In article , Gary Schafer
writes:

Speaking of AM modulation,, we all know that the carrier amplitude
does not change with modulation. Or does it?

Yes and no.

It's a situation of subjective understanding of the basic modulation
formulas which define the amplitude of an "RF" waveform as a
function of TIME [usually denoted as RF voltage "e (t)" meaning the
voltage at any given point in time].

With a REPETITIVE modulation waveform of a single, pure audio
sinewave, AND the modulation percentage LESS than 100%, the
carrier frequency amplitude does indeed remain the same. I put some
words into all-caps for emphasis...those are required definitions for
proof of both the math AND a bench test set-up using a very narrow
bandwidth selective detector.

One example witnessed (outside of formal schooling labs) used an
audio tone of 10 KHz for amplitude modulation of a 1.5 MHz RF stable
continuous wave carrier. With a 100 Hz (approximate) bandwidth
of the detector (multiple-down-conversion receiver), the carrier
frequency amplitude remained constant despite the modulation
percentage changed over 10 to 90 percent. Retuning the detector to
1.49 or 1.51 MHz center frequency, the amplitude of the sidebands
varied in direct proportion to the modulation percentage.

That setup was right according to theory for a REPETITIVE modulation
signal as measured in the FREQUENCY domain.

But, but, but...according to a high-Z scope probe of the modulated RF,
the amplitude was varying! Why? The oscilloscope was just linearly
combining ALL the RF products, the carrier and the two sidebands.
The scope "saw" everything on a broadband basis and the display to
humans was the very SAME RF but in the TIME domain.

But...all the above is for a REPETITVE modulation signal condition.
That's relatively easy to determine mathematically since all that is
or has to be manipulated are the carrier frequency and modulation
frequency and their relative amplitudes. What can get truly hairy
is when the modulation signal is NOT repretitive...such as voice or
music.

Here is a question that has plagued many for years:
If you have a plate modulated transmitter, the plate voltage will
swing down to zero and up to two times the plate voltage with 100%
modulation. At 100% negative modulation the plate voltage is cutoff
for the instant of the modulation negative peak.

How is the carrier still transmitted during the time there is zero
plate voltage?

If we lower the modulation frequency to say 1 cps or even lower, 1
cycle per minute, then wouldn't the transmitter final be completely
off for half that time and unable to produce any carrier output??

I don't blame you for being puzzled...I used to be so for many
years long ago, too. :-)

Most new commercial AM transmitters of today combine the
"modulator" with the power amplifier supply voltage, getting rid of
the old (sometimes mammoth) AF power amplifier in series with
the tube plate supply. Yes, in the TIME domain, the RF power
output does indeed vary at any point in time according to the
modulation. [that still follows the general math formula, "e(t)"]

You can take the modulation frequency and run it as low as
possible. With AM there is no change in total RF amplitude
over frequency (with FM and PM there is). If you've got an
instantaneous time window power meter you can measure it
directly (but ain't no such animal quite yet).

If you set up a FREQUENCY domain test as first described, you
will, indeed, measure NO carrier amplitude change with a very
narrow bandwidth selective detector at any modulation percentage
less than 100% using a REPETITIVE modulation signal.

Actual modulation isn't "repetitive" in the sense that a signal
generator single audio tone is repetitive. What is a truly TERRIBLY
COMPLEX task is both mathematical and practical PROOF of
RF spectral components (frequency domain) versus RF time
domain amplitudes when the modulation is not repetitive. Please
don't go there unless you are a math genius...I wasn't and tried,
got sent to a B. Ford Clinic for a long term. :-)

In a receiver's conventional AM detector, the recovered audio is
a combination of: (1). The diode, already non-linear, is a mixer
that combines carrier and sidebands producing an output that is
the difference of all of them; (2). The diode recovers the time
domain amplitude of the RF, runs it through a low-pass filter to
leave only the audio modulation...and also allows averaging of the
RF signal amplitude over a longer time. Both (1) and (2) are
technically correct.

With a pure SSB signal there is a constant RF amplitude with a
constant-amplitude repetitive modulation signal, exactly as it
would be if the RF output was from a Class C stage. Single
frequency if the modulation signal is a pure audio tone. With a
non-repetitive modulation the total RF power output varies with
the modulation amplitude. The common SSB demodulator
("product detector") is really a MIXER combining the SSB input
with a constant, LOCAL RF carrier ("BFO") with the difference
product output...which recovers the original modulation signal.

Question is, at what point does the carrier start to be effected?

Beyond 100% modulation. The most extreme is a common
radar pulse, very short in time duration, very long (relative) in
repetition time. There's a formula long derived for the amplitude
of the spectra of that, commonly referred to as "Sine x over x"
when spoken. That sets the receiver bandwidth needed to recover
a target return.

I've gotten waist-deep into "matched filter" signals, such as using
a 1 MHz bandwidth filter to recover 1 microSecond RF pulses.
(bandwidth is equivalent to the inverse of on-time of signal, hence
the term "matched" for the filter) Most folks, me included, were
utterly amazed at the filtered RF output envelope when a detector
was tuned off to one side by 1, 2, or 3 MHz. Not at all intuitive.
The math got a bit hairy on that and I just accepted the late Jack
Breckman's explanation (of RCA Camden) since it worked on the
bench as predicted.

It's all a matter of how the observer is observing RF things, time
domain versus frequency domain...and whether the modulation is
repetitive single frequency or multiple, non-repetitive. The math for
a repetitive modulation signal works out as the rule for practical
hardware that has to handle non-repetitive, multi-frequency
modulation signals.

When combining two basic modulation forms, things get so hairy
its got fur all over. So, like someone explain how an ordinary
computer modem can send 56 Kilobits per second over a 3 KHz
bandwidth circuit? :-)

Len Anderson
retired (from regular hours) electronic engineer person