TUNING OF OSCILLATING CIRCUITS BY
PLATE CURRENT VARIATIONS
I. INTRODUCTION
1. Observations Which Led to Investigation.-During the course of
investigations of antenna models* and short wave transmitters,t it
was observed that whenever a circuit coupled with a short wave
transmitter is tuned to approach resonance, variations of plate cur-
rent take place, which under certain conditions become so marked
that the setting for resonance can be determined by observing the
amount of change indicated by the ammeter or voltmeter. Espec-
ially for measurements in circuits oscillating with a frequency of 30
to 60 megacycles such a method promised to be very useful. The
introduction of meters in the directly or indirectly coupled oscillating
circuit involves a change of frequency and a redistribution of po-
tential along the circuit; both these effects influence the measure-
ments, introducing errors. If it were possible to determine point of
resonance by merely observing a meter in the plate or grid circuit of
the oscillator a serious source of errors could be eliminated. Prelim-
inary experiments which were made showed that this method can be
used conveniently in many cases; in the attempt to develop this
method, however, some interesting phenomena were observed which
made it doubtful whether this method of tuning can be applied in all
cases. Thus, for instance, while in most of the short wave experi-
ments a decrease in the plate current was observed whenever a
coupled circuit approached resonance, similar experiments with long
waves often showed a less marked effect of opposite direction, i.e.,
the plate current usually increased when resonance was approached.
In other cases no change in plate current could be observed.
2. Object of Investigation.-A systematic study was therefore
undertaken to find the conditions which influence the plate current
variations, and to develop a method of applying these variations for
the tuning of oscillating circuits. The influence of filament current,
of plate voltage, of coupling, and of resistance of oscillating circuits
had to be investigated. The conditions were sought which would
give the largest response with the least influence upon the constants of
*"Investigation of Antennae by Means of Models," Univ. of Ill. Eng. Exp. Sta. Bul. 147, Sec. 22,
p. 31 1925.
t "Short Wave Transmitters and Methods of Tuning," Univ. of Ill. Eng. Exp. Sta. Bul. 161, Sec. 27,
p. 51, 1927.
ILLINOIS ENGINEERING EXPERIMENT STATION
the circuits. It was also found necessary to compare the characteristic
peaks of variation of current in the plate circuit with those in the grid
circuit, and to determine whether and to what degree of sharpness
both may indicate the resonance point. Finally, the adaptability of
this method to the tuning of antennae, wavemeters, and parallel wire
measuring systems, and to the determination of logarithmic decre-
ments had to be tested.
This investigation was carried out during 1925-26 and finished in
1927. Some of the results of this investigation were presented at the
meeting of the American Physical Society in New York, February
22-23, 1929.*
3. Acknowledgments.-The authors wish to acknowledge their in-
debtedness to PROF. E. B. PAINE for his encouragement and interest
in this investigation. They also wish to express their thanks to PROF.
MORGAN BROOKS, PROF. H. A. BROWN, DR. A. P. CARMAN and DR.
C. T. KNIPP for suggestions which aided in a clearer presentation of
the results.
This investigation has been a part of the work of the Engineering
Experiment Station of the University of Illinois, of which DEAN M. S.
KETCHUM is the Director, and of the Department of Electrical En-
gineering of which PROF. ELLERY B. PAINE is the head.
Acknowledgment is also due to F. T. Tingley, graduate student of
Electrical Engineering, for checking the measurements of logarithmic
decrement.
II. METHODS OF COMPENSATING D-C. COMPONENT FLOWING
THROUGH PLATE CURRENT INDICATOR
4. Observation of Total Average Plate Current.-The variation of
the plate current produced by coupling a resonant circuit with the
thermionic tube oscillator is very small as compared with the total
plate current. In order to measure these variations directly the
coupling coefficient of the two circuits must be made large enough.
Thus, for instance, in the case represented by curve a of Fig. 28 of
Bulletin 161, the plate current decreased from 47 milliamperes to 27,
that is about 43 per cent, due entirely to close coupling, which pro-
duced a considerable reaction on the oscillating circuit, so that by the
coupling the oscillating current Io was considerably reduced, as indi-
*See Abstract, Phys. Rev., Vol. 33, p. 634. "Determination of Frequency and Decrement by
Means of Plate Current Variations of Thermionic Oscillator Tubes."
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 9
(} L31,'JjIjCs (2 LJ^jSJCJ
eBy mea'2s of a' 'es/.a'02cm7e 3'd y lvea''s of a r,/s,,foyce al'nd
sepc'a/l-e ha'Vel'y ctr-ass lt' fca'fa',1r71 ba'//'eny a 5crass 1/e
'01.71e cellrel7l y7/e-/ c/-/e w/rel7i-^/w/y
Osc///a'or Co7pensaA-or
(c)
FIG. 1. METHODS OF COMPENSATION OF D.C. COMPONENT OF PLATE CURRENT
cated by the curve b. With decreasing coupling the plate current var-
iations became so small that they could hardly be measured by ob-
serving the total plate current I,. As all measurements should pro-
duce the smallest possible reaction upon the oscillator methods have
been devised to compensate the d-c. current in such a way that the
meter indicates predominantly the change of the current.
5. Resistance Shunt Method.-The usual method, Fig. la, consists
in shunting across the plate ammeter Am a source of electro-motive
force D in series with a variable resistance Re. The potential differ-
ence across the ammeter is thus compensated by another electro-
motive force by adjusting the resistance Re. The current through
the ammeter can be reduced to zero for any current flowing in the
plate circuit. The ammeter is conveniently of a type permitting
rapid changes in sensitivity by means of shunts S controlled by a
dial switch. The procedure usually consists of detuning the coupled
circuit II; adjusting the resistance Re, until the ammeter shows zero;
ILLINOIS ENGINEERING EXPERIMENT STATION
then increasing the sensitivity of the ammeter by changing the shunt
S, and readjusting the resistance Re, to bring the pointer to a conven-
ient place on the scale. Now if the condenser C3 is varied, in order
to tune the circuit II into resonance with I a variation of the plate
current takes place. The meter is connected so that for an increment
of the plate current the pointer will move to the right, for a decre-
ment to the left; and the deflection will give a measure of the plate
current variations. Simple as this method appears to be difficulties
are experienced by a continuous drift of the pointer. The drift was
found to be produced by gradual discharge of the batteries A, B,
and D.
A slight improvement results from the use of a common battery
for the filament current and the compensating shunt of the ammeter,
as shown in Fig. lb. The number of batteries is here reduced, and
so are the sources producing the drift of the ammeter pointer. Never-
theless, this method cannot be applied for reliable measurements of
change in plate current of the order of a few micro-amperes. The
plate current is an exponential function of the current heating the
cathode of the oscillating tube v. A slight decrease in the voltage of
the filament battery produces a very large decrease of the electron
flow through the tube, while the current through the compensating
shunt, being a linear function of the filament voltage, produces a
small change in the indication of the ammeter. The total variation
is the difference of the two decrements. The resulting current may
vary to such an extent that the taking of measurements required for
a complete resonance curve is made impossible by the pointer drift-
ing off the scale.
6. Thermionic Shunt Method.-There are other sources of plate
current fluctuations besides that described in Section 5, such as the
effect of room temperature change upon the resistance of the differ-
ent rheostats in use, and the decrease in resistance of the filament
with decrease of temperature. A reliable method had to be developed
in which the variation of plate current due to a coupled circuit would
be independent of the slight decay in the electron emission of the
filament. In principle, this consists in the use of a thermionic shunt
connected across the plate current meter in such a way that equal
drifts are produced in the plate currents of both tubes; Fig. ic shows
this method diagrammatically. The meter Am is traversed by the
difference of two plate currents flowing in opposite directions, one
originating in the oscillating tube v, and the other in the compensat-
ing tube v'. Two separate sets of A and B batteries are used for
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 11
feeding the two tubes. The type of batteries used should be similar,
so that the time and rate of charge and discharge may be the same.
The compensating tube is chosen with characteristics and filament
resistance similar to that of the oscillating tube. It was found ex-
pedient to adjust the slope of the plate voltage-plate current char-
acteristic of the compensating tube v' by introducing a variable load-
ing resistance R,' in the plate circuit. This resistance and the voltage
of B' are so adjusted that the slope of the characteristic of the loaded
compensating tube is approximately the same as that of the oscillat-
ing tube v. Under such conditions the d-c. component of the plate
current can be entirely compensated, and the pointer of the ammeter
kept free of drift for a length of time sufficient to make a complete
series of measurements. The ammeter which was used throughout
the investigation had five sensitivity ranges, a switch on the meter
inserting the necessary shunts. The compensation could be accom-
plished with such precision that variations of plate current could be
measured using the most sensitive range, 0 to 100 micro-amperes,
even though the variations amounted to several milliamperes. If, for
instance, increasing the capacitance of the condenser in the coupled
circuit produced an increase of plate current, the capacitance was fur-
ther increased until the plate current variation reached the largest in-
crement measurable with the most sensitive scale. By decreasing the
rheostat R,' the pointer was brought back to 0, and the process of
tuning was then continued until full scale deflection was again reached.
By repeating this operation the increments I, could be read accu-
rately over the entire resonance curve. For every change of filament
current, plate voltage, or coupling, the conditions in the compensat-
ing circuit had to be readjusted. The general procedure was to keep
the filament currents in both tubes the same, and to find the proper
values of plate voltage and external plate resistance for the compen-
sator to give the desired compensation of the current and the slope.
7. Influence of Inductance and Capacitance of Plate Current Am-
meter.-Precautions had to be taken to eliminate the influence of the
high frequency currents upon the direct current indicating instrument
Am. Also, the moving coil and the various shunts of the meter rep-
resents a system of impedances varying when the instrument is
switched from one sensitivity range to another, and for different
positions of the scale on the same range. The deflection of the am-
meter is thus considerably altered by stray effects. The appearances
of the curves thus obtained differed from each other, depending on
the sensitivity range used for the measurements. This difficulty was
ILLINOIS ENGINEERING EXPERIMENT STATION
entirely eliminated by connecting in addition to the condenser C1
another bypass condenser C1i across the leads of the ammeter Am,
and by inserting in addition to the choke coil L1, the coils L1'. It was
then ascertained- by testing that the same character of resonance
curves was obtained no matter to what sensitivity the instrument was
adjusted. With this arrangement, for which specific data are given
in the index accompanying Fig. 1, a systematic study was made of
the influence of different factors upon the plate current variations
obtained when a coupled circuit II was brought into resonance with
the oscillating circuit I. So the influence of filament current, of plate
potential, of coupling coefficient, of resistance of the coupled circuit,
and of resistance of the oscillating circuit was studied.
DATA FOR FIG. 1
A = Filament battery-5 storage cells
Am = Plate current milliammeter-supplied with a shunt for 0, 0.1, 1, 10,
100, 1000 ma.
B = Plate battery-6 amp. hr.
Ci = Bypass condenser-2, mica, capacity 0.002 4f
Ci' = Bypass condenser-mica, capacity 0.003 Af
Ca = Variable condenser of coupled circuit (G.R. Precision Type 227)-
capacity 0.0015 Af
Ca = Mica cartridge grid condenser-capacity 0.003 pf
C9' = Mica cartridge grid condenser-capacity 0.001 4f
Co = Variable condenser of oscillating circuit-capacity 0.003 Af
D = Compensating battery-6 amp. hr.
L, = R.F. choke coil
Li' = R.F. choke coils, 8 in. x 15 in. single layer 1100 T, 95 mh.
L2 = Inductance in capacity branch of oscillating circuit
L3 = Coil of G.R. Precision Wavemeter
Lo = Inductance, edgewise wound copper strip, 15 cm. diameter, 0.5 cm.
spacing
R. = Compensating resistance
Rf = Filament rheostat
Rz' = 1100 and 12,000 ohm stovepipe rheostats in series
R ' = Cartridge grid leak
R, = Grid leak 5000 ohms
- = Ammeter shunt
Th = Thermo-ammeter
V = Vacuum tube of oscillator
V' = Vacuum tube of compensator
Characteristic Data of Oscillator Tubes:
UX-210 UV-202
Max. Filament Voltage, volts ........ 7.5 7.5
Max. Filament Current, amperes..... 1.25 2.35
Max. Operating Plate Voltage, volts.. 350 350
Max. Plate Current, ampere......... 0.060 0.050
Amplification Factor p.............. 8 7.5
Normal output, watts ............... 7.5 5
Type of filament................... Thoriated Tungsten Pure Tungsten
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 13
K
K
K)
----Effect/l'e Crac'er/t/,C-, o**'i"
W½/?f Lvo'a'-^T^
S.- (b), ,, Effeci"'-e
,V Cha,'vc/e/'zs/'c, Vo L oad
-'i 3 r- --
8 --0-- _ ___ _- --
f (/J, ao
.0 0.
r3/ o.4
4-- - - - - 7c' 3./.<.- -2
T&rid &'I-,_e'=
Fia. 2.
ze9 eo 0/ e' e.?3 E4 e.5-
'/,"a',z'e,,' C$&rre/n/ t7 A 1 e1,-res
CHARACTERISTICS OF OSCILLATING TUBE AS A FUNCTION OF
FILAMENT CURRENT
Ký
III. FACTORS INFLUENCING SHAPE OF PLATE CURRENT
TUNING CURVES
8. Influence of Filament Current.-Preliminary to measuring the
plate current variations, the characteristics of the oscillator tubes
were taken. A variety of types of tubes were tested. As all of them
showed measurable variations of plate current when a coupled circuit
was tuned, two types, UV-202 and UX-210, were chosen for a closer
study.
Of each type, two oscillator tubes were selected showing similar
characteristics. When in the course of the investigation one of them
showed marked changes in its characteristics due to prolonged use,
it was replaced by the other. For instance the study of the influence
of filament current at constant potential (Fig. 5) was made with one
tube type UV-202, while the study of the influence of plate poten-
tial at constant filament current (Fig. 9) was made with the other tube
of the same type.
ILLINOIS ENGINEERING EXPERIMENT STATION
Co7ace,7ser z'7/ ,Se1/,g of Copl/ed C/,cc'/-
Fia. 3. PLATE CURRENT TUNING CURVES FOR DIFFERENT VALUES OF
FILAMENT CURRENT
Figure 2 represents the characteristics of the Radiotron UV-202 as
functions of filament current at a constant plate potential of 100 volts.
The "static characteiistic" curve c shows how the plate current varied
when, by disconnecting the condenser Co of 2400 if. capacitance
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 15
Fia. 4. PLATE CURRENT VARIATIONS PRODUCED BY ADJUSTING A COUPLED
CIRCUIT INTO RESONANCE WITH THE OSCILLATOR AS FUNCTION
OF FILAMENT CURRENT
(Fig. ic), the tube was stopped from oscillating. The "effective char-
acteristic"* curve b shows the plate current I, when the tube was
oscillating, the oscillating current Io being shown by curve d.
Curve a shows that coupling the oscillator with another circuit
*The term "effective characteristic" as defined here will be used throughout the investigation.
ILLINOIS ENGINEERING EXPERIMENT STATION
changes the shape and slope of the effective characteristic curve.
These changes and the intersection of the characteristics b and a ob-
tained for the oscillator when unloaded and when loaded by a coupled
circuit play an important part in the formation of the plate current
tuning curves, as will be shown in Section 17.
Figure 3 shows four groups of plate current tuning curves obtained
for different values of the filament current I, of the oscillating tube
UV-202, starting from the lowest value at which the tube would oscil-
late. Observing the character of the curves it is noticed that by grad-
ually increasing the filament current the peaks of the curves diminish
in height so that at a filament current of 1.92 amperes no variation
whatever of the plate current is produced by the coupled circuit. The
filament current If, being continuously increased it was found that
the curve shows a depression at resonance instead of a peak, the de-
pression increasing with increasing filament current, as shown in
Fig. 3a. At a filament current of 2.00 amperes a change in the char-
acter of the variations takes place. The depression begins to ap-
proach the zero line, as indicated in Fig. 3b. At the same time the
formation of a peak on each side of the depression sets in, these peaks
becoming more and more prominent and coming closer and closer to-
gether, and the depression gradually disappearing. At I, = 2.04
amperes the curves resume the form of typical resonance curves with
increasing peaks as If is increased. At a current Iy = 2.07 amperes,
another tendency becomes marked. This stage is shown by the group
of curves in Fig. 3c, which indicate that the values of the peaks grad-
ually decrease without, however, becoming zero. For I, = 2.15 am-
peres, a minimum is reached. From this point on the peaks of the
plate current tuning curves begin to increase again with increasing
If, as shown by the group of curves plotted in Fig. 3d. Character-
istic of all groups of curves in Fig. 3 is the fact that the position of
resonance of the coupled circuit always coincides either with a peak
or with a depression of the curves. In order to facilitate a comparison
of the relative sharpness of these resonance curves two dotted lines
are shown, separated from the resonance point by a distance cor-
responding to 1 per cent dissonance.
By inspecting the curve in Fig. 4 a general picture is obtained of
how the variation of plate current due to coupling of a resonant cir-
cuit depends on the filament current. This curve was obtained from
Fig. 3 by plotting the resonance values of the plate current variations
against the filament current. Sections a, b, c, and d of the curve in
Fig. 4 correspond to the values taken from the respective groups of
curves in Fig. 3. Along the entire range of the curve (Fig. 4) there are
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 17
only two definite values of filament current, I/ = 1.92 and If" =
2.02 amperes, for which a coupled resonant circuit exerts no influence
whatever upon the plate current. Between these two critical values
is confined a narrow region where the coupled circuit causes a de-
pression of the plate current. Remarkable is the narrow zone ex-
tending on both sides of the second zero point I/' = 2.02 amperes,
and marked by a dotted line. All of the plate current tuning curves
within this region show two maxima with one minimum situated be-
tween them. The points along the dotted line give the values of plate
current variations for those characteristic maxima. The rest of the
curve has positive values of plate current variations showing that pre-
dominantly the plate current tuning curves are peaked.
9. Influence of Plate Voltage.-For the study of the influence of
the plate voltage ten series of measurements were taken, each series
for a different filament current, and each representing a family of
14 curves taken for a range of plate voltages of from 25 to 400 volts.
The most characteristic curves for a UV-202 tube are shown in Figs. 5
and 6. Figure 5 shows that at 36 volts, a region of voltage at which the
tube just starts to oscillate steadily, the plate current variation curves
showed a distinct depression whenever the coupled circuit was in reso-
nance with the oscillating circuit. As the voltage was increased the de-
pression became smaller and smaller. At about 60 volts three char-
acteristic points appeared on the curve, there being a maximum on
either side of the depression. At 100 volts, the plotted increments of
plate current acquired the shape of resonance curves with peaks be-
coming more and more prominent as the voltage was increased. The
dotted lines K-L and P-Q crossing the curves are drawn at a distance
corresponding to 1 per cent dissonance. A general view of how plate
current variations depend on plate voltage is obtained by inspecting
Fig. 6, in which the values of the plate current variations for reso-
nance are plotted against the plate voltage. The plate current varia-
tions are directly transposed from Fig. 5 to Fig. 6. We find here
again, as in Fig. 4, the existence of two regions and of a critical value
of potential for which AI, at resonance is zero. In one of them, rep-
resented by branch a, b, the characteristic of the plate current varia-
tion is a depression, while that for branch c is a peak. Similarly for a
certain region, extending from 70 to 90 volts, the curves show depres-
sions and maxima. This region is marked in Fig. 6 by a dotted line
which represents the value of the maxima.
In order to show the character of the curves when the ordinates
represent the total plate current, including the variations produced by
ILLINOIS ENGINEERING EXPERIMENT STATION
Con/denser D/2/ Sew/7yg of
Couo/ea' C/'cu//?
FIG. 5. PLATE CURRENT TUNING CURVES
FOR DIFFERENT VALUES OF PLATE VOLT-
AGE
FIG. 6. CURVE SHOWING VALUES OF
VARIATION OF P L A T E CURRENT
PRODUCED BY ADJUSTING A
COUPLED CIRCUIT I N T O RESO-
NANCE WITH THE OSCILLATOR AS
FUNCTION OF PLATE VOLTAGE
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 19
0 /00 ~ 300 400
Co7a/<y7se-o Dlav/ Se1/'n P/07e Vol/ta/ e
of Cocupl/ed Circuit Z. in vo/tS
FiG. 7. PLATE CURRENT TUNING CURVES
FOR DIFFERENT VALUES OF PLATE VOLT-
AGE AS THEY APPEAR WHEN TAKEN
WITHOUT COMPENSATION OF STEADY
PART OF PLATE CURRENT
FIG. 8. CURVEs SHOWING
VALUES OF VARIATION OF
PLATE CURRENT PRODUCED
BY ADJUSTING A COUPLED
CIRCUIT INTO RESONANCE
WITH THE OSCILLATOR AS
FUNCTION OF PLATE VOLT-
AGE
ILLINOIS ENGINEERING EXPERIMENT STATION
a coupled circuit (without use of compensation), a family of curves is
shown in Fig. 7. These were plotted from observations made when
the filament current was kept constant at 2.30 amperes, the coupling
at 0.35 per cent, and the plate voltage only was varied. The advan-
tage of compensating the steady component of the plate current is
readily seen by comparing these curves with those of Fig. 5.
Instead of reproducing families of curves obtained for other fila-
ment currents, Fig. 8 shows the values of plate current variation for
the resonance condition only, as a function of plate voltage for three
values of filament current, If = 1.93, 2.18, 2.30 amperes, respectively.
The distinction of Fig. 8a from Figs. 8b and 8c is the absence of the
dotted line indicating a region in which the plate current variation has
the three characteristic points, two maxima and one minimum.
Figure 8a represents one of a number of families of curves in which the
plate current variations show either a maximum or a depression.
10. Influence of Coupling.-In order to study the influence of
coupling upon the plate current tuning curves, data were taken for
different distances between the coil of the oscillator and that of the
tuned circuit. The coupling coefficient for each distance was deter-
mined by measuring the change of frequency produced by shorting
the coil of the coupled circuit. As this change of frequency was ex-
tremely small, a double heterodyne method was used. Details of this
method are described in Appendix A and the results of these measure-
ments are represented by Fig. 23a, the curve giving the coefficient of
coupling for each distance between the centers of the particular coils
used in the investigation.
The plate voltage was kept constant, E, = 100 volts, while the
filament current was varied from 1.88 to 2.35 amperes. For each
value of filament current a series of measurements of plate current
variations was made for different values of coupling. The most char-
acteristic results for type UV-202 tubes are represented in Figs. 9 and
10; Figs. 9a, 9c, 10a, and 10c give groups of curves showing the rela-
tion between the tuning of the coupled circuit and the plate current
variation produced in the oscillator; Figs. 9b, 9d, 10b, and 10d show
how the magnitude of the plate current variations at resonance varies
with the coupling coefficient. The dotted line in Fig 10d indicates the
zone where two characteristic points besides the one at resonance ap-
pear on the curve. For couplings greater than 0.01 the known phe-
nomenon of the oscillations becoming unstable at resonance (often
called ziehen effect) takes place. In this case, as in the usual resonance
curve, the maximum of the variation does not appear at the point of
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 21
Cond9eser li9/ Se/i/'g of Coe0f/ce'i/ of
CcOn/ft/ea' Ci/'l Covp/lg'
FIG. 9. RELATION BETWEEN PLATE CURRENT VARIATIONS AND CO-
EFFICIENT OF COUPLING
resonance, but is displaced more or less depending on the degree of
coupling and on the direction of varying the frequency of the coupled
circuit, i.e., whether the observations are made while going up or
going down the scale of frequency.
By inspecting the curves it is found that the effect of increasing
the distance between the coils, which is equivalent to decreasing the
ILLINOIS ENGINEERING EXPERIMENT STATION
Coeff/'Aclent/ of Cou04p/i
aos ad/ 0oo5f wo1/9 ao4/z
/10 O 30 40 SO
i/&
Condenser /a7/ Setwny 9/sstance between C
of Coul/eod C/rct// Centers /;7 cm.
FIG. 10. RELATION BETWEEN PLATE CURRENT VARIATIONS AND
COEFFICIENT OF COUPLING
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 23
FIG. 11. EFFECTS OF RESISTANCE INSERTED IN AN OSCILLATING CIRCUIT, PRODUCED
BY ADJUSTING A COUPLED CIRCUIT INTO RESONANCE WITH THE OSCILLATOR
coupling, is to diminish the variation of plate current. Under certain
conditions, however, the variation becomes zero (critical value of
coupling), and at a still smaller coupling changes sign. For instance,
Fig. 10d shows the zero variation point to be at a distance of 35 cm.,
corresponding to a coefficient K = 0.003. For still smaller coupling
coefficients the plate current tuning curves show a change from a de-
pression to a peak.
11. Influence of Resistance.-The character and the magnitude of
the plate current variation of the oscillator, produced by the coupled
ILLINOIS ENGINEERING EXPERIMENT STATION
circuit, depends also on the resistance of the oscillator circuit. Fig-
ure lla shows two typical curves obtained by observing the plate
current variations AI, for different values of resistances inserted in
the inductance branch of the oscillator circuit when the coupled cir-
cuit was adjusted for resonance. The 7.5-watt tube used in the oscil-
lator had a thoriated filament, and was of the Type UX-210. The
internal resistance of the oscillating circuit was 1.5 ohms. For
a filament current I, = 1.00 ampere and a plate voltage of 200 volts
the coupled circuit caused a depression-AIl of 1.12 ma., the depres-
sion decreasing with the resistance. For values of the inserted resist-
ance greater than 0.64 ohm, AI, assumed positive values. Another
curve was obtained by increasing the filament current If to 1.25 am-
peres while the plate voltage remained 200 volts. The variations of
plate current AI, changed from positive to negative values for a re-
sistance of 0.76 ohms (point 0'), reaching a maximum of depression-
AIp = 1.64 ma. for 1.48 ohms, and passing again through zero for
3.16 ohms. The values of radio-frequency current Io in the oscillator
circuit, corresponding to the inserted resistances, are plotted in the
curves of Fig. lib. The effect of increasing the plate voltage was to
shift the transition point 0 " toward larger values of inserted resist-
ance.
From theoretical considerations it was important to know whether
the character of the maximum plate current variations due to a coup-
led resonant circuit would be changed by inserting a resistance in the
capacitance branch of the oscillator instead of in the inductance
branch, as has been done in the experiments recorded in Fig. lla. Two
series of measurements were made with the oscillator driven by a UX-
210 7.5-watt tube at 300 volts plate potential and 1.25 amp. filament
current. The first series is plotted in Fig. 12. The abscissas represent
values of resistances in ohms inserted in the capacitance branch of the
oscillator circuit.
The ordinates for curves a, b, and c were obtained in the following
way: Let I, represent the plate current when the oscillating circuit
was opened and therefore inactive; I,' the plate current when the os-
cillating circuit was closed and active, but the coupled circuit was
completely detuned or removed; Ip,' the plate current when the oscil-
lator was active, but the coupled circuit was in resonance. Then the
ordinates of curves a, b, and c are determined by the plate current
differences:
a = I,' - Ip
b = I" - I,
c = - a = I" - I' = A,,
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 25
0 / 3 4 5- 6"
FIG. 12. INFLUENCE OF RESISTANCE INSERTED IN PRIMARY OSCILLATING
CIRCUIT ON VARIATION OF PLATE CURRENT AND OSCILLATING
CURRENT, PRODUCED BY A TUNED COUPLED CIRCUIT
For point Q on curve a, I,' - I, = 0, and R = 0.45 ohms, the plate
current remained the same whether the tube was in an oscillating or
a non-oscillating state. Curve a thus shows the difference I," - Ip
as a function of the inserted resistance R when the coupled circuit
was completely detuned or removed, while curve b gives the same
relation for a coupled circuit (K = 0.0035) tuned in resonance with
the oscillator. The difference of the ordinates of curves a and b results
in a curve c, which is equivalent to the variation of plate current AI,
due to the presence of the resonant circuit. As in the former cases,
for a definite critical value of inserted resistance (R = 3.37 ohms),
a transition point 0 on curve c was obtained, above which the reso-
ILLINOIS ENGINEERING EXPERIMENT STATION
240
206
/60
80
40
'C
. F_____y .
13. CRITICAL PLATE POTENTIAL As FUNCTION OF THE RATIO C/L
13. CRITICAL PLATE POTENTIAL AS FUNCTION OF THE RATIO C//L
nant coupled circuit produced a depression and below which a peak
resulted in the plate current variation tuning curve. Curves d and e
give the oscillating radio-frequency currents lo', Io", respectively, in
amperes, measured simultaneously with the plate currents I,' and I, ".
The values of Io" are smaller than those of Io', indicating that the
coupled circuit exerts a reaction upon the oscillating circuit, reducing
the effective current in the latter by about 10 per cent.
The second series of measurements was made with resistances in-
serted in the inductance branch of the oscillating circuit. Curves of
similar character and with ordinates of the same order of magnitude
were obtained, with the exception that the resultant curve c showed
a shift towards larger values of R (3.6 ohms).
12. Influence of Damping.-For the study of the influence which
the load produces upon the character of the plate current tuning curves
I.'
~1.~
N.
N
N
Tae d/%2/10
A= 240 Me,'e-.s
R= 18 Ohi'3
4_ = / Atz'pere
4s/' -/^y^ I
--&___ __ __ .
4
-J
P
0
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 27
23
22
Z/
1½
/20
Ioo.
lso
/0
80
60
40
0
ao
Co7den/?set- L/i/ Se/tiAg of Coi/o/e' C/r-c//i>
Fia. 14. PLATE CURRENT AND GRID CURRENT TUNING CURVES AND BJERKNES
RESONANCE CURVE OBTAINED AT 333.1 KC. WITHOUT THE USE OF COMPENSATOR
it is useful to know not only the influence of the resistance but also
that of the other factors which determine the logarithmic decrement
= 152 Rw CF. Measurements were therefore made with an os-
LH
C
cillator circuit in which the ratio - could be varied over a large range
L
for a constant frequency, constant filament current, and nearly con-
stant resistance. The coupling was not measured, but was kept small
enough not to affect the character of the curves. The frequency used
was 1250 kc., the total resistance of the oscillating circuit was 1.8
ohms, and the capacitance of the circuit was varied from 160 to 400
jutf. Instead of taking the entire system of plate current curves the
ILLINOIS ENGINEERING EXPERIMENT STATION
++
bd
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 29
measurements were limited to the determination for every value of the
C
ratio - that particular plate potential at which no change whatever
L
in the plate current was produced by a coupled circuit adjusted to
resonance. This critical plate potential is important because it indi-
cates the transition point at which the plate current tuning curves
change their character from depressions to peaks. (See, for instance,
point where curve crosses zero line 0 in Figs. 8a, 8b, and 8c). In Fig.
C
13 the critical potentials E,' are plotted against the ratio -. It can
L
be concluded from the curves that increasing the damping shifts the
critical voltage at an increasing rate to higher potentials.
13. Influence of Frequency.-The plate current variations pro-
duced by tuning a circuit coupled with the oscillator have been in-
vestigated over a wide range of frequencies. Frequency bands as low
as 149.9 kc. (X = 2000 m.) and as high as 999 300 kc. (X = 3m.) were
used for this purpose. The general character of the plate current
tuning curves was found to be similar for all frequencies, the types of
the curves obtained depending on the filament current, plate voltage,
coupling, and damping of the oscillator. For every frequency investi-
gated the particular conditions could be found at which the plate
current tuning curves showed either peaks or depressions, or the in-
termediate shapes. Figure 14 and the set of curves a, and a' in Fig. 15
may serve as examples for the following frequencies: 333.1, 1499,
3748, 21 420, and 63 120 kc. The abscissas are settings of the con-
denser in the coupled circuit. Curves marked al show depressions,
while those marked a' indicate peaked curves. The conditions under
which they have been obtained are given in Table 1. Thus it may be
demonstrated that, by choosing proper conditions, the various types
of plate tuning curves investigated can be obtained at any radio-
frequency. The peaked curves always appear at higher plate voltages
than those showing a depression.
The curves for AI, in Fig. 15b give a remarkable example of a
plate current tuning curve obtained under conditions such that the
amplitude of oscillations of the tube was far too small to be measured
by the usual thermo-electric instruments. However by a d-c. micro-
ammeter inserted in the plate circuit, and compensated as described
in Section 6, plate current variations of 24 micro-amperes were pro-
duced by adjusting a wavemeter for resonance. The applied voltage
at which the curve was obtained was only 8 volts, that is about 2 per
cent of the normal operating voltage.
ILLINOIS ENGINEERING EXPERIMENT STATION
C)
0
0
C)
0))
C-,
CC'
0 0 C o000
0 t00
Co100
Co
0 O ONOtOOO
Co0CO0O'O
NCO CONNC~-
=====^ t -30 N N
N NCO O C CON N
N N CO i-i-CO CO
Co Co
>0»N
b O00 C
0 Co Co -
00SC Co O CoCo C
. o
C)
S*** 3 b*~
0T
f0
oo.
o>
'
C)
C)
d
C)
C)
0).
|J
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 31
Wioer'ee/ler 5e,, e '/n ' Sc /, ,/e z2//ir//or7s
FIG. 16. GRID CURRENT TUNING CURVES OBTAINED AT DIFFERENT
PLATE POTENTIALS
14. Influence of Types of Tubes and of Oscillator Circuits.-In-
spection of the data specified in Table 1 shows that the plate current
tuning curves al and a' of Fig. 15 represent examples chosen from
measurements with a variety of types of oscillators and oscillating
tubes. Besides the types mentioned a great many other tubes and
oscillators were tested. From the similarity of these curves it may be
ILLINOIS ENGINEERING EXPERIMENT STATION
concluded that the plate characteristic current variations as produced
by tuning of coupled circuits represent a quite general property of
oscillators driven by thermionic tubes.
15. Grid Current Tuning Curves.-Simultaneously with the varia-
tions of plate current, variations of the grid current were also meas-
ured. The latter are represented in Figs. 14 and 15 by the curves b,
showing a depression. In order to ascertain that this is the prevalent
type of grid current tuning curve, measurements of grid current varia-
tions were made with a Radiotron tube, Type UV-202, over a range
of plate voltages of from 37 to 400 volts. From the results plotted
in a system of curves (Fig. 16) it appears that for any plate potential
a more or less pronounced minimum in the grid current tuning curve
is produced when the coupled circuit consisting of a wavemeter is
adjusted for resonance.
16. Properties of Plate Current Tuning Curves.-The plate current
tuning curves assume complicated forms in the vicinity of the critical
potential, and also for coupling above the critical value. However,
it is possible to apply the right potential, and also to choose the
mutual inductance between the two coupled circuits so that the coup-
ling coefficient remains below the critical values. Then the shape of
the plate current tuning curves assumes the simplest form, showing
distinctly one maximum or one minimum. These characteristic
points were found to correspond to the condition of resonance between
the oscillating and the coupled circuit. To verify this correlation a
great number of observations were made by simultaneous measure-
ments of plate current variations AI,, grid current I,, high frequency
current Is in the coupled circuit, and also of the current Io in the pri-
mary oscillating circuit as functions of the degree of detuning (dis-
sonance). The curves in Figs. 14 and 15 show these relations. The
n122 relation is plotted with ordinates proportional to the deflection
of a Weston thermo-galvanometer and represents a true resonance
curve.
The maxima or minima of these curves coincide with the ordinate
corresponding to the resonance setting of the condenser of the coupled
circuit. The depression in the curve for Io at resonance decreases
rapidly for smaller coupling coefficients.
It was important to know how close the plate current tuning
curves resemble the true resonance curve. Figure 17 gives the result
of a comparison. The two curves plotted are based on values of AI,
and n122 taken for this purpose from Fig. 14. Multiplying the values
of the ordinates of each curve by the factor m, = 0.645 and m2 =
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 33
IT
I
^
^
i
I
^
Co2/c/ef7set/r 1/e7/ Se/ti c'f Co'/e6/ C/Ci///
Fia. 17. COMPARISON OF A PLATE CURRENT TUNING CURVE WITH A
BJERKNES RESONANCE CURVE
0.0087, respectively, two new curves of Fig. 17 were obtained, having
equal maximum values at resonance. The agreement in this as in
many other cases was found to be close; however, in some cases more
or less marked deviations from the true resonance curves were
obtained.
ILLINOIS ENGINEERING EXPERIMENT STATION
17. Interpretation of Plate Current Tuning Curves.-A completely
satisfactory explanation of the various forms of plate current tuning
curves cannot be offered at the present stage of our knowledge of the
complicated phenomena which take place in the oscillating tube.
However, it is possible to interpret all of the described variations of
plate current on the basis of the effective characteristics. It is well
known that loading the oscillating tube changes its effective charac-
teristic. In Fig. 18 the curves b, and bo indicate the plate potential-
plate current relation for the tube when it was in the oscillating state.
The curves are not similar. Curve b. was obtained when the oscil-
lator had no external load whatever, while bo corresponds to the con-
dition when the oscillator was loaded by a coupled circuit adjusted
to resonance. For the detuned coupled circuit a family of such curves
bi, b2, b3-b. would be obtained, each curve giving the effective char-
acteristic for the particular degree of dissonance.
The differences between the ordinates bo-bn, bi-b., b2-b., etc.,
taken for a particular plate voltage and plotted against the degree
of dissonance, produce a plate current tuning curve for that voltage.
A system of such curves is obtained when the differences of ordinates
are taken from the curve, Fig. 18, along a number of other plate
voltage ordinates.
As an example of the correctness of this interpretation a group of
plate current tuning curves is shown in Fig. 19, obtained with a
Radiotron tube, Type UX-210, under conditions as denoted in the
drawing. To prevent confusion only two effective characteristics of
the same tube are shown in Fig. 18, curves b. and bo. They were
taken at the same time as the measurements represented in Fig. 19.
The differences AI, = b. - b. which are given by the curve c should
represent the ordinates- of the plate current tuning curves for the par-
ticular case of resonance of oscillator and coupled circuit. That this
is actually the case can be ascertained by inspecting the curve c of
Fig. 18, and the ordinates for resonance in Fig. 19. For instance, the
peak P of the plate current curve in Fig. 19 obtained with a plate
voltage of 100.3 volts has the same ordinates (Alp, = +0.84 ma.) as
the point P of curve c in Fig. 18 corresponding to E, = 100.3 volts.
Likewise for E, = 50.5 volts the depression D (AI, = -0.43 ma.)
in Fig. 19 agrees with the value of bo - b, for the point D on curve c,
Fig. 18, for the same voltage.
Remarkable in Fig. 19 is the curve obtained with a plate voltage
E, = 62.3 volts; it has two peaks, one on either side of the resonance
point, and is noted by a depression nearly reaching the abscissa axis.
By projecting the lowest point, 0, of the depression upon the curve c
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 35
_z l! a "/ 's,,o/,z .
M El
sa to .
Fa
E- H '
O F
0
z
*a a
<sa
F. Si&
0
CL
G°
.Cr
%
VeW ///^ '.ý?, /-- .9">/01d
ILLINOIS ENGINEERING EXPERIMENT STATION
of Fig. 18, and by inspecting the effective characteristic at the par-
ticular plate voltage, an intersection of curves bo and b. is found in
point 0' very near this voltage. The fact that the point of intersec-
tion AI, = b. - b. = 0 appears at 60 volts explains why a very small
plate current variation was obtained at 62.3 volts.
The same method of studying effective characteristics and check-
ing them with plate current tuning curves was applied for tuning
curves obtained for constant plate voltage and variable filament
current. So, for instance, in Fig. 2 the intersection between the two
effective characteristics a and b occurs at a point P corresponding to
a filament current of 2.02 amp. The plate current tuning curve for
this filament current is reproduced in Fig. 3(b) and shows indeed
AIl = 0 at resonance. In this case also the results justify the fore-
going interpretation.
The various types of the plate current tuning curves may be inter-
preted in terms of the properties of the effective characteristic curves.
Whenever, by varying the frequency of the coupled circuit, a family
of characteristics is obtained which intersect each other all at one
point, the plate current variations form resonance curves. Conditions
corresponding to any group of values of ordinates, obtained by cross-
ing the effective characteristics on one side of their point of intersec-
tion, produce the usual peaked resonance curve. An inverse reso-
nance curve showing a depression is produced by a group of ordinates
crossing the effective characteristics on the other side of their point
of intersection. If, however, in a family of effective characteristics
the curves intersect each other at various points deviations from the
resonance curves follow. Ordinates obtained by crossing the charac-
teristics near the zone of their intersections give complex plate current
tuning curves, often with a minimum stituated between two maxima.
IV. PRACTICAL APPLICATIONS
18. Determination of Oscillation Frequency of Circuits.-The char-
acteristic plate current variations, assuming a maximum increase or
a maximum decrease when a coupled circuit is tuned to resonance,
give a convenient means for the determination of the frequency of
oscillation and of the damping of circuits. If a wavemeter is used for
the coupled circuit, as was the case in most of the measurements in
this investigation, the frequency of the oscillating circuit is deter-
mined by adjusting its setting for a maximum increase or decrease of
plate current variations. The latter are observed by means of a milli-
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 37
or micro-ammeter whose current is compensated by any of the meth-
ods indicated in Chapter II. Of these methods, the thermionic shunt
method described in Section 6 gives the possibility of obtaining stable
indications with a micro-ammeter, and of using couplings so small
that a sharp plate current tuning curve results from the measure-
ments. Should the plate current variations at resonance be too small,
larger variations may be obtained by readjusting the filament current
or plate voltage of the oscillator. Conditions have to be chosen so as
to work outside the critical zone, which, as has been shown in Section
17, corresponds to the zone of intersection of two effective character-
istics of the oscillator. This zone is restricted to a narrow margin of
filament currents and plate voltages. Also the zone where the plate
tuning curves show depressions is narrower in comparison with that
where the plate tuning curves have a pronounced peak. The latter
is the prevalent form and therefore can be easily obtained, while other
forms must be searched for. For measuring purposes the use of the
peaked form of plate tuning curves is to be preferred because they
show greater maximum values of AI, than other forms of curves.
For the compensation of the current flowing through the plate
ammeter the following must be considered: The sensitivity of the
meter is first diminished by a shunt so as to allow just an indication
of the magnitude and character of the plate current variations due to
tuning the wavemeter. If the variations indicate a peak at resonance,
the compensation is gradually adjusted to bring the pointer to the
zero position, while the shunt is set step by step for a higher sensi-
tivity of the meter. If the current variations indicate a depression
at resonance the same procedure is used until the desired sensitivity
is reached, but the compensation is finally adjusted to indicate a full
scale reading. While the compensation is being adjusted the setting
of the wavemeter must be as far as possible from the position of reso-
nance.
By utilizing the plate current variations for frequency determin-
ation, the high-frequency current indicator which is usually inserted
directly or inductively in the wavemeter circuit can be entirely ex-
cluded. The damping of the measuring circuit is thus reduced, and
the precision of frequency measurements is considerably increased.
19. Determination of Logarithmic Damping Decrement of Circuits.-
It was found that the plate current tuning curves can also be applied
for measuring the damping decrement of circuits with an accuracy
equal to that obtainable with a thermo-galvanometer inserted in the
circuit whose damping is measured. Indeed, measurements showed
ILLINOIS ENGINEERING EXPERIMENT STATION
that the width of the plate tuning curves for ordinates equal to half
values of the resonance ordinate increases with the resistance inserted
in the coupled circuit. Similarity of these tuning curves with the
usual Bjerknes resonance curves, as shown for instance in Fig. 17,
leads to the conclusion that approximate values of the logarithmic
decrement 5 can be calculated from the plate current variations using
the relation
Cr - C, 1
S C1W AIr / AI - 1
when Air is the value of the plate current variation produced by the
wavemeter at the resonance frequency corresponding to the conden-
ser setting C, and AI1 the plate current variation at another frequency
corresponding to the condenser setting C1.
The advantage of this new method for measuring the logarithmic
damping decrement is derived by excluding from the measuring cir-
cuit sources of damping due to the resistance of thermocouples or of
other current indicating devices.
In order to obtain accurate plate current tuning curves for this
purpose it is necessary to ascertain first that there is no drifting of
the pointer of the plate current meter. Usually drifting takes place
when the condition of the oscillator or batteries is different from that
of the compensator. The observations must be taken rapidly enough
to limit the error to negligible values, or the method of determining
total differences may be applied. It consists in measuring for every
chosen setting of the wavemeter the plate current Alp', and also in
observing the plate current AIp" when the wavemeter condenser is
quickly shifted to a position entirely out of resonance, at which no
plate current variation whatever takes place. The total variation
Al, = AIR' - Ai, "
is independent of the drift taking place between two consecutive po-
sitions of the wavemeter. Many of the curves in this investigation
were obtained in this way.
The following data of measurement of the logarithmic damping
decrement of a wavemeter circuit may serve as an example of the use
of the plate current variations for the determination of damping.
The condenser of the wavemeter had at resonance a capacity of
C2 = 542 micro-micro-farads, corresponding to a wavelength X =
166.2 m. (f = 1 807 300). In the plate circuit of the oscillator, sup-
plied with a UX-210 7-watt tube, was inserted a micro-ammeter and
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 39
a compensating arrangement according to the diagram in Fig. lb.
This meter was not fully compensated and showed a current I" =
llUa when the wavemeter was completely detuned or removed. At
resonance the meter indicated AI/' = 79pa. Thus the increase of
plate current due to the wavemeter having been set for resonance was
AIr = 79 - 11 = 68iua. The wavemeter was then detuned until
68
Ali assumed half the value of AI, or AI1 - 2 + 11 = 45ya. This
value was obtained at the condenser setting C1 = 890, while the set-
ting for resonance was Cr = 907.5. Because of the linear relation
between the capacitance and indications of the wavemeter setting, the
latter were used in evaluating the above formula for the logarithmic
decrement
3.14(907.5 - 890) / 1
= 890 68 0.0617
34-1
The equivalent resistance of the wavemeter circuit is given by the
known relation
R A 0.0617 x 166.2
R 5918 C 5918 x 542 x 10-6 = 319 ohms
This calculated value was then checked by measurements. The
method of substitution was used for this purpose. A manganin wire
2 mils in diameter and 0.8 cm. long was inserted in the wavemeter
circuit coupled with the oscillator. The resistance of the wire was
TABLE 2
DATA FOR FIG. 19
1 2 3 4 5
nI' AI, =I' - 11
C a = nl2 p amp. p amp. m AI
863 2 19.5 8.5 2.56
882 6 31.5 20.5 6.17
892 12 48.5 37.5 11.3
900 17 67.5 56.5 17
902 19 73.5 62.5 18.9
905 20 78 67 20.2
907.5 20.5 79 68 20.5
910 20 77 66 19.9
914 17 69 58 17.5
922 12 50.5 39.5 11.9
935 6 32 21 6.34
962 2 18 7 2.11
ILLINOIS ENGINEERING EXPERIMENT STATION
1.95 ohms and reduced the resonance deflection of the thermo-gal-
vanometer from its original value of a, = 80 to al = 30. From these
observations the resistance of the wavemeter circuit was found to be
AR 1.95
R - = 3.09 ohms
-- - 1
a, 30
in close agreement with the value calculated from the logarithmic
decrement determined from the plate current tuning curve.
Table 2 contains data of both the plate tuning curve AI, and the
resonance curve nI2 taken simultaneously for the purpose of checking
these measurements. Both curves are plotted in Fig. 20.
Column 1 gives the condenser setting; column 2, the deflection of
the thermo-galvanometer inserted in the wavemeter circuit; column
3, the reading of the partly compensated plate current meter; column
4, the increase of plate current AI, obtained by subtracting from the
previous column lla, corresponding to the indication of the plate
current meter when the wavemeter was removed entirely or detuned.
The last column, 5, shows the values of column 4 multiplied by a
factor
amax 20.5
S- = - = 0.302
Alp max 68
From the agreement between the values of a = nI' for the reso-
nance curve and the values mM, for the plate current tuning curve
it follows that the two curves are similar.
20. Application to Parallel Wire Measuring Bridge.-In measur-
ing frequencies higher than 30 megacycles two additional advantages
accrue by the application of the plate current variations. In the usual
wavemeter circuit a thermo-electric instrument is included, which has
to indicate values of high frequency currents as functions of the degree
of dissonance. However, in circuits oscillating with very high fre-
quencies the distribution of current and potential plays an important
part in the indication of the meter. The instrument not only in-
creases the resistance of the circuit, but also changes the distribution
of the current. Furthermore, the effective resistance of the instru-
ment is influenced by its position relative to the nodal zones, and also
by the frequency of the oscillations. All these difficulties may be
overcome by excluding the instrument from the wavemeter circuit
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 41
C'ot7/enser- i0/1 Sel//g' aof C eIl/ez/ CircugeZ
FIG. 20. SIMILARITY OF A PLATE CURRENT TUNING CURVE WITH THE
CORRESPONDING BJERKNES CURVE
and applying instead plate current variations of the oscillator to indi-
cate resonance between the two circuits.
This method was found especially convenient in connection with
the parallel wire measuring bridge, as used for the calibration of short
wave transmitters.* The insertion of a current indicator in such a
bridge system increases its attenuation factor and necessitates special
corrections due to the end effects of the terminals, thermocouple, and
galvanometer. It is possible to eliminate this error by moving the
*Univ. of Ill. Eng. Exp. Sta. Bul. 147, p. 25. May 25, 1925.
Jour. Opt. Soo. of Am. Vol. 11, p. 641, Dec., 1925.
Research. Electrotechnic. Lab. Tokyo, No. 177, Aug., 1926.
ILLINOIS ENGINEERING EXPERIMENT STATION
bridge contact slide away from the first nodal point until another node
is reached. The distance between the consecutive nodes determines
then the half wave length. The limitation of space in a laboratory,
however, does not always permit the use of this procedure. By using
the method of observing plate current variation of the oscillator it
is possible to remove the measuring instrument from the parallel wire
system, and to obtain even more accurate results with wires only one-
half wave in length.
In order to illustrate the advantage of this method the results of
a series of measurements are plotted in Fig. 21. The oscillator was
set for X = 5.78 m. (51 870 kilocycles), and the parallel wire system,
with a Weston thermo-galvanometer inserted at one end, was tuned
to resonance by varying its length. In Fig. 21a the plate current
variations AIp together with the grid current variations AI, and the
indications of the thermo-galvanometer n121 are plotted against the
length of the parallel wire system. When the thermo-galvanometer
was shorted a much sharper curve was obtained (Fig. 21b). Compu-
tation showed a 40 per cent decrease of damping. Also the length of
the parallel wire system changed from 287.7 cm. to 289.0 cm. due to
the absence of the disturbing end effect of the instrument. Leaving
all conditions the same except the plate voltage, which was reduced
from 250 volts to 50 volts, another set of curves (Figs. 21c and 21d)
resulted, showing for AI, a depression instead of a peak. Neverthe-
less, the comparison of the AI, curves shows the same reduction of
40 per cent in damping and consequently the same increase in sharp-
ness of tuning, produced by shorting the indicator. It may be noted
in connection with Fig. 21c that the energy exciting the parallel wire
system was too small for the thermo-galvanometer to give any indi-
cation of the bridge current, but was sufficient to react upon the
oscillator and to produce a decrease in the plate current.
21. Tuning of Antennae and Transmitting Circuits.-If the coup-
led circuit consists of an antenna and a variable inductance or con-
denser without any current indicating instrument, it is, nevertheless,
possible to tune the antenna to the oscillator by observing the plate
current variations. In most cases the coupling coefficient will be
sufficiently large to produce a measurable variation without the aid
of compensation. However, the compensation provides means of an-
alyzing the character of the variation over a range of frequencies
extending 5 per cent and more below and above resonance.
For normal operating conditions the shape of the plate current
tuning curves usually approaches that of pure resonance curves and,
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 43
'I
K,
iN
N
Lenzgh oe Pagr//e/ a/-e' .Sgy.fe/ e /117 meteu5
FIG. 21. PLATE CURRENT TUNING CURVES AND GRID CURRENT TUNING
CURVES OBTAINED WITH A LECHER PARALLEL WIRE SYSTEM
ILLINOIS ENGINEERING EXPERIMENT STATION
-/C--o - C
/ncr'ease of/ frequeiecy fro,7}
2s /o "cOrdses ro'ta't2 of cc',' -
d&e2ser to fhe r/g'tt ;/,'/i +zgC
//2C/reo'se of p/e/te c'r'/p, tecr-e<s< of f/equeA'cy A>irv'
+LI., Q'c/ivao'es e/!c/o,7aget! A1. 4 to f'cwse.5 ro/a'io/' of co'z-
FIG. 22. DIAGRAMS SHOWING METHODS OF AUTOMATIC STABILIZATION OF
THE FREQUENCY OF COUPLED CIRCUITS
when reduced to equal height, their width increases as the ohmic and
radiation resistance of the antenna increases. Coupling coefficients
above the critical value may be noticed on the sudden jerky plate
current variation taking place just before or just after the resonance
condition is passed, depending on whether the tuning process pro-
ceeds from lower to higher frequencies or in the opposite direction.
Plate current variations were studied when the coupled circuit con-
sisted of a small antenna of the v-type, as illustrated by Fig. 15 on
page 41 of Bulletin No. 147, and had a frequency of 37.93 megacycles
(X = 7.9 m.). The same character of the variations was obtained as
that represented by the AI, curves of Fig. 15 illustrating the relations
for closed circuits. The only difference observed in the shape of the
curves when reduced to equal height was their greater width, as
should be expected if the antenna damping caused by the radiation
resistance is taken into consideration.
22. Control of Frequency Variations.-Theoretically the method of
balancing the plate current flowing through an indicator should
render it possible to study the changes in frequency occurring in a
thermionic oscillator coupled with another tuned circuit. It may also
be possible to control automatically the frequency changes in a cir-
cuit so as to obtain a stabilized source of oscillations. Preliminary
experiments were made with two relays inserted in the plate circuit.
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 45
A remote control impulse driving motor* M (Fig. 22) was used in
connection with relays. The contact lever R' of one of the relays
closed the circuit actuating magnet M', similarly the contact lever R"
of the other relay closed the circuit actuating magnet M ". The com-
pensating resistances n', n " and the direction of the plate current I,
exciting the relays was so adjusted that the armature of the magnet
M' moved whenever a plate current increase took place and the arm-
ature of M " moved whenever the plate current decreased due to a
change in frequency. A vernier condenser of 20ppjuf, shunting the con-
denser of the oscillator and mechanically coupled with M, could be
thus rotated by the magnets of the impulse motor in one or the other
direction. The oscillating circuit was adjusted to be slightly out of
resonance with a coupled circuit, its frequency fo corresponding to a
point o of the resonance curve (Fig. 22). The result was that the
total capacitance of the oscillating circuit automatically decreased or
increased by a value AC whenever the frequency variation fo - f, or
f2 - fo produced plate current impulses AI, in negative or positive
directions, respectively. Similar automatic frequency stabilization
was sustained when the capacitance of the coupled circuit was varied
slightly by means of a vernier condenser. Experiments showed, how-
ever, that though the current compensation could be made sufficiently
stable for a period of time required for taking a series of resonance
curves, it was not possible to eliminate entirely slight but continuous
diminution of the plate current. The slightest decrease of the plate
current, if continued for hours, requires periodical readjustments of
the relays.
V. SUMMARY AND CONCLUSIONS
23. Summary and Conclusions.-A summary of the principal re-
sults of this investigation and the conclusions to be drawn are as
follows:
(1) A method has been developed for a quantitative study of the
variations of current observed in the plate circuit of vacuum tube
oscillators when the constants of a coupled circuit are varied.
(2) By plotting plate current variations against the variable
capacitance of the coupled circuit characteristic plate current tuning
curves are obtained.
(3) Plate current tuning curves can be obtained at all frequencies
investigated within the range of 150 to 100 000 kc. (X = 2000 m. to
X = 3 m.).t
*The motor is described in Bulletin No. 161 on pages 54 and 55. In Fig. 29 of that bulletin the
motor is marked M. In the diagram of connections in Fig. 30 the two driving magnets are marked
M' and M" respectively.
tThis range has been extended recently to audio-frequencies from 3 to 15 k. c.
ILLINOIS ENGINEERING EXPERIMENT STATION
(4) The influence of filament current and plate voltage upon the
shape of the tuning curves was investigated. The existence of criti-
cal values (see Sections 8-12) for each of these variables was dis-
covered. Above the critical values the current variations are posi-
tive, below the critical values they are negative.
(5) The influence of increasing the damping coefficient of the os-
cillator circuit is to shift the critical potentials towards higher values.
(6) For the coupling coefficient there are two critical values: at
the lower one the amplitude of the plate current tuning curves changes
from positive to negative values, at the higher the amplitude jumps
(near resonance) to positions below or above that at resonance (zieh-
en effect).
(7) The plate current tuning curves possess the following prop-
erties:
(a) Above and below the critical values of plate voltage, of
filament current, and of the smaller coupling coefficient, the
curves AI = f(w) approach closely the Bjerknes type, I2eff =
f(w), resonance curves.
(b) At resonance the curves show either peaks or depressions,
increasing with the coupling coefficient.
(c) The width of the curves when reduced to equal height
increases with the damping coefficient of the coupled circuit.
(d) In the region close to the critical values the curves usually
show a variety of complex shapes, having one maximum situated
symmetrically between two minima, or one minimum between
two maxima.
(e) The grid current tuning curves always show a depression
at resonance.
(f) The peak or depression of the plate current tuning curve,
the minimum of the grid current tuning curve, and the peak of
the Bjerknes curve have all a common abscissa corresponding
to the resonance frequency.
(8) It was experimentally verified that the formation of plate cur-
rent tuning curves is due to the oscillating tube varying its effective
characteristic with frequency and load influenced by the coupled
circuit.
(9) Plate current variations may be applied for precise determina-
tion of frequency, and for approximate measurement of the damping
of oscillating circuits. Their use in connection with the tuning of
wavemeters, parallel wire Lecher systems, antennae, and transmit-
ting circuits has been tested.
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 47
(10) A double heterodyne method of measuring small coupling
coefficients has been developed.
(11) A method has been devised for automatic frequency stabili-
zation of oscillating circuits.
APPENDIX A
1. Method of Measuring Small Coupling Coefficients.-For measur-
ing accurately the coefficient of coupling the usual method consists
in finding the two frequencies characteristic of coupled circuits, one
frequency being higher and the other lower than the fundamental of
each of the circuits. For coupling coefficients greater than 5 per cent
this method gives satisfactory results when one of the circuits is
excited by free oscillations produced by quenched spark methods.
For smaller coupling coefficients this method is very inaccurate, and
is limited by the condition that the condensers of the continuous
wave oscillators will not stand the potential applied for the production
of damped oscillations by means of sparks. Kiebitz suggested a
method* based upon the variation of frequency of oscillating circuit
produced by shorting the coupling coil of the coupled circuit. The
variation of the frequency is determined by a wavemeter circuit and
thermocouple arrangement. For very small coupling coefficients this
method of determining the frequency change introduces considerable
errors, due to the fact that the peaks of the resonance curves are not
sufficiently sharp to determine the shift produced by shorting the
coupling coil.
Figure 23 shows diagrammatically the arrangement which was
used in this investigation and which allowed measuring coupling
coefficients down to 0.001. To the condenser Co, of the oscillating
circuit I a small calibrated precision condenser C. was added. The
condenser was of a stepped disc constructiont permitting a variation
of capacitance of about 5 micro-micro-farads for a rotation of 180 de-
grees. The coil L3 of the coupled circuit II was placed at the distance
d from coil Lo for which the coupling coefficient had to be determined.
If there is no other inductance in circuit II besides that of L3, no other
part of the circuit II is required to be connected with it during the
measurement. Another radio frequency oscillator III was placed
with its coil L4 at a distance great enough not to influence the fre-
quency of the first oscillator and just sufficiently coupled to produce
*Kiebitz F. "Eine neue Methode zur Messung von Koppelungagraden und Induktionsgroessen."
Verb. d. Deutsch. Phys. Ges. Vol. 15, 1913, p. 1240.
t"Investigation of Antennae by Means of Mode's," Univ. of Ill. Eng. Exp. Sta. Bul. 147, See. 21,
p. 29, 1925.
ILLINOIS ENGINEERING EXPERIMENT STATION
D/sta7nce, d, 8e/1ieen Ce/7/er3 o/6 C'//S /,I c.
FIG. 23. MEASURED COUPLING COEFFICIENTS AS FUNCTION OF DISTANCE BE-
TWEEN COILS, DETERMINED BY THE DOUBLE HETERODYNE METHOD
a beat note of the frequency 1000, audible in the loudspeaker T. The
amplifier of the loudspeaker was connected with the winding R of a
telephone transformer whose coil S was inserted in the plate circuit
of the oscillator III.
The oscillator III was adjusted to the frequency of the circuit I
until no beat tone was heard in the loudspeaker. The coil L3 was then
shorted. The effect was to decrease the inductance Lo by the mutual
inductance between L3 and Lo. The frequency of circuit I thus in-
creased, and the beat tone in the loudspeaker indicated the change
of frequency. The beats, however, can be heard only when the coup-
ling coefficient is large enough to produce a frequency change larger
than the dead zone usually appearing in heterodyne methods, plus
the range of low frequencies for which the ear is not very receptive.
For smaller coupling coefficients the range of measurements was
extended by the following additional arrangement: A tuning fork
oscillator supplied 1000 cycle currents to the loudspeaker by means of
the winding P of the telephone transformer. A variable air-core
coupler A was inserted for the purpose of controlling the intensity
of the 1000 cycle tone emitted by the loudspeaker. Oscillator III
was then adjusted to produce a heterodyne beat of approximately
1000 cycles, the frequency of oscillator I was corrected by means of
TUNING OSCILLATING CIRCUITS BY PLATE CURRENT VARIATIONS 49
the condenser Cm, giving a setting corresponding to a capacitance Co,
so that zero beat was produced with the tuning fork oscillator.
The coupling coil L3 was then shorted, producing by its inductive
influence upon the frequency of circuit I an audible beat in the loud-
speaker. By increasing the capacitance of the variable air condenser
Cm until the zero beat is again reached, another setting corresponding
to a capacity C is obtained. From these data the coupling coefficient
C - Co
is calculated from the relation k'2 = . Instead of first using
the coupled coil open and then shorting, it was found more conven-
ient to set the coil in position shorted, and then to remove it alto-
gether. The measured values of the coupling coefficient are plotted
in Fig. 23 as a function of the distance d between the centers of the
two coils.
NOTE.-This part of the investigation was completed March, 1927. A mathematical analysis of
a similar method was published by C. B. Aiken, Proc. Inst. Rad. Engrs. Vol. 16, p. 125, 1928.