August 1939 QST
Wax nostalgic about and learn from the history of early electronics. See articles
QST, published December 1915 - present (visit ARRL
for info). All copyrights hereby acknowledged.
Frequency modulation (FM) was, is, and
shall always be: x(t) = Xc·cos [Ωct + β·sin (Ωmt)],
where the carrier is xc(t) = Xc·cos (Ωct), and
the modulating signal is xm(t) = β·sin (Ωmt). Yea verily,
Edwin H. Armstrong. Amen, brothers and sisters of radio. The methods
for generating and degenerating[sic] FM might vary, but the fundamentals do not
vary. Mr. Armstrong developed and patented his system of frequency modulation in
the late 1920s and early 1930s, so when this article appeared in QST in
1939, FM was still fairly new - or even unknown - to most people. Household radio
dials still had only markings for the commercial AM band (520 - 1720 kHz) and,
in a few cases, a couple shortwave bands (also AM). The information presented here
is suitable for study by anyone at any time.
See June 2, 2020 update from RF Cafe visitor Mike, WN2A.
Frequency Modulation Fundamentals
How Frequency Modulation Works; Its Advantages in Overcoming Noise and Interference
By Daniel E. Noble, W1CAS
Fig. 1 - Illustrating amplitude and frequency modulation.
A, the motor-driven alternator used as an example; B, output with constant field
and constant speed (sine wave); C, output with constant speed and variable field
(amplitude modulation); D, constant amplitude and variable speed (frequency modulation).
Fig. 2 - Vector Diagram of phase modulation. The modulator
vector reverses, producing a resultant Θ degrees ahead or behind the carrier vector.
This is equivalent to a sudden change in the time axis, with the result that the
frequency changes. The vector will oscillate back and forth between A and B at the
modulating frequency. The more rapid the oscillation the faster the change in the
time axis, therefore the greater the frequency deviation produced.
Fig. 3 - A practicable frequency-modulator circuit, after
Weir. The oscillator is frequency-modulated by the a.f.c. tube (modulator) which
causes a frequency deviation in proportion to the amplitude of the audio voltage.
A small part of the output signal is fed to the converter tube, which is heterodyned
by a stable crystal oscillator to give a beat frequency at 1500 kc. The i.f. output
operates the rectifier (discriminator) and by providing the modulator with a d.c.
bias which varies when the mean oscillator frequency tends to change (a.f.c. action)
maintains the carrier frequency constant. Deviations of approximately 30 to 40 kc.
may be obtained in the region of 20 Mc. using a 6L6 modulator and 6F6 oscillator.
The stability of the system will be determined by the discriminator circuit stability.
Fig. 4 - Essentials of a superheat receiver suitable for
Fig 5. - Elementary detector circuit for frequency-modulated
waves. CD is tuned to the lower extremity of useful side bands, AB to the upper
extremity. The voltage appearing across either circuit is determined by the amplitude
of the audio modulating voltage. A hybrid wave appears across each circuit. Rectification
recovers the audio component.
Fig. 6 - The discriminator circuit combines the functions
of frequency detector and rectifier to recover the audio signal.
Fig. 7 - A parallel-resonant circuit will act as a frequency
detector when tuned to carrier at points A or B. With the circuit tuned so that
the carrier is at A. The voltage across the circuit will rise and fall in step with
the deviation produced by the modulating voltage; the result is an amplitude- modulated
wave which is also frequency-modulated. A rectifier will recover the amplitude audio
Transmitter house and six-bay turnstile antenna at W1XPW, a 1000-watt
experimental frequency-modulated transmitter located on top of West Peak, Meriden
Mountain, near Meriden, Conn. The transmitter operates on 43.4 megacycles. WDRC,
Inc., is the owner.
Two 50,000-watt experimental transmitters and several lower-powered transmitters
will be placed in regular operation in the Fall using the Armstrong frequency-modulation
system. The marked noise suppression which is the important characteristic of the
system will make possible a new standard of high-fidelity reception. The writer
has been asked to explain the action of this frequency-modulation system without
too much technical terminology. With all qualifications aside, the picture looks
something like this:
Every amateur knows what frequency modulation is - it's something in his transmitter
operation that he doesn't want! To make the picture a little more exact, we shall
make use of a pure sine wave alternator. A pure sine wave is a single-frequency
wave; that is, no side bands and no harmonics will be associated with it. A perfect
frequency meter could locate only one frequency with such a wave. If our alternator
is the usual motor-driven type with an external field supply, we can vary the voltage
output of the alternator by varying the field current. Let's vary the field current
slowly up and down and observe the result. First, the output voltage of the alternator
will increase and decrease, and we have a condition commonly referred to as amplitude
modulation. See Fig. 1 (A, B, and C). Second, the output wave is no longer
a pure sine wave, and if we examine the wave with our perfect frequency meter we
shall find several frequencies present, because only the pure sine wave will be
limited to a single frequency. So much for amplitude modulation.
Now regulate the field supply so that the amplitude of the alternator output
will not change while the driving motor is made to speed up and slow down. The frequency
of the alternator will be determined by the speed of the motor; if we speed up the
motor the output frequency will increase, and it will decrease when the motor slows
down. Assuming that the amplitude of the output remains constant, we have produced
a frequency-modulated wave by the simple process of speeding up and slowing down
the motor. What has happened to the wave? First, obviously the wave is no longer
a pure sine wave, since the frequency is changing. Second, since the wave is not
a pure sine wave, several frequencies will be present (theoretically, an infinite
number). When we neglect inertia and speed up and slow down the motor in such a
way that the change in speed is at the rate of ten cycles per second, and the cycles
are perfect sine-wave cycles, we will produce a frequency series for a 1000-cycle
generator something like this: . . . 1000 - 30, 1000 - 20, 1000 - 10, 1000, 1000
+ 10, 1000 + 20, 1000 + 30 . . . and so on to an infinite number of side bands.
Although frequency modulation will produce a composite wave made up of the carrier,
plus and minus a regular harmonic series of the modulating-signal frequency and
the carrier, we are fortunate in the fact that the amplitudes of the side bands
decrease rapidly as the signal harmonic number increases.
To go back to our motor-generator again, the motor was speeded up and slowed
down to produce our frequency modulation but we didn't say how much we speeded it
up or how much we slowed it down. We can change the motor speed so that the frequency
will vary instantaneously as follows: 1000 --> 1025 --> 1000 --> 975 -->
1000 cycles, and make the entire excursion in one-tenth of a second for a modulating
frequency of ten cycles per second. Or we can go 1000 -->1050 --> 1000 -->
950 --> 1000 in one-tenth of a second for a 10-cycle modulation frequency. The
difference is found in the more extended change in frequency in the second case.
This change is called the "deviation." For the first case the deviation is 25 cycles
and for the second, 50 cycles. Deviation is then the maximum instantaneous change
in frequency. Just to increase the confusion, we might add that we can't find the
deviation with the frequency meter since no continuous spectrum is produced but,
rather, we produce discrete side bands which may be detected and their physical
existence made evident by means of our frequency meter. These side bands may be
found far beyond the limits of the deviation. We might define the maximum instantaneous
frequency for our special case as the frequency we would get from our alternator
if we held the speed constant when the maximum speed was reached. We do not actually
produce such a maximum frequency because the speed does not remain constant. All
this leads to conclusion that we can expect the band-width of the frequency modulated
wave to be greater than twice the deviation.
Producing Frequency Modulation
A frequency-modulated wave may be produced much more readily with vacuum tube
equipment than with rotating machinery. Rotating a condenser back and forth to change
the capacity in an oscillator circuit will produce a frequency-modulated wave. Placing
a condenser microphone in an oscillator circuit in such a way that changes in the
microphone capacity will influence the frequency of the oscillator is an obvious
means of producing a modulated wave. The circuit used in automatic frequency control
systems is an excellent frequency-modulation system.
The modulation method invented by Major Edwin Armstrong is very stable since
the carrier is controlled by a quartz crystal oscillator. A 200-kc. oscillator supplies
voltage to a phase-shift network from which two components of the carrier are extracted,
differing only in phase. One component is 90° out of phase with the other. Mathematically,
the difference between the amplitude-modulated wave and the frequency-modulated
wave is the difference in the phase relations between side bands and carrier. If
the side bands of an amplitude-modulated wave could be extracted from the carrier,
shifted in phase 90°, and then recombined with the carrier, a frequency- modulated
wave would result. Major Armstrong did not extract the side bands but he did arrange
to produce side bands without a carrier by means of a balanced modulator working
with one of the 200-kc. components mentioned above, and then to combine the side
bands with the second component in such a way that the side bands were 90° out of
phase with the normal arrangement for carrier and side bands in the amplitude modulated
wave. His result was a frequency-modulated wave of the special type sometimes referred
to as a "phase-modulated" wave. Another way to describe the action of Major Armstrong's
modulator is to say that he combined a carrier voltage with a side-band voltage
which had been rotated through 90°. This gives us the simple picture of two vectors
90° out of phase combining to give the resultant voltage. Fig. 2 will assist
the reader to visualize the process. As the side-band voltage is increased and decreased,
the resultant of the two vectors is caused to shift phase. The shift in phase corresponds
to a frequency change, and the amount of frequency change produced will depend upon
the magnitude of the phase shift and upon how rapidly the phase shift is taking
place. Since the magnitude and the speed of the phase shift is determined by the
side-band vector, the deviation produced will be determined by the magnitude and
the frequency of the modulating signal. The only difference between pure frequency
modulation1 and phase modulation is the fact that the deviation is a
function of the amplitude only of the modulating signal for pure frequency modulation
while the frequency of the signal also determines the deviation for phase modulation.
A network placed in the audio input amplifier making the output signal voltage inversely
proportional to frequency will make the overall response independent of signal frequency,
and thus the phase modulator will produce a pure frequency-modulated wave. The actual
deviation produced at 200 kc. is small, something of the order of 15 to 20 cycles.
Therefore, a series of doublers must be introduced to increase the maximum deviation
to 100 kc. A total of twelve or thirteen doubler stages is used to reach the required
A system of modulation suggested by Murray C. Crosby and developed by Irving
R. Weir makes use of the automatic frequency control variable oscillator for modulating
the frequency, and of the a.f.c. discriminator circuit for stabilizing the oscillator
carrier. Fig. 3 illustrates the type of circuit used. The modulator tube injects
90° out-of-phase current into the oscillator tank circuit. The effect of changing
the modulator injector current is comparable to changing the tank capacity in the
oscillator circuit. The stabilizing circuit functions in the usual a.f.c. manner.
The receiver requirements are not so complicated as one might suspect. The usual
super-heterodyne is used with a few additions and changes. The pass band must be
greater than twice the transmitter deviation. A limiter precedes the detector, and
this limiter has the very important function of "wiping off" any amplitude modulation
which may have been introduced by noise voltages. The limiter passes on the frequency-modulated
wave with constant amplitude to the frequency detector, which changes the frequency-modulated
wave into a hybrid wave with both amplitude and frequency modulation components.
An ordinary detector then recovers the signal from the amplitude component. Fig. 4
illustrates the line-up. Figs. 5 and 6 show two frequency detectors.
A simple circuit of the type shown in Fig. 7 also will act as a frequency
detector. The carrier is tuned in on one side of the resonance curve. A steady-state
r.f. voltage will result from the unmodulated carrier, and modulation will produce
instantaneous frequency changes. Taking A as the operating point, any change corresponding
to an increase in frequency of the signal will increase the amplitude of the voltage
across the parallel-resonant circuit, and an equivalent decrease in frequency will
decrease the voltage across the circuit. Therefore, since the modulation produces
magnitudes of frequency change or deviation corresponding to the amplitude of the
audio modulating signal, and since the rate at which the changes or deviations take
place corresponds to the frequency of the audio signal, the voltage appearing across
the parallel-resonant circuit will be amplitude-modulated. Frequency modulation
will also be present but we are no longer interested in that. Rectification will
recover the audio signal. Any receiver of the usual type can be made to receive
frequency- modulated signals after a fashion by detuning slightly, but the reader
is assured that the "fashion" is not very satisfactory.
Remarkable results in the suppression of noise and interference are possible
with the frequency modulation system. Since the limiter wipes off all amplitude
variations, noise of this type must appear as frequency modulation produced by the
phase shift resulting from the combination of the signal and noise voltages. For
the case where the peak noise amplitude is half the signal amplitude and the phase
relation between signal and noise is ninety degrees, the maximum phase shift would
be approximately 26.5°. Very little frequency modulation will be produced if this
phase shift is the result of noise modulated by a low-frequency audio component,
but the frequency modulation will increase directly with the frequency of the audio
noise component. The receiver will display greatest susceptibility to noise frequencies
above audibility. Logical design of the receiver would call for a sharp cut-off
of the audio amplifier response or, better still, a falling high-frequency characteristic
which will reduce the hiss response. A simple predistortion network at the transmitter
will present a compensating rising high-frequency response so that the overall response
of the system is flat. This is the arrangement used in the stations now on the air.
The very remarkable effect of the limiter action upon the suppression of interference
has been demonstrated by Weir.2 He reports that with two stations operating
on the same channel the stronger station would prevail 100 per cent at the receiver
whenever the stronger station's signal was more than twice the strength of the weaker
signal. He also reports in the same paper that no interference area of the usual
kind existed where the signals were of nearly the same amplitude. In this area the
movement of the antenna a few inches would throw one program out and bring in the
other one. The presence of standing waves accounts for the phenomenon since the
nodes would permit the selection of the required voltage radio.
Mathematically the action of the limiter is rather complicated, but the results
of the limiter action are an overall effect of cutting the amplitude of the received
voltage in such a way that the strong signal component dominates while the weak
signal is suppressed. In other words, the strong signal will always take control
of the receiver. The frequency-modulation system permits2 as much as
25 dB gain in signal-plus-noise- to-noise ratio over that possible with an amplitude
system of equal carrier strength.
While this gain in equivalent power is due in part to the limiter action it is
also the result of the very interesting effect which makes the magnitude of the
recovered power at the receiver a function of the modulation deviation. If a deviation
of 50 kc. produces voltage A at the receiver, then a deviation of 100 kc. will produce
a voltage two times A at the receiver. Here the received voltage has been doubled
without changing the carrier power at the transmitter. In the amplitude case the
peak carrier power must increase four times when the modulation changes from zero
to 100 per cent. Since without the power change the received voltage increases for
the frequency-modulated system with an increase in deviation, it follows that the
advantage of the system over the amplitude system will increase as the deviation
is increased. The practicable limits must be determined by available channel width.
The Federal Communications Commission has assigned 200-kc. channels for the broadcast
stations now in operation. For this channel width the deviation will probably be
restricted to 80 kc. or less. Present standards seem to point to a modulation index
(that is: ratio of deviation to audio frequency) of 80,000/15,000' or approximately
Necessarily this is a very sketchy account of Major Armstrong's invention. The
writer hopes that it may serve as an introduction to the subject, and for those
who are interested in the more detailed and technical aspects a carefully selected
bibliography is appended.
- The term "phase modulation" is something of a pain. Actually there are as many
types of frequency modulation as there may be functions of X. Phase modulation is
one type. The type referred to as "pure" frequency modulation is the unadulterated,
holy, sweet, etc. variety in which the deviation produced is a linear function of
the modulating signal amplitude only. "Phase modulation" is still "frequency modulation."
- I.R. Weir, "Field Tests and Amplitude Modulation with Ultra-High-Frequency Waves,"
Part I. General Electric Review, may 1939.
Selected Frequency Modulation Bibliography
1. Carson, John R. "Notes on the Theory of Modulation," Proceedings IRE, Vol.
10, No.1, February, 1922. First paper in which the frequency-modulated wave is analyzed
mathematically and the required "band width" determined.
2. Armstrong, Edwin H. "A Method of Reducing Disturbances in Radio Signaling
by a System of Frequency Modulation." Proc. I.R.E., Vol. 24, No.5, May, 1936. Undoubtedly
the classical paper in the field. The first published account of the wide-band frequency
3. Crosby, Murray C. "Frequency Modulation Noise Characteristics." Proc. I.R.E.,
Vol. 25, No.4, April, 1937. Mathematical treatment and experimental verification
of wide-band frequency modulation vs. amplitude noise suppression.
4. Roder, Hans. "Frequency Modulation." Electronics, Vol. 10, No.5, May, 1937.
Mathematical analysis of validity of noise-suppression effect in wide-band frequency
5. Carson, John R. and Fry, Thornton C. "Variable Frequency Electric Circuit
Theory with Application to the Theory of Frequency Modulation." Bell System Technical
Journal, Vol. 16, No.4. Fundamental formulas for variable frequency electric circuit
theory are developed. Transmission, reception and detection of frequency modulated
waves are studied analytically.
6. Roder, Hans. "Tuned Circuits and a Frequency Modulated Signal." Proc. I.R.E.,
Vol. 25, No. 12, Mathematical treatment of tuned circuits.
7. Weir, I. R. "Field Tests of Frequency-and-Amplitude-Modulation with Ultra-High-Frequency
Waves." General Electric Review, May, 1939, Part I; June, 1939, Part II. A very
important paper of interest to both the technical and non-technical readers. Describes
a simplified transmitter.
8. Day, John R . "A Receiver for Frequency Modulation." Electronics, June, 1939.
The first published constructional data for a seven-tube frequency-modulation receiver.
Mike, WN2A, wrote the following in response to this
"Frequency Modulation Fundamentals" article:
Again, you hit it out of the ballpark, Kirt!
Great article out of QST.
Absolutely accurate to credit "The Old Man" Edwin Armstrong for the invention/development
of FM and much more, plus the work of Dan Noble, who worked with the Connecticut
State Police and Motorola as Director of Research. Also many, many others. Some
that have never been properly credited. Guys like Bob Morris, W2LV and Frank Gunther,
W2ALS. They were both interviewed by Ken Burns for "Empire of the Air".
I was fortunate enough to talk to both of these guys after I got my Tech license
in 1970. My immediate supervisor/mentor from 1972 until he retired in ~1990, was
George. He was a superb mentor, who espoused the best engineering methods and as
he would say " the price of success is constant vigilance." George had worked for
Armstrong at the pioneering FM station, W2XMN in the late 40's and early 50's. George
had several stories about working for "The Old Man."
1) George was a young guy, just back from WWII and many communication assignments
during the war: Chain Home Radar, Normandy, the Bulge, all with the Army. His fluent
German and technical skills (that ARRL membership card gave him away!) got noticed
by the Army and before long he was put to some rather dangerous assignments doing
Decoy work at (and behind) enemy lines. After the war, Armstrong hired George while
he was finishing up his degree. Armstrong would grab a bunch of heavy turnstile
antennas and bound up the tower, while George struggled to keep up with "The Old
Man." Armstrong was very adept at tower climbing, even in his later years.
2) What do you use for a dummy load for 50,000 watts (Average, not ERP!) ?? Armstrong
and his team loaded up the chain link fence that ran through a shallow pond near
the transmitter house. They matched it up and it "made the ducks very happy in the
winter!" Apparently it could melt the ice on the pond.
3) The best story I have to relate to you is the Capacitor Failure story: Armstrong
spent off-time at his house, way out on Long Island. Of course, he was never really
away from his work, he kept an FM radio monitor on all the time. If the station
went off the air, or there was any other problem, you knew it! I was told, he gave
you about 10 minutes before he called you, if it went off the air. So late one night,
George was doing his homework at W2XMN when something loud exploded. George knew
he only had a few minutes to diagnose the problem. So he was running around and
saw that the high-voltage capacitors exploded and there was a big mess. He couldn't
understand why the fuses had not blown. So he looks into the fuse box and sees pennies
where fuses should have been. The Phone rings...right on time....it was Armstrong.
His voice always in the same deliberate measured way, almost a drawl... "George...
the station is down..." George responds (actually quite proud of himself now that
he diagnosed the problem first) says, "Yes , I found the problem!...the High Voltage
Capacitors blew, 'cause some idiot put pennies in the fuse box!!" After a pause,
Armstrong responds, "ohhhh George, I must be that idiot... I was trying to find
the failure mode in the power supply...guess you found it... Good Night, Click"
George was speechless.
As you maintain an incredible website that always keeps an eye on both the past
(and future) of electronics technology, I thought you would appreciate these stories.
George was always very reserved about telling these stories and others, but I
have no doubt of their authenticity. Armstrong was my mentor's mentor?--Cool!
73's-Be Safe! Mike, WN2A
Posted May 29, 2020
(updated from original post on 5/30/2013)