Fred McKenzie wrote:
It has been about 35 years since I had a class in school where SSB-FM was
discussed. I recall that if you derive the equations for both AM and FM
SSB, they are identical for practical purposes if the FM signal has low
deviation (low modulation index?).

You're probably thinking of AM vs. narrow band FM. Although the equations
look very similar on paper and the MAGNITUDE spectrum is identical, the
phase spectrum is different in that -- in the phasor domain -- AM always
sits at 0 degrees and just grows and shrinks with modulation (overmodulation
pushes it over to 180 degrees, BTW). NBFM, on the other hand, still has the
carrier at 0 degrees but grows and shrinks along the imaginary axis. Hence
the angle of the phasor is small but time-varying (which implies that the
instantaneous frequency is varying as well -- but of course you already knew
that since we called this whole mess 'frequency modulation'). The angle is
about 15 degrees for a modulation index of 0.3 (what my notes claim as a
good cutoff for NBFM) and about 5 degrees at 0.1.

See the message I posted earlier tonight for a discussion of whether or not
you can recover NBFM with an envelope detector as of course one often does
with AM (the difficulty is due to that phasor's wiggling...). I think not,
but there's plenty I don't have a clue about... yet!

What's the modulation index on two meters anyway?

---Joel Kolstad
....who does know that a wideband FM receiver has no problem whatsoever
receiving NBFM...

Looking at Two Meter FM, the deviation typically peaks at about 5 KHz.
If you listen to your local repeater with an SSB rig such as the IC-706,
it will be obvious that it isn't a clean signal! However, a 3 KHz
deviation FM signal on HF (below 29 MHz) will sound much cleaner when
tuned as SSB, and you may not notice it isn't AM-SSB.

Sometimes I really get curious and want to know about something.

I haven't seen the Ham Radio article, but I'm thinking if the whole
idea had any merit it would be a popular mode by now.

Bruce-

It has been about 35 years since I had a class in school where SSB-FM was
discussed. I recall that if you derive the equations for both AM and FM SSB,
they are identical for practical purposes if the FM signal has low deviation
(low modulation index?).

Looking at Two Meter FM, the deviation typically peaks at about 5 KHz. If you
listen to your local repeater with an SSB rig such as the IC-706, it will be
obvious that it isn't a clean signal! However, a 3 KHz deviation FM signal on
HF (below 29 MHz) will sound much cleaner when tuned as SSB, and you may not
notice it isn't AM-SSB.

With this in mind, consider that AM-SSB and FM-SSB might just be two ways to
generate an SSB signal, assuming you use a filter to eliminate the carrier and
other sideband.

By the way, an IC-706, especially one with the TCXO, often has a more accurate
frequency read-out than a typical Two Meter rig. Therefore you can use it to
check a repeater's frequency by tuning it as if it were an SSB station while
someone is speaking. It is easy enough to check the IC-706 against WWV on HF.

73, Fred, K4DII

In article , W7TI
writes:

On Wed, 22 Oct 2003 06:52:37 -0700, "Joel Kolstad"
wrote:

After all... in the presense of some AM on regular double side band FM, most
receivers still perform just fine, don't they?
_________________________________________________ ________

In the USA, the FCC used to prohibit simultaneous amplitude and
frequency modulation. I did a search of Part 97 rules and I don't see
that exact wording now, but I would still tread lightly in this area.
Provided all the sidebands are confined to a band no wider than
conventional AM, you probably won't be bothered by Uncle Charlie but
caution is advised.
--
Bill, W7TI

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.

A general problem with understanding the concept is the simplicity
of the explanations of AM in today's amateur radio. The mathematical
representations of all modulations have been known and distributed in
text books for decades...my introduction to that was "Electronic
Designer's Handbook by Landee, Davis, Albrecht, McGraw-Hill 1957,
Section 5. Those who can follow the series expressions in a
summation formula, study it, will understand how a phasing-type SSB
modulator and demodulator can work. It is much harder to look at the
expressions and "see" FM or PM; Hewlett-Packard's Agilent site has
a neat little animated Java display that may help some on that.

Filter-type SSB from AM is almost intuitive when the AM spectrum is
shown. That is easy to comprehend...once all accept that the content
of each AM sideband has the same information. (there are still some
long-timers who refuse to accept that the carrier RF energy doesn't
change in AM at less than 100% modulation, heh heh) FM and PM
sidebands are definitely NOT easy to visualize since their individual
amplitudes and phases change depending on modulation index and
modulating frequency. There isn't any corresponding similarity of
FM and PM to AM for the repetition of sidebands' information when
looking at the spectral content.

What Slater was discussing in that January 1977 HR article was what
a group of researchers had already been doing in the early 1970s to
see if there were alternatives to SSB-like frequency multiplexing in
multi-channel circuits. Part of that investigation was to get around
some of the patents still existing on frequency multiplexing via single
sideband techniques (pioneered first on long-distance telephony, by
the way). Another part was to simplify (if possible) the circuitry
involved when carrying a LOT of channels. Equipent of 3 to 4 decades
ago was a lot bulkier than it is now for non-digital multiplexing. The
"narrowband" necessities of working in small-bandspace amateur bands
was not a prime criteria for that research.

Slater explained much of the above in that article and didn't claim any
exciting narrowband results of previous art. The (mislabeled in my
opinion) "single-sideband FM" technique of combining FM and AM
is simply a DIFFERENT way to communicate information.

A truly different way of modulation exists in everyone's telephone line
modem that can send/receive up to 56 Kilobits/Sec in a bandwidth of
only 3 KHz. That is a combination of AM and PM. That isn't intuitive
to AM-oriented minds and there still exist arguments in newsgroups
that such high rates "aren't possible!" :-) Yet most of us POTS users
with computers regularly get 33 to 56 KBPS rates over 2.5 to 3.0 KHz
bandwidth telephone circuits.

I've not seen much on that "single-sideband FM" stuff in the professional
literature after 1980. Based on what was published in the 1970s, it was
an interesting technique but did not come up with any advantages for
commercial or military adoption or much further work. I think it does
show that old paradigms aren't always worth four nickels and that, truly,
thinking outside the box might come up with something new and useful.

Just some comments from
Len Anderson
retired (from regular hours) electronic engineer person

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

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...

Joel Kolstad wrote:
. . .
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.

I'm afraid you lost me with the "baseband" FM signal. Would you provide
a carrier frequency, modulation frequency, and deviation or modulation
index as an example?

The lower and upper sidebands of an FM signal do contain the same
information when the modulation is a single sine wave, even though the
sidebands aren't identical. But when you modulate with a complex
waveform, you might find that some of the information which is adding in
one sideband is subtracting in the other, and you might not be able to
recover the modulating waveform from only one or the other -- sort of
like you can't get two separate stereo channels from just the sum
signal. I don't know if that's true, but it wouldn't surprise me. And,
as I pointed out in another posting, the entire modulation information
isn't even contained in *both* sidebands except under very special
conditions -- some is in the carrier. Another question, of course, is
whether you can get close enough to be useful. Perhaps with NBFM, at
least, you could.

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?

Cos^2(x) = abs(cos(x)) = 1/2 * (1 + cos(2x)). As you've noted, the DC
term can be blocked with a capacitor, so you'd end up with a cosine wave
at twice the frequency.

But I've never heard of trying to detect NBFM directly with an envelope
detector like you'd detect AM. The trick we used in ye olden tymes was
called "slope detection". You tuned the signal so it was on the edge of
the IF filter. The filter slope converted the FM to AM, which was then
detected with the normal AM envelope detector. If you tuned directly to
the carrier frequency, you didn't hear any modulation to speak of.

Roy Lewallen, W7EL

Joel Kolstad wrote:
. . .
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.

I'm afraid you lost me with the "baseband" FM signal. Would you provide
a carrier frequency, modulation frequency, and deviation or modulation
index as an example?

The lower and upper sidebands of an FM signal do contain the same
information when the modulation is a single sine wave, even though the
sidebands aren't identical. But when you modulate with a complex
waveform, you might find that some of the information which is adding in
one sideband is subtracting in the other, and you might not be able to
recover the modulating waveform from only one or the other -- sort of
like you can't get two separate stereo channels from just the sum
signal. I don't know if that's true, but it wouldn't surprise me. And,
as I pointed out in another posting, the entire modulation information
isn't even contained in *both* sidebands except under very special
conditions -- some is in the carrier. Another question, of course, is
whether you can get close enough to be useful. Perhaps with NBFM, at
least, you could.

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?

Cos^2(x) = abs(cos(x)) = 1/2 * (1 + cos(2x)). As you've noted, the DC
term can be blocked with a capacitor, so you'd end up with a cosine wave
at twice the frequency.

But I've never heard of trying to detect NBFM directly with an envelope
detector like you'd detect AM. The trick we used in ye olden tymes was
called "slope detection". You tuned the signal so it was on the edge of
the IF filter. The filter slope converted the FM to AM, which was then
detected with the normal AM envelope detector. If you tuned directly to
the carrier frequency, you didn't hear any modulation to speak of.

Roy Lewallen, W7EL

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