PULSE-WIDTH AND PULSE-TIME MDULATORS
by
Seth H. Washburn
B. S. Mass. Inst. of Technology 1944
SUBMITTED IN PARTIAL FULFILLMENT OF TIE
REQUIREENTS FOR THE DEGREE OF
MASTER OF SCIENCE
-
from the
VASSACHUSETTS INSTITUTE OF TECHNOLOGY
1947
Signature redacted
Signature of Author
Department of Electrical Engineering, May 22, 1947
Signature of Professor
in Charge of Research
Signature redacted
Signature of Chairman of Department
Committee on Graduate Students
Signature redacted
-ii(.I Q
TABLE OF CONTENTS
Page
INTRODUCTION........................1
Chapter I.
A.
A Brief Discussion of Pulse-Width
and Pulse-Time 1fodulation..........,...1
1. Pulse-Vidth Modulation....,........,.l
2. Pulse-Time "&Iodulation.................8
3. Demodulation ........
B.
....
.
..
..
9
The Historical Background.............10
1. The Heising Modulator................10
2. Finch's Modulation System............12
3. R. D. Kell's Modulators...........'...14
4. Cathode-Ray-Tube Modulators..........16
5. Modulators for Multiplex Systems.....18
Nature of Problem under Concideration.20
C.
Chapter II.
A.
THE MIXER-TYPE MODULATORS............24
The Kell-Kretzmer Circuit.............24
1. Kell-Kretzmer Circuit Design.........25
2. Experimental Procedure...............26
3. Experimental Results....
B.
.29
An OriginalModulator.................33
1. The CircuitDesign...................33
2. Experimental Results................36
C.
Stability of Mixer-Type Modulators....38
28"783.
-iii-
Page
Chapter III.
THE NULTIVIBRATOR 1LDULATORS........43
The First Multivibrator Modulator.....48
A.
1. Circuit Design....................48
2, Experimental Results................0.50
A Second Multivibrator Modulator......56
B.
1. Design of the Circuit................56
2. Experimental Results................57
C.
Stability of the Multivibrator
Modulators.
Chapter IV.
. ..
..
..
..
..
..
. ..
. ..
.
. .....
61
CONCLUSION AND INTERPRETATION OF
tRESULTS . . . . . . . .. . . . . .. .. . . ... * . . * *.. . 65
BIBLIOGRAPHY.............................72
-iv-
ACKNRIfEDGENENT
The author wishes to express his gratitude
to the supervisor of this thesis, Professor L. B.
Arguimbau, for his patient assistance. Professor
Arguimbau, as well as serving as the source of essential advice and guidance, provided a certain freshness of approach which was, at many times, most
sorely needed. Many thanks are also due Professor
H. J. Zimmermann and Mr. E. R. Kretzmer for the
time they spent in helping the author wrestle with
the problem of multivibrator modulation.
-l-
CHAPTER I
INTRODUCTION
A.
A Brief Discussion of Pulse-Width and Pulse-Time
Modulation.
Modulption may be defined as "the process of
producing a wave, some characteristic of which varies
as a function of the instantaneous amplitude of a
second wave, the modulating signal." Thus, pulse modulation refers to the modulation of a chain of rectangular pulses by a signal voltage. Characteristics
of a pulse chain which may be varied are the widths
of the pulses, the positions, or times, of the pulses
with respect to other pulses in the chain, the amplitudes
of the pulses, and, finally, the pulse-i-epetition
frequency. In this discussion only the first two methods
are of interest.
1. Pulse-Width Modulation.
In pulse-width modulation, the widths or durations
of the pulses are varied as a function of the instantaneous amplitude of the signal wave. For example,
consider a train of pulses of voltage amplitude E,
duration d, and pulse repetition rate p, as shown in
Figure la. Consider also a signal voltage of complex
waveform as in Figure 1b. It
is possible by electronic
..
2-.
means to combine the two waveforms in the process
of modulation so that the resultant waveform will
appear as in Figure 1c.
(a) Unmodulated Pulse Train
(b) Signal Voltage
(c) Width-Modulated Train
Figure 1.
Pulse-Width Modulation.
The widths of the pulses in the modulated
chain depend on the amplitude of the signal at certain
instants, either fixed in time or at times dependent
on the signal itself. If the pulse widths are a
function of the signal amplitude at instants corresponding to the midpointl of each pulse in the unmodulated chain, as shown in Figure 2, the modulation
would be termed "symmetrical" since the pulses vary
in width symmetrically about their midpoints. In
effect, the signal waveform is "sampled' at regular
time intervals, t, in Figure 2, the widths of the
pulses in the chain depending upon the amplitudes of
these samples.
Signal
i
Width-Modulated Pulse Train
Figure 2. Symmetrical Width-Modulation.
Apposed to symmetrical width modulation is the
asymmetrical, or disymmetrical, type. Here, the leading
and lagging edges of the pulses vary in position by
unequal amounts. There are two general modes of
asymmetrical modulation, In "Mode 1," shown in Figure 3,
the pulse edges shift by an amount dependent on the
signal voltage at fixed instants; namely, at the
instants of the leading and lagging edges of the unmodulated pulses. Thus, the leading edge of each pulse
in the modulated chain will be shifted as a function
of the signal at one fixed instant, and the position
-4-
of the lagging edge is a function of the signal at
another fixed instant.
Sigal
Width-Modulated Pulse Train
Figure 3.
Asymmetrical Width Modulation, Mode 1.
Dotted lines indicate positions of unmodulated pulses.
In the second mode of operation, illustrated
in Figure 4, the shifts of the pulse edges are again
asymmetrical, but the magnitudes of the shifts depend
not upon the amplitudes of the signal voltage at fixed
times but on the signal at the actual instants at
which the leading and lagging edges of the pulses in
the modulated chain occur. Thus, in "Mode 2" operation,
the pulse widths are a function of the signal amplitude
at instants which are themselves a function of the
signal amplitude.
E. R. Kretzmer, of the Electronics Research
Laboratories at Massachusetts Institute of Technology,
has shown that a Foutier series may be derived for
Signal
IF,
Width-Modulated Pulse Train
Figure 4.
Asymmetrical Width Modulation, Mode 2.
"Mode 2" pulse-width modulation. For a width-modulated
pulse train with voltage amplitude of unity, an unmodulated pulse width of d' ( sec.), pulse repetition
rate p (rad./sec.), and signal frequency q (rad./sec.),
the f ollowing series obtains:
pd'(l+ks int
)+ 21JJ
41W
+
Iona, ,-
+I
0.01,--
#j.g, n
(n f)
sin(nRpd')) cos (npt
)
e,
2
2
(npd') sin (npd') (cos (np~mg) t+c os (np-mq) t)
2
(ndi)
2
2
cos (ap~d') (sin (np*-mq) t-sin (np-mq) t
2
v,.here k
modulat ion index
(dma.- &'in,
( tax.+ d'mi n..
and m and n are integers.
This is-.obtaindd by -subs titut
ing- in'to the"-filzilikr-
series for a rectangular pulse chain,
ZZ1 s in(]Ud)l cos (npt)
2
v.=, n
*
e rp
2-W
the equation indicating the dependence of d upon the
signal: dz (d'+kd'(sin qt), where d' is the unmodulated
pulse width, and simplifying the result. Kretzmer has
adequately justified this substitution in his paper.
From the above expression for the modulated
chain it can be seen that this chain contains a directcurrent component of amplitude
(pd')/(2r), a signal-
frequency component of amplitude (pdA)/(2w), and an
infinite number of components with frequencies (np~mq)
and amplitudes dependent on the Bessel Function of
(npd'k)/2.
It is interesting to note that, in the above
expression, n cannot equal zero. This indicates that
components of frequencies mq are not possible. In other
words, harmonics of the signal frequency, theoretically,
are riot geerafted in Atbe .- odulation process.
Obviously, the higher the pulse repetition rate
in comparison with the signal frequency, the smaller
will be the amplitudes of the undesired (nprmq)
components. It has been found that a ratio of p/q
equal to 2.5 or 3.0 is high enough for practical
A
purposes.
The series which expresses the width-modulated
3
chain obtained by "Mode 1" modulation is as follows:
..
so
mnp) c os((np~mq)(t-')
k
m~Jnd
e a
+
(1)
J
m)
d
+ y(-177 Jj'/2) (n+s1
cos ((np-mq) (t- d'))
J(d'k(np+sqj)
sin ((np*sq)
2 sin(npd'/2) cos(pn(t-d'/2))
nTr
where sviatb, and a and b are integers.
All other letters are as defined above. This expression
for the
is derived in a manner similar to that used
"lMde 2" series, except that the process is somewhat
3
longer and more involved.
The expression indicates the presence of
(np*mq) components as well as signal frequency and
direct-current components. It can be seen that, in
addition, since n can equal zero, harmonics of the
signal frequency are generated in the modulation
to
process. By setting n equal to zero and m equal
the
one, two, and three, it is easily found that
magnitude of the signal frequency component is
/
J, (kdq).
(ej= 2e=i
The second harmonic is given by
le.1
J, (2dkq)
2 4_XL
The expression for the third harmonic is
2
7ri
Js(3dkQ)
3q/p*
-8.
Other methods of modulation which are based
on these two modes are, of course, possible. One example
might produce a modulated pulse train in which the
leeding edges of the pulses were fixed in position and
the lagging edges varied in position in accordance with
either "Mode 1" or "Mode 2." Another possibility might
be a train in which the leading edges varied as in "Mode
1" and the lagging edges, as in "Mode 2.
2. Pulse-Time Modulation.
In pulse-time modulation, the positions, or times,
of the pulses in the modulated chain vary as a function
of the signal voltage. There is a clear correspondence
between pulse-width and pulse-time modulation since
any time-modulated chain may be thought of as the
difference between two width-modulated trains. Figure
5 illustrates a time-modulated chain composed of
pairs of pulses, the first pulse in each pair fixed
in time, and the second vaiying as a function of the
signal. The figure also shows the corresponding widthmodulated chains.
It can be seen that the discussion of "Mode 1"
and "Mode 2" modulation will also apply to pulsetime modulation. Expressions for time-varying pulse
chains may be written directly from the known series
for the corresponding width-modulated pulse train.
-9-
Time -odulated
Train
Corresponding Width-Modulated Trains
Figure 5.
Pulse-Time Modulation.
Because of the simple relationship between timemodulation and width-modulation it is obvious that
corresponding chains will have the same frequency
components (though the amplitudes of corresponding
components will be different).
3. Demodulation.
Demodulation is the process of recovering the
signal waveform from the modulated pulse train. The
standard method of demodulation is by the use of a
low-pass filter
adjusted to pass only signal frequencies.
Of course, those (nptaq) components with frequencies
less than that of the highest signal frequency to be
passed will appear at the output of the filter, as
well as the signal frequencies. Also, some harmonics
-10-
of the signal frequencies, either caused by nonlinearity of modulation or inherent in the mode of
modulation, will be passed by the demodulating filter.
In order to demodulate a chain of time-varying
pulses by means of a low-pass filter, the chain is
converted to the corresponding width-modulated pulse
train. Thus, to determine the components appearing in
the output of any pulse-time or pulse-width system,
it is sufficient to investigate only the corresponding
w-idth-varying pulse chain.
B.
The Historical Background.
1. The Heising Modulator.
R. A. Heising of the American Telephone and
Telegraph Company applied for a patent on the fundamental pulse modulator in 1924. In his system, an
audio signal voltage was added to a 20,000 cps,
sinusoidal waveform, and the summation was passed
through two overdriven amplifier stages, as shown in
Figure 6. The overdriven amplifiers were biased in
such a manner as to clip the tops and bottoms from
the input summation waveform. Thus, the output consisted of a series of nearly-rectangular widthvarying pulses. The signal waveform,
the summation
wave, and the output of the overdriven amplifier
-
-11
Figure 6. Heising's Pulse Modulator.
stages are pictured in Figure 7.
Examination of. this modulation method indicates
that there was some lack of linearity in the system.
The base widths of the pulses at the output of the
overdriven amplifiers will depend upon the distances,
or times, between points of intersection of the summation waveform and the line of cut-off voltage for
the first amplifier tube. If the modulation were to be
exactly linear, these distances would need to vary
linearly with the signal amplitude. It is obvious
that, in the Heising modulator, the points of intersection between the summation waveform and the cutoff voltage line do not vary linearly with the amplitude
of the signal, but rather as a trigonometric function
of the signal amplitude. As the ratio of the amplitude
of the sign wave to that of the signal is increased,
the non-linearity decreases, since the points of
intersection fall upon the more nearly straight
portions of the sine wave. Thus, for a very small
-12-
Sumnxat ion Wavef orm
Output of Modulator
Figure 7.
Waveforms in Heising's Modulator.
percentage modulation, the harmonic distortion would be
low.
It should be noted that Heising's modulation
was essentially of the "Mode 2" type since the widths
of the pulses in the modulated chain depended on the
signal amplitude not at fixed intervals but at instants
determined by the signal amplitude itself.
2, Finch's Modulation System.
In 1929, J. L. Finch of the Radio Corporation
of America substituted a supersonic saw-tooth voltage
wave f or the sinusoid of Heising. The summation of the
saw-tooth and signal voltages was fed to the grid of
-13-
a triode amplifier, as shown in Figure 8, driving the
tube below cut-off for a portion of each negative
swing of the summation wave. The tops of the summation
waveform were clipped by a glow-discharge tube in the
AM6
8*
Figure 8.
Finch's Pulse Modulator.
plate circuit of this overdriven triode stage. The
resulting waveform was further shaped by two more
overdriven stages to give a final output of widthvarying pulses.
Since a saw-tooth rather than a sinusoid
was mixed with the signal, the modulation was,
of the
theoretically, perfectly linear. The widths
at
pulses var.ied directly as the signal amplitude
pulses
the instants of the leading edges of the
in the modulated chain as in "Mode 2" modulation,
as a
The lagging edges were fixed in position
can be
result of the shape of the saw-tooth. It
pulses at
seen that the widths of the rectangular
could be
the output, with no modulating signal,
.14-
varied by adjusting the bias voltages on the first
overdriven triode and glow-discharge tube. If these
biases were of such values as to give output pulses
of a duration equal to one-half the pulse repetition
frequency, a modulation index of unity (or 100 percent modulation) would be obtained when the peak-topeak signal voltage at the secondary of the input
transformer was equal to the saw-tooth voltage swing.
3. R. R, Kell's Modulators.
R. D. Kell, in 1934, applied for a patent on
a pulse modulator somewhat similar to that of Finch!
However, instead of mixing a sawtooth wave with the
modulating signal voltage across a common resistor,
Kell applied a supersonic triangular wave to the grid
of a pettode, and coupled the signal to the cathode,
as diagramed in Figure 9. Thus, the mixing process
was accomplished by the tube. The pebtode also
served as a clipper since the grid was biased at the
cut-off point, with no input. An overdriven triode
served to remove the peaks of the output of the mixerclipper, and further pulse-shaping was carried out
by two more overdriven stages.
The similarity between Kell's system and that
of J. L. Finch is evident, and, except for the
-15-
JUL
Figure 9. R. D. Kell's Modulator.
substitution of a triangular waveform for the sawtooth, the observed waveforms at various points in this
system are similar to those obtained at corresponding
points in Finch's modulator. Since a triangular wave
-was employed, both leading and lagging edges of the
pulses in the modulated chain varied in position.
Again, the modulator was of the "Mode 2" type.
Kell suggested a modification to his basic modulator in which a reristop-capacitor differentiating
network and negative-pulse inverter were placed after
the clippers in the basic circuit. The inverter had
for an output a series of short pulses marking the
leading and lagging edge of each input width-modulated
pulse, as shown in Figure 10. Thus, he obtained a
chain of time-varying pulses. At the receiver, the
pulse-time modulated chiin was converted to the corresponding chain of width-varying pulses by means of
-16-
Figure 10.
Kell s Conversion from Width-
Varying to Time-Varying Pulses,
a free-running multivibrator. This multivibrator was
synchronized by the time-varying pulses in such a
manner as to produce the desired width-modulated train
at the output.
4. The Cathode-RZa-Tube Modulators.
An entirely different method of modulation was
devised by R. E. Shelby in 1937, and later modified by
by W. T. Beatty. The heart of this method was a cathoderay tube with the normal electron gun and electrostatic
deflection plate assembly but with a specially-shaped
anode. The output of the modulator was taken from this
anode.
Pulses were generated between the anode and
ground by the electron beam which was caused to sweep
repeatedly at a constant rate over the anode. The section
of the anode swept over by the beam was controlled by
the modulating signal which was coupled to the
-17-
deflection plates. Thus, the width or position of the
output pulses, depending on the design of the anode,
could be made a linear function of the signal amplitude.
A typical modulator of this type had for an
anode a plate, triangular in shape, in a plane normal
to the axis of the tube, as in Figure 11. The electron
beam was swept across the triangle by sweep voltages
Figure 11.
Anode of Typical Beatty 'Modulator.
applied to the hoizontal deflection plates. The signal
varied the potentials of the vertical plates, thereby
moving the sweep in a vertical direction. The widths
of the output pulses depended upon the section of the
anode swept over and, therefore, on the signal voltage.
Since modulation by means of specially- designed tubes was beyond the scope of this thesis, the
brief mention above of the cathode-ray-tube modulators
should suffice. For further information on these
modulators, as well as on the history of pulse modulation in general, the reader is referred to the
Electrical Engineering Department seminat paper by
the author.
-18-
f.
Modulators for Multiplex Systems.
Probably the most practical application of
pulse modulation is in the field of multiplex communication. Several pulse systems providing for the transmission of a group of communication-channels using a
single transmitter were devised during the war years.
The most important of these were the AJ/TRC-5 and
AN/TRC-6.
These systems are basically very similar. The
pulse chain which keys the radio--frequency transmitter
is composed of a train of fixed marker pulses, as
illustrated in Figure 12, each followed by timemodulated channel pulses, one for each channel to be
transmitted. There is a modulator for each channel
which varies the position of the proper channel pulse
with relation to the common marker pulse.
As.I
M ARKEA
Figure 12.
PULSE
!. 7/t
CHANNEL PVLFiS"
AN/TRC-6 Multiplex Pulse Chain.
The pulse chain in Figure 12 Jir labelled to
indicate the time relationships existing for the
AN/TRC-6. One hundred percent modulation of one channel
p
-.19-
causes the corresponding channel pulse to shift by six
microseconds to either side of its unmodulated position,
a total pulse displacement of 12 microseconds. Therefore,
rith a maximum positive displacement of one
pulse and a maximum negative displacement of the next
adjacent pulse, the time interval between the trailing
edge of the former and the leading edge of the latter
is about 2 microseconds. This interval is called the
safety, or guard, interval, and is necessary to reduce interference between channels.
Unfortunately, no detailed information of an
unclassified nature has been published concerning the
modulation methods employed in these systems. Although
a brief account of the modulator used in the AT/TRC-6
is contained in one of the available references, the
writer has been informed that this account is inaccurate,
and that actual modulator is still
under
military classification.
Assuming that width-modulated pulses are produced by the modulator and that these pulses are,
in turn, converted to corresponding time-varying
pulses, it can be seen that 100 percent modulation
of the time-varying pulse would not necessarily
*
According to information received from
Prof. S. T. Martin, Mass. Inst. of Tech.
]
-20-
correspond to 100 percent modulation of the widthvarying pulse. For example, consider the second
channel pulse in the chain shown in Figure 12. If this
pulse is converted from a width-modulated pulse whose
leading edge is fixed and occurs at the instant of the
marker pulse, the index of modulation of the widthvarying pulse necessary to give 100 percent modulation
of the time-varying pulse would be: (dmax.-d'min./
dmax.+d'min. ) x 12/54 . 0.22. On the other hand, a timing
system might conceivably be used which would generate
the leading edge of the width-modulated pulse at some
fixed time after the marker pulse. Thus, no fixed
relation can be derived between the modulation index
of the width-modulation and the percentage modulation
of the time-modulation without detailed knowledge
of the system under consideration.
C.
Nature of Problem Under Consideration.
In the published work on pulse modulation
there has been little
information on the design and
operation of pulse modulators from the standpoint of
harmonic distortion. Theoretically,
as shown by the
expression for the modulated pulse chain, any modulation method which produces a train in which the
widths of the pulses (or the positions of the
-21-
pulses in a corresponding time-modulated chain) depend
upon the signal amplitude at the instants of the
leading and lagging edges will not generate harmonics
of the signal frequency. Such a method should be
superior to a system in which signal harmonics are
inherent, as in a modulator of the "Mode 1" type.
However, it might be that, by reason of increased
stability or simplicity of design, the second system
would be preferable to the first.
Also, although the mathematics might indicate
no harmonic distortion, the modulator itself might
operate non-linearly in such a way as to introduce
the undesired harmonics.
It was decided to investigate the behavior
of several modulators, all employing standard vacuum
tubes, in regards to the generation of harmonics of
the modulating signal as a function of the modulating frequency and the modulation index. Moreover, some information as to the stability of the
modulators in the face of changes in vacuum-tube
characteristics would be derived.
Unfortunately,
time did not permit as complete
an invstigation as originally envisioned.
possible, however,
It was
to take sufficient data on the
modulators considered so that conclusions could be
-22-
drawn as to the comparitive merits of each. The investigation was largely experimental since, except in the
case of the basic modes of operation as discussed in
the first part 6f this chapter, the mathematical analysis was too lengthy to warrant its inclusion in the
relatively short time allowed for this thesis research.
All the modulators designed had width-modulated
pulse chains as outputs. Any one of them, however,
could be used as pulse-time modulators by the addition
of a differentiating network and negative-pulse inverter
at the output. Since, in any pulse system, a timemodulated train is converted to the corresponding
width-modulated
train before demodulation,
it
is un-
necessary to investigate the time-modulated train in
order to draw conclusions as to the quality of modulation. Thus, in general, Pny conclusions as to a
given modulator will hold whether it is to, be used
in a pulse-width or pulse-time application. Any
distortion which appears as a result of converting
the width-modulated train to a pulse-time train is
not a function of the basic modulation.
On the other hand, inwlight of the preceding
discussion of multiplex pulse chains, a modulator
which generated low distortion for small percentage
modulation but high distortion for larger percentages
.23-
might be used to advantage in a pulse-time system. In
such a system a small variation in pulse width would
give a 100 percent of the final time-varying pulse.
Of course, the above paragraph would not apply for
modulators which varied the pulse positions directly,
without first generating a width-modulated chain.
However, the writer was unable to design or find any
account in published literature of such a modulator
other than the specially-designed cathode-ray tube.
This is not meant to imply, of course, that such a
system is impossible.
-24-
CHAPTER II
THE MIXER-TYPE MODULATORS
A.
The Kell-Kretzmer Circuit.
The first modulator to be constructed was very
similar to that patented by R. D. Kell. The circuit
was taken,
2
in large measure, from work of E. R. Kretzmer.
In operation, the modulatbr mixed the modulating signal with a triangular waveform. This summation was
amplified and clipped to produce at the output a
chain of width-varying rectangular pulses.
A repetition frequency of 20,000 cps. was arbitrarily selected for the triangular wave. As stated
above, it has been shown that the interference frequencies, i.e., the sum and difference of multiples
of pulse repetition frequency and signal frequency, will
be small for practical purposes if the ratio of pulse
frequency to signal frequency is 2.5 or above. Thus,
a pulse frequency of 20,000 cps. will allow a maximum signal frequency of 8,000 cps. This maximum is
considerably higher than would be necessary in a
system to be used solely for communications purposes.
However, if a degree of fidelity were desired, as in
the transmission of music, a maximum signal frequency
of 8,000 cps. is none too high.
-25-
1. Kell-Kretzmer Circuit Design.
The circuit diagram of the Kell-Kretzmer modulator is shown in Figure 13. A square-wave with a
pulse repetition rate of 20,000 cps. was passed
through a resistor-capacitor integrator with a timeconstant of 100 microseconds. Thus, the voltage waveform across the condenser C, was triangular in
shape. The familiar equation for the instantaneous
potential across the capacitance for a step-voltage
)E, where E is the paplitude of the
input is e= (1- e
step input, T is the time-constant of the integrator,
and t is the time between the step and the instant of
measurement of e. The amplitude of the triangular
wave, then, was e = (l- e
OlK
6SN7
)E 0.22E.
1N
0
-EOeurr
.C
300v
AfVl -**
5sNAL
'/SOV
Figure 13.
i'
I~
a
-
-~~~~2
The Kell-Kretzmer Modulator.
This triangular waveform was amplified by the
triode V, . This tube was biased by the action of C,,and
R,. C tended to charge to the peak of the triangular
-26-
wave so that grid current was drawn only at the instants of the positive peaks of this wave, A cathodefollower VA coupled the triode V,
to the mixer.
As in the Kell modulator, the triangular wave
was impressed on the grid of the modulator V,, and the
signal was applied through a coupling transformer to
the cathode. This tube, without input voltages, was
biased to the cut-off point by a variable-bias source.
Thus, the mixer also'clipped the negative swings of
the summation of signal and triangular wave. The
amplitude of the triangular wave was adjusted so
that no grid current would be drawn for 100 percent
modulation.
Overdriven amplifiers V. and V,,
similar to
Kell's, completed the clipping prooess. In order to
prevent a variation of bias at low frequencies, fixed
biasing was employed. Especial care was taken to
reduce power-frequency iterfetence. Signal-carrying
leads were carefully shielded, and filament leads
were well segregated. The filaments were held at a
d-c voltage of +20 volts with respect to the cathodes
to eliminate emission between heaters and cathodes.
2. Experimental Procedure.
A block diagram of the test set-up is shown
in Figure 14. A General Radio Square-Wave Generator
-27-
154U~AM-WANg
staivAl.
GEN6EATOR
Low-PASS
/a3AN-
PASS
CArmoos-AAY
WAvE
OsCILLosc.,a
ANAY.zaeR
Figure 14. Block Diagram of Experimental Set-up.
Mpdel 769 supplied & square wave to the integrating
circuit in the modulator. The modulating signal was
obtained from a Hewlett-Packard Audio Oscillator,
Model 200b. Since second and third harmonics of the
order of 0.3 and 0.1 percent of the fundamental,.-respectively, appeared at the output of the audio oscillator, a band-pass or low-pass filter was inserted
between the oscillator and the modulator. Thus, the
signal which was applied to the modulator had a harmonic distortion of less than 0.02 percent of the
fundamental component.
The pulse-chain output of the modulator was
fed to a load consisting of either a low-pass filter
if
the signal was to be recovered,
or aeresistinde
box.
A Dumont Cathode-Ray Oscilloscope, Model 208,
.28-
was used to view the waveforms at various points
throughout the circuit. The sweep of the oscilloscope
was synchronized with a voltage either from the squarewave generator or from the signal source, depending
upon the waveform of interest.
To measure the amplitudes of the harmonic
components in the modulated pulse chain, a General
Radio Wave Analyzer, Model 736-A, was employed. The
fact that harmonics were present in the output of the
audio oscillator proved fortunate. The wave analyzer
was connected to the oscillator, and was tuned to
the approximate frequency of the desired harmonic. The
exact setting of the analyzer could be obtained by
tuning for maximum swing caused by the harmonic. Thus,
even though small errors in calibration existed
either in the audio oscillator or in the analyzer,
it
was still
possible to adjust the desired frequency
quickly and easily.
After the correct dial settings for the
second, third, and fourth harmonics had been obtained,
the analyzer was connected to the output of the modulator for actual measurement. By carrying out this
system of comparative calibration at frequent intervals,
one could be sure that measurements were being made
of the harmonic components and not of extraneous
-29-
interference voltages.
Since the harmonic distortion of modulation as
a function of frequency was to be investigated, various
frequencies of the modulating signal were selected.
In order to permit valid measurements it was necessary
to choose these frequencies carefully so that no harmonic would have the same frequency as any of the
larger (np mq) components. As the pulse repetition
frequency was 20,000 cps., such.signal'frequenties.las
100, 200, 400, 500, 800, 1000, 1200, 1500, 2000, 4000,
5000, and 8000 cps. were avoided.
3. Experimental Results.
Amplitudes of the fundamental and all measurable
harmonics of the signal frequency as a function of the
modulation index,
(cmax.- dmin.)/(d'iax.+d'min.), were
measured at the output of the mixer tube and also at the
output of the overall modulator at three signal frequencies, 355, 1170, and 3550 cps. Waveforms, shown in
Figure 15, were observed at various points in the
circuit to check, at intervals, on the operation of
the modulator. Care was taken to keep the mixer-grid
bias at the cut-off point, thus assuring an output
wave in which the unmodulated pulse widths were equal
to one-half the pulse repetition period.
No Modulation
50 % Modulation
Output of Mixer Tube
Output of Clippers
Figure 15.
Waveforms of Kell-Kretzmer Modulator.
The results of the measurements are represented
on Graph I. It was found that the harmonic content for
any value of modulation was independent of the signal
frequency. Therefore, only those measurements taken
for a signal frequency of 3550 cps. are shown.
Obviously, the performance of this modulator is
not of very high quality. If the modulator were to be
used in a system where the total allowable harmonic
distortion was to be below three percent, the modulation index could never be permitted to exceed
about 0.5, or 50 percent modulation. It is of interest that, although the second-harmonic distortion
at the output of the mixer reaches a maximum of 10.2
percent of the fundamental, the second-harmonic
component at the output of the entire system has a
maximum of only about 311 percent. The action of the
(IL
0
4
0i.4
ri
F--
KI
0.-
-7vANMWVO~~nas
Q0
4-4vq.N::wC
-32-
clipper-amplifiers is, apparently, to decrease the
second-harmonic distortion and increase the distortion
caused by the third harmonic of the signal frequency.
It is impossible to judge from the data in
GraphiI .the degree of distortion which can be credited
to the clipper-amplifiers. Apparently: though, the
major source of the distortion lies in the process of
mixing the modulating signal with the triangular wav.
This distortion might be a result of non-lineprity of
the sides of the triangular w.ave or non-linearity in
the operation of the mixer tube.
It will be remembered that the mixing triode
was biased at cut-off, with no input signal, and was
driven by the modulating signal and triangular wave
to a point just below that at which grid current
would be drawn. Because of this, the operating point
traveled over a considerable portion of the plate
voltage-plate current characteristics of the tube,
from cut-off to e,= 0. For this reason,
it
was believed
that the major part of the distortion was caused by
the non-linearity of the mixer tube. It was decided
to design a modulator in which the mixer tube would be
driven over only a small and linear portion of its
characteristics. Also, a more effective clipping
system would be devised to replace the tetrode clippers
-33-
of the Kell-Kretzmer circuit.
B.
An Original Modulator.
1. The Circuit Design.
A circuit diagram of the resultant original
modulator is shown in Figure 16. The triangular-wave
generator was identical to that used in the KellKretzmer modulator except for an increased time-constant of the integrating circuit. This increase insured greater linearity of the sides of the triangular
waveform. This wave and the signal were mixed in the
triode amplifier V, , at a very low amplitude level.
The low-level mixing, together with the feedback
caused by the un-bypassed cathode resistor, promised
good linearity in the mixing process. The grid-toplate amplification of this stage was approximately nine.
ISOIC
465mr-
Figure 16.
Sty TSIC
6*
AMC
Circuit Diagram of Original Modulator.
Further amplification was secured by the use
of a second triode V2, also with degenerative feed-
-34-
back. The feedback was made greater in this second
stage than in the first since the input signal was of
greater amplitude. As a result, the gain of this stage
was only 2.5. Fixed grid bias was employed for both
.
V, and V2
Double-diodes provided the required clipping
at the output of V,. In the absence of a modulating
signal, the input to V3 was a triangular wave with a
peak-to-peak amplitude of about 55 volts, The conducting plate-cathode
resistance of each diode section
was approximately 1500 ohms. Thus, the waveform at
the output of V3 appeared as in Figure 17.
It will be noted that Q.3 volt peaks remain
on the somewhat-rectangular pulses at the output of
V3 . These are caused by the fact that the conducting
resistance of the diodes is not negligible.
It
is
true that the magnitudes of these peaks could have
been reduced either by decreasing the amplitude of
the input triangular wave or by increasing the
input series resistor R,. However, if the amplitude
of the input wave wexe decreased, the slopes of the
leading and lagging edges of the output pulses
would be less.
An increase in the value of R1 would also
decrease these slopes. The wiring and tube capac-
M
-'35-
Output of First Double-Diode.
Output of Second Double-Diode.
Figure 17.
Waveforms in Clipping Circuit with
No Modulation.
itances across the input of the diode must be charged
through R,. Thus, an increase in R, will increase the
charging time-constant, effecting a decrease in the
slope of the wave across the diodes.
To remove the peaks from the waveform at the
output of the first double-diode V3 , a triode amplifier
and a second double-diode were employed. The output
of this second clipper V., shown also in Figure 17,
was the final rectangular pulse chain. The variablebiasing circuit at the input of Vs made it possible
to adjust the unmodulated widths of the output pulses.
Plainly, this modulator is basically very
similar to the Kell-Kretzmer system. The major differences lie in the low-level mixer and the doublediode clipping circuit.
.36-
The modulator was tested in exactly the same
manner as that used for the Kell-Kretzmer circuit.
Harmonic components were measured at various points
in the circuit as a function of the modulation index.
It was found that the amplitudes of these components
were again independant of signal frequency so that
only the results obtained f or a single signal frequency need be recorded.
2. Experimental Results.
The resulting data are plotted in Graph II.
It is obvious that this modulator shows a considerable
improvement over the Kell-Kretzmer system in regards
to harmonic generation.
The percentage
of the second-
harmonic component for the overall circuit reaches
a maximum of 0.34 percent at a modulation index of
0.9. The percentage of third-harmonic distortion remains below 0,02 percent for all values of modulation
index.
Apparently, each stage, as well as the signal
transformer, adds a small amount of harmonic distortion. In hopes of eliminating some of this distortion, a direct coupling to the cathode of the
mixer was substituted for the transformer. An inpe dance -matching cathodd-follower was placed be tween
the signal filter
and the mixer. No noticeable
~~~~1~~ 7
4
:t)
GRAPH II
Harmonic Distortion in the
Original Mixer,'Type Modulator
JO
Ue surable harmonic
components are plotted as a
function of modulation index.
Signal frequency in all cases
was 550 cps., and the pulse
frequeney, 20,0YO eps.
X
P
~~14
Seth H. Washburn
April 5, 1947
4R
d
a
0
I
Um
'IN
1d
'C
4
~,t9
.
.
.
-
113
I
t!L
~Io
wvanWirdr
a
iii'
improvement resulted as the cathode-follower generated
about the same values of second-harmonic component
as had the original transformer.
The only third-harmonic component to be plotted
in Graph II was that at the modulator output. This
component was so small that it
was difficult to
measure with accuracy. The fourth .signal harmonic
was too weak to record.
Unlike the -clipping circuit in the Kell-Kretzmer modulator, the double-diode circuit had no effect
on the harmonic content of the wave passed through it.
Thus, harmonic percentages measured at the output
of the modulator were essentially equal to those at
the input of the clippers.
C.
Stability of Mixer-Type Modulators.
As has been seen, the operation of the mixer-
type modulators is basically as follows. A triangular
wave is passed through a clipping circuit. The modulating signal effectively varies the points on
the triangular wave where clipping occurs. Because
of this, any change in amplification factor /A or
dynamic plate resistance
."
,
occuring in any tube
passing the triangular wave, which varies these
clipping points will affect the widths of the pulses
in the output chain.
.39.
AM
AAJA
Figure 18.
Degenerative-Feedback Amplifier.
r
Figure 19.
Output of Amplifier, showing Effect
of Amplitude Change on Pulse Width.
Consider a single triode with cathode feedback, as shown in Figure 18. The output of this tube
is a triangular waveform of peak-to-peak voltage
amplitude 2E and period 2T, as in Figure 19. The
dotted line in the figure indicates the clipping
point, the point at which the clippers in the output
of the modulator operate. Thus, the widths of the
unmodulated pulses at the output will be d. Let
d/T equal a. Referring again to Figure 19, it
seen that, by simple geometry, (d/T)
=
can be'
(aE/E).
Suppose that some change in tube characteristics
-40-
causes a change AE in the output voltage amplitude.
This, in turn,- will change the output-pulse duration
by 4d. Again by geometry,
d+d
AE + aE
AE+E
T
T
Then,
Ad AE aE
T AE+E
a
and,
Ad: AE(1- a)
T
+dd
T
.pa
T
AE-aE
4E+E
4_d= 4E (1 -al
d
4E-+E
T
d
AE
(1
E+6E
a
)
The per-unit change in d will then be:
If the change in E, CE, is very small compared with E,
d
(1)
)
.d
a
E
This equation gives the per-unit change in
pulse duration with a per-unit change in the amplitude
of the output triangular wave. The next step is to
discover the effect of changes of tube constants on
this output amplitude.
For the amplifier in Figure 18,
tA= RL+r,+
+(,"l)RoK
where A
is the grid-to-plate
gain.
p
is the amplification
factor.
re is the dynamic plate
resistance.
-41-
We are concerned with changes in -AI
with
changes in rp and A. From elementary calculus, d JAI x
(AM/-r,)dr,-+ (JiAI/J ) dA.
Thus, the chrnge in JAI will
equal the change in JAI due to a variation in rp with
A
constant plus that due to a variation in
,&
with rp
held constant, if all changes are very small.
a variation in rp.
Consider first
-.A R &.
.+ rM+ (.+1) R4
alAl
j r,
The per-unit change in JAI will be:
IAI
JAI B *,r,+ (C+l)P IAI RrO+(/^+l)R_ 6
rp
R+r,+ (+1R
.Ar
F,= (Jsj
\
jre-
Considering a change in.p,
1
-R&Ric
_AIA
R.
(+1)R*
R,.+ r,+R
JAI
JAIL
.
Then,
A (1-IA1
Now suppose that the input triangular .wave
has a peak-to-peek amplitude of 2e. Then E -. AI e , and
(aEA)a (A1A$A).
4E=ALAI e . Thus,
Substituting equations.,( 2 ) and (3) into (1);
for a variation in r,:
j.d,
d
-.
I'
.A
r
" R.
)
rp-4)
rp
(2)
42-.
and for a variation in A:
d
d
~)a/
R&/
a (1- - /At
(5)
The factor a will remain constant as long as
the triangular wave is unmodulated. If the unmodulated
output-pulse width is one-half the period of the
triangular wave, a will equal unity and d will be unaffected by changes in r,
andp.
However, when the signal is introduced,
the value
of a will change for each succeeding cycle of the
triangular wave. The stability expressions show that,
as a decreases,
the greater will be the effect of a
change in ^ or in r,.on the output pulse. Thus, it
appears that a greater degree of stability exists for
a condition of small percentage modulation and an unmodulated pulse width of one-half the pulse repetition
period.
Considering the mixer tube V
in the original
modulator circuit, shown in Figure 16, where R,=100k,
Rk= 5ktA.
2O,
and r,
10k, the per-unit stability
values are f ound to be:
d
and
. - -.
a
.~ (1 -
)rp
a) +0.535)
-
an -6A
.43-
CHAPTER III
THE MULTIVIBRATOR MODULATORS
Although the second mixer-type modulator tested
was most encouraging in its very small harmonic generation, it was thought that some other circuit, of
simpler design, might also give good results. The
cathode-coupled multivibrator suggested itself as a
basic circuit from which to work, It was hoped that- a
modulator with fewer tubes and of the same order of
stability and distortion as the mixer-type of modulator might result. As shall be seen, this hope was
not realized,
at least in regards to stability and
harmonic distortion.
The cathode-coupled multivibrator, as illustrated in Figure 20, operates in a manner very similar to that of the more common plate-coupled multivibrator. Consider the circuit at rest. Since the
grid of VA is returned to Ebb through Rga, Va draws
a relatively high value of plate current. For this
reason, the- potential drop across Rk is large. The
grid-cathode potential for Va is about zero volts
since RgA has a high resistance, of the order of one
megohm.
If suitable values for R, and RA have been
chosen, the grid-to-ground potential of V,
is low
-44-
V
RZ
Figure 20.
R
RA
R,
R~
2
Ric
Cathode-Coupled Multivibrator.
compared with the cathode-to-ground voltage el,,
V,
and
is cut-off.
These steady-state conditions obtain until the
circuit is triggered. A positive pulse of amplitude
sufficient to cut-on tube V, is applied to the grid
of V, . As this pulse starts the conduction of V, , the
plate of VA falls in potential, and, since the voltage
across the condenser CA cannot change instantaneously,
the grid of V 2 also drops. The decrease in grid-toground voltage for V. causes the cathode voltage to
decrease, which,
in turn, increases the drop in vol-
tage on the plate of V,. This process, an almost instantaneous one, continues until the grid-cathode
voltage on V, has fallen considerably below cut-off.
The plate and cathode voltages on V, will depend
upon the plate current drawn by V,.
CA discharges through Rga and V.,
and, as it
-45-
discharges, the grid-to-ground potential increases.
When the grid of V, reaches cut-off, V, will start to
draw current, the cathode will rise in potential, and
the plate of V, will also rise, thus cutting off V,.
The circuit returns to the steady-state donditions,
CA quickly recharging through R. 5. and the grid of
VA. The multivibrator remains in this steady-state
condition.until the next triggering pulse.
The duration of the multivibrator output pulse,
or gate, t depends upon the discharge time-constant
of CA in series with Rga, the plate resistance of V,,
and B.c* If Rga is large compared with the other
resistances, this time-constant is approximately equal
to C,,XRgz. The duration of the output gate also depends on the initial value of the exponential in the
en,
waveform,
shown in Figure 21, and also upon the
value of the same exponential when it
reaches the cut-
off point for V., If both these values are measured
in volts deviation from the steady-state value of Ebb,
the gate time can be expressed as
t
T
mi(
Initial Value
LTJlnL Final Value
where Toes is the time-constant C,RgA.
From the waveforms in Figure 21, it
can be
seen that the initial value of the exponential is
..46-
Mtv"Aih
Fwr.h.
Ebb1
eka
ecna,
Plate-Ground VoltageV,
Grid-Ground Voltage, V
oOv
Cathode-Ground Voltage
Plate-Ground Voltage, V&
Waveforms for Cathode-Coupled Multivibrator.
(Trigger at t,
)
Figure 21.
(Ebb+ A ebn - ekz) , and the final Value equals (Ebb+
jEcoi-ek, ).
EcoI is the grid-cathode cut-off voltage
for VA at the end of the gate.
ST
t
aTagIn
Therefore,
Ebb+ebn
Ebb-JE c osj -eks
- ek,
The initial value of ecn, is a linear function
of the plate current of V, during the gate, since Aebn
varies linearly with the plate current of V, . Also,
since IEcoI and ek, vary linearly with the plate
current of V, , the final value of the exponential will
also be a direct function of this current. The plate
current taries directly with Ece.,, over the linear
portion of the tube's characteristics, and, thus, the
initial and final values vary linearly with E...
If the average current through Q
during the
gate pulse remains constant for various pulse widths,
the pulse width will vary as a direct function of
E.,. Since the current through C
equals approximately
(Ebb -ecn,)Rga,
this requirement merely states that the
average.e.nmust be a constant. Thus,
(Ebb-t Aebn -eka) + (Ebb+ IEco.1
-ek,)
K
For a change in E,,, Ebb and eka are constants.
Since Aebn equals Ebb- ebn,, the above can be simK,. Therefore,
plified to (-ebn, +)EcoA-ek,)
L0(-ebn,+EcoI-ek, ) =
(2)
It is obvious that Aebn,/E,, and Aek,/E,
are merely the grid-to-plate and grid-to-cathode
gains, respectively; and that Eco, is a linear function
of ek,, Then,
Aebn=
-APAEC.
A ek
Aac4E..
-bAtEa.,
AEcoz
Substituting these identities into equation (2),
Ap -bAk-Ak 0
or
A,- (1 *b)Af
(3)
For a triode with unbiased cathode,
R ..
r, + R,,+
"
Ap
A,= R,
.
Ra.n
,"Rj
Ak AR
= + r, -*R,,
5+1
Substituting into (3),
R1.
(1 + b)R
Iwhere b =IE(.aLOEb
(4)
S Ath /tek
Since the method used to derive this relation
-48.
is not rigorous, the equation (4)
can be regarded as
only approximate. However, it can be seen that it is
possible to cause the gate width to vary directly
with the control voltage Eg,,.
A.
The First Multivibrator Modulator,
The brief analysis above suggests that it
might be possible to couple the modulating signal to
the grid of V,
in the multivibrator, and make the
output-gate width vary as a function of the signal.
A circuit, shown in Figure 22, incorporating the cathode-coupled multivibrator was designed and constructed,
1. Circuit Design.
Examination of the plate current-plate voltage
characteristics of the 6SN7 double-triode show that
Eco/ Eb equals 0.06. Substituting this value into
equation (4) above, it is found that R, should be
1.06 times the value of Rx. By cut-and-try methods
of assuming values of Reand RK and computing the
pulse widths as a function of E4.,, it was found that
for Ri=7.5k and Rs,322.5k, the pulse width varied
3.2 microseconds for a change in 1 volt in E,... This
assumes a CaR3L time-constant of 500 microseconds, a
high value calculated to make the discharge exponential
of e..a essentially linear.
-.
49-
Voo
toou 5#7
a
First Multivibrator Modulator,
For higher values of B.xand lower values of Rj
,
Figure 22.
sap, 7.5 22.
this sensitivity was increased. Since the increased
sensitivity did not seem desirable from the standpoint of stability, the values of Rm= 7,5k and R, L422.5k
were employed. The cut-and-try methods also showed
that if a variation of 0 to 50 microseconds in pulse
width were desired, Econ should be variable from 25 to
50 volts. The 25k resistor in the grid circuit of V,
served to decouple the signal and the trigger inputs.
The method of testing this modulator was
essentially the same as that used for previous circuits.
The multivibrator was triggered at a rate of 10,000cps.
This trigger was obtained by differentiating the output of the square-wave generator and then clipping
the resultant negative pulses with a diode limiter.
The harmonic content of the width-modulated pulse
chain at the output of the multivibrator was meas-
-50-
ured by the General Radio Wave Analyzer. Again, signal
frequencies of 355, 1170, and 3550 cps. were used to
investigate the effect of signal frequency on modulation linearity.
Since the output of the multivibrator consisted
of pulses the leading edges of which were fixed in
time, it was convenient to measure the percentage
modulation in terms of the number of microseconds the
lagging edges varied from their unmodulated positions.
Thus, the harmonic content was recorded as a function
of the amount of this deviation. These measurements
were made at three values of unmodulated-pulse width:
10, 17, and 20 microseconds.
2. Experimental Results.
The results of the measurements taken with
the multivibrator modulator are illustrated in Graphs
III, IV, and V. Certain features are apparent at
once. First, the harmonic distortion increases as the
signal frequency increases. Then, the harmonic distortion is greater for larger values of the unmodulated pulse widths. The amount of distortion also
appears to be greater than would be expected merely
from the slight non-linearity of the exponential
discharge curve of egm.
gild.
I
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-54-
A closer examination of the modulation process
may indicate an explanation of these results.
It
has
been shown on preceding pages that the pulse width
varies almost linearly with the control voltage Eco.
However, this dependence assumed that Ecoswas a d-c,
or very slowly varying, voltage. If the control voltage varies rapidly,
the value of Econat the end of
the pulse will not be the same as that at the beginning of the pulse.
The pulse duration depends upon the initial
value of the exponential curve of e",.and its value
at the end of the pulse. These values are, respectively,
(Ebb-+ ,ebn
-
ek,) and (Ebb-tlEco-ek,). Aebn depends on
the control voltage at the leading ledge of the pulse,
and JEco4. and ek, are functions of E...at the end of
the pulse. Thus, the pulse width depends upon the
signal voltage at the instant of the pulse leading
edge, a fixed instant, and also upon the signal
voltage at the instant of the pulse lagging edge, a
varying instant.
It was seen in Chapter I that if the pulse
width varied as a, function of the signal at the instants of the varying edges themselves, "Mode 2" modulation, there was no harmonic distortion inherent
.55-
in the modulation system. On the other hand, if the
pulse duration depended on the signal at fixed instants, as in "Mode 1" operation, harmonics of the
signal frequency would appear in the modulated pulse
train.
The multivibrator modulator, therefore, appears
to incorporate both modes of operation. Thus, it
should reasonably follow thpt harmonic distortion is
inherent in the system. On page 7, it has been seen
that, for "Mode 1" this distortion increases as the
signal frequency increases, as the unmodulated pulse
width increases,
and also as the modulation index,
or pulse-edge deviation increases. Graphs III, IV,
and V show that the harmonic distortion of the multivibrator modulator behaves similarly. It is, therefore, believed that the major portion of the observed distortion is inherent in the system. Unfortunately, a mathematical analysis of the system
to check this belief could not be made in the time
available.
In light of the large distortion pro-
duced by the modulator, it is doubtful whether such
an analysis would be, practically, of sufficient
value to justify the large amount of time necessary
to carry out the analysis.
-56-
B.
..
A Second Multivibrator Modulator,
Design of the Circuit,
A modulator employing a slightly different
method of signal injection was designed, in which the
signal varied the potential of the control grid'of V.,
as in Figure 23. However,
this circuit proved to be
subject to the same inherent non-linearity of modulation as that found in the first modulator. Again
the pulse duration depended upon the signal voltage
at the beginning of the pulse, since e ra was a function of the new E.. Also, the duration was a function
of the signal at the pulse end, since the signal varied
the instant at which the grid of Va reached cut-off
at the conclusion of the exponential.
300v
Sk
22.5
.Ij1
65s7r
2
V,
Itu
szp
;
Figure 23.
aS fE7
20
k
7.r
VC
a.
Tiet
Second Multivibrator Modulator.
Since the signal varied the initial and final
-57-
values of the discharge exponential by like amounts
(assuming a signal of low amplitude and frequency) for
any circuit-component values, no analysis similar to
that on page 4 7 was necessary. By cut-and-try experimental methods it was found that the 2 megohm resistor
in the signal input circuit was sufficient to decouple
the signal source from the modulator.
2, Experimental Results.
The harmonic components present in the output
wave, shown in Graphs VI, VII, and VIII, were obtained
in exactly the same manner as that used for the first
multivibrator modulator. Again, it is seen that the
distortion increases as a function of the signal
frequency, the amount of modulation, and the unmodu-.
lated pulse width. This was to be expected as a result of the inherent distortion present in a modulator,
the output pulses of which have a width partially
dependent upon the signal at fixed instants.
The distortion for a given pulse width, frequency, and lagging-edge displacement is slightly
higher for the second harmonic than it
was for the
first. This may be due to an increased dependence, in
the second modulator, on the signal amplitude at the
fixed instants of the output pulse leading edges.
013
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-61-
In this second moldulator, the value of ex
varies in
a one-to-one ratio with the signal voltage. Also, there
is some signal leak through the 500 micro-microfarad
discharge capacitor causing a very small variation of
debn. The initial value of the exponential rise of
een depends upon both of these factors. In the first
modulator, debn varied as the signal but not to as
great an extent as ek, in the second. For this reason,
it appears that the second modulator might be subject
to greater inherent distortion than was the first.
It
is believed that if the mathematical analysis of a
system in which the pulse width depended on the signal
at both fixed and varying instants were carried out,
the above conclusion would be found justified. As
stated above, however, such an analysis might possibly
have little practical value.
C.
Stab
of the Multivibrator Modulators.
A study of the stability of the stability of
the multivibrator modulators resolves itself into
a consideration of how changes in tube constants will
affect the duration of the output gate. Thus, it is
only necessary to analyze the basic cathode-coupled
multivibrator in regards to changes in the amplification factor.
and the plate resistance r,
for
-62-
each of thetto triodes in the circuit.
The basic equation for the duration of the
output pulse, as has been seen, is:
t
T,
Ebb-4ebn-ea
ln
(1)
(Ebb-# Mcftl - eu,
From the waveforms on page46, it is obvious
that Aebn a Ebb - Ebn, . Now Ebn, , ex, , and e ft
are frac-
tions of Ebb as follows:
Ebn, =
Ebb
ek,
=
Ebb
eka
=
Ebb (R6,,+Rk)
,
where
tubes V,
r,
Rk
,
f
and Y
4- Rk
Rk
are the static plate resistances of
and VA, during and before the pulse, res-
pectively.
Also, let
,&mEbb/E,,.
1. Substituting these
relationships intb the basic equation,
t -Tasn
(1
n1Fp*Rk) - Rk/(Ra..+FrA+Rk)
T Ru/(R+
+eR/&.+
- Rk/(Rb,-. Fp, -+Rk)
(2)
Now let (R,+ Y,,. Rk)
R,
and (R45 #f,-tFRk) = Rz.
Substituting R, and Ra into equation 2,
t :
T
1n
*
1+- R,/R, -_Rk/R.)
1- +4.
- Rk/R,
T. l R, RA+R&R&,-ORkR,
=~~
TRlnI Ra
Evidently,
( 1 -+ 1 /^) - RR'
t depends upon the tube constants
-63-
,,
7,, ,
and^. The effect of a change in each on the
pulse duration t can be found by taking partial derivatives with respect to each in turn.
it
Ty, = To'
Ta
(l+ /.&&)Ra
R, Rj, * R, Ra., -- RkO,
=
osR,+ (Rs RL.) /(R,7-Rk)
e)) Rk(4
it
( 3)
TDi- RA-
.:
J,
R, /*&
T,,L (1+1/.,)R,- Rk
=
T
Fl + 1/^r) R, R, - RkRx
T,
1
(1-tA.)R,-Rk
-R,
Rs,
R 0( R- Rg R, - RkR, (1 +1/,6.)RRC-RkRL)
)
t
R, Ra /&
(1+1/,)RR-R
(R)
T RC -(R.R ) /(R,+ R&,)
From the appearance of equations (4) and (5),
it is obvious that it is impossible to choose circuit
constants such that either bt/laT., or Jt/fp, will be
zero. However, the effectof changes in Fp, and F,, may
be minimized by making R,,, R&, and Rk as small as
possible, in comparison with f,, and i,,. 'Since rp,
and f,, will themselves depend on Ra,, Rx, and Rk, only
a succession of trial values substituted into the
equations will indicate the quantitative effects of
various values of the resistances.
The plate resistances F,, and fp. are very susceptible to changes in Ebb. A change in plate-supply
voltage will produce a variation in
,, and fp., the
-64-
magnitude of which will depend on the operating points
of V,
and V . However,
a glance at the plate char-
acteristic curves will indicate that a one percent
variation in Ebb may cause an equally large percentage
variation in the static plate resistances.
For an idea of the magnitudes of Jt/J'1 ., Jt/dfa,
and 4t/d^, the equations have been applied to the
first multivibrator modulator. If the circuit is
adjusted for an unmodulated pulse width of 12 microseconds, it may be determined from plate characteristics
of the 6SN7 that f,, will be 43.3k and fp,, 10.0k.
Substituting these values into equations (3), (4),
and (5), together with the values of the circuit constants, it
is found that
t/JceaT,,(0.00385), Jt/df,.=
T,,,(-0.OO476), and ut/dip~a
the final percentage
T,,,(0.005). From these,
stability relations may be ob-
tained: dt/t = 2.54e/,A/. , dt/t = -8.1d9,/!,, and
dt/t
1.9 afp/r,
Since Afp,/f,,
and AiF,/rp.
are of opposite
signs, it might be possible to choose circuit constants in such a manner that variations of
p. and fr.,
due to variations in Ebb, might be cancelled against
each other. However, changes in either f, or F& not
dependent upon Ebb would still
be large.
-65-.
CHAPTER IV
CONCLUSION AN
INTERPRETATION OF RESULTS
In the evaluation of the pulse modulators designed and tested, certain obvious conclusions may
be drawn. First, it has been seen that a carefullydesigned mixer-type modulator introduces less harmonic distortion in the modulation process than does
a modulator of the multivibrator type. This appears
to be true, in general, for any index of modulation
and signal-to-pulse frequency ratio. The mixer-type
modulator could be so designed that the maximum
total harmonic distortion present in the output pulse
chain was less than 0.3 percent of the fundamental
component. To obtain this low value of distortion,
it was necessary to mix the triangular wave with the
signal at a very low level and to amplify the summation with good linearity before clipping.
Secondly, the mixer-type modulator is found
to be inherently more stable than the mnltivibrator
modulator for changes in vacuum-tube characteristics.
This is apparent from the dependency of the multivibrator output on the static plate resistance of the
tubes in the circuit. A change in the emission of
W
-66-
of a vacuum-tube will cause a pronounced variation in
the static plate resistance of that tube. In comparing
the stability of the two types of modulators, it can
be noted that any change in the operating point of
a tube in the multivibrator circuit will affect the
width of the output pulses. The stability of the mixer
modulator depends primarily upon the stability of the
dynamic plate resistance of circuit tubes. Thus, if
the operating region is small, this region may be
shifted an appreciable amount without much effect on
the dynamic plate resistance, and, hence, on the
output pulse, of the tube. The per-unit relationships derived for both types are also indicative of
the comparitive stability of the two modulators.
In favor of the multivibrator modulator, it
is true that a circuit of the multivibrator type affords
a considerable saving in the number of circuit components and tubes to be used.
It is, apparently, the general consensus of
opinion that the most practical application for pulse
modulation lies in the field of multiplex transmission.
A modulator, to be of use in a multiplex system, as
described in Chapter I, must provide a pulse varying
in time with respect to a fixed pulse. The multi-
II
-67-
vibrator modulator would seem to be eminently qualified for application in this field, except for its
high inherent distortion generation. However,
the
multivibrator modulator could be employed if size and
weight requirements made the mixer-type modulator undesirable.
Suppose that the maximum allowable harmonic
distortion were to be limited to three percent. This
distortion, in the multivibrator, depends upon three
factors: the unmodulated pulse width, the amount of
modulation, and the pulse-to-signal frequency ratio,
As stated in Chapter I, the ratio of pulse repetition
frequency to maximum signal frequency should be
greater than 2.5 to 1. However, the use of much higher
ratios increases the difficulty of amplifying the modulated pulse train at the 'receiver. Then, a ratio of
about 3 to 1 is normally employed. Also,
it
would be
desirable to allow as much pulse shift due to modulation as possible.
Referring to Graph III, with these requirements
in mind, it can be seen that, for an unmodulated pulse
width of d, the maximum modulation or pulse displacement possible would be about 7 microseconds for da
20Asec., 9 microseconds for dx 17^sec., and 14 micro-
-68-
seconds for d: 10sec, The allowable pulse displacement is limited by the time between unmodulated channel pulses. in the final multiplex pulse chain. If this
time were 14 microseconds, as in the AN/TRC-6, the
maximum pulse shift due to modulation would be about
t6 microseconds, or a total of 12 microseconds pulse
displacement or deviation. Thus, the width of the unmodulated pulse at the output of each multivibrator
modulator must be less than 10 microseconds.
Of course, the mixer-type modulator may easily
be converted for use with a multiplex system. Instead
of employing a triangular wave, a wave consisting of
saw-teeth, each with a vertical leading edge, as in
Figure 24, could be mixed with the signal. The output
of the modulator would then be a chain of widthvarying pulses, each having a fixed leading edge. A
differentiating circuit, similar to that to be used
with the multivibrator modulator, could supply the
desired position-varying pulse. Here, the problem of
distortion would not exist; the only consideration
determining the width of the unmodulated pulse at the
output of the mixer modulator would be that of
stability.
Full modulation of the multiplex channel pulse
will correspond to some fraction of 100 percent mod-
-69-
Figure 24.
Saw-Tooth Wave for Use with
Multiplex Mixer-Type Modulator,
ulation of the width-varying pulse at the output of the
basic modulator. It is apparent that the smaller this
fraction is, the larger will be the effect of a small
change in the width of the width-modulated pulse on
the percentage modulation of the channel pulse. Thus,
for a small fraction, the final result of instability
in the modulator will be great. It should be advantageaous then to make the modulation index for the
width-modulator as great as possible. If the width of
the unmodulated pulse was equal to one-half the total
displacement of the position-varying channel pulse,
100 percent modulation of the channel pulse would
correspond to a modulation index of unity for the
width-modulator. However, a modulation index of unity
cannot be obtained in actual practice.
In Chapter I, it was shown that for good stability, the duration of the unmodulated pulses in the
output of the mixer modulator should be one-half the
duration of each mixer saw-tooth. It was also found
-70-
that a small percentage of modulation would be less
affected by changes in tube characteristics than a
large percentage. This last is in direct opposition
to the conclusion reached in the last paragraph, in
which it seemed that a large index of modulation was
desirable. In the design of a practical system, it
would be necessary to reconcile the two conclusions,
taking a mean value for the percentage
of modulation
for the mixer-type modulator.
The equations expressing the stability of the
multivibrator modulators indicate that trouble would
be experienced if the vacuum-tube characteristics
or
the plate-supply voltage had a tendency to drift. It
would be necessary to make frequent checks and adjustments of.the modulators to compensate for these
variations.
This lack of good stability in the multivibrator
modulator, as well as its inherent harmonic distortion leads to the final 'conclusion that, unless
it is of primary importance to employ a modulator
having small size and weight, the multivibrator does
not lend itself to pulse-modulation applications.
It is also concluded that, because of low distortion,
good stability, and relative simplicity of design,
the mixer-type modulator will give satisfactory results,
whether it
is to be used with a pulse-width or pulse-
time modulation system.
-72-
BIBLIOGRAPHY
1.
Standards on Transmitters and Receivers (New
York: The Institute of Radio Engineers, 1938), 3.
2.
E. R. Kretzmer, Fidelity in Pulse-Time Modulation,
Thesis for M. S. Degree, M. I. T., (1946).
3.
Fredendall, Schlesinger, and Schroeder, "Transmission of Television Sound on the Picture Carrier,"
Proc.
4.
.RE., 34(1946), no 2, 49,
R. A. Heising, "Transmission System," U.S.
Patent 1,655,543, (1928).
5,
J. L. Finch, "Signalling System," U.S. Patent
1,887,237,
6.
(1932).
R. D. Kell, "Signalling System," U.S. Patent
2,061,734, (1936).
7.
R. E. Shelby, "Improvements in or relating to
Cathode-ray Tubes," British Patent 493,010, (1938).
8.
W. A. Beatty, "Pulse Modulation System," U.S.
Patent 2,256,336, (1940), (Duplicate of British
Patent 523,575).
9.
W. A. Beatty, "Pulse Generating and Pulse
Modulating System," U.S. Patent 2,265,337,
10.
S. H. Washburn, The H
(1940).
of Pulse Modulation,
E.E. Seminar, 11. I. T., (1947).
-73-
11.
T. Gootee, "Radio Relay Communications," Radio
News, 35(1946), no 5, 16.
12.
"Pulse Position Lrodulation Technic," Electronic
Industries, 4(1945), no 12, 82.
13.
D. L. Shapiro, Analysis of Diode Limiter, Thesis
for B. S. Degree, V. I. T., (1941).
14.
V. I. T. Radar School Staff, Principles of
Radar (2nd ed,; New York: McGraw-Hill Book
Company, Inc., 1946), 2-53 - 2-58,