In article , Gary Schafer
writes:

I understand all of the points that you have made and agree that
looking at a spectrum analyzer with a modulated signal, less than 100%
modulation, shows a constant carrier. I also agree that looking at the
time domain with a scope shows the composite of the carrier and side
bands.
I understand that AM modulation and demodulation is a mixing process
that takes place.

My question of "at what point does the carrier start to be effected" I
was referring to low frequency modulation. Meaning when would you
start to notice the carrier change.

As long as the AM is less than 100% there won't be any change.

The qualifier there is the MEASURING INSTRUMENT that is
looking at the carrier.

With low and very low modulation frequencies, the sidebands
created will be very close to the carrier frequency. If the measuring
instrument cannot select just the carrier, then the instrument
"sees" both the carrier and sidebands...and that gets into the
time domain again which WILL show an APPARENT amplitude
modulation of the carrier (instrument is looking at everything).

I don't know how you would observe the carrier in the frequency domain
with very low frequency modulation as the side bands would be so close
to the carrier.

DSP along with very narrow final IF filtering can do it, but that isn't
absolutely necessary to prove the point.

Using "ordinary" narrowband filtering like a very sharp skirt 500 Hz
BW filter and variable frequency audio modulation from about 1 KHz
on up to some higher, one can separately measure the carrier and
sideband amplitudes. It will also show that the sidebands and
carrier do not change amplitude for a change in modulation
frequency, which is predicted by the general AM equations. Ergo,
decreasing the modulation frequency will not change amplitude
but one bumps into the problem of instrument/receiver selectivity.
That problem is one of instrumentation, not theory.

In my scenario of plate modulating a transmitter with a very low
modulation frequency (sine or square wave), on the negative part of
the modulation cycle the plate voltage will be zero for a significant
amount of time of the carrier frequency. The modulation frequency
could be 1 cycle per day if we chose. In that case the plate voltage
would be zero for 1/2 a day (square wave modulation) and twice the DC
plate voltage for the other half day. During the time the plate
voltage is zero there would be no RF out of the transmitter as there
would be no plate voltage.

It's a problem of observation again. Even with a rate of 1 cycle per
day, the sidebands are still going to be there and the observing
instrument is going to be looking at carrier AND sidebands at the
same time.

That would be right at 100% modulation, has to be if the carrier
envelope is observed to go to zero. At 99.999% (or however close
one wants to get to 100 but not reach it) modulation, the theory
for frequency domain still holds. Above that 100% modulation,
another theory has to be there.

For greater-than-100% modulation, an extreme case would be on-
off keying "CW." Sidebands are still generated, but those are due
to the very fast transition from off to on and on to off. Those sidebands
definitely exist and can be heard as "clicks" away from the carrier.
In designs of on-off keyed carrier transmitters, the good rule is to limit
the transition rate, to keep it slower rather than faster. [that's in the
ARRL Handbook, BTW] Slowing the transition rate reduces the
sidebands caused by transient effects (the on-off thing).

Modulation indexes greater than 100% fall under different theory.
For on-off keyed "CW" transmitters, the transient effect sideband
generation is much farther away from the carrier than low-frequency
audio at less than 100% modulation. It can be observed (heard)
readily with a strong signal.

This is where I get into trouble visualizing the "carrier staying
constant with modulation". As the above scenario, there would be zero
output so zero carrier for 1/2 a day. The other 1/2 day the plate
voltage would be twice so we could say that the carrier power during
that time would be twice what it would be with no modulation and that
the average carrier power would be constant. (averaged over the entire
day).

But we know that the extra power supplied by the modulator appears in
the side bands and not the carrier.

What is happening?

A lack of a definitive terribly-selective observation instrument is what
is happening.

Theory predicts no change in sideband amplitude with AM's modulating
frequency and practical testing with instruments proves that, right down
to the limit of the instruments. So, lowering the modulation frequency
to very low, even sub-audio, doesn't change anything. The instruments
run out of selectivity and start measuring the combination of all
products at the same time. Instrumentation will observe time domain
(the envelope) instead of frequency domain (individual sidebands).

There's really nothing wrong with theory or the practicality of it all.
The general equations for modulated RF use a single frequency for
modulation in the textbooks because that is the easiest to show to a
student. A few will show the equations with two, possibly three
frequencies...but those quickly become VERY cumbersome to
handle, are avoided when starting in on teaching of modulation theory.
The simple examples are good enough to figure out necessary
communications bandwidth...which is what counts in the practical
situation of making hardware that works for AM or FM or PM.

In the real world, everyone is really working in time domain. But, the
frequency domain theory tells what the bandwidth has to be for all
to get time domain information. In SSB with very attenuated carrier
level, that single sideband is carrying ALL the information needed.
We can't "hear" RF so the very amplitude stable receiver carrier
frequency resupply allows recovery of the original audio. With very
very stable propagation and a constant circuit strength, the original
audio could go way down in frequency to DC. The SSB receiver could
theoretically recover everything all the way down to DC...except the
practicality of minimizing the total SSB bandwidth and suppressing
the carrier puts the low frequency cutoff around 300 to 200 Hz.

The carrier isn't transmitted, and it is substituted in the receiver at a
stable amplitude in a SSB total circuit. Yet, theoretically it would be
possible to get a very low modulation rate but nobody cares to do so.
There ARE remote telemetering FM systems that DO go all the way
down to DC...but most communications applications have a practical
low-frequency cutoff. Theory allows it but practicality dictates other-
wise. The same in instrumentation recording/observing what is
happening...that also has practical limitations.

If most folks stop at the "traditional" AM modulation envelope scope
photos, fine. One can go fairly far just on those. To go farther, one
has to delve into the theory just as deeply, perhaps moreso. Staying
with the simplistic AM envelope-only view is what made a lot of hams
angry in the 1950s when SSB was being adopted very quickly in
amateur radio. They couldn't grasp phasing well; it didn't have any
relation to the "traditional" AM modulation envelope concept. They
couldn't grasp the frequency domain well, either, but that was a bit
simpler than phasing vectors and caught on better than phasing
explanations. :-)

Basic theory is still good, still useable. Nothing has been violated
for the three basic modulation types. Practical hardware by the ton
has shown that theory is indeed correct in radio and on landline (the
first "SSB" was in long-distance wired telephony).

BLENDING two basic modulation types takes a LOT more skull
sweat to grasp and nothing can be "proved" using simplistic
statements or examples (like AM from just RF envelope scope
shots) either for or against.

I like to use the POTS modem example...getting (essentially
equivalent) 56 K rate communications through a 3 KHz bandwidth
circuit. That uses a combination of AM and PM. Blends two basic
types of modulation, but in a certain way. Nearly all of us use one
to communicate on the Internet and it works fine, is faster than some
ISP computers, heh heh. So, the simplistic explanations of "one
can't get that fast a communication rate through a narrow bandwidth!"
falls flat on its 0 state when there are all these practical examples
showing it does work. It isn't magic. It's just a clever way to blend
two kinds of modulation for a specific purpose. It works.

In the "single-sideband FM" examples, one cannot use the simplistic
rules for FM in regards to bandwidth or rate. Those experiments were
combining things in a non-traditional way. It isn't strictly single
sideband, either, but many are off-put by the name given it.

Len Anderson
retired (from regular hours) electronic engineer person