You have to be careful in what you call the "carrier". As soon as you
start modulating the "carrier", you have more than one frequency
component. At that time, only the component at the frequency of the
original unmodulated signal is called the "carrier". So you have a
modulated RF signal, part of which is the "carrier", and part of which
is sidebands.

General frequency domain analysis makes the assumption that each
frequency component has existed forever and will exist forever. So under
conditions of modulation with a periodic signal, you have three
components: A "carrier", which is not modulated, but a steady, single
frequency, constant amplitude signal; and two sidebands, each of which
is a frequency shifted (and, for the LSB, reversed) replica of the
modulating waveform.

You can take each of these waveforms, add them together in the time
domain, and get the familiar modulated envelope.

So, the short answer is that the carrier, which is a frequency domain
concept, is there even if you're modulating at 0.001 Hz. But to observe
it, you've got to watch for much longer than 1000 seconds. You simply
can't do a meaningful spectrum analysis of a signal in a time that's not
a lot longer than the modulation period.

Roy Lewallen, W7EL

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

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??

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


73
Gary K4FMX

You have to be careful in what you call the "carrier". As soon as you
start modulating the "carrier", you have more than one frequency
component. At that time, only the component at the frequency of the
original unmodulated signal is called the "carrier". So you have a
modulated RF signal, part of which is the "carrier", and part of which
is sidebands.

General frequency domain analysis makes the assumption that each
frequency component has existed forever and will exist forever. So under
conditions of modulation with a periodic signal, you have three
components: A "carrier", which is not modulated, but a steady, single
frequency, constant amplitude signal; and two sidebands, each of which
is a frequency shifted (and, for the LSB, reversed) replica of the
modulating waveform.

You can take each of these waveforms, add them together in the time
domain, and get the familiar modulated envelope.

So, the short answer is that the carrier, which is a frequency domain
concept, is there even if you're modulating at 0.001 Hz. But to observe
it, you've got to watch for much longer than 1000 seconds. You simply
can't do a meaningful spectrum analysis of a signal in a time that's not
a lot longer than the modulation period.

Roy Lewallen, W7EL

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

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??

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


73
Gary K4FMX

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

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

Roy Lewallen wrote:
The amplitudes of the sideband components are symmetrical (at least for
modulation by a single sine wave), but the phases aren't. The phases of
all the upper sideband components are in phase with the carrier; in the
lower sideband, the odd order components (and only the odd order ones)
are reversed in phase.

I certainly didn't realize that until you pointed it out; I was generalzing
from the narrowband FM situation where only the first sideband components
are necessarily maintained and incorrectly assuming the same phase
differences applied to the general case.

However...

Say you start with a baseband FM signal. Let's call the two sides of its
Fourier transform L and R for the 'left' and 'right' halves. Now we mix up
to the desired carrier frequency. At -f_c we have L at even greater
negative frequencies and R at smaller negative frequencies. Ditto at f_c.
If we now apply a low pass filter to select the lower sideband, we end up
with R and L -- No information has been lost! (Likewise, with a high pass
filter you have L and R left -- Same deal.)

Fundamentally mixing ANY signal followed by SSB filtering shouldn't lose
information. Yes, in practice we'll be talking about VSB instead of SSB,
but I still think we're OK.

Speaking of narrowband FM (NBFM)... and at the risk of splitting this
topic... I had a discussion today with someone over the ability to use an
envelope detector to recover narrowband FM signals. The output of the
envelope detector is approximately 1+0.5*cos^2(2*pi*f*t), where f was the
original modulating signal. The '1' will be killed by a capacitor, but that
leaves the cosine squared term... which seems impossible to easily change
back into cosine, since sqrt(x^2)=abs(x) and therefore it would appear that
we've irreversably lost information. Comments?

---Joel Kolstad
....ambitious novice who'll be licensed shortly...
....and I still think C-QUAM AM stereo is quite clever...

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

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??

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


73
Gary K4FMX


On Wed, 22 Oct 2003 20:39:20 -0700, Roy Lewallen
wrote:

The amplitudes of the sideband components are symmetrical (at least for
modulation by a single sine wave), but the phases aren't. The phases of
all the upper sideband components are in phase with the carrier; in the
lower sideband, the odd order components (and only the odd order ones)
are reversed in phase. With multitone modulation, things get a whole lot
more complex. Unlike AM, FM is nonlinear, so there are sideband
components from each tone, plus components from their sum, difference,
and harmonics. The inability to use superposition makes analysis of
frequency modulation with complex waveforms a great deal more difficult
than AM.

Note also that unlike AM, whatever fraction of the carrier that's left
when transmitting FM also contains part of the modulation information.
Of course, at certain modulation indices with pure sine wave modulation,
the carrier goes to zero, meaning that all the modulation information is
in the sidebands. But this happens only under specific modulation
conditions, so you'd certainly have an information-carrying carrier
component present when modulating with a voice, for example.

Roy Lewallen, W7EL

Joel Kolstad wrote:
Avery Fineman wrote:

There isn't any corresponding similarity of
FM and PM to AM for the repetition of sidebands' information when
looking at the spectral content.


Umm... last I looked the spectrum of FM and PM was symmetrical about the
carrier frequency? (Well, the lower sideband is 180 degrees out of phase
with the upper, but that's true of AM as well.) Looking at a single sine
wave input to an FM or phase modulator, this comes about from the Bessel
function expansion of the sidetones and J-n(x)=-Jn(x)?

I know you're far more experienced in this area than I am, however, so I'll
let you explain what I'm misinterpreting here!

---Joel Kolstad

In article , "Joel Kolstad"
writes:

Avery Fineman wrote:
There isn't any corresponding similarity of
FM and PM to AM for the repetition of sidebands' information when
looking at the spectral content.

Umm... last I looked the spectrum of FM and PM was symmetrical about the
carrier frequency? (Well, the lower sideband is 180 degrees out of phase
with the upper, but that's true of AM as well.) Looking at a single sine
wave input to an FM or phase modulator, this comes about from the Bessel
function expansion of the sidetones and J-n(x)=-Jn(x)?

Yes. More or less.

I know you're far more experienced in this area than I am, however, so I'll
let you explain what I'm misinterpreting here!

Noooo...I'm not going to. About a million subjective years ago I had to
slog through a solution and series expansion with the only "help" I got
being a suggestion to use Bessel Functions of the First Kind.

In doing so - AND thinking about it in the process - I learned quite a
bit about the math AND the modulation process. Very useful later on.
ALL learning takes place in one's own noggin...doesn't matter whether
one is in a formal class or alone being "lectured" by print on paper
through the eyeballs.

Over on the Agilent website, I would suggest downloading their free
Application Note 150-1. That is really a subtle selling thing for their
very fine spectrum analyzers but it is also a darn good treatise on
modulation and modulation spectra for all the basic types. It should
(unless altered there) include that nice little animated display of
sidebands versus modulation index. I've always admired those H-P
appnotes, valuing most as nice little tutorials on specialized subjects.

Richard Slater in the mentioned January '77 HR article was trying to
explain a combination of FM and AM. In order to get a proper "feel"
for that (in my opinion), one needs the experience of juggling those
series terms in the expanded equation form. There IS one hint and
that is the not-quite symmetry (in numeric values) of FM and PM
spectra as compared to AM spectra. True "single-sideband" has a
possibility only on true symmetry. FM and PM spectra, by
themselves, don't have that symmetry in the expanded form. I'm
not going to discuss that one since it should be apparent.

If you want some source code on calculating the numeric values of
Bessel Functions of the First Kind, I'll be happy to post it here under
some thread. It's short and not complicated and a #$%^!!! faster than
slugging through 5-place tables with slide rule and/or four-function
mechanical calculator. Been there, done too much of that. Computers
aren't just for chat rooms, are very nice for numeric calculations of the
large kind. :-)

Len Anderson
retired (from regular hours) electronic engineer person

The amplitudes of the sideband components are symmetrical (at least for
modulation by a single sine wave), but the phases aren't. The phases of
all the upper sideband components are in phase with the carrier; in the
lower sideband, the odd order components (and only the odd order ones)
are reversed in phase. With multitone modulation, things get a whole lot
more complex. Unlike AM, FM is nonlinear, so there are sideband
components from each tone, plus components from their sum, difference,
and harmonics. The inability to use superposition makes analysis of
frequency modulation with complex waveforms a great deal more difficult
than AM.

Note also that unlike AM, whatever fraction of the carrier that's left
when transmitting FM also contains part of the modulation information.
Of course, at certain modulation indices with pure sine wave modulation,
the carrier goes to zero, meaning that all the modulation information is
in the sidebands. But this happens only under specific modulation
conditions, so you'd certainly have an information-carrying carrier
component present when modulating with a voice, for example.

Roy Lewallen, W7EL

Joel Kolstad wrote:
Avery Fineman wrote:

There isn't any corresponding similarity of
FM and PM to AM for the repetition of sidebands' information when
looking at the spectral content.


Umm... last I looked the spectrum of FM and PM was symmetrical about the
carrier frequency? (Well, the lower sideband is 180 degrees out of phase
with the upper, but that's true of AM as well.) Looking at a single sine
wave input to an FM or phase modulator, this comes about from the Bessel
function expansion of the sidetones and J-n(x)=-Jn(x)?

I know you're far more experienced in this area than I am, however, so I'll
let you explain what I'm misinterpreting here!

---Joel Kolstad

Avery Fineman wrote:
There isn't any corresponding similarity of
FM and PM to AM for the repetition of sidebands' information when
looking at the spectral content.

Umm... last I looked the spectrum of FM and PM was symmetrical about the
carrier frequency? (Well, the lower sideband is 180 degrees out of phase
with the upper, but that's true of AM as well.) Looking at a single sine
wave input to an FM or phase modulator, this comes about from the Bessel
function expansion of the sidetones and J-n(x)=-Jn(x)?

I know you're far more experienced in this area than I am, however, so I'll
let you explain what I'm misinterpreting here!

---Joel Kolstad

On 22 Oct 2003 20:21:16 GMT, (Avery Fineman)
wrote:

Bill, I just dug out the 1977 issues of HR from storage and looked
the article over. Author Richard Slater (W3EJD) said almost the
same thing at the end of the article on page 15 under "closing
comments." The nomenclatures for different modulations were
formalized by the ITU-R since then but the FCC still doesn't have
anything covering this "single-sideband FM" modulation type for
U. S. amateur radio.

The ITU-R emission designations are quite outdated and many modern
emissions use din commercial and military systems would be designated
as XXX. In each case the X means "none above" in the corresponding
column.

Anyway, why should the amateur radio regulations contain these ITU-R
designations ? Here in Finland, ITU-R emission designations were
removed from amateur radio regulations and exam in 1997 and only band
specific power and bandwidth limits are used. I haven't heard of any
problems due to this decision.

Paul OH3LWR