On Thu, 23 Oct 2003 19:51:49 -0700, Roy Lewallen
wrote:

Now, imagine that you can draw three sine waves on a long piece of
paper. They would have the frequencies and amplitudes of the three
spectral components above. These are the time domain representations of
the three frequency domain components. (In that sense, you *can* speak
of a carrier or a sideband in the time domain -- so I was perhaps unduly
dogmatic about that point.) But here's the important thing to keep in
mind -- all three of these components have constant amplitudes. They
extend from the beginning of time to the end of time, and don't start,
stop, or change at any time. That's what those spectral lines mean, and
what we get when we transform them back to the time domain.

It is quite easy to visualise this using a spreadsheet program.
However, it would be easier to use a much higher modulation frequency
compared to the carrier frequency. Assuming a carrier frequency of
1000 Hz and a modulating frequency of 100 Hz, so the sidebands would
be at 900 and 1100 Hz.

In column A put the time t and for each line increment the value by
0.0001 s or 0.00005 s.

In column B calculate 0.5*sin(2*pi*900*t).
In column C calculate 1.0*sin(2*pi*1000*t).
In column D calculate 0.5*sin(2*pi*1100*t).
In column E calculate the sum of columns B, C and D.

Duplicate these lines 500 to 1000 times and draw a graph, with column
A or time as the X-axis and display columns B, C, D and E as separate
graphs on the Y-axis.

Paul OH3LWR

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

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

I've read through some of the replies and didn't see what I thought was a good
answer to "where can I find a good explanation". We've been doing a series of
technical seminars at work, and one of the first ones covered AM and FM
modulation. (FYI...we build equipment that is very good at analyzing spectral
content of signals, so it's an area we care quite a bit about.) We used a
vector diagram that I think is fairly easy to understand. Wish I could draw it
here! I'll try to describe it verbally in a way you could draw it yourself,
and think about it.

For AM: Draw a vector starting at the origin and going one unit right. This
is the carrier, at time=0. It rotates counterclockwise (by convention) at the
carrier frequency. Now consider, say, 50% modulation with some sinewave, maybe
1/1000 the carrier freq. To represent this, draw two more vectors. The way
we've done it is to start them both at the right end of the first (carrier)
vector. Both are 1/4 unit long. To start, at time=0, draw them both further
to the right from the carrier. Since they are both adding to the carrier, the
net at that point in time is 1.5 units long. Now if the carrier didn't move
(zero freq), one of the little vectors would rotate clockwise and one would
rotate counterclockwise, at just the same rates. (Careful here! The one going
clockwise represents your "negative freq" if you will, but there is NO MATH,
just a picture, so don't let your mind lock up on this one!) They'd get to be
both pointing to the left at just the same time, and at that time they'd
subtract from the carrier and leave you with a vector 0.5 units long. But
before you got to that point, you'd have one of them pointing straight up, and
one pointing down, and they'd cancel out, leaving just the carrier. Now just
imagine all that happening as the carrier rotates them around... it's all just
the same but produces the carrier plus the two sidebands. One key thing to get
from this picture is that the two modulation vectors always sum together to a
vector which is parallel to the carrier vector (or else zero length).

For FM: Draw the same picture, but now the modulation vectors both start
pointing up, at 90 degrees to the carrier. As they rotate around, they always
sum to something that is perpendicular to the carrier vector. Hmmmm...but
notice that if they are very short, the net result is practically the same
length as the carrier vector all the time, but if they are a bit longer, you'd
have the carrier amplitude changing. Draw the picture to see that! Let's say
that each of the two are 1/10 as long as the carrier, so that the result is a
right triangle with the carrier 1 unit long and the modulation 1/5 unit long.
So the net in that case would be sqrt(1^2 + 0.2^2) = 1.02. But this is FM, and
the amplitude is not allowed to change. So we have to put in a correction.
One way to do that is to add a couple more vectors which correct this initial
error. If you think it through, you'll see they have to rotate twice as fast
as the initial two modulation vectors. So the initial ones represent the first
sidebands, and the next pair represent the second sidebands...and if you draw
it out right, you'll be able to see how the whole set of sidebands comes about.
So...why is it FM? Because the sidebands rotate the carrier phase. In fact,
that's how you have to draw the set of modulation vectors: to sum up to a
carrier whose phase is modulated (which is the same as FM, of course, for this
single sine freq modulation).

But notice that if the modulation is low enough, practically all the modulation
energy is in those initial two sidebands, represented by the first two vectors.
Now if you transmitted ONLY those two and removed the carrier, and someone on
the other end inserted the carrier at t=0 pointing UP instead of to the right,
why you'd have -- AM! Or at least something very, very close to AM. So, I
think it should be clear from that, that single sideband FM (assuming very low
modulation index) should be practically equivalent to single sideband AM.

By the way, back several years ago there was a lot of interest in finding ways
to make more efficient AM broadcast transmitters. If you use a class C power
amplifier, you can get good RF-generator efficiency, but the modulator running
class AB or B is inefficient. And if you do the modulation at a low level, you
have to run the RF chain AB or B. So one of the ways invented to get AM was to
generate two FM signals, which of course can be amplified by class C power
amps, whose modulation was generated through a pretty special DSP algorithm, so
that when you combined the RF outputs of the two FM transmitters you got,
ta-da, AM! I always thought that was pretty cool, but I don't think it ever
caught on in a big way, because folk have come up with other ways of
efficiently generating AM.

Cheers,
Tom


(Bruce Kizerian) wrote in message
. com...
Can anyone direct me to some good understandable references on single
sideband frequency modulation? I have no real practical reason for
wanting to know about this. It is interesting to me in a "mathetical"
sort of way. Of course, that is dangerous for me because my brain gets
very stubborn when I try to do math. Such ideas as "negative
frequency" kind of send my mental faculties into total shutdown.

But I read schematic very well. It is a visual language I can usually
understand. Seems like years ago there was an article on SSB FM in Ham
Radio. That would probably be a good start. If anyone can send me a
copy of that article I would be much appreciative.

Thanks in advance

Bruce kk7zz

www.elmerdude.com



Cheers,
Tom

I've read through some of the replies and didn't see what I thought was a good
answer to "where can I find a good explanation". We've been doing a series of
technical seminars at work, and one of the first ones covered AM and FM
modulation. (FYI...we build equipment that is very good at analyzing spectral
content of signals, so it's an area we care quite a bit about.) We used a
vector diagram that I think is fairly easy to understand. Wish I could draw it
here! I'll try to describe it verbally in a way you could draw it yourself,
and think about it.

For AM: Draw a vector starting at the origin and going one unit right. This
is the carrier, at time=0. It rotates counterclockwise (by convention) at the
carrier frequency. Now consider, say, 50% modulation with some sinewave, maybe
1/1000 the carrier freq. To represent this, draw two more vectors. The way
we've done it is to start them both at the right end of the first (carrier)
vector. Both are 1/4 unit long. To start, at time=0, draw them both further
to the right from the carrier. Since they are both adding to the carrier, the
net at that point in time is 1.5 units long. Now if the carrier didn't move
(zero freq), one of the little vectors would rotate clockwise and one would
rotate counterclockwise, at just the same rates. (Careful here! The one going
clockwise represents your "negative freq" if you will, but there is NO MATH,
just a picture, so don't let your mind lock up on this one!) They'd get to be
both pointing to the left at just the same time, and at that time they'd
subtract from the carrier and leave you with a vector 0.5 units long. But
before you got to that point, you'd have one of them pointing straight up, and
one pointing down, and they'd cancel out, leaving just the carrier. Now just
imagine all that happening as the carrier rotates them around... it's all just
the same but produces the carrier plus the two sidebands. One key thing to get
from this picture is that the two modulation vectors always sum together to a
vector which is parallel to the carrier vector (or else zero length).

For FM: Draw the same picture, but now the modulation vectors both start
pointing up, at 90 degrees to the carrier. As they rotate around, they always
sum to something that is perpendicular to the carrier vector. Hmmmm...but
notice that if they are very short, the net result is practically the same
length as the carrier vector all the time, but if they are a bit longer, you'd
have the carrier amplitude changing. Draw the picture to see that! Let's say
that each of the two are 1/10 as long as the carrier, so that the result is a
right triangle with the carrier 1 unit long and the modulation 1/5 unit long.
So the net in that case would be sqrt(1^2 + 0.2^2) = 1.02. But this is FM, and
the amplitude is not allowed to change. So we have to put in a correction.
One way to do that is to add a couple more vectors which correct this initial
error. If you think it through, you'll see they have to rotate twice as fast
as the initial two modulation vectors. So the initial ones represent the first
sidebands, and the next pair represent the second sidebands...and if you draw
it out right, you'll be able to see how the whole set of sidebands comes about.
So...why is it FM? Because the sidebands rotate the carrier phase. In fact,
that's how you have to draw the set of modulation vectors: to sum up to a
carrier whose phase is modulated (which is the same as FM, of course, for this
single sine freq modulation).

But notice that if the modulation is low enough, practically all the modulation
energy is in those initial two sidebands, represented by the first two vectors.
Now if you transmitted ONLY those two and removed the carrier, and someone on
the other end inserted the carrier at t=0 pointing UP instead of to the right,
why you'd have -- AM! Or at least something very, very close to AM. So, I
think it should be clear from that, that single sideband FM (assuming very low
modulation index) should be practically equivalent to single sideband AM.

By the way, back several years ago there was a lot of interest in finding ways
to make more efficient AM broadcast transmitters. If you use a class C power
amplifier, you can get good RF-generator efficiency, but the modulator running
class AB or B is inefficient. And if you do the modulation at a low level, you
have to run the RF chain AB or B. So one of the ways invented to get AM was to
generate two FM signals, which of course can be amplified by class C power
amps, whose modulation was generated through a pretty special DSP algorithm, so
that when you combined the RF outputs of the two FM transmitters you got,
ta-da, AM! I always thought that was pretty cool, but I don't think it ever
caught on in a big way, because folk have come up with other ways of
efficiently generating AM.

Cheers,
Tom


(Bruce Kizerian) wrote in message
. com...
Can anyone direct me to some good understandable references on single
sideband frequency modulation? I have no real practical reason for
wanting to know about this. It is interesting to me in a "mathetical"
sort of way. Of course, that is dangerous for me because my brain gets
very stubborn when I try to do math. Such ideas as "negative
frequency" kind of send my mental faculties into total shutdown.

But I read schematic very well. It is a visual language I can usually
understand. Seems like years ago there was an article on SSB FM in Ham
Radio. That would probably be a good start. If anyone can send me a
copy of that article I would be much appreciative.

Thanks in advance

Bruce kk7zz

www.elmerdude.com



Cheers,
Tom

Let's start at the other end and see what happens;

If we have a final amp with 1000 dc volts on the plate and we want to
plate modulate it to 100% or very near so, we need 1000 volts peak to
peak audio to do it.
On positive audio peaks the dc plate voltage and the positive peak
audio voltage will add together to provide 2000 volts plate voltage.

On negative audio peaks the negative audio voltage will subtract from
the dc plate voltage with a net of zero volts left on the plate at
that time. (or very nearly zero volts if we do not quite hit 100%)

How does the tube put out any power (carrier) at the time there is
near zero plate voltage on it?

The negative audio cycle portion is going to be much longer than many
rf cycles so the tank circuit is not going to maintain it on its own.

Why does the carrier stay full?


73
Gary K4FMX



On 25 Oct 2003 03:52:07 GMT, (Avery Fineman)
wrote:

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

Let's start at the other end and see what happens;

If we have a final amp with 1000 dc volts on the plate and we want to
plate modulate it to 100% or very near so, we need 1000 volts peak to
peak audio to do it.
On positive audio peaks the dc plate voltage and the positive peak
audio voltage will add together to provide 2000 volts plate voltage.

On negative audio peaks the negative audio voltage will subtract from
the dc plate voltage with a net of zero volts left on the plate at
that time. (or very nearly zero volts if we do not quite hit 100%)

How does the tube put out any power (carrier) at the time there is
near zero plate voltage on it?

The negative audio cycle portion is going to be much longer than many
rf cycles so the tank circuit is not going to maintain it on its own.

Why does the carrier stay full?


73
Gary K4FMX



On 25 Oct 2003 03:52:07 GMT, (Avery Fineman)
wrote:

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

In article , Gary Schafer
writes:

Let's start at the other end and see what happens;

If we have a final amp with 1000 dc volts on the plate and we want to
plate modulate it to 100% or very near so, we need 1000 volts peak to
peak audio to do it.
On positive audio peaks the dc plate voltage and the positive peak
audio voltage will add together to provide 2000 volts plate voltage.

On negative audio peaks the negative audio voltage will subtract from
the dc plate voltage with a net of zero volts left on the plate at
that time. (or very nearly zero volts if we do not quite hit 100%)

How does the tube put out any power (carrier) at the time there is
near zero plate voltage on it?

The negative audio cycle portion is going to be much longer than many
rf cycles so the tank circuit is not going to maintain it on its own.

Why does the carrier stay full?

Gary, you are trying to mix the frequency domain and time domain
information...and then confusing steady-state conditions in the time
domain with repetitive conditions.

The "carrier amplitude is constant" holds true over repetitive audio
modulation. In conventional AM, with repetitive modulation from a
pure tone, there are three RF spectral products. If you deliberately
notch out the carrier component in a receiver, and then reinsert a
steady-state, synchronized carrier frequency component in its
place, you will recover the original modulation audio. The receiver
demodulator sees only a steady, constant-amplitude carrier
frequency component. There is absolutely no carrier amplitude
variation then. But the original modulation audio is demodulated
exactly as if it were the done with the original transmitted carrier.
SSB reception is done all the time that way (except the carrier
amplitude is so low it might as well be zero).

That's a practical test proving only that the carrier amplitude does
not have any change insofar as demodulation is concerned.

As a practical test of just the transmitter, let's consider your basic
old-style AM description...Class-C RF PA with linear plate volts v.
power output characteristic, modulation by the plate voltage. That
plate voltage is 1 KV steady-state. In steady-state, RF output has
a single RF component, the carrier frequency. One.

RF spectral component will follow the general time-domain RF
equations with no modulation. [easy math there]

Apply modulation to the plate voltage with a pure tone. Plate
voltage swings UP as well as DOWN equally. [theoretical perfect
linear situation] Same rate of UP and DOWN. [start thinking dv/dt]

Look at the spectral components with this pure tone modulation.
Now we have THREE, not just one. Any high resolution spectrum
analyzer sampling the RF output will provide practical proof of that.

So, if you want to examine the total RF in a time-domain situation,
you MUST examine it as amplitude versus an infinitely-thin slice of
TIME. You cannot take a finite time chunk out of the RF envelope
and "prove" anything...anymore than you can justify the existance of
three RF components, not just TWO. [if this were the real classroom,
you would have to prove that on the whiteboard and justify it in full
public view...and maybe have to show the class the spectrum
analyzer output]. Remember that the modulation signal also exists
in a time domain and is constantly changing.

If the "carrier sinewave goes to zero and thus power output is zero,"
how do you justify that, a half repetition time of the modulation signal
later, "carrier sinewave goes to twice amplitude and power output is
double"? You are trying an analogy that has a special condition, by
neglecting the RATE of the modulation. It is always changing just as
the carrier frequency sinewave is changing. You want to stop time
for the modulation to show repetitive RF carrier sinusoids and that is
NOT modulation. It is just adjustment of the RF output via plate
voltage. No modulation at all.

The basic equation of an AM RF amplitude holds for those infinitely-
small slices of TIME. The series expansion of that basic equation
will show the spectral components that exist in the frequency domain.
Nothing has been violated in the math and practical measurements
will prove the existance and nature of the spectral components.

For those that like the vector presentation of things, trying to look at
a longer-than-infinitely-small slice of time or just the negative or
positive modulation swings is the SAME as removal of the modulation
signal vector. Such wouldn't exist in that hypothetical situation. It
would be only the RF carrier vector rotating all by itself.

In basic FM or PM, there's NO change in RF envelope amplitude with
a perfect source of FM or PM. "The carrier swings from side to side
with modulation," right? Okay, then how come for why does the
carrier spectral frequency component go to ZERO with a certain
modulation/deviation level and STAY there as long as the modulation
is held at that level? RF envelope amplitude will remain constant.
Good old spectrum analyzer has practical proof of that. [common way
of precise calibration of modulation index with FM] The FM is "just
swinging frequency up and down" is much too simple an explanation,
excellent for quick-training technicians who have to keep ready-
built stuff running, not very good for those who have to use true basics
for design, very bad for those involved with unusual combinations of
modulation.

If you go back to your original situation and have this theoretical
power meter working with conventional AM, prove there are ANY
sidebands generated from the modulation of plant voltage...or one
or two or more. :-) Going to be a difficult task doing that, yet there
obviously ARE sidebands generated with conventional AM and each
set has the same information. Lose one and modulation continues.
Prove it solely from the time-domain modulation envelope. Prove
the carrier component amplitude varies or remains constant.

Hint: You will wind up doing as another Johnny Carson did way
back in 1922 (or thereabouts) when the basic modulation equations
were presented on paper. [John R. Carson, I'm not going to argue
the year, that's in good textbooks for the persnickety] With
conventional AM the CARRIER FREQUENCY COMPONENT
amplitude remains the same for any modulation percentage less
than 100. Period. I not gonna argue this anymore. :-)

Len Anderson
retired (from regular hours) electornic engineer person

In article , Gary Schafer
writes:

Let's start at the other end and see what happens;

If we have a final amp with 1000 dc volts on the plate and we want to
plate modulate it to 100% or very near so, we need 1000 volts peak to
peak audio to do it.
On positive audio peaks the dc plate voltage and the positive peak
audio voltage will add together to provide 2000 volts plate voltage.

On negative audio peaks the negative audio voltage will subtract from
the dc plate voltage with a net of zero volts left on the plate at
that time. (or very nearly zero volts if we do not quite hit 100%)

How does the tube put out any power (carrier) at the time there is
near zero plate voltage on it?

The negative audio cycle portion is going to be much longer than many
rf cycles so the tank circuit is not going to maintain it on its own.

Why does the carrier stay full?

Gary, you are trying to mix the frequency domain and time domain
information...and then confusing steady-state conditions in the time
domain with repetitive conditions.

The "carrier amplitude is constant" holds true over repetitive audio
modulation. In conventional AM, with repetitive modulation from a
pure tone, there are three RF spectral products. If you deliberately
notch out the carrier component in a receiver, and then reinsert a
steady-state, synchronized carrier frequency component in its
place, you will recover the original modulation audio. The receiver
demodulator sees only a steady, constant-amplitude carrier
frequency component. There is absolutely no carrier amplitude
variation then. But the original modulation audio is demodulated
exactly as if it were the done with the original transmitted carrier.
SSB reception is done all the time that way (except the carrier
amplitude is so low it might as well be zero).

That's a practical test proving only that the carrier amplitude does
not have any change insofar as demodulation is concerned.

As a practical test of just the transmitter, let's consider your basic
old-style AM description...Class-C RF PA with linear plate volts v.
power output characteristic, modulation by the plate voltage. That
plate voltage is 1 KV steady-state. In steady-state, RF output has
a single RF component, the carrier frequency. One.

RF spectral component will follow the general time-domain RF
equations with no modulation. [easy math there]

Apply modulation to the plate voltage with a pure tone. Plate
voltage swings UP as well as DOWN equally. [theoretical perfect
linear situation] Same rate of UP and DOWN. [start thinking dv/dt]

Look at the spectral components with this pure tone modulation.
Now we have THREE, not just one. Any high resolution spectrum
analyzer sampling the RF output will provide practical proof of that.

So, if you want to examine the total RF in a time-domain situation,
you MUST examine it as amplitude versus an infinitely-thin slice of
TIME. You cannot take a finite time chunk out of the RF envelope
and "prove" anything...anymore than you can justify the existance of
three RF components, not just TWO. [if this were the real classroom,
you would have to prove that on the whiteboard and justify it in full
public view...and maybe have to show the class the spectrum
analyzer output]. Remember that the modulation signal also exists
in a time domain and is constantly changing.

If the "carrier sinewave goes to zero and thus power output is zero,"
how do you justify that, a half repetition time of the modulation signal
later, "carrier sinewave goes to twice amplitude and power output is
double"? You are trying an analogy that has a special condition, by
neglecting the RATE of the modulation. It is always changing just as
the carrier frequency sinewave is changing. You want to stop time
for the modulation to show repetitive RF carrier sinusoids and that is
NOT modulation. It is just adjustment of the RF output via plate
voltage. No modulation at all.

The basic equation of an AM RF amplitude holds for those infinitely-
small slices of TIME. The series expansion of that basic equation
will show the spectral components that exist in the frequency domain.
Nothing has been violated in the math and practical measurements
will prove the existance and nature of the spectral components.

For those that like the vector presentation of things, trying to look at
a longer-than-infinitely-small slice of time or just the negative or
positive modulation swings is the SAME as removal of the modulation
signal vector. Such wouldn't exist in that hypothetical situation. It
would be only the RF carrier vector rotating all by itself.

In basic FM or PM, there's NO change in RF envelope amplitude with
a perfect source of FM or PM. "The carrier swings from side to side
with modulation," right? Okay, then how come for why does the
carrier spectral frequency component go to ZERO with a certain
modulation/deviation level and STAY there as long as the modulation
is held at that level? RF envelope amplitude will remain constant.
Good old spectrum analyzer has practical proof of that. [common way
of precise calibration of modulation index with FM] The FM is "just
swinging frequency up and down" is much too simple an explanation,
excellent for quick-training technicians who have to keep ready-
built stuff running, not very good for those who have to use true basics
for design, very bad for those involved with unusual combinations of
modulation.

If you go back to your original situation and have this theoretical
power meter working with conventional AM, prove there are ANY
sidebands generated from the modulation of plant voltage...or one
or two or more. :-) Going to be a difficult task doing that, yet there
obviously ARE sidebands generated with conventional AM and each
set has the same information. Lose one and modulation continues.
Prove it solely from the time-domain modulation envelope. Prove
the carrier component amplitude varies or remains constant.

Hint: You will wind up doing as another Johnny Carson did way
back in 1922 (or thereabouts) when the basic modulation equations
were presented on paper. [John R. Carson, I'm not going to argue
the year, that's in good textbooks for the persnickety] With
conventional AM the CARRIER FREQUENCY COMPONENT
amplitude remains the same for any modulation percentage less
than 100. Period. I not gonna argue this anymore. :-)

Len Anderson
retired (from regular hours) electornic engineer person

Avery Fineman wrote:
So, if you want to examine the total RF in a time-domain situation,
you MUST examine it as amplitude versus an infinitely-thin slice of
TIME.

You might want to remind everyone that the mathematical Fourier transform of
a signal is an integral that extends from time=minus infinity to plus
infinity. Since Real Spectrum Analyzers (or network analyzer) need to
produce results in something, oh, less than infinite time (probably less
than the time between now and the next donut break), they're necessarily
limited in the low frequency detail they can provide. True, if Gary's
transmitter is transmitting a zero at the moment he connects a spectrum
analyzer, he won't see anything at all on the display, but as you point
out -- this is an equipment problem, not a mathematical one.

I'm still a believer in SSB-FM, BTW. :-) But I have enough respect for you
that I won't attempt to argue it further without first finding the time to
prepare a few drawings to demonsrate why!

---Joel Kolstad