dependence of the amplification on y for these cases in
1Fig.9 is depicted curve A.
;an the sane values of a hookup with a single circuit gives greater ampli-
fication in the presence of matching than a network with a band filter.
eqs.(10), (11), and (23) it follows that, at the same m1 the value of y
large for a hookup with a single circuit.
From
appears
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In the case of a band filter with parallel and series circuits (curves B and C
in Fig.9), the amplification has different values for the same values of yl.
The curves C in Fig.9 correspond to the case of optimum coupling and the
curves 13 to matching across the collector. In conformity with eq. (35) obtained
above, the case of optimum coupling leads to a slightly larger amplification than
matching across the collector. This is connected to the fact that, at optimum coup-
ling, the coupling factor is 0 = 1 and, at the same time, to the fact of matching?
across the collector fl< 1. In the presence of matching across the collector in a
hookup with parallt1 and series circuits, the amplification Kop at yi = y2 becomes
equal to the amplification of systems considered above for the same values of yl.
This result follows directly from a .comparison of eq.(31), under the corresponding
assumption of y = y2, with eas.(13) and (24). Actually, it can be seen in rig.9
that the curves B intersect the curve A at yi =Y2. In this way, all the considered
hookups, except the last with optimum coupling, lead in the presence of matching to
the same amplification factor for the same values of y. At y14 y2, a hookup with a
parallel and a series circuit gives, in this way, a greater amplification than a
hookup with a simple band filter or than a hookup with a single circuit correspond-
ing to a ,-factor relationship equal to Y1. An increase in Y2 leads to a rise in
amplification for a hookup with parallel and series circuits. An increase in Yo may
take place according to eq.(32), due to an increase in the input resistance of the
,succeeding triode 7in and due to a diminution in the characteristic losses 4. At
inormal values of yl, equal to 4 - 6, a hookup with parallel and series circuits and11
0
optimum coupling (curves C in Fig.9 at y2 = 4 and y9 = 6) gives the greatest amMi-
oc,
? ?
fication.
A comparison of the adjacent-channel selectivity for all hookups under consid-
eration, under the condition that frequenc: distortions along the edge of the band
in 10 kc are equal to 3 db, and at y 4 leads to the following deduction (cf. the
0 0
Table p 46).
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fr
0 a,
For amplifiers with band filters, the adjacent-channel selectivity is here cal-
culated according to eq. (36). It follows from these data that, with the same ampli-
fication, a hookup with a single circuit possesses the least selectivity.
A hookup with a band filter and a hookup with parallel and series circuits,
a)
?
10 4,65.10'
S And Q
Se, db
Q work
Se, db
()work
d)
b) c)
Q) f)
7 7,s 7,8 8,45
16,1
H 16,1 20,5
oc=
7 7,8 7,8 8,45
46,5 68,5 68,5 87
a) Frequency, b) Amplifier with single circuit; c) Amplifier with a band filter.
d) Amplifier with parallel and series circuits. e) Balancing across the collector.
f) Optimum coupling
matched along the collector and having the same amplification, are characterized by
the same selectivity. A hookup with parallel and series circuits in the presence
of optimum coupling is characterized by a higher adjacent-channel selectivity.
Article received by Wditors 9 May 1955.
BIBLIOGRAPHY
0
1. - Problems in Radar Engineering. Ho.2 (1952), pp.68 - 86 (Crystal Triodes)
2. Siforov,V.I. - Radio Receiving Systems. Voyenizdat (1951)
3. - Crystal Rectifiers and Amplifiers. Edited by Prof.S.G.Kalashnikov, p.49
0
0 0
46 STAT
c'
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0
!!IG!!-11112),UEIICY DMA a-BAND TR/1113FM TP3
s by
S.G.Kalikhman
Active Member of the Society
On the basis of the well-known method for converting balanced
filters into unbalanced ones, practical schematics for broad-band
transformers are obtained, and the engineering formulas are de-
rived for calculating their components. Experimental data are
cited from actually constructed high-frequency broad-band trans-
formers with flat frequency-response curves, designated for op-
eration in the 0.15 - 100 megacycle band.
1. Basic Principles
In practice, the projecting of high-frequency radio receiving equipment often
requires a matching of the resistances in the broad band of the received frequencies.
Such problems are encountered, for example, in matching the antenna feeders with the
input circuits of short-wave, ultrashort-wave, or of television receivers during the
matching of vacuum-tube band amplifiers with the main line in the multichannel col-
lective antenna (Bib1.1), etc.
The resonance methods, well-known from the theory of radio reception, used for
solving problems of matching resistances on one frequency 1'0, are completely unsuit-
able in cases where the band of the transmitted frequencies CI F becomes commensurable
with its mean frequency. Under these conditions, the problem is solved by the use
of band filters, based on the matching of the characteristic resistances. So that
these filters may have the proper characteristic for the transformation of resis-
tances, they should be unbalanced, i.e., their characteristic resistances at the
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0
ends should be different.
The construction of unbalanced (transforming) band sections is based on two
well-known equivalences (Bib1.2):
1. The ideal transformer with a (voltage) transformation factor n, whose pri-
mary winding is shunted by the resistance Zo, is equivalent to a T-shaped quadripole
(Fig.1) whose components are determined by the equations
4==(1- n)Z0
(1)
Zr1 = n (n - 1) Zo,
(2)
Zr: =---
(3)
2. The ideal transformer with a transformation factor n, whose primary winding
is connected with the source emf across the resistance Zo, is equivalent to a Pi-
Fig.1
a) Ideal transformer - p
0
/7
Ji---c?
N I
20-
4 2 4
L _ J
a)
Fig.2
a) Ideal transformer - p
shaped quadripole (Fig.2) whose components are determined by the equations
ZPA = Zo,
n 1
P
c
=-= 114
/48
1 n
0
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2. Desi of the Transformers
'le will use the indicated equivalences for converting balanced filters (proto-
t7pes) with equal characteristic resistances into transforming band filters, having
different characteristic resistances at the ends. Let us take as a protot:pe a T-
shaped link whose characteristic resistances are
- 2 = ? 4 ..;c) (Fig.3)-
Fig.3
the line A - A and include the
to n (Figs.). and 5). Using the law
We will consider the links of t7pes
IIIl
and IVKI* presenting the great-
high-frequency engineering (cf.
e will split the circuit along
1112, 1113, I
t interest
es
Tables 1, 2, 3).
ideal transformer with a transformation factor equal
of lumped resistances and having replaced, on
the system consisting of a parallel resis-
for
the basis of the
first equivalence,
A 8 1 1
I 12:Xt, 2-J(0
VIM MN NM Om
1 ? ?
1
k
Fig.4
tance XL2 and an ideal transformer by the T-shaped quadripole (Fig.1), we will ob-
tain an equivalent circuit (Fig.6). The elements ri?, ZB, and Zc of this hookup are
deter( 1) - (3) with the substitution of So in XL, = 6)12.
TrAnsiormer-re
Fig.5
Fig.6
0
mined b: eqs.
We will consider the particular case: Z2 = Xc2 = m (the prototype 1112,
Table 1, ro.2). In this case, the circuit (Fig.6) after summation of its elements,
leads to a T-shaped unbalanced quadripole (Fig.7), whose elements are
ation of filters according to T. Ye. 3hi (31b1.2).
TAT
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C1 1.1 1.3 r
Io-W3c
1.1 114Y?
4
Fig.7
L,
2
= it n (n ? 1) L21,
Fig.8
Li _II= nL2,
Cl 2 CI?
Cit =--
2C,
0
The obtained conversion of the elements of prototype 1112 has a physica.14mean-
ing at least when LI) 0, LII % 0, according to which the theoretically limiting
transformation factor is determined lc the inequality
1 n m 1 +- ,
L, . ?
2L2 (12)
-21.2
The limits in the ratio of the transfornation factor can be principally defined
by replacing the autotransformer circuit of the filter (Fig.7) by a transformer cir-
cuit (Fig.8); we then have
-1- L2,
L,-- n2 (--1--;21- L2)1
1 +1.1121.2
(13)
(ILO
(15)
Equations .(13) and (1h) show that 11.1> 0 and Lv> 0 for any value of n.
it is not difficult to convert into transformer filters the T-
\
of types liii, 1113, 1114 and IVK. It
By an
analogous method,
shaped and Pi-shaped links and the half-links
can be shown (Bib1.3) that:
a) For links with capacitance transformations
50
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Table B.

b)
4.)
d)a)
F,C7
1 l'i Li 1:1
L, tz R .
1
-9 2 ' 2C.
Weg-g- C2 "0
1
-151I`--11--.0.
ir r. C-I:cr:-/;' 1., irlf2-4) '
o-rtriCrs--11 y
R
0
2C,
1 1724 ,
i 2
rill,
fi
?
C 1
_z__c
-; "2- Lialf-f2 LI '',-4 ifrii ' *1-1f6r,+OR
0. 424 n z
r .11 I.L.f-t1-1 1 . .
rff 2
(fort+ -2- al. n --e. )
2c,
2C,
4
C - --
1 r n
r f2 f
2
-1-12 2C, 1 24
oratP-1 1-43
4 4
n
/4 fiR .
L ' .2- + L2; Cz -2C, ; 11-74(6-6)'
2f i
0---1 i___,
....-
R -??? 112R
r
' t 4
L - nill
+/. 1;
I 0 62+4
(Iv any n)
6
K-
i
c-2shiig?6-)f.
1. 2 2.i n 4rf,'
i
--y--; Cr --r-;
4- --L 4111-0 R
2L:
fi
T2
-
ril Zfo2
f re - -
3
-1:11 2C, -il 2C,
tan**
?R Cr-.77.%
L C.
y
Li. -,rC
0 1 2
1, R
,z+ .-1
fl V 1
1-P-1
Li- 2 . K---T-- c..-
'
Az
2C,
211
fi - f
1 o
C1.1 In 1.8
( for ally n)
Lel., CI-2C,, G-7,-
L, 1
L6-112 (1-2 -allf--IFF
13
r A' x
1 I
2f z
f -f\i-T,27.-
1 ? fi f2
i
/ o i',2 . ft
f -f
a 0
T 111 m
c, , I: 6,
oon-0-0
,0
' 7)5(ft ' , T(4 on R
1 - -1 +L; C -2C1 ,
-17 2 2 i
a; 1
Le-a2L2' C1.72-?1(-ff
0
1.4 1.8
( jor Any n.)
L -1 2bz
- -1 a2 C,
X 2 ' t r nz ,
1
ry "1/ II- 2Tiz
1
1 Irri ft.)
0?".- fi)A1
f- r I X
. ? 1;412
f
I 2 0
r ET x
L2 CI Cc8
cw-crtrnitro?..tr
R -... fd?i(fi III`
C, L,
tratp-0
fr
?
L,
LI- .; CI-21;
i-
111 z ez C 1
LI, Cr 1
1
L-:1-,C--,C-2 T---
z 2
t 24i
i fiz+ f22
11.C. r
0
r-c,V
1

41 ft t fz-
20
f -IL1
I i f } r?
I 2
1' ? f
r 0
Oor n .?-.- ---.1
2c,
r.
L1i -L2' C' -'- '
I I n
1
2 47T 1472
T1YH
, C1
orms-ii-ri
R-.- )1?C
ft*
48 Ca 1
( I n' R
T f,
._7(:7_7 i c _CZ
' 2C,
1,,2 C2 C
1 f,_ _2 r.
0
Cz-r 1.1:
(for 7 !--; ; I .2,- )
a 7 7
L. 1,- Lza
L 4 re Li
0,1541 L,- 2C,
7 L,-F ,, ?
p-..- 6) c ....._.,7 a - c. .
r firm
%
c,--
rfo fr)
i
1 __
1 r(f2:6-)R
Lit 11 L, . n- I
Cr
cii*rts i I". ' r"Cz+24 a
gill-ni
(for a1- . o- 7r, CI- az t 1
r.... -;11:.- ) Lu-1.2Cc
2t,
f 1 '
zir
\1---,i1-z
i r /1 +/-2
1
-foil 11:_
a
r IY m
L, L C., L n-1
- 2C, --ir
1 ' , Cf - nig
1 2 2C, 2C1
Ca- , c, 7
F " 7
L C-1, ci+crr C, 2c,(i ")
''L
i'lk..f; T CdC4 3f
CI; ;7-2 4 -712-
11-L2/12,
( fora E i 4 f"c-;-.. . )
51
???????
a)
+3
0
5-1
fit
Cd
c) Computed values for the
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?
a)
CI
9
+1?-1Vn
2/.2
----a--
W?1?---
' 212
-
1114
66
L
21 r C2
2
Wo:/7 2L
--17-1V
T1113
- ao?
F, &
'TT?,
c
vt- -9
.
2Lz 21.
3
IF
(
6 4'
.
TivN
5
T IV If
r WI(
b)
I 1LZ
u*rit. Cd T n-P
o
14-15";
kr.;)ii
27.'s
R
' I
( for any n)
o
K r
1
0 t ,
3(6',LT
( for any a)
C,
? -1--
c;
_a
Table 2
c)
d)
c, ...1c,+ ?
2 ' Off,f11,"
2L,.; kl-ft)C,ft_d _ Ft
Co- ?711-
I 11 7
C,
C, f n ,
ft"
2F2
6-4/7
- F
?-?11-1,
y f; 4 tz.--
A
R
'-1 ji (f; 4 0
1.?-21.2-14; c7 ,
L, c---a-
La-h2La : L -I-' If--)
C2 2 4)14
t.2 I g-OR
L, 2L2;
?
1r
Ls-it(2,4-71.2);C,
L11-2L112; K
? C2
uff--j17-2
rfr
( for ? 1 4..,)
C 17
I 2L I Z
-- II-i{(1-n)C, I
I
1s
/I . t.'7
L3
c,
rto - -F,
F0-11-67;
(6-41R
4iff,2
4-i-C27?
F F
o
212.
F V " 7 -2
r
F.- F.
C 1
2 271fr ft)'?
F
o
2Po2
F-r
I 0 F 4 F
F-
o Fi2 4 k,
? FO
52
elements; d) Natural frequencies of the link circuits;
e) For any n
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2
a)
EL
Table 3
h)
1.1 CPQ
0-r1SITLri.
3
4
12R
Cl; Tcicii
(for n c14-Ct)
( for any ti)
3
n2,0
4
c)
2C,
1.1- 2', r 77-; r(f2-1,*)
6-6
C,=2C1-V ; C,- or ff
czi.
/112 kt-nycl+ yi,L2 xpf;
VI 4 L2
w
c, 44. LFCTF-te?fi )'; ro
3
T.LE'm
2
3
112R
4
(-4 -+C1411-4
(for n
' 4C,
R.
C,
L,
( for arty
? n
2C,
=ELE ;
2r 2; +6
; 41(42 411,1 R
=6-1.+1-L 2C,;
2
fo-ff
1
La'2L2; K= iff+ .111 412')
Y 4L2 c
(f2-1;2 0P c = 1
2 7(6- ft )R
47T
5
T11K
3
-n2R
4
1
= z
+2L ; K-
n 2
v
n22L2, C1=2C,
C,T= -2CL112
2
1. K
epa LI 3
CCI fle...fLI
rI
?o 4
'for1+ -4ri?;)
2C
rIi
L11-2L2 n2 ;
(: =
112
11-1 2r;
(..1=
53
Lr.11(?)
L -
2 4ir fo
6-6
4iffo2R
1
n(firrY
the transformer band T-shaped
b)
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1 < nlim < 1 ? ?
2C '
(16)
b) For half-links, the values of num coincide with the corresponding eqs.(12)
and (16) under the condition of changing 212 to 412 and 2C1 to 4C1.
The revisions of the computing formulas for more important types of links and
half-links are cited in Tables 1, 2, and 3. For controlling the computed results,
)31
V
V
Fig.9
La
a) Half-link of the prototypes; b) Links
of the prototypes; c) Half-link of the
prototype IVK; d) Link of the prototype
IVK
Fig.10
the values of the characteristic-frequencies of the individual circuits of the fil-
ter are listed there.
After substituting into the expressions for num, the values Li, 121 Cl, and C2
determine the limiting frequencies fl and f2 and the load resistance R = Wo. From
this it is clear that a dependence exists between num and the pass band of the fil-
ter. These dependences, found by us for the considered types of links and half-
links, are listed in Table 4 and in Fig.9.
Above it was mentioned that the transformer circuit of the filter, in principle,
54 STAT
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can be completed with an transformation factor n. However, in reality the attain-
able value of n is determined by the possibility of obtaining a physical result from
the computed values of the inductances, capacitances, and coupling factor K. The
magnitude of K is determined by the ratio of the inductances Ll and 12 which, in
turn, can be expressed by the cutoff frequency (cf Table 1 - 3).
Substituting the above expressions for Li and 12 in the formula for K, we ob-
tain the relationship establishing, for links and half-links, the following depend-
ence (Fig.10) between the permissible pass bands (cutoff frequencies fi and f2) and
the given coupling factor K.
a) Transformer half-link and link of type III:
000
== f
o =
1
)/I -
3 = /- 1 K
11 V -17-7,7
b) Transformer half-link and link of type IVk
2 -- I( V i -
p;;.?..
1
)
K -
pivg
(17)
(18)
(19)
(20)
An analysis of the obtained dependences permits the following deductions:
1. The theoretical limiting coefficients of full transformation are determined
1'0
the limiting frequencies (i = ----, i.e., by the pass band of the filter.
fl
2. The link of any t:,-pe filter permits a significantly larger transformation of
the resistances than a half-link.
3. The filter II. has the greatest efficiency for converting impedances.
TK g The
Q03
gain in the transformation factor, guaranteed by a filter of this type in comparison
with filters of other types, is characterized by the curves in Fig.9.
4. During an uninterrupted increase of the pass band, the transforming charac-
teristics of all the filters are gradually flattened. Here it should be mentioned
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that the transformer developed by V.D.Kuznetsov for changing from 'a four-wire feeder
to a coaxial cable (Bibl.h) can be considered as a particular solution of the above-
a)
e)
f)
b)
a) n
co I
(0-
h) n< 1
noItr.)
m -I- 1
12
ft
a) n 1
(H) .
Urn(-1)2
b) n 1
? 1/2
I'm ___ co + 1
^
Table 4.
c)
-j- I
lini .4 I
?
- d)
n
lini
"Inn
n i? 1
b) n < 1 b) n
111 ?1
thn
+ 1
n
h) n ? 1
tS" ?1
n h?rn ':-.? '
1.
I1t1
? I
ni K.)
5 - I
ilm
+
n Lim
12
n I
n ?rn
n ? ? 1)
"
b) n
t
rt Iht
. 57 (;), I)
" IM I
= A
f
6
a) Form of the link; b) n(k) is the limiting transformation factor in the Si4er of
lim
ozoo
type IVK; c) n ? is the limiting transformation factor in the filters of types
1111, 1112, 1113, and 1114; d) 41r)11 is the relative efficiency of the filter of
:type IVK; e) Complete link;. f.) Half-link
explained general problem of the designing transformer filters (in Table 2 this
56
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transformer is listed as No.3).
3. Certain Features in the Designing of Transformer Filters in the 0.15 - 100 Mega-
c-cle Band. and Experimental Data
As demonstrated above,
possess maximum efficiency,
(Tables 1 and 2, Nos.2 - 4)
sistances on any band.
In practice, however,
the coils, the actual pass
termination of the coupling
transformers
whose prototypes are links of type IVK,
of transformers with a magnetic coupling
permit any desired transformation of the re-
so that types
in principle
as
a result of the imperfect magnetic coupling between
band has
factor should precede the designing of transformers
a critical value. Therefore, an experimental de-
for
a given case.
It is possible to list the following coupling factors reached in practice.
long-wave and 'medium-wave bands (0.15 - 1.6 mc), high coupling factors
iron cores with an initial magnetic permeability of 11 = 300
band (6 - 20 mc), the use of carbon or iron
(90 -
In
are obtained by using
to 500 gauss/oersted. In the short-wave
cores with 400 gauss/Oe
and of
factors of the order of 75 -
limiting coupling factors have a magnitude of the order of 50:.
eIr.nowin- '"e actual nagnitude of the coupling faeiior, the permissible pass band
? s
0
(7ig.10) can be determined from eq.(17) - (20). If the restriction as to pps band
8 ?
is less severe, filters with capacitance transformations should be uset In this
.
??
Line-wire windings guarantees obtaining coupling
In the ultrashort-wave band (48 - 100 mc), the
case, using the curve in Fig.91 the magnitude of the transformation coefficient of
?
one link n for the given pass banfl p - - can be obtained. After this, it is not
r,
'lifficult to deternine the number of Unix, necessary for obtaining the desired co-
efficient of transformation. Je may remark that a filter with capacitance transfor-
simpler in design. Therefore, in
desirable.
in the input
mation, despite a greater number of elements, is
cases where economic considerations can be ignored, its use is more
Intense interest is exhibited in the use of transformer filters
?
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circuits or in the terminal stages of vacuum-tube amplifiers and receivers. In this
case the critical value of the transformation of the resistances, as a rule, is de-
termined by either the input or output ca-
g
r, 2 pacitance. We will discuss certain prac-
tical considerations for choosing the cut-
-
C.
krnall
tO I
a
U.1
1.1A1
11,1. I
)1.2 1
L.A) b)
al 0/5 C2 71,b 4'11:d *c:p.
f, mc
Fig.11
a) Long-wave and medium-wave band;
b) Short-wave band
41)
WI
0,6
0.4
a)
4tkedb
I
?
-- I- :_s_ _L
40 50 611 70 d0 91)
!
100 mc
Fig. J._2 'a
a) Ultrashort-wave transformer,
75,- 25 ohms (n = 3)
off frequencies and of the Q,-factor of the
filter coils.
The irregularity of the transformer
frequency characteristic in the limiting
pass bands is determined by the values
chosen for the cutoff frequencies f1 and f2
and f2. Experience shows that irregulari-
ties in the frequency characteristics ?-1 db
and +3 db are guaranteed at values of the
cutoff frequencies fi and f2 exceeding the
pass band limiting frequencies by ? 20%
and ?10, re?pectively. At Q-factors of
of Q 50 and at a pass band
0.15 with damping, caused by ac-
the coils
AF
of ----
fo
tive losses in
the transformer sections,
it can be disregarded.
?
To confirm the possibility of using
0
the obtained relationships we will cite
some experimental data. Figure ha gives
the schematic of an all-wave radio broad
casting transformer. The diagram includes a.ferrite transformer (2) with ?0 =
= 400 gauss/Oe for operation on long and medium-wave bands (0.15 - 1.6 mc) and a
band transformer filter (1) (denoted by No.7 in Table 1) for the short-wave band
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Cita!, o
(6 - 15 mc). In the long and medium-wave band, the ferrite transformer differs lit-
tle from the ideal transformer (coupling factor K = 98, assigned capacitance of the
coils 3 - /0-112). ['hanks to this, the replacement of a cbmplicated transformer cir-
cuit by a simple ferrite transformer is permissible. As can be seen from the curves
of Figalb, the irregularity of the frequency characteristics in a given band does
frequency characteristics, obtained for
not exceed ?0.6 db.
The analogous
ultrashort-wave transformers (75 - 25 ohms, n = 3) are cited in Fig.12.
Eot citing the characteristics, we point out that, with the help of analogous
0
transforming filterspin the input stage of each channel, amplificationscpere obtained
0
equal to lh db on an 8-megacyale ban. In all cases, the practical frequency charac-
teristics obtained were of the plane type.
Conclusiori
00? 0?00) 0
On the basis of the cited theoretical and experimental material, the following
deductiAns can be made. Tne'n-adered method of designing band filters overcomes,
to a significant degree, the shortcomings caused by the Emperfections of high-
60
?
circuits (significant inductance diffusion in the inductively connected
frevency
circuits, distriNted capacitances
ence o2 other parasitic elements
of TT transformers on a given Pass band of frequencies,
0
of the coils,
induptance of the wiring, and pres-
%
in the high-frequency c0
ircuits), and permits the
0
construction
gliters similar to those of ideal transformers.
eito!p-4;:ito
which have pa-
Article received by the "Alitors 19 1:e4,- 195)1.
?
BIPLICC2AP?:
1. Kalikhman,S.Cr. - An A11-2:ave Antenna Systen for the Collective Reception of
2adio Broadcast Programs of Ultrashortave Broadcasting and Television.
Paper read before the Session of JEOP and E imeni A.S.Popov, June (1950
2. Shi,T.:e. - -luadripoles and electric filters. ST-azizdat (1930
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orb
???
3. KalikhmanIS.G. - The Transformation of Impedance's in the Wide-Frecilency Band.
Report IRPA. Issue II. Lenizdat (1954)
J. AysenbergIG.Z. - Antennas for the National Radio Link Svyazizdat (1948)
?
?
?
?
?
? 0
?
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used:
CALCULATIOII OF A7 ICI= VOLTAGE STABILIZER
by
G.S.Veksler
Active I.:ember of the Society
The calculation of a stabilizer is presented in which the following
factors are inter-related: integral stabilization factor of the hookup;
stabilivolt, its rated current; input voltage,
the stabilizer. The value of the possible maximum
stabilization factors for each of the stabilivolts
firing voltage of the
and the efficiency of
and minimum integral
is established.
1. In designing an ionic stabilizer (Fig.1), the following denotations are
U2n is the rated voltage at the load resistance; +e, -f are the deviations of
the voltage U2 from U2n in :;; I2n is the rated load current; 4-c, -d are the devia-
tions of the current 12 from 12n in :.:; +a, -b are the deviations of the voltage U1
?? ?.
at the input from the rated voltage Uln in i; n is the efficiency of tl,esostabilizing
0??
for the input volt-
device (often not given); Ku is the integral stabilization factor
age, defined as
a b
Ku= .
e f
Besides this, the parameters of the stabilivolt are given: Uz is the firing
voltage; Ie min perm. Ic max are the minimum and maximum permissible currents
through the stabilivolt; Ri is the internal (dynamic) resistance,
in the stabilization band.
As a result of this calculation it is necessary to determine:
f tle additional resistance r, which would
oftheinputvoltagelJ'and the value o
1
taken as constant
the rated value
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guarantee
also at mi
integral
the firing of the stabilivolt at minimum input voltage Uhl (1 - and
100
*nimum load resistance R(1 - which mould permit obtaining the wanted
100
stabilization factor Ku with the given efficiency n while preventing an
output beyond the permissible current limits through the stabilivolt.
The published calculations of ionic stabilizers (Bib1.11 2, 3, and 4) cannot be
considered
acceptable, since in these papers (Bib1.1, 2, and 4) the defined quanti-
ties are not correlated with the voltage
for firing the stabilivolt, while in other
papers (Bib1.1 and 4) changes in the loado
are not considered, and in some papers
(Bib1.3 and 4) the permissible oscilla-
tions f the output voltage are not taken
Fig.1
Below, a method for calculating a
shortcomings is described, correlating
its efficiency, and excluding the recalculations required by other methods of com-
puting.
2. From the condition for obtaining the
input voltage and load resistance, we have
into account.
voltage stabilizer, free of the indicated
stabilizer integral stabilization factor and
Let the
ation of the
rent through
Then,
r
124 (1 + ioo
c
firing of the
U111(1? 100)
U,
stabilivolt at minimum
(1)
deviation of the input voltage 1 U1 from the rated value produce a devi-
output voltage AU2 from the rated value, and during this time the cur-
the stabilivolt changes its value by Al from the rated value.
(2)
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Since
then, substituting eq.(3) in eq.(2), we get
U1=---1/e(1 L41-? ----)r.
R
?
0
(3)
Taking I'd RIO U I
-- (1.7b
[I'm" err"? 12m (r 1+:
From eos.(17a) and (17b) we determine the limiting (though in practice unattain-
able) integral stabilization factors of the stabilivolt in hookup:
30
20
10
--. -,
-......2,
-,
5
_
0
10
Fig.5
KUtriAz 2
b-0
u,? (1 --lb-1)
U3
Ri ? IC,":? pfrft, ( la )
U2?( U
i - u")
Kn = ,
m;r1 11.m j ? 1 c
MAK perm
/10 - O.
(19)
Table 2 contains the values of the
limiting integral stabilization factors
for certain t:Tes of stabilivolts. The
possible values of Ku depend on 12n, and.
b, c and d should lie between Kur?colim and Knmin lim.
Co ?'-o
For orientation in the selection of a permissible value for K the plotted
-u,
0
? values in Fig.5 Ku
0 .
max
(b), line 1, and Kin (bIrl), at a = 55, c = d = 105, lines L.
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I
and 5, are common for CG-1P, CG-3C, and CG-4C in the working band of the currents
5 - 30 ma. Line (1) denotes Kur,?2 for any currents; line (2) is the Kumaxl for
= 20 na (from the condition guaranteeing firing); line (3) is the Kunp,c1 for
I2n
I2n = 50 ma; line (k) is the Kunin for Ion = 50 ma; and line (5) is the Ku . for
I2n = 20 ma. The region of possible Ku; at Ion = 50 ma, is deleted.
If for, finding Ku according to eq. (17a) it is possible to use as.5 for any
-'-
values of I2 a, _, L... Id,
then the values of I' determined from Fig. 5, are
r7, c and "umin'
correct at least for the quantities Ion, a, c, and d, indicated on the graph. In
Other cases, :u,in is determined from en. (17b).
5. The proposed Ku should be smaller than I "
L.,
"ma2 obtained from eq. (17a); in ad-
dition, the propose KuI2n should be smaller than (NuIon)mx:, deternined from
eo.(11). Katurall:, the Ku with the proposed Ion should at he same time satisfy
both inequalities (11) and (17a). For the same Values of I2n, from eq.(11) K
uma:a
will be the it; for others, it will be 7
-una:c2 from eq. (17a).
In Fig.5, Ku(b) is plotted for I2n = 20 ma (line 2) an for I2n = 50 na(line 3).
Thus it follows from Fig. 5, for I2n = 20 nal that Ku will be defined b-., Kuricx2 from
eq. (17a), i.e., line 1, while for Ion = 50 ma, the value of Ku will be defined by.
Yur,22,?1 from en.(11), i.e., line 3. The permissible magnitudes of Ku should lie in
the region bordered by Kunin and by the smallest values of Kumax.
'lased on the above statements, the calculation of a stabilizer should begin by
cheching whether it conforms to the inequality (11). Then, the value Kur,,i, for
'or an esti-
the given I2n, is obtained from eq.(11). Using en.(17a), find Kumax.,.
mate, take the smaller of these two K1
Ina:c .
If Ku > Kuraa:c of the fact that firing is not guaranteed (11) or because of the
???.
fact that Icrin 4 ICTrin lin- (17a), then it is impossible to design the wanted
stabilizer.
?
If Ku ? Kunin (Icnax /cmax then it is possible to construct the stabi-
lizer, if the proposed magnitude of Ku is obtained, considering for this that Ku =
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=? *
Alitin ?
of el f and Imaxc
With this specification, Ku can be approached to a definite magnitude n, and the
calculation can be completed.
0
The suggested method frees the designer from recalculations, which are frequent-
ly necessary at the end of the calculation, due to incompleteness of one of the in-
equalities, (16a) or (16b)**.
6. Approximate calculation of a stabilizer.
Given U2n = 150 B, I2n = 20 nal a = 5, b = 155, c = d = 105, e = f = 15, from
At constant values for a and b, this leads to a decrease in the values
this:
K.=
e+1
a ? b
?10 awl KI2,, = 0,2.
his is correlated with the increase in n, Uln, and the decrease in Yn (cf.Figs.2,
3, Q, with which it must be reconciled, or else it is impossible to complete the
projected assignment.
**If Ku.?eisdetermined from eq.(17a), and not from eq.(11), then I2nn,x can be
found from eqs.(17a) and (17b), by which stabilization is still possible. In this
regime, Icmin = Icnin lim and Icmax = Icmax lim and the full band currents of the
stabilizer are used.
Having equated the right-hand sides of eqs.(17a) and (17b), we get
12K 7,
0
1
[
b \ i r t..d_ 1 ic mArperm
luti) WO ]
a U21, b
? ?
lut) U luO
- Ic + ?
min pitfrl ajm
(20)
In Fig.5, this extremely rare state is determined by the intersection of the
line Ku min for I2nmax and line 1.
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It is necessary to determine: U ln, r, Icmin' Icmax' Icn, nn-
Calculation Sequence
1. Select the stabilivolt CG-4C (cf.Table 2). 0 0 0
0
2. From eq.(11) we have (NuI2n)max = 0.59; 0.59 0.2 and the inequality (11) is
satisfied.
3. When I,)n = 20 ma from NuIprinax = 0.59, we get 1Uraaxi = 29.5.
h. From eq. (17a), we have Kura:: = 26.5.
5. We then -take Kumitx = 26.5; 26.5 > 10 so that the inequality (17a) is satisfied.
6. From eq. (17b), we have Kunin = 12.3; 10 4 12.3 sO that inequality (11b) is not
satizfied; consequently, it is necessary to raise Ri,1 to lcu.. . ?
7. ..;e then take Ku = 12.3, and by this obtain NuI2n = 0.2L6< 0.59.
8. From eq.(6), we have n = 2.38.
?
9. From eq.(13)4 Icn
? 10. From eq.(15a), Icmin = 11 ma; 11 ma > 5 ma.
ft...0.0 ?
U. From eq.(15b), Icmax = 30 ma; 30 ma = 30 ma.
12. From eq.(5), Ula = 357 volts. ?
?
13. From eq. (h), r = 4680 ohms.
14. From eq.(9), nn = 0.19.
0 o c-V coo
?
OD
?
CORRECTIOK
From eq.(3) for Ick. = 11 ma and Icmax = 30 ma, we have 6112 = 3.04 volts.
Then, e + f = 2.025; 2-; had been given.
Article received by the Editors 7 January 1955.
DIBLI0G2AP1 Y
- Calculation of a Voltage Stabilizer with Glow Discharge Tubes.
Vestnik Svyazi, issue of Tekhnika Svyazi No. 11 (1949)
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?
2. Efrussi,M. - Gas Voltage Stabilizers. "Radio" No.6. (1951)
3. Goltdreer,I.G. - Voltage Stabilizers. DEI (1952)
4. Donch-Bruyevich,A.M. - The Use of Electron Tubes in Experimental Physics.
GITTL (1954)
?
0
a:* -1-74-0
?
SO ?
?
72
o 0
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A 123T.1:0D FOR IMP:EASING TIIE ACCURACY OF FREQUENCY ANALYZEP.S WITH AN
ELECTRON-33MT INDICATOR
by
0 IT.F.Vollerner
Active 1:ember of the Society
In the article a schematic is examined for raising the accuracy
of a frequency analyzer with an electron-beam indicator, possessing
a higher degree of accuracy as a result of excluding the error of
the frequency scale.
In modern radio engineering, a wide range of different frequency analyzers
exists in addition to various types of spectrometers, panoramic receivers, and
cathode-ray curve tracers, permitting observation on a screen of the spectrum, char-
acteristics, etc. being studied.
The basic elements of such devices are a frequency-modulating (FR) generator -
voltage source with constant amplitude and a frequency varying within a given inter-
val - and an electron-beam tube functioning as an indicator. On the tube screen the
studied characteristics, frequency spectrums, etc. are observed. Block diagrams of
such devices are very well-known (Fig.1).
The accuracy of frequency metering in devices carried out according to such a
block diagram, is primaril7 determined by the stability of the modulating character-
=. (U) ?
istic of the FR generator w
We will consider this question in more
proportional to the instantaneous value
d for determining the instantaneous
detail.
the x-axis,
The deviation of the beam along
of the voltage (current) at the
fre-
amplifier outlet of the channel x,
quency. From the deviation of the
components of the examined voltage
is use
beam along the y-axis, the level of the frequency
can be determined; or else the transmission fac-
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? 0 ?
tor at the given frequency of the examined quadripole.
The input voltage of the amplifier channel xl determining the deviation of the
SS
a)
b)
f
E -dt
Fig.1
a) Sawtooth-voltage generator; b) FH generator; c) Investigated object
?
beam along the x-axis (and consequently also the frequency metering) and appearing
?
at the same time as the modulating voltage of the EH generator, is connected at least
indirecta.y throusl-?4.14e-rnod-Sen...ahaeatthe rntart?ous
frequency. If, for some reason, the modulation characteristic of the Fg generator
changes, significant errors arise during frequency metering in accordance with the
pre-charted scale. This is the main shortcoming of frequency analyzers constructed
b)
Fig.2
?
a) Sawtooth-voltage generator; b) FM generator; c)
d) Frequency discriminator
D.
ed object;
?
according to a block diagram such as that shown in Fig.1, especially when the tubes
in the frequency modulation circuit vary, since the modulation characteristic of .
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the FM generator in this case depends mainly on the form of the tube characteristic,
which changes significantly during operation and varies with changes in the state of
the power supply.
The block diagaaamAn Fig.21 which uses connection in series, is free of the in-
3 0
0 ,
diated shortcomings (Bib1.3). In this hookup, the error of the frequency scale,
caused by a change in the shaTe of the modulating characteristic (a) = W(u), is prac-
tically excluded. The voltage for the deviation along the x,-axis, i.e., the frequen-
cy scale, is taken from the output of the frequency discriminator, so that the
coupling between the instantaneous voltage frequency, created by the FR generator,
0
0
and the instantaneous6voltage (current) in the channel x is of the direct type; this
coupling i determined by the frequency discriminator charae2xistic ud?6N/10J).
--az-nr.----lbrft-Fs'ffacl-Parie-sfoTe'offeritr-araFaTt'eFiWreFf'clitr'iW4ErerSithil
reasonable performance does not depend on the form of the electron tube characteris-
tics, the stability of the discriminator can be significantly higher than'the sta-
bility of the modulation characteristic of the FM generator.
The suggested schematic is also interesting in that, with the proper choice of
the discriminator characteristic, a stable frequency scale of the analyzer with the
necessary degree of accuracy for example, can be obtained, such as an evenly divided
(linear) scale, close to the logarithmic scale, etc.
When designing frequency analyzers in accordance with the block diagram of
Fig.2, it is not necessary to make strict requirements as to the fIlm of the modu-
lating characteristic of the FM generator; it is correct within the limits in which,
due to the change in form (slope) of the modulating characteristic, the rate of
?
change of the freauency, influencing the resolution and other parameters of the an-
alyzer, is not observed to vary (Bib1.1 and 2). The value of this block diagram
lies alsooin the possibility of changing the frequency scale of the device, without
additional errors, by proper selection of the separate sections of the scale for a
detailed analysis, by a change in the mean frequency of the FM generator, or by a
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?
,
decrease in the frequency deviation and an increase of the amplification in the chan-
nel of the frequency axis (correspondingly shortening, if necessary, the analyzing
time). At correctly selected parameters of the spectrometer, this block diagram per-
mits, without additional errors, changing from automatic scanning to manual scanning
by replacing the sawtooth voltage leading to the Fg generator with a constant volt-
age, whose magnitude varies during adjustment of the analyzer to manual scanning
(for example, by the potentiometer).
In designing frequency analyzers according to the block diagram in Fig.2, broad-
band frequency discriminators (with a large 1.where Af is the pass band and f is
Af
the mean frequency) must be used.
Broad-band discriminators can be
f
completed in the same manner as a network with
.=4,101c1;17M4Igar/L.?(32111'4)* F?1"'
circuit must have a law resistance
dett7rerifeTfilritiZra:"Fet'arl.ZaSJZ.
-
obtaining a broad-band frequency discriminator its
and thus also a low equivalent resistance. As a result of this, the transmission
factor of the discriminator drops sharply, and to obtain significant voltages at its
output relatively powerful tubes, with a large current, must be used. One can rough-
ly double the output voltage of the discriminator with strongly coupled circuits, at
given Q-factors of the circuits and the current of the tubes, by connecting the
first circuit of the discriminator in the cathode of the tube. This arrangement (a
circuit with a grounded plate) eliminates the necessity of a special shunting resis-
tance, lowering the Q-factor of the first circuit to the required magnitude.
? Article received by the Editors 7 Jul: 1955
?
BIDLIOGRAPT:
?
1. Deranek,L.A. - Acoustic Yeasul-ements. IL (1952)
2. Kharkevich,A.A. - Spectra and Analysis. GI (1952)
3. - Description of Heterod:ne Spectrometers in the Bands 0.3 - 10 kc, 4 - 100 kc,
and 30 - 500 kc Kiev Political Institute. Faculty for Radio Receiver
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?
Design (1950 ? 1952)
1.. ? Frecluenc:- :lodulation and its Application. ST-azizdat (191,13)
?
?
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?va.r.m-.7" ? as? .==sea.,2*
?
? ?
?
?
0
?
?
77 STAT 0
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??=is ?s0
?
?
THE EFFECT OF CAPACITANCE OF A SPACE CHARGE AND NOMINEARITY OF A TUBE
CHARACTERISTIC ON THE FREQUENCY OF A SEIF-OSCIIIATOR
by
G.T.Shitikov
Active Member of the Society
The causes of the effect of power-supply voltages on the
frequency of a self-oscillator in wide frequency spacing are
examined. It is demonstrated that the capacitance, produced
?
by the space charge of a tube,Declassified in Part - Sanitized Copy Approved for Release 2013/05/22 : CIA-RDP81-01043R002000090003-3
charge of the tube (dynamic capacitance), this problem is not quantitatively inves-
tigated in the technical literature; there is merely an indication of the presence
of such an influence.
Our task is a quantitative evaluation of all destabilizing factors connected
e of the self-oscillator at optimum tube coupling with the circuit
with th operation
("optimum link" is what we call the minimum coupling for obtaining stable self-
oscillations). The problem of decreasing the coupling of a tube with a circuit is
of great significancer?inasmuch as the partial (optimum) coupling of a tube with a
circuit basically permits a decrease in the destabilizing effect of the oscillator
tube as a whole, as estaliEfailf:Fgrev----ca,_?1111.,_ 6 *.
The upper frequency limit, which will be investigated here, are frequencia'bTL-v==
the order of tens of megacycles. One can consider that up to these frequencies the
effect produced by the electron transit time of the tube, is negligible. The depen-
dence of the frequency of the oscillator on its operating state when the transit
time of the electrons between the electrodes of the tube is commensurable with the
period of oscillation, demands special investigation.
Cumeasere
Since we are primarily concerned with finding ways of increasing the frequency
stabilit7 of the self-oscillator rather than with determining the amount of frequen-
cy instability of unstable self-oscillators, the general prerequite for the ini-
tial operating conditions of the oscillator is its operation in the left-hand segment
*In the paper (Bib1.6), published in the magazine "IEST" No.12 for 1940, I made the
deduction "...the stability of an oscillator during changes in the tube parameters
and its operating ,conditions does not depend on the?L/C ratio of the oscillatory.cir-
cuit". Clapp, in his historic survey "Frequency-Stable L,C Oscillators", published
in PI? E (August 195h) writes: "Vackar (19h9), Gouriet (1950), and Edson (1953) es-
tablished that, while working in a linear sl,ate, the stability does not depend on
the ratio of L to C". In this way, we have an? almost complete coincidence in deduc -
0
ns however, my deductions were made 9 to years earlier.
?
79,
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CZ*
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of the tube characteristic. This practically prevents one of the most important de-
stabilizing factors - the influence of grid currents.
The practical realization of such an operating state of the oscillator encoun-
ters no serious difficulties.
citance on the Oscillation Fre
2. Effect of Dvnamic Ca
For studying the effect of dynamic capacitance on the frequency of an oscilla-
tor, it is primarily necessary to know the magnitude of this capacitance and its
correlation with other characteristics of the tube. Research shows that this capac-
itance, for each type of tube and for each given tube, is determined just like any
? ..... .Dthere. parameter of the tube. As far as the nature of its dependence on the operat-
ing state of the tube,is cO-1166Ffiell;-,1t-most,_qpsoly resembles the transconductance
_J_. _w
...
? ... .....,....._ _
of the characteristic; this is due to the transconductance of the characTUTTM.--,..,
which, in turn, is closely related to the presence of a space charge.
In Figs.1, 2 and 3 are plotted the interdependence of the transconductance of
e 4 =so
S.
4
encv of an Oscillator
CP
0,5
2I1127L
? ? ? 14-14,-9,1v
coo
Ua.- U:6C,
/ '
Fig.1
the characteristic and the dynamic capacitance with various voltages on the first
grid for certain modern pentodes, including the equivalent triode. As is seen from
the graphs, these dependences are close to linear; however, their slope is essen-
Cd,"4
Oka
? ? ? U?r gr114v
45
Fig.2
45
2 P 2 9 I-
? ? 1/x? 'Sy
?O. 11,-11, "46
Fig.3
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tia.117 different for various plate voltages, by which the transconductance of the
slope increases on lowering the plate voltage. This means that, on lowering the
voltage, the transconductance of the characteristic decreases faster than the magni-
tude of the dynamic capacitance.
:ath a change in the filament voltage (Fig. 4) within the limits permissible for
normal operation of the tube, the slope of the characteristics of the interdepen-
dence of the dynamic capacitance and the transconductance changes less, and then to
the opposite side, i.e., with a lowering of the filament voltage, the magnitude of
the dynamic capacitance declines more rapidly.
e400 ?
Under actual operating conditions of the tube generator (working with plate-
current cutoff) the alternating voltage on the grid significantly overlaps the lin- ?
?
ear part of the tube characteristic, so that this voltage reacts on the nonlinear
capacitive reactance of the tube. If the grid voltage is considered sinusoidal (it
will be shown below tha',.:iiri5Fffeti?t-ual..-Inis,alway3 close to sinusoidal),
? then the current, flovring across the nonlinear capacitive reactance, can be expanded
into a Fourier series and, after separating the first harmonic of this current, the
?
This
mean magnitude of the dynamic capacitance can be determined for the period.
?
capacitance (designated belay as active dynamic capacitance) will be connected by a
given transmission factor to the fundamental capacitance of?ithe oscillator circuit,
since ever:- other interelectrode capacitance of the tube is connected to it. The
? *only difference is that, in practice, the statistical interelectrode capacitances do
not depend on the magnitude 4 the power-supply voltages, while the active value of
?
the dynamic capacitance does.
:ere the main point of the
?
the frequency of the oscillator is due to the dynamic
Oi
mechanism of the paver supply voltage influence on
capacitance of the tube.
We will assume at first that
will next discuss this problem quantitati
the dynamic capacitance increases during a change
than continuously, immediately attaining its maximum value.
veL.
in the grid voltage in jumps rather
tification for
The jus
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1=060
such an assumption is that the entire existing system of calculating tube generators
according to the broken-line characteristics is based on this, considering that the
transconductance of the characteristic is either equal to zero or has a completely
determined constant value. Then, based on the dependence between the current and
the voltage under a capacitive load, We Get
coCdU,? sin w t, (1)
?
0 QM* 0
6 Ow
WO ?
Fig.4
where ed is the dynamic
(in the beginning it is
constant value when the
capacitance of the tube
assumed that it has a
grid voltage is equal to
or greater than the cutoff voltage and that it is
equal to zero when the grid voltage is equal to
? .
or less than the cutoff voltage; Uck denotes the.
?
. C3,1:00?5=3 .:==l1C) C=
amplitude value of the grid voltage.
If we designate b7 G that half of the period during which the capacitive cur-
rent is flowing, then the maximum value of this current, based on eq. (1), is equal
to
? (0CdU ? sin 43
(2)
(at values of 0 90? the magnitude of the current imwill be highest when wt = 90?;
however this does not change the final results).
From eqs.(1) and (2) we find
till sin Oh
(3)
After an expansion into series, we find the amplitude of the first harmonic
i stir
i =-- 0 t dt
cin S
- a
8')
it sin 04
iw
(H sin N cosel
?
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or, after corresponding substitutions, we conclusively get the magnitude of the ca-
pacitive susceptance for the first harmonic of the current:
, 0 - sin A ces0
gc=m8 urc.
The magnitude .) where is the reductnio
1
from the theory of transmitters, is equal to the
0 - sin 0 cos 0
-0
ne. is well knovn
mum transconductance o4' the characteristic for the period to the
ance.
omplet1ng the substitu'ion, we get
(5)
factor which,
ratio of the maxi-
mean transconduct-
? wCd
0? . -
krz
(Woe 4.4206.0. cz.=taran... CV CVCP73 Crg ? -
In this wly, the ragnitude of the ac:t ive dynamic capacitance can be presented
?
?
as
7ouation (6)
Cd
a
tic
Jr
completel7-
As an
?
Cd
C der ?
a
? (6)
8
shows that, at a linear dependence between the transconductance
of the characteristic and the
namic capacitance, the active val-
? ..
of the dynamic capacitance has
7ig.5
ue
the same dependence on its maximum
value as the mean transconductance.
Although these deductions are made
examination of
on the basis of an
idealized characteristics of the
transconductanse and the dynamic
capacitance, nonetheless they are
?
correct for the actual characteristics of the tube.
illustration of the explanation, Fig:5 gives the characteristics of the
STAT
00 0
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40,
40
current ic, flowing through the dynamic capacitance with its actual (solid line) and
idealized (broken line) characteristic, in the case of operation of the generator
with a cutoff of 8 = 900 (according to the idealized characteristic). In the same
graph, the plate current ia of the tube for the idealized and the actual characteris-
tics is plotted.
?
If the dependence between S and Cd is not
identity of
capacitance
acteristic.
linear, there will not be a complete
the coefficients ai for the dynamic
and the transconductance of the char-
However, for the majority of modern
-
disregarded. For example, for the dependence
Fig.6
plotted in Fig.3 (an unfavorable case), the dis-
crepancy of ai for Cd and S does not exceed 105.
:le will next discuss a study of actual schematics of tube generators with self-
excitation. For any circuit of a triode generator (generalized schematic shown in
Fig.6) during its steady state, there should exist equality between the negative re-
sistance of the tube and the positive resistance of the circuit in the plate-cathode
section
= z,, .
s-*.
?
where S is the transconductance of the tube characteristic; P is the internal resis-
tance of the tube; c is the ratio of the voltage between the cathode and the anode
to the voltage of the grid-cathode, i.e.,
L.
"
a--,"
'dr?!
z ZOk(ZI A' .1-
Zem + ZaK
?
Jhen the generated frequency is close to the frequency of the oscillatory cir-
S TAT
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S
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'cuit, we can write
Zor p:N R.,
(io)
where R0 is the complete resistance of the oscillatory circuit during resonance,
PTR.:where U0 is the voltage in the entire circuit.
?.. 1,0
..We will designate
?
(a)
where Uac is the voltage between the grid and plate of the tube.
We will denote by p the coupling factor of the tube with the circuit. Then, on
the basis of eqs.(75778-irM773.Titr-t11-47.43.2242,12-...tato.acount that Uc = Ucl
Uak, we get
?
Since, during resonance, we have
(.1 1)t 1/
(a2)
Ro =
w co'
(13)
where Q is the Q-factor of the circuit and Co is the total cacacitancei4 the oscil-
latory circuit, then
(1 ? r.)2 a; Cn
a
(10
Equation ()0 characterizes the dependence of the coupling factor p of the tube
with the circuit on the parameters of the circuit, the tube, and its operating state.
Based on this expression, it is possible to calculate the magnitude inserted into
the capacitance circuit from any interelectrode capacitance and the extent of its
effect on the generator frequency. The magnitude of the insertion into the circuit
of Ale capacitance from the interelectrode grid-cathode capacitance is determined,
85
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ea
=LexSa
with sufficient accuracy, by the expression
?
P2
A Ccle + CK .
or
Furthermore, using the simple correlation
A I A Co,
2c0
(15)
(16)
=14 .
(where f is the fundamental frequency and Af is the change in frequency) and using
eqs.(1h) and (15), the magnitude of the frequency correction for the interelectrode
can be obtained:
At.--
1 \
a Q (S ?
However, in the given case we are interested in tilt effect of the dynamic capac-
itance of the tube on the genera-
tor frequency.* It was established
above that the dependence of the
, kilital;
0 -
.
- active value of this capacitance
? 40 -
on the operating conditions is de-
termined by eq.(6), under the con-
Fig.7
dition that a sinusoidal voltage
is supplied to the grid of the tube. We will now examine to what degree this condi-
tion is satisfied in actual networks of tube generators having partial coupling of
the tube with the circuit. For the analysis, we will take the two mopt characteris-
? ?
tic schematics of the triode generator - the hookup with capacitive coupling and the
hookup with inductive coupling shown respectively in Figs.7a and 7b. In these hook-
ups, the dynamic capacitances are indicated by the circular broken lines. Applying
eq. (1) for the fundamental frequency and higher harmonics to the grid circuit of
86
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these hookups, and using eqs,(10, (15) and (16), we find: for the hookup with ca-
pacitive coupling
n-00
n-00 ?
Cd V. PCd in
Csai 4-1 In (I + G) Co al/In
n-2
for the hookup with inductive coupling
n-00
tin
=_? ? Ped I
rt,
(1 + a) Coal n-2 it
(18)
(18a)
?
where Un is the voltage in the grid circuit from the nth harmonic of the current
flowing through the nonlinear (dynamic) capacitance: n is tfie number of the harmonic;
In is the current of 1th%first harmonic; C2 is
the general capacitance of the grid-cathode section of the tube.
It is not difficult to see that, at normal operation of the generator, and at a
sufficiently high -2-factor of the circuit, the left-hand side of eqs.(18) and (18a)
??
does not exceed 1;-;. Such a numerical order can be obtained in any other hookup of
a triode generator with partial coupling of the tube to the circuit.
This proves the reliabilit- of the magnitude of the active t-narni.c capacitance
determined from eq.(6). Then, substituting in eq.(17) the value of Cdoe from eq.(6)
for CeR, we get
lcd
0Q(S
Eouation (19) is used for determining the frequency correction due to the dynam-
ic capacitance; it is deduced on the basis of the general theory of triode genera-
tors and is therefore applicaqe to any form of hookup with partial coupling of the
tube to he circuit and with operating conditions of the generator close to normal.
Using Eq.(19), knowing the values of the quantities entering into this formula,
and having determined the dependence S, Cd, and Tj of the given tube on the applied
(19)
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voltages (according to statistical characteristics), one can easily calculate the
change in the generator frequency during a change in the power-supply voltages.
Inasmuch as, during a decrease in the plate voltage, the transconductance of the
characteristic decreases faster than the dynamic capacitance, while this decrease is
slower during a drop in the filament voltage, then [in agreement with eq.(19)] a low-
ering of the plate voltage will lead to a lowering of the frequency, while a lower-
('
ing of the filament voltage will result in an increase in frequency. ?
3. Influence of the Hi her Harmonics on the Generator Frequency at 0
of the Tube with the Circuit
? ?
timum Cou linF
?
For the generalized hookup of a tapped-coil oscillator (Fig.6), based on the
aa
aa,
cqp moo ? waft
condition that balance of the phases is present, the following expression is valid
(Dib1.7, 8):
Za. (Z,, 4 Z2,). ( 4, + 1 ) =
Z,,, + Zac + Zatc?Z(K+ Zac 11 i
,
1
1
n ? co
n
-
z"m d_
ZORM (Zexn 4. ;111 (....._______
Z, An ? Z ,cn 4- ZaAn ZcA78-1- Zorn
1 )
EL
ta. \t
(20)
( lot 1 '
where 'al is the component of the first harmonic of the plate current;
?
Ian is the component of the nth harmonic of the plate current;
is the amplification factor of the tube;
7
-ah) -ch) .ac are the impedances of the corresponding sections of the hookup
?
2,akn) -ckn) -acn
The discussion below is applicable to actual circuits of generators. We will
pa: special attention to the tapped-capacitor network, which offers the possibility
of obtaining the best indexes for frequenc: stabilit: and for simplicity in struc-
tural solutions. In its most general outline, this schematic is shown in Fig.; as
indicated below?Qyer: other network of a tapped-capacitor oscillator (Colpitts
for the fundamental frequency;
are the same for the nth harmonic.
88
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?
osci a or is a special case of this schematic. The necessity of inserting the ca-
pacitance 0i, into the circuit is due to the fact that, at sufficiently small values
of the capacitances 02 and C3, the capacitance C4
(i.e., the plate-grid capacitance of the tube)
may greatly affect the final results. ie will
assume that the active resistance of the circuit
is concentrated in the inductance (that it does
not have aonoticeable limit, since the Q-factor
? ?
of modern capacitors is many times larger than
Fig.8
the Q-factor of the inductance coils. Then, after certain transformations of
eq. (20), we get for the imaginary
?
ra2,--?-60-Ege.f?fg?,t) ?-.7?Eari_ _x [r 2+ XOR XCKR(11 +
x2
XaK x12n r)7) 2
0 r ac
xnn x?,) ( \ I
k at )
(21)
where 'ac is the active resistance of the entire circuit for the
fundamental freouency;
rn is the same for the corresponding number of the har-
monic;
Irak/ xac, xck are the reactances of the corresponding chain circuits
for the fundamental frequency;
0
7''-acn, :::ckn are the same for the nth harmonic;
xo= xak xac xck is the reactance impedance of the entire circuit for
the fundamental frequency;
=
is thesame for the nth harmonic.
xon xakn xacn xckn
Before continuing with the transformations of eq. (21), we will designate
= ALO,
89
(22)
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?
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where w is the working angular velocity; wo is the resonant angular velocity of the
circuit.
Since the magnitude Aw is small in comparison tow, it is not difficult to find
(23)
?
We will further designate
22 a f
co2 0 (1 -r )
0
C4
a ==
C,
Cce
m
Co
(24)
(25)
where Coe is the total capacitance of the link, comprised of C1IC21C31 and C4.
We will assume the following limiting condition:
ecermaeascmAsevtes wrrauns.3117...ermsrp f.oe-a ezzact.ammcer.ft ?
i.e., we stipulate that the ratio of the total capacitance of the divisor to the en-
tire circuit capacitance must not be less than the determined magnitude (nonobserv-
ance of this condition leads to a sharp increase in the frequency correction of the
generator and to instability of its operation).
We will further take into account that, for a fractional frequency change due
Af 1
to a nonlinear correction, the inequality
xo 4:rac and that, for the higher harmonics, we have xon ?,rn, since the system
for the higher harmonics is located far from resonance (excluding special points,
inductance 1,0 will be in reso-
ics). Then, after several calcu-
Q
is valid, from which it follows
that
where the capacitance Ck together with the circuit
nance on the frequency of one of the higher harmon
lations and transformations of eq. (21), we get fin
?
0
0
ally
n--30
[1 ? a(1 + E jp._L_+-1+
n-2 I I +1
90
-+
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?
?
".1quation
1- 02 ? 1) (1 --p) 4- n2 ml)x
lf
1 p n2 0 .? m) ?
pin1(1 ?nu-- II i it (1 4 :) (nt ? ) 1
1
2QII.1 + m(1 ? p) + a(1-1-3)1Pint T.T.T:
4 a(1 + 0)(112-14 ?1217in VIIL-?" ,)2
(27)
quenc: due to the influence of the higher harmonics for the generalized network of
offers the
? 0
(27)
opportunit:- of calculating the correction of the fre-
MO
13.g?
c's
?esus ?
a tapned.--aracitcr oscillator (7ig.C). ':e will assume that the capacitances 02 and
..
--
- e significantl: larger ',:lan the capacitance i.e., in compliance with
-, 4-
,
eq.(2'4), the quantit:- a will be sraall. Then, equating the term a in eq.(27) to zero,
':e g,et the freouenc:- correction for the schematic in Fi0.9a, i.e.,
?
/ 2
n-oe
[11-11-
1 + 3
In' ? (1 ? TO mP 1-,17
I,?
rtl (I ? ? II
2Q1,71[ 1 4 in 1 ? p)1[
e then assume that m = 1 (the schematic in rig. 9b corresponds to this case),
?
sc that the 2reouenr7 correction will be
f =
n-
S1
,,-2
? 1
+ a
(n2 ? 1) (1 ?
2 Q2 2 ? p)
p---1
n2 pl.
I
?
?
I
1 Italy
? 1 ( fat
?
oil 0
?
(-)o) ?
?0
"urther we w-411 nonsider the case when '-' 4 1 n = 1 (Fig .?c); then the freouen-
/ ?2 .
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cy correction is
?
f I n
'
#1 11 (411)3
n ?2
11+0_ -
11
L4.1
2(11 mt.
Lastly, for the usual tapped-capacitor network, (Fig.9d),
i.e., when a = 0,
p = 1, in = 1, we have
f
?
n?
[v.
.4?J 1 + a j
n ?2
?
I /?? \is
I ( LL )3
(31)
rt 2 ? 1 k 6/4 )
rii-1 \
n-2
2(23
?11
2 Q2 r1+I
+0
- - - a:matzo:2am etteez,mwsuEts......tges, lZYMMIZONI,C. CLEJSrlat %Mt
Equations (27) - (31) permit computing the frequency correction due to higher
harmonics for any hookup of a tapped-capacitor oscillator. It is not difficult to
prove that the frequency corrections can be actually separated not only according to
magnitude but also according to sign, for various networks as well as for the same
network at various values entering into it.
It must be remarked that, due to the presence of the interelectrode capacitance
? ?Cothe tube and the self-capacitance of the coil, the inductance of the schematics
in Fig.9a, b, g does not exist in the pure form. The error in calculating the fre-
produced by disregarding these capaci-
quency correction due to the higher harmonics,
tances can be quite significant, especially at
change in sign of the correction). Therefore,
[eq.(31)] well-known in the theory (Bib1.3, 4), is,
short and meter waves; for these wavelengths, ea.(30)
high frequencies (almost up to a
the frequency correction for the
usual tapped-capacitor network
not applicable in practice for
must be used.
1:e will next examine the network of a tapped-coil oscillator with partial coup-
ling of the tube to the circuit (Fig.10). Based on eq. (20) and applying such meth-
ods as used for deducing the expressions for tapped-capacitor networks, we find the -
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.f requency correction
In deriving
0
M
eq. (32),
n 03
'S1
+ a
I? -2
vre
nearest higher harmonics (the
n4 rail
? ?P)
n3
2 Q p + a ?1
a r?1
co
I1 n4 /in V
2QJ ,2 _1
n k rd, ) ?
(32)
consider that, for the fundamental frequency and the
second and third harmonics), the capacitive reactance
of the interelectrode capacitances (in 7ig.10
these are shown as broken lines) are actually
larger than the inductive reactance of the sec-
tions of the inductance corirte"-?-17--pa,
them. with a sufficiently high Q-factor of the
circuit, this limiting is not essential.
it can be seen that, in the
same as for a tapped-coil net-
In contrast to the frequency
Fig.10
given case, the frequency correction
work with total coupling of
correction due to dynamic
monies has the same
since the transconductance
of the harmonics)
the tube
capacitance, the frequenc7 correction due to higher har-
sign with a one-sign change of the plate and filament voltages,
of the characteristic (and conseTiently the coefficients
decreases with a decrease in the plate voltage as well As with a
From eq. (32)
is actually the
to the circuit.
decrease in the filament voltage.
4. Variation in the Generator Freauenc- due to the Shuntin Action of the Internal )
r.esistance of the Tube
The shunting action of the internal resistance of the tube introduces the addi-
racxak into the oscillatory -circuit. After substituting,
tional reactance xo = -
rAa
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in this expression, the quantities xo, rac, and xak it takes the following form, for
the schematic given in Fig.8:
0
PGII -1-01
4 nj QmC.(1-1-0)Riai
For a tapped-coil netorrh (Fig.10) we will have
?
ID
?
-I
I'
Q C0(1 o) Ri ai ?
It is not difficult to see that the frequency correction
a change in the operating condition of the generator only because of the value Riai.
lae will transform this value
(33)
(33)
(34)
can change during
(35)
?
?? ?
? ? ?
? - ???-?
The amplification factor of the
tio of the interelectrode grid-cathode
tube is expressed, as is well known, by a ra-
capacitance to the plate-cathode capacitance.
Undoubtedly, we should include the static as well as the dynamic capacitance in the
interelectrode grid-cathode capacitance. Then, during operation of a tube with a
cutoff we get the following value for 11
?
Cd
ccK
ai
=
?-?1211!
Inn
Taking into account the values for p., eq.(33) takes the form
Lf /"CaNS11?a(1-1-01
?
j I njQin Co (I + G) (3i Cd)
(36)
(37)
Equation (37) permits computing the magnitude of the frequency change during a
change in the power-supplY voltage, due to the shunting action of the plate resist-
ance. For this it is necessary'to know the change in the magnitude of Cd, ai and S,
as we have seen, is necessary also for calculating other frequency correc-
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tions.
The peculiar feature of the given frequency correction is that its absolute
magnitude does not depend directly on the frequency. Therefore, it will have a more
relative valuation at comparatively low frequencies.
Besides the above frequency corrections, there is room for a frequency correc-
tion due to the currents of the higher harmonics, formed in the grid circuit on ac-
count of the nonlinearity of the dynamic capacitance.
?
ditional shift in the phase of the grid voltage.
changes comparatively little with a change
quency corrections, its relative magnitude
carded in the discussion.
.1.14,14.1,-,11,.. ? Raft
tr,m,
5. Comarative Evaluation of the Obtained Results
Fripm the above explanation, it follows that the mechanism of the effect of a
change in the power supply voltages is characterized by a series of frequency correc-
tions, determined by eq. (19) for the frequency correction due to the dynamic capaci-
tance of the tube, by eqs.(27) - (32) for the frequency correction due to the non-
linearity of the tube characteristic, and by e. (37) for the frequency correction
?
due to the shunting action
of the internal resistance of the oscillating tube.
Taking into account that all these corrections are individually and in total
sufficiently small, it is possible to assume that they act independently of each
other. Therefore a computation of the change in frequency of the generator, for
each factor, can be rade separately and later combined.
Considering the diversity of the factors influencing the change in freqlency,
it is difficult to determine in a general form the relative magnitude of each of
these corrections in different zones of the band and for various values of the quan-
tities entering them. Actually, it is Possible to state only one: the relative
magnitude of the frequency correction, due to dynamic capacitance, increases with an
in
These currents create an ad-
The magnitude of this correction
in the overall sum of fre-
so that it can be disre-
frequency;
is not great,
irtfayrt.rgtmearf.........oematmcle_atinermrse
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increase in the operating frequency.
However, the problem can be greatly simplified (nonetheless evaluating by this
the whole pattern), if the calculations of the changes in the generator frequency
during changes in the power-supply voltages are carried out for the most character-
istic cases in practice and in a wide interval of operating frequencies.
We will assume as the limit of variation in the working frequencies, the range
from 0.2 x 106 cycles to 60 x 106 cycles. We will take into account that, for the
frequency 0.4 x 106 cps, the Q-factor of the oscillating circuit of the generator is
equal to Q = 125 and the full circuit capacitance Co = 300?4Lf. 'We will further
take into account that the Q-factor of the circuit changes monotonously in propor-
tion to the root of the fourth power of the frequency, while the circuit capacitance
is inversely proportional to the square root of the frequency. The circuit coils
are of thq_gul2z2a_p_r_kmco_xithout a corex_4nd.their_inductance is determined by
the given frequency and the capacitance of the circuit. We will consider that the
special (distributed) capacitance of the circuit coil changes according to a law op-
posite to the change of its .1-factor. As the oscillating tube we will use a tube of
the type 12Zh1L, working equal]; well in all given intervals of the operating fre-
quencies.
Inasmuch as we are not interested in the frequency corrections themselves but
only in their change with a deviation in the power-supply voltages from the rating
for the given relative magnitude, the magnitude of the change in these voltages must
be known. In operation, the latter constitutes 10 - 20. We will take it as equal
to 207J.
Let us make calculations applicable to two cases - to a hookup with a capaci-
:bive coupling (Fig.) in the most general form, when m = 0.2 and to the same network
but with the a capacitance Ck, decreased to the possible limit (m = 1), i.e., at
self-capacitance of the inductance coil. As for the capacitance Ch, it is in both
cases taken equal to the interelectrode capacitance of the tube Cac (counting the
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. ? -
7
i I
I .1 ;11.
T
-
- ' ?
lOr
i ' 1?
'1..
\(
V-
r ? ?
,r)
1? ---r--?
c cc. NT to
CO
(NJ en NI*
9'7
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capacitance between the leads and the capacitance of the tube socket), since the ar-
tificial increase of this capacitance can in no way be justified.
In Figs.11 and 12 the results of 'the above calculations are plotted in the form
of a graph. Here a denotes the curves for the frequency change due to the influence
of the higher harmonics, r those due to the shunting action of the plate resistance,
c those due to the d7namic capacitance and S is the total change in frequency. In
both cases, the generator was examined under two operating conditions
=o.5 and cr = 2.
From the analysis of the obtained results it follows that
1. Bothnetworks are of equal value in an evaluation of the frequency change
???? ? ?? . .? as
C=D
due to the d:rnarnic capacitance of the tube; at the same time, they are basically dif-
ferent in an evaluation of the destabilizing influence of the higher harmonics. The
St=15.???J=2.....Gs
influence?OT?frie?iliturete,---;trozic-ea.pa?GI?tanr...e,s_221d the self-capacitance of the induc-
tance coil (C4 and Ck) in the second case is so significant that it cannot be ig-
nored without committing a serious error, especially at the higher frequencies.
2. At a properly selected schematic, the frequency change due to the influence
?
of the d7namic capacitance is dominant in the entire band of the short and meter
waves.
6. Material for
D.
erimental Research
To check experimentally the above cases, a working circuit, based on the basic
diagram in Fig., was selected. At a proper selection of the quantities entering
into it, this hookup can be converted into the schematic shown in Fig.9.
The *research was carried out on the tube 12M1L, including the equivalent tri-
ode. In order to decrease measuring errors as mach as possible, the plate voltage
did not vary by 20, but by 845 (from 60 to 110 v), which corresponded to a varia-
2.3 ma 3.13 ma
tion in the transconductance of the tube characteristic S from to
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' The maximum dynamic capacitance of the tube Cd - 1.2 11? f (at Uci = 0) was practicai.-.1
ly
constant for various values of the plate voltage. At a variation in the quanti-i
ties entering eqs.(19), (27) - (31), and (37) the capacitances of the network were
changed in a corresponding manner. The interelectrode capacitances of the tube and
the self-capacitance of the inductance coil, were useq as the lower limit of the
values for the capacitances C2, C3, C4, and Cit; here likewise eq. (26) was valid.
The inductance coil was in all cases of the single-layer, cylindrical (except in the
specified cases) type, in a red copper shield.
The calculated and measured values of the frequency change for the self-
oscillator are presented in Tables 1, 2, and 3.
Table 1
?
Fundamental frequency f = 26.2 x 106 cps; inductance of the circuit L = 1.05 x
x 10-6 henry; Q-factor of the circuit Q = 200 (measured values)
0,107
0,113
0,111
O,23
0,291
0,11
0,133
0,375
0,5
0,38
0,3.3
0,337
0,35
0,117
0,98
0,98
0,98-
0,98
0,53
0,69
1,51
0,28
0,17
a
0,44
0,44
0,98
0,109
0,116
0,11
/
AY, (
11a3
0,16
0,21
0,145
0,121
0,19
0,13.1
cps
1650
1320
897
275
160
1290
1190
A-1 T, cPs
50
16
33
22
23
55
28
Ail lc, cps
1730
1730
1730
1730
2970
2570
1160
fs, crs
3430
3320
3066.
2590
2027
3153
3845
2378
AACcps
3180
2620
9250
:3400
3500
2490
- f,
+3,3
- 3,61 1,1
-10
--7,3
+ 9,9
- 4,5
.0/0
L161,
d)
Qat,- Ailf,-+
+ f + f r?
f
a) :marks; b) Calculated; c) Calculated according to eq.(27); d) Calculated
according to ea.(37); e) Calculated according to eq.(19); f) Measured.
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The Tables indicate that the discrepancy between
values of the frequency change of the self-oscillator
accuracy of the measurements, taking into account the
the calculated and measured
lies within the limits of the
diversity of the factors in-
fluencing this change.
In order to determine the possibility of using inductance coils with a carbonyl
Table 2
L 12,2.10
?
I. cps
6,95.108
4,95.108
1
4,99.108
? 124
0,473
0,29
9
4,98. 108
124
?
0,473
? ?
138
0,126
0,0')3
0,975
1'14
----
0,485
0,267
---
0,29
0.5
1.065 ._
---------
a
0,11
32
0,12
21
4
b)
c)
0,11
32
8
w.:(LE2-12
Ito
0,12
Ad fa. CPS
394
d) ?
AA fr, cps
37
6
Weft Q)
AAfs'''AA/C1
4- Ir
i)
54
Mf, cps
172
90
128
94
94
0
210
AA /5, cps .
603
220
? 4,5
AA /4. cps
510
127
+1
AA is /4,0/0
-1- 18
AA /4
It,
?
a) Remarks; b) Calculated; c) Calculated according to eq.(27); d) Calculated
according to eq.(37); e) Calculated according to eq.(19); f) Measured
?
iron core for the experiment, whose results are presented in Table 3, a single-layer
coil was replaced by an inductance coil with a carbonyl iron core. A closed (pot-
shaped) core of a diameter of 22 in was selected; the inductance of the coil in this
core and its Q-factor were
The frequency in this case changed a few tens of times
?
roughly the same as the inductance and the Q7-factor of
?
more
the single-layer coil.
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than in a single-layer inductance coil. This could have been merely due to the non-
linearity of the magnetic permeability of the core.
Consequently, when using carbonyl iron cores in contour coils, the instabili-
ties of the generator frequency are of a much higher order, incompatible with the
se ?
Table 3
L 260.10-6 cps
-
I.cps 0,756.10,1 0,105.10
Itio
106
r_
?
a)
trf
0,97
0,9
0,343
/'
0,18
. ? 0,14
0,37
1,06
0,53
? Arr
LX ( I
,
0,15
-
0,13
0.13
b)
cP5
0,03
0,3
4,36
c)
cPs
0,22
0.4.
030
d)
13.ef. cps
1,5
1,6
1,41
a)
AA is, cps
4,69
2,35
6,50
f
"
? AA /c
cps
5
3
6
1)
a) 7.emmirh,s; b)gioCalculated; c) Calculated according to eq.(27); d) Calculated
according to ea.(37); e) Calculated according to eq.(19); Measured ,
concept of a.high-stability oscillator. The given theory is naturally not extended
to this case.
7. General Conclusions
? v
The influence of payer-supply voltages on the frequency of an oscillator is de-
termined basically by three unstabilizing factors: the active value of the dynamic
101
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than in a single-layer inductance coil. This could have been merely due to the non-
linearity of the magnetic permeability of the core.
Consequently, when using carbonyl iron cores in contour coils, the instabili-
ties of the generator frequency are of a much higher order, incompatible with the
I. cps
In
Table 3
260.10-6 Cps
_
0,77.11,4 0,756.10d 0,105. 1(,e
160 ltiO 106
0,97 0,9 0,343
0,18 . ? 0,14
(1,37 1MG 0,53
a)
.0.-?=sum..._.......testanneetscur.M-,,p,,,,,,,ro-reaprer.racf ameaseesecreee.seeett.GMeley_sArunesessMtelet,sheeetefertra...?cn
......_ .?. - - ..-...-. ...
C, 01)
01 0,002 A trr...teeesinala-srveseummv, essffm-remen. I. APORIPM?kall. PT% I.S
. ... ? . .. I
... ..... ...........
a.,....: ( /,:n .2 0,1", 0,13 0?13 b)
?? , , ... I 1 _
1.1 f?, cps 0,03 0,3 .1,36 c)
_IA f,. cps 0,22 0,4", 050 d)
AA f. cps
..I$. cps
f4, cps
1,5
1,6 1,44 a)
4,69 2,35
5 :3
AA ta -1 AA fc+
6,50 ?FMf,
?????INVON
?
a) emarks; b) Calculated; c) Calculated according to eq.(27); d) Calculated
according to eo.(37); e) Calculated according to ec.(19); Measured .
concept of a high-stability oscillator. The given theory is naturally not extended
to this case.
7. General Conclusions
The influence of power-supply voltages on the frequency of an oscillator is de-
termined basically by three unstabilizing factors: the active value of the egwric
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capacitance of the tube; the higher harmonics; the internal resistance of the gen-
erator.
For short and especially for meter waves, the main factor determining the vari-
ation in the generator frequency due to power-supply voltages, is the change in the
active value of the dynamic capacitance of the tube.
The variation in frequency due to the dynamic capacitance is characterized by
its independence (at optimum coupling of the tube with the circuit) from the form of
the network and from the characteristic of the circuit (L/C ratio); at a given fre-
quency, this variation is determined only by the basic parameters of the tube and
the circuit (S, Cd, and Q), and likewise by the relationship between the grid and
plate coupling ?.
The metlei-ial presented in the present article proves
ing continuous-band oscillators with very small frequency
--iri-fhe-power-cupply-matagps (up to 1 x 10-6) and permit's
the feasibility of design-
variations during a change
a calculation of this vari-
ation with a sufficient degree of accuracy.
Article received by the Editors 20 July 1955
BIBLIOGRAF7
1. Kotzarevju.B. - The Dependence of the Oscillator Frequency on its Operating
Conditions. Vestnik Elehtrotekhniki, No.10 (1931)
2. Krylov,IX. and BogolyubovIN.N. - New Methods in Nonlinear Mechanics. ONTI (1934)
q?
? ? ?
3. Shembell,B.K. - Deviation of the Generator Oscillation Frequency from the Natural
Frequency of the Linear Circuit. ZhTF (Sh.Tekhn.Fiz.) Vol.IX, No.7 (1939)
L. YevtyanovIS.I. - Calculation of Self-Oscillation Frequency. Radiotekhnika,
No.2 (19)6)
5. Shitikov,G.T. - Investigation of the Influence of the Tube on the Oscillator
Frequency. IEST No. (1940)
.7
6. Shitikov,G.T. - Influence of the Circuit Characteristic on the Oscillator Stabil-
102
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?
it:,- and the Permissible Amplification Factor in Systems with Single-Element
Tuning. IEST No.12 (1940)
7. Groslikovskiy,Ya. - Generation of High-Frequency Oscillations and Frequency Sta-
bilization. IL (1953)
8. YevtyanovIS.I. - Radio Transmitting Systems. Svyazizdat, Moscow (1950)
0 ?
011
MO
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CALCULATION OF THE AMPLITUDE CHARACTERISTICS OF LIMITERS
by
Ya.Z.Tsypkin
Active Member of the Society
? ?
The amplitude characteristic of a limiter is expressed
indirectly by the dynamic characteristic of the tube, which
simplifies calculations and establishes a link between the
properties of these characteristics.
?
The amplitude of the output voltage of a limiter, consisting of a tube and a
filter and passing the first harmonic (Fig.1), as is well known (Bib1.1), is equal
to
...????=??????????????? _41,er.271=60.1????riar? m?IMANMA?????:=Menv 4emeNee
U m out =B11,
(1)
where B is a constant, determined by the network of the filter;
is the amplitude of the first harmonic of the plate current of the tube.
This amplitude depends on the fixed bias Esm and the amplitude of the input
voltage Um in and is determined according to the dynamic characteristic of the tube
SO
= F (e), (2)
on the basis of the well-known formula:
2 7
/1
x J
? ?
F (Es?, Um,.ncosp)cospdp.
For an analysis of Ill a previous report (Bib1.12 derives an approximation of
the dynamic characteristic by straight-line segmenting and integration by sections,
analogous to the method used in the simplest case in courses on the theory'd com-
all
,
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putation of transmitting systems (Bib1.2).
A similar method was used in another
in wt
ESI71
b)
Fig.1
a) Tube; b) Filter
straight line Ek, the bias
to determine the value, according to the formula or tabular functions
lu I
paper (Bib1.3) for determining the higher
as well as the first harmonics of the plate
current.
For determining I in agreement with
this method, it is neceesary to compute
the angle of cutoff 0.k along the points of
discontinuity of the segment of the
0
Earn and the amplitude of the oscillating component Um in;
1 1
(cos ) == -114K ? ? -i sin 2figi
K 1. 2, 3, .
mua.titay?tr?lese-iunct-rbtrs-by-th-ear.ge-.,>f--,eaop_e_r)f_..th_e.t,
straight line and add the obtained products.
All'"
these operations must be r,epeated for each value of Umin
1 which makes a
A
?
calculation of I quite cumbersome. To clarify the influence of Earn or of the form
of the dynamic tube characteristic on the amplitude characteristic, the calculation
must be repeated.
Nonetheless, it is possible to express i, with sufficient accuracy for prac-
?
characteristic of the tube F and by this not
lif the calculation, but also establish a definite link between and
tice, indirectly through the dynamic
ony simply
both Um out and F(e). This possibility was used by the author for establishing a
close connection between the "mean transconductancen or, as it is called in the
theory of automatic control, the complex amplification factor, and the characteris-
tic of the nonlinear element (Bib1.4).
?
We will substitute the variable cos T = y. Then,
tions (Bib1.4) and substitution of the value of I in e
after elementary calcula-
105
q.(1), we can put the expres-
S TAT
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sion of the amplitude characteristic of the limiter in the form
21 r F 3 E sm.; ?, v) v
Urn out = '1== ay.
-1
(4)
For computing this expression the quadratic equations of V.A.Steklov, can be
used:
? ?
where
or
where
?
?
I .1 dy [f ) j ( 1) + 2./ (
(6) .
(;) ?
?61
?
(y)1
, f f(1)+J(-1)
aY = t(--)+ t(_.)+ ? j ?y2 6
-1
+ 1(24) f Y2: )4. f (0) I+ R,:,
2" ? 1.2'
1%. I < 1.
(5)
If we eliminate thc remaining terms R6 and R12, we will find the, approximate
expressions of the integral in the wanted form. Obviously, the expression obtained
from eq.(6) in the usual case will be more accurate than that obtained from eq.(5).
Putting, in eqs.(5) and (6)*,
= r (Es. Um 4. Y"
?
?
*Further, it is assumed that F(e) corresponds to a continuous curve.
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?
we get, after substituting them in eq. (14.) an4 eliminating the remaining terms, the
approximate expressions for the amplitude characteristic of the limiter in the form
UmB r
.a F am+ Urni - F (Esr,? Urn in) +
-FF(1:sn,+-1.1)",;?)
and, with greater accuracy,
Limem1==4H44F(E3m4-tim;#)
4-F(Esnci-4:Lc,A) F(Esm bC11.)1-1-
11:g [ F (F: Urn ;,;) F E sm U m
77n
' " in)]
1
F (Es,,, Urn -I-
The presented formulas indirectly connect
limiter Um out with the dynamic characteristic
is relatively simple. In cases where its accuracy is not sufficient, one can use
1 differs from eq.(8) by the last two
(7)
(8)
the amplitude characteristic of the
of the tube i = F(e). Equation (7)
eq.(8)* which, disregarding the factor
terms:
1
2
)1';C F (E 771-
3m + U m;? Fs,?
2 2
?
t?.
2 in),
If the dynamic characteristic of the tube is given analytically, then by sub-
stituting its expression in eqs.(7) or (8), we find the approximate analytical ex-
pression for the amplitude characteristic of the limiter.
If, as usually happens, the dynmnic characteristic of the tube is given graphi-
cally (Fig.2a), it is possible to find the amplitude characteristic of the limiter
by a simple plotting of the graph. .For this, using the dynamic characteristic
of F (e), the curve F( 1 e) is constructed by doubling the abscissas of F(e). In-
2
*Equations (7) and (8) become accurate
the 4th and 10th degree, respectively;
ordinates" (Bib1.5).
if F(e) can be represented by polynomials of
then, eq.(7) will yield the "formula of the
107
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serting the ordinates of these curves (Fig.2b),
the origin of the coordinates by the amount Esm
left at Esm< 0), we find F(Esm + e) + F(Esm +
1
curve F(Esm - e) + F(Esm - ---e) is obtained by
2
tamed earlier relative to the ordinates (curve
we get F(e) + F( 1 e). Displacing
2
(to the right at Esm > 0 and to the
....2e), (curve 1 in Fig.2b). The
2
the mirror image of the curve ob-
2 in Fig.2b). Since it is assumed
=Ft')
+3
a)
?
Fig.2
that Um in = e > 0, it is suflicf'enz tc-get-a-mirrop-image-of-the section oa...9f
curve 2, lying to the left of the ordinates (the mirror section is indicated by the
solid line). The difference between curves 1 and 2 at Um in = e >0 (curve 3 in
3
Fig.2b), in agreement with eq.(7), is equal to __Um out. Changing the scale along
the ordinates times, we get a graph for the amplitude characteristic of the urn-
iter. If, for any reason, extreme accuracy in computing the amplitude characteris-
tic of the limiter is necessary, then eq.(8) can be used.
In that case, the scale of curve 3 in Fig.2b changes along the ordinates ___
6
times and the curve
VT IF (1;? ,? 4,) ? F (E 1?, -
is added to it, which is constructed in the same way as that obtained above.
Article received by the Editors 26 August 1955
108
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BIBLIOGRAPHY
1. SidoravIV.14. - Calculation of the Amplitude Characteristics of Limiters.
Radiotekhnika, Vo1.8, No.5 (1953)
2. Berg,A.I. - Theory and Computation of Tube Generators (1935)
3. Person,S.V. - A Method for EXpanding thellorking Characteristics into a Fourier
Series. Elektrichestvo No.3 (1948)
4. TsypkinlYa.Z. - Concerning the Coupling of an Equivalent Complex Amplification
Factor of a Nonliilear Element with its Characteristic. Automation and
Telemechanics (in printing)
5. Krylov,N.N. - Electrical Processes in Nonlinear Elements of Radio Receivers
(1949)
109
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LIST OF THE ARTICLES WHICH APPEARED IN ?RADIO ENGI
in 1955
DUE
INT! JOURNAL
Author
Abramovich,G.P.
Agafonov,V.M.
AltermanlYa.L. and
Livshits,A.R.
Antseliovich,Ye.S.
Antseliovich,Ye.S.
Artym,A.D.
Artym,A.D.
BarchukovIA.I.,
Vasiltyev,G.A.
Zhabotinskiy,M.E.
and Osipov,B.D.
Baranultko,V.A. and
Fedotov,I.V.
Belkin,B.G.
Beikin;B.G.
Blokh,E.L. and
Kharkevich,A.A.
Blokh,E.L. and
KharkevichIA.A.
BorodichIS.V.
Title of Article
Os
Concerning a Universal System.of Units
Matrix Coefficients for Two Types of Cells from
the Cutoffs of Two Interacting Long Lines
A Pulse Amplifier with a Two-Channel Feedback
Concerning the Broadening of the Frequency Trans-
mission Band of an Input Transformer
Influence of the Nonlinearity of the Iriternar"
Resistance of a Tube, in Calculating Resistor-
Coupled Amplifiers
Calculation of the Nonlinearity of the Internal
Resistance of a Pentode During an Analysis of
---the---eperation. of Besistor-Coupled;Amplifiers
A New Method of Phase Modulation
Raising the Efficiency of Reactance Tubes
An Electromechanical Klystron Frequency
Letter to the Editor ?Radio Echo from Lightning"
A New Generator of Noise Voltages
A New Method for Measuring Nonlinear Distortions
in
in Loudspeakers
The Geometric Theory of the Threshhold Carrying
Capacity of a Link System
An Answer to the Reprimand by L.M.Finka
Journal
Issue
?
Concerning the Nonlinear Distortions Caused by
Mismatching of the Antenna Feeder in Multichannel
*FM Systems
1
?
4
7
5
3
7
1
6
3
13.
4
9
7
10
10
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Author
Title of Article
Breytbart,A.Ya.,
Lyudmirskiy,I.L.,
Preobrazhenskiy,B.I.
Bunimovich,V.I.
Velcsler,G.S.
Velikin, Ya. I. 1
Geltmont,Z.Ya. and
Zelyakh,E.V.
VereshchaginlYa.M.
Vol,V.A.
VoUerner,N.F.
Voltpert,A.R.
Sources of Disturbances in Television Sets
and Protective Devices
On Passage of a Signal and Noises through a
Limiter and a Differentiating System
Calculation of an Ionic Voltage Stabilizer
A Piezoelectric Filter for the Upper Frequencies
Quadratic Amplitude-Phase Modulation
An Amplifier for a Stroboscopic Oscillograph
A Method for Raising the Accuracy of Frequency
Analyzers with an Electron-Beam Indicator
ory-o--
Certain Applications
Journal
Issue
1
6
32
3
3
10
az
Receiving Antennas and on
11
Voltpyan,V.G.
Voltf,V.M.
Voltf,V.M.
Gutkin1L:S. and
Kuemin,A.D.
Dekabrun,L.L.
Dementlyev,Ye.P.
Zhitomirskiy11h.I.
Zingerenko ,A .1i.
? see
Zyuko.,A.G.
?
of the Principle of Reciprocity
On the Sensitivity of Frequency Detectors with
Resonant Circuits
An Evaluation of the Qualitative Indexes of
Sound Transmitting Devices
The Nonlinear Conversion of Signals of a Compound
Form
The Influence d'Electron Inertia in Diode Frequency
Detection
K-Stabilizers for Voltage of Laboratory Rectifiers
Noises of Super-High Frequency Amplifiers
Determining the Probability of Jamming, Caused by
Interference Signals
Determining the Duration of the Build-Up of Transient
Functions According to the Amplitude-Frequency
Characteristics of Transmitting Systems
A Comparitive Evaluation of the Channels of a Link
for Various Modulation Systems According to their
Carrying Capacity
111
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3
11
9
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1
10
7
6
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Author
Ivanov,I.I.
Ivanov, I.V.
Irisova,N.A.,
Zhabotinskiy,M.Ye.,
Veselago,V.G.
? Kalinin,A;I.
Kalikhman,S.G.
Kashell,A.A.
Klyat skin, I .G.
Kogan, S. S.
Kononovich,L.M.
Kontorovich,M.I.
Kocherzhevskiy,G.N.
Kravchenko,B.A.
Krize,S.N.
Kriksunov,V.G.
Kuznetsov,V.D.
Kulikovskiy,A.A.
Kulikovskiy,A.A.
Title of Article
Journal
Issue
Remarks on the Book by N.M.Izyunova
Pulse Spark Excitation of Oscillations on the
Centimeter Wave Band
Frequency Stabilization of the Three-Centimeter
Klystron with the Aid of Spectral Lines
Calculation of the Field Strength of Ultrashort
Waves in the ?Illuminatedu Region of Space
High-Frequency Broad-Band Transformers
Selection of Elements for Separating Filters
During the Operation of Two Medium-Wave and
Long-Wave Band Transmitters on One Antenna
On a Universal System of Units
Narrow-Band Quartz Filters for Intertube Connection
Selection of a Hookup for Feedback in RC Generators
On the Basic Equations of a Tube Generator in an
Established Regime in the Presence of Grid
Currents
Radiation of a Slot in an Ideally Conductive
Round Disk
Harmonic Analysis of the Plate Pulse Current of a
?
Generator for Approximation of the Plate-Grid
Characteristic of a Tube by a Straight-Line Break
Transcient Characteristics of Compound Pulse
Systems Consisting of Heterogeneous Sections
On Establishing the Oscillation Amplitude in the
Circuits of RC Oscillators
Shunt Vibrators
Processes of Installation at Detection of Pulse
Signals
A Comparison of the Theories of Tube and Semicon-
ductor Amplifiers, and the Possibility of their
Generalization
112
10
12
4
9
12
11
2
1
5
9
10
6
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Author
Title of Article
Journal
Issue
Kushmanov,I.V.
LevensternII.I.,
Kostandi,G.G.
Levin,G.A., Levi
B.R.
Levitan,GvI. ?
Levin,G.A.,
Goloychiner,M.M.
Leytes R.D., Gutman,
Loshakov L.N.
Mashkovtsev,Yu.P.
Miz3ruk,L.Ya.
Mikaelyan,A.L.
Mikael,yan, A . L. ,
Pistoltkors,A.A.
Mikaelyan,A.L.
Model?,A.M.
Model? Z I. ,
Nesvizhskiy,Yu.B
Morozov,I.I.
Nazarov,V.G.
Neyman , M. S.
Calculation of Correction Circuits for Broad-
Band Amplifiers with the Help of RC Circuits
Triode Converters of Neter Wave Frequencies
The Time Characteristics of Pulse Signals, Having
Passed Through a Linear System
Calculation of Rectifiers with Electron Stabiliza-
tion
An Analysis of Quantum Moises with Pulse-Code
Modulation
On a Method for Studying Transient Processes in a
Linear Systeth
On a Case of Matching of RadITTWavegUld-e0
On the Amplitude-Frequency and Phase Characteristics
of Broad-Band Amplifiers
Calculation of a Cathode Detector
Calculation Methods for the Dielectric and Magnetic
Permeability of Artificial Media
Electromagnetic Waves in Magnetized Ferrite in the
Presence of Conducting Planes
Magneto-Optic Effects in a Rectangular Waveguide,
Filled with an Electron Gas
The Propagation of Plane Electromagnetic Waves in
Space, Filled with Plane-Parallel Grids
of Bridge T-Networks with Auxiliary
Power from HF Generators
The Temperature-Frequency Characteristics of Electro-
lytic Capacitors
Dielectric Amplifiers
Step-by-Step Method of Calculating Waveguide and
Oscillatory Systems
133
9
6
1
2
8
6
3
5
1
3
9
6
7
5
8
1
STAT
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e
T011:.na1
Tr.vvie
? n 1::_cnals and the rleneral
1.? :,114 orlat Li? 1".?ocesses
?
a :.(7-,4-". for ?)et- ninr 'se v.-we:- -0: 71.11se
-or:cr.:1;3-1-5
Tnvent," : ?-?.n -el:: n
? ? ? '???? ?
?
a. , I el r?-)v,
?-c4 I? c-21.0."..?? 2,-.? ? -;e-,
? Io 'UT's
)11_ n.10-7 c'1n.atC ' 31.11 It r n';
"13 .1C ifi C1'.3 in e? ''n-
;el c,?t
3C.T, T
I-I
n4 ISO ? ni,-; 3 1 1??_1
oi
3 ? 1:1 4 ; " c Fe ? ,c.??,
? -1"
C.
? ,Irse ,1
on .1's : .1-22 irier
an n Ye FTh c .? -?lit, L 11,:c
?c?
zns, , 115 'le
:1?131.onry,
'r"'1 i 7 e:- ,????_t,',? a 1 n7r... -?? ,, .
Trrulsient. -1-ara:?4e .i.'"3 Ie
"et wor1-3
`1")e or. cf :',1(.11 "ave. ; 1? a
n ? lp-1 -1.cn
.cac lion of Icriare 1"?17.5c,7 "
an Tnte.rval f7; on a Line 1-le'c
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Author
Title of Article
Journal
Issue
Tyminskiy,R.M.
Fayzulayev,B.N.
Fayzulayev, B. N.
Fedotov,Ya .A.
Fedorov, N. N.
FiLippov, L. I.
Fink,L.M.
Fradin, A . Z
--01:efidskiy,V.A.
Khaykin,S.E.
Kharkevich,A.A.,
Blokh,E.L
Khmellnitskiy,Ye.P.
Khronylch,M.K.
Tsykin, G. S.
Tsykin, G. S.
Tsypkin,Ya.Z.
Chaykovskiy,V.I.
Cherne,Kh.I.
,Shapiro,D.N.
On Certain Features of Modulation
The Pip of the Pulse Characteristic in Networks
with a Correction of the Build-Up Front
Calculation of a Cathode Repeater in Pulse
Operation
On Calculation Methods for Amplifying Networks with
Crystal Triodes
Nonlinear Distortions in Oscillation Generators with
1/Inertia Nonlinearityu in the Oscillating Circuit
Potential Noiseproof Feature for the Reception of
Pulse Radio Signals
Letter to the Editor
7
5
8
11
10
10
On the Antenna Effect of a Balanced Feeder 2
Radioastronomy
On the Critical Carrying, Capacity of a Link
?
System
On a Method of Significantly Raising the Oscillating
Power and Efficiency of an Oscillator, Operating in
the Excess Voltage Regime
Transient Processes in a Class B Power Amplifier
Calculation of a Cathode Repeater
Selection of Operating Conditions, Calculation of
the Load, and Determination of the Nonlinear Dis-
tortions in Amplification Stages with Semiconductor
Triodes of the Plane Type
Calculation of the Amplitude Characteristics of.
Limiters
Reception of Pulse Signals by the Method of Re-
ciprocal Correlation
On the Theory of a Single-Tube RC Oscillator
Calculation of the Efficiency of Shield Cans
115
?
?
?
4
2
8
9
1
8
12
6
2
4
STAT
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Author
SheMbelf,B.K.
Title of Article
A Calculation Method for Generators with
Piezoelectric Frequency Stabilization
Shitikov,G.T. Effect of the Capacitance of a Space Charge and the
Nonlinearity of the Tube Characteristic on the
Generator Frequency
Shteyn,N.I., Eydus Theory and Calculation of a Transitron Generator 7
Journal
Issue
7
G.S.
Yurov,Yu.Ya.
Yampolskiy,V.G.
Yampolskiy,V.G.
IYastrebtsova,T.N.,
4
1
MID ssIII SI..
Equivalent Networks of Multigrid Electron Tubes
An Approximate Method for Determining the Effect of
?
Phase Distortions in the Aperture of a Space
Antenna on its Radiation Characteristic 5
The Oblique Incidence of a Plane Wave on a Wire Grid 9
On a Method of Quenching the Free Oscillations of
Quartz 7
3
OTHERS
P.I.Lukirski
A.L.Mints. On his 60th Birthday
Scientific-Technical Conference on Matters Pertaining
to Television
Sixty Years of Radio
The All-Union Scientific-Technical Society of Radio
Engineering and Telecommunication Imeni A.S.Popov 4
?
A.G.Arenberg. On his 50th BirthdaY 5
Scientific-Technical Conference on the Sound Quality
of Radio Broadcasting Receivers 5
All-Union Scientific Session Devoted to the "Dnyu Radii' 7
F.A.Lbov. On his 60th Birthday 7
All-Union Scientific Session Devoted to the "Dnyu Radio" 8
10
1
2
2
/I.
I.G.Klyatskin. On his 60th Birthday
Scientific-Technical Conference in Leningrad Devoted
to the 60th Anniversary of the Invention of Radio
316
10
STAT
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NEI BOOKS
Ya.S.Itskhokiy. Nonlinear Radio Engineering. Published by "Soviet Radio?.
Moscow, 1955, 508 pp. Price: 18r. 50k.
The book is devoted to a study of the most important general properties of non-
linear elements, circuits and basic nonlinear conversions. The principal problems
of self-excitation of self-oscillators (RC tube, klystron, TN tube, and magnetron)
are explained. The reaction of the external efficiency on a nonlinear oscillating
system (regeneration and holding of self-oscillation frequencies) is examined. About
?
500 problems with answers are given in.the text; some of these with the solutions.
Particular attention is given in the book to a through study of the essence of the
physical processes in the basic nonlinear systems.
The book is designed for students of radiotechnological colleges and for radio
S.I.Bychkov. Magnetron Transmitters. Edited by S.A.Droboli. Voenizdat, Moscow,
1955, 216 pp. Price: 5r. 85k.
The principle of action and the classification of magnetron oscillators, the
fundamentals of multiresonance magnetrons, the construction, electric characteris-
tics and modulation of magnetron oscillators, a high-frequency assembly, and control
of the operation of a magnetron transmitter are examined.
K.P.Yegorov and G.P.Tikhanov. Construction of Equipment for Long-Distance
Links. Gosenergoizdat, Moscow-Leningrad, 1955, 423 pp. Price: 14r.
Basic data on the design of components and unitsof equipment for a long-distance,
distance link is explained as well as the construction of the apparatus as a whole.
The .book was compiled for engineers, but can also be used by technicians and stu-
dents of advanced courses in the corresponding polytechnic institutes.
Dzh.K.Sausvort. Principles and Application of Waveguide Transmission. Pub-
117
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lis ed b:- "adio?, :"oscolt, 19'7, 700 pp. Price: 33r. 50k.
In the book, t;.e basic theories for tran5-mittinc electroriacsnetic enerr-- b-- wave-
rui des is explained, and tl:e construction and eper-Ition of nurieroun liaverui de clement:
and units, used tn super-! 2requenc:- tee, nirr.:e, are?ale::;ibee.. The book can be
J.1000sa,
4 used an a reerence a: I i,u1 ? te-,-lide h7 scien'Af'ic ?.:or!-ers, enr,ineern, anzl .s? tudents
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The col.lection includes arL'cles devotel to the desigi and opera' in of the ex-
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students of advance:1 courses, and thcse vorkin?! -.?ith the technione of 2-1,1ir 1 inks.
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