[AMRadio] The Physical Reality of Sidebands in the AM signal

Donald Chester k4kyv at charter.net
Thu Sep 29 13:50:17 EDT 2016

>From the beginnings of radiotelephony there has been a question whether
sidebands exist as physical reality or only in the mathematics of modulation
theory.  In the early 20's this was a hotly debated topic, with a noted
group of British engineers maintaining that sidebands existed only in the
mathematics, while an equally well-remembered group of American engineers
argued that sidebands do, in fact physically exist.

Today, the issue seems settled once and for all.  We can tune our modern-day
highly selective receivers through double-sideband and single-sideband voice
signals, and tune in upper or lower sideband, and even adjust the
selectivity to the point that we can tune in the carrier minus the
sidebands.  Nearly everyone accepts the notion that sidebands do indeed
exist physically...  or do they?  

Maybe it's a matter of how we observe the signal, and our result is modified
by our measuring techniques. Those who have studied quantum mechanics will
recall the Heisenberg uncertainty Principle, which states that it is
impossible to know both the position (physical location) and velocity (speed
and direction) of a particle at the same time, along with the related
"Observer Effect", which states that you cannot observe a system without
changing something in the system. In the following thought experiment, we
take this to an analogy with an amplitude modulated radio signal.

Imagine a cw transmitter equipped with an electronic keyer.  Also imagine
that there is no shaping circuitry, so that the carrier is instantly
switched between full output and zero output. Such a signal can be expected
to generate extremely broad key clicks above and below the fundamental
frequency because of the sharp corners of the keying waveform.  Set the
keying speed up to max, and send a series of dits.  If the keyer is adjusted
properly, the dits and spaces will be of equal length, identical to a full
carrier AM signal 100 percent modulated by a perfect square wave.

Suppose the keyer is adjusted to send, say, 20 dits per second when the
"dit" paddle is held down. The result is a 20 Hz square-wave-modulated AM
signal.  Now turn the speed up. If the keyer has the capability, run it up
to 100 dits per second.  If you tune in the signal using a receiver with
very narrow selectivity (100 Hz or less, easily achievable using today's
technology), you can actually tune in the carrier, and then as you move the
dial slightly you can tune in sideband components 100, 300, 500 Hz, etc.
removed from the carrier frequency. A square wave consists of a fundamental
frequency plus an infinite series of odd harmonics of diminishing amplitude.
Theoretically you would hear carrier components spaced every 200 Hz
throughout the spectrum.  In a practical case, due to the finite noise
floor, the diminishing amplitude of the sideband components and selectivity
of the tuned circuits in the transmitter tank circuit and antenna itself,
these sideband components eventually become inaudibly buried in the
background noise as the receiver is tuned away from the carrier frequency.

Suppose we now gradually slow down the keyer.  As we change to lower keying
speed, it takes more and more selectivity to discriminate between carrier
and sideband components, as the modulation frequency becomes lower and the
sideband components become spaced more closely together. Let's observe what
happens when we slow the dit rate down to 10 dits per second. Now the
fundamental modulation frequency is 10 Hz, and we can hear sideband
components at 10 Hz, 30 Hz, 50 Hz, 70 Hz removed from the carrier,
continuing above and below the carrier frequency at intervals of 20 Hz until
we reach a point  where the signals disappear into the background noise.  In
order to distinguish individual sideband components, we need selectivity on
the order of 10 Hz, which is possible if we use resonant i.f. selectivity
filters with extremely high "Q".  This can be accomplished using crystal
filters, regenerative amplifiers or even conventional L-C tuned circuits if
we carefully design the components to have high enough Q. 

As we achieve extreme selectivity with these high Q resonant circuits, we
observe a sometimes annoying characteristic familiarly known as "ringing."
This ringing effect is due to the "flywheel effect" of a tuned circuit, the
same "flywheel effect" that allows a class-C tube type final or class-E
solid state final to generate a harmonic-free sinewave rf carrier waveform.
The selective rf tank circuit stores energy which is re-released to fill in
missing parts of the sinewave, thus filtering out the harmonics inherent to
operation of these classes of amplifier.  CW operators are very aware of the
ringing effect of very narrow receiving filters, which can make the dits and
dahs of high speed CW run together, causing the signal to be just as
difficult to read with the narrow filter in line, as the same CW signal
would be with a wider filter, even one that admits harmful adjacent channel
interference.  Kind of a damned if you do, damned if you don't scenario.
Now, let's continue with our thought experiment, taking our example of code
speed and selectivity to absurdity.  We can slow down our keyer to a
microscopic fraction of a Hertz, to the point where each dit is six months
long, and the space between dits is also six months long.  In effect, we are
transmitting an unmodulated carrier for six months, then shutting down the
transmitter for six months. But still, this is only a matter of the degree
of code speed; the signal waveform is still identical to the AM transmitter
tone modulated with a perfect square wave, but whose frequency is one cycle
per year, or 3.17 X (10 to the -8) Hz.  That means that in theory, the
steady uninterrupted carrier is still being transmitted, along with a series
of sideband components spaced every 6.34 X (10 to the -8) Hz.

Now, carriers spaced every 6.34 X (10 to the -8) Hz apart are inarguably
VERY close together, to the point that building a filter capable of
separating them would likely be of complexity on the order of a successful
expedition to Mars, but still theoretically possible. Let us assume we are
able to build such a filter.  We would undoubtedly have to resort to
superconductivity in the tuned circuits, requiring components cooled to near
absolute zero, and thoroughly shield every rf carrying conductor to prevent
radiation loss, but here we are talking about something hypothetical,
without the practical restraints of cost, construction time and availability
of material.  Anyway, let us just assume we were able to successfully build
the required selectivity filter.

The receiver would indeed be able to discriminate between sidebands and
carrier of the one cycle/year or 3.17 X (10 to the -8) Hz modulated AM
signal, identical to a CW transmitter with carrier on for six months and off
for six months.  So how can we detect a steady carrier while the transmitter
is shut off for six months?  The answer lies in our receiver.  In order to
achieve high enough selectivity to separate carrier and sideband components
at such a low modulating frequency and close spacing, the Q of the tuned
circuit would have to be so high that the flywheel effect, or ringing of the
filter, would maintain the missing RF carrier during the six-month key-up

This takes us back to the longstanding debate over the reality of sidebands.
If we use a wideband receiver such as a crystal set with little or no
front-end selectivity, we can indeed think of the AM signal precisely as a
steady carrier that varies in amplitude in step with the modulating
frequency.  This is always the case if the total bandwidth of the signal is
negligible compared to the selectivity of the receiver.  Once we achieve
selectivity of the same order as the bandwidth of the signal, which has been
the norm for practical receivers dating from the late 1900's up to the
present, reception of the signal behaves according to the principle of a
steady carrier with distinctly observable upper and lower sidebands.  The
"holes" in the carrier at 100% negative modulation are inaudible due to the
flywheel effect of the tuned circuits, even though those same "holes" may be
observable on the envelope pattern of an oscilloscope.

An oscilloscope set up for envelope pattern, with the deflection plates
coupled directly to a sample of the transmitter's output, is a wideband
device much like a crystal set. It allows us to physically observe the AM
signal as a carrier of varying amplitude. A spectrum analyser on the other
hand, is an instrument of high selectivity, namely a selective receiver
programmed to sweep back and forth across a predetermined band of spectrum
while visually displaying the amplitude of the signal falling into its
passband at each instant. It clearly displays distinct upper and lower
sidebands with a steady carrier in between.

Furthermore, it has often been observed that the envelope pattern of a
signal as displayed from a scope connected to the i.f. output of a distant
receiver can be quite different from what is  seen on a monitor scope at the
transmitter site.  This is yet another example of how the pattern is altered
(distorted) by the selective components of the receiver.

In conclusion, there is no correct yes or no answer to the age-old question
whether or not sidebands are physical reality, or exist only in the
mathematics of modulation theory. It all depends on how you physically
observe the signal.  Sidebands physically exist only if you use an
instrument selective enough to observe them. Putting it another way, their
existence depends on whether we observe the signal in the time domain or the
frequency domain. Remember the Heisenberg Uncertainty Principle and the
associated Observer Effect?

Don k4kyv

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