Re: Radio waves...

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

Donald Simanek wrote:

> In amplitude modulation, a carrier frequency is mixed additively with the
> audio frequency wave. The resultant wave therefore has a spectrum of
> frequencies above and below the carrier frequency.

Actually for AM the modulation is impressed *multiplicatively* (with a DC
bias on the audio signal greater than the peak signal amplitude) and not
additively.  Maybe you meant something else by the term but if the audio
signal is just added to the rf signal no modulation develops and the
resultant is a simple linear superposition of signals with no modulation of
the rf carrier at all.  If such a superposition was to be run through a
*nonlinear* device then some audio modulation of the rf carrier would result
(along with many other audio signals and rf harmonics, etc. which could be
eliminated by a sufficiently narrow filter whose pass-band was centered on
the rf carrier frequency), but then in this case the signal is no longer
*additively* impressed.  Maybe you used the term "additively" in a way
different than as a superposition?

>                                                   (I'm leaving out the
> complication of the 455 kHz frequency used in superhet radios.) Thus the
> entire signal occupies approximately 15 kHz on either side of the carrier
> (the AM system doesn't transmit hi-fi up to 20 kHz audio, it only goes to
> 15 kHz if memory serves). Thus the two sidebands contain identical
> information, the carrier carries none. In some commercial and short-wave
> radio band the carrier is suppressed before transmission. In some the
> carrier and one sideband is suppressed. These conserve bandwidth and
> transmitted power. In either case, a carrier is supplied at the receiving
> end for the demodulation process. 

What you say is true about carrier suppression and single sideband SSB
transmissions, but the frequency bandwidths listed above are not allowed for
ordinary medium wave AM transmissions.  A standard AM channel is 10 kHz wide
which allows a 5 kHz width for each sideband.  This restriction requires that
AM radio signals carry no audio information at frequencies above 5 kHz.  This
is the major reason for the poor fidelity of AM broadcasts.  Maybe you are
thinking of the L - R channel AM modulation carried on a stereo FM
subcarrier. In this case the L - R channel is AM modulated on a 38Khz
subcarrier (the subcarrier is then suppressed before superposing the signal
onto the regular L + R audio signal. The combined signal is then FM modulated
on the FM rf signal.  In this case the side bands for the L - R signal have
15Khz width on each side of the 38 kHz subcarrier.  After demodulation when
this signal is algebraically combined with the L + R signal, both the L and R
channels are obtained.  Both audio signals (L + R and L - R) have a 15 kHz
bandwith for the audio signals.  For broadcast FM signals the audio frequency
response bandwidth is 0 - 15 kHz.

> Am radio in the US retains both bands and the carrier. I've heard some
> proposals of AM stereo by putting one channel of audio on each sideband.
> Ordinary radios would get the mixed (mono) signal, but radios could be
> designed to separate the sidebands and get stereo. I haven't kept up with
> this, it may already be used.

AM stereo *is* in use on some radio stations.  Since the fidelity is so low
it is kind of a waste of resources to bother with it though.  As far as I
know, I think the technique that you mentioned (of having each sideband carry
a different audio channel to get stereo) is not used.  I think the reason is
that this method would result in unacceptable distortion of the signal at
high modulation levels when it is tuned in by a mono radio that is not
designed for stereo reception.  This is because beating a single sideband
against a carrier will reproduce the original audio modulation only at low
modulation levels (i.e. low percent amplitude fluctuations).  In order for
the envelope to accurately reproduce the actual signal at high modulation
levels then both sidebands are needed.  I believe the multiplexing technique
adopted for AM stereo is to superimpose just the sidebands of the AM
modulated signal for the L - R channel onto the full AM signal for the L + R
channel.  The phase of the rf carrier used in modulating the L - R signal is
shifted 90 degrees with respect to the carrier used to modulate the L + R
channel.  What results is a rf wave with an amplitude modulation carrying the
L + R channel while the frequency of the wave is phase modulated PM with the
L - R channel.  A mono radio tuned to this signal just detects the AM
envelope with the L + R signal and it ignores the L - R PM signal.  The
reason that this works is that if one takes an AM modulated wave and then
subtracts out the carrier and then reinserts a new carrier that is phase-
shifted by 90 degrees, the resulting signal is phase modulated but not
amplitude modulated.  It is straightforward to show algebraically that by
doing such a phase-shifted trick that the (phase-shifted) carrier goes
through a zero crossing just when the sideband signal is cresting/troughing
in phase, and the sideband signal also is going through a zero crossing just
when the carrier is cresting/troughing in phase.  In contrast, an ordinary AM
wave always has its phase (crests, troughs, and zero crossings) remain
undisturbed by the modulation on its amplitude -- no matter what the harmonic
content of the sidebands is (as long as the audio signal doesn't overmodulate
the carrier and clip it off on the audio troughs).  In this case the side-
band signal always adds purely in-phase or purely out-of-phase to the carrier
causing only constructive interference which increases the carrier wave
amplitude, or only destructive interference which subtracts from the carrier
wave amplitude.  Actually this technique of superposing two channels worth of
sidebands from an AM modulated signal using a 90 degree (AKA quadrature
modulation) is also used in a (NTSC) television signal to carry the two color
channels on a common subcarrier.  This multiplexed signal has the entire
subcarrier removed however before the two sets of sidebands are added to the
video signal.  When these two channels are demodulated and algebraically
combined with the ordinary monochrome signal, then signals for all three
primary colors (RGB) are then reconstituted for driving the CRT electron
guns.  (BTW the main mathematical reason why quadrature techniques can
multplex two channels on one carrier is that a sine wave is orthogonal to a
cosine wave of the same frequency.)

> In FM radio they wisely allocated enough bandwidth to each station to
> include adio up to 20kHz, and a subcarrier for the stereo difference
> signal, and still another subcarrier for other services (background music
> for stores and businesses, second language services, etc.) I suspect this
> second subcarrier isn't much used anymore. TV bandwidth also accomodates
> subcarriers for color signal, stereo sound, and still another for
> closed-captioning, second language, etc.) 

As I said above FM audio signals carry audio frequency information up to
15kHz, not 20 kHz.  The FCC allows 100% FM modulation to correspond to a
carrier frequency shift of +- 75 kHz from the nominal unmodulated carrier
frequency.  This makes an FM channel nominally 150 kHz wide but the FCC
has FM channels separated by 200 kHz on the band.  This extra width is
because FM sidebands are intrinically wider than AM sidebands (whose width is
just the band width of the audio signal).  The Fourier analysis of a FM
signal is extremely complicated.  For an AM signal the sideband frequencies
are at f_c + f_a and f_c - f_a when the rf carrier has frequency f_c and the
audio signal has frequency f_a.  OTOH, for a FM signal the corresponding
sideband frequencies are f_c - f_a, f_c - 2*f_a, f_c - 3*f_a, ... f_c + f_a,
f_c + 2*f_a, f_c + 3* f_a, ....   This infinite series of side band
frequencies typically converges fast but the full signal still needs lots of
bandwidth anyway to carry the audio signal with full fidelity.

The full multiplexed audio signal impressed on the FM rf carrier has the
following frequency layout: 0 - 15 kHZ is the L + R  signal, at 19 kHz is a
weak pure sine wave pilot tone used to signal the receiver that the broadcast
is in stereo (the presence of this tone tells the receiver to turn on the
"stereo" light on the dial for the tuned station, 23 - 38 kHz is the lower
sideband for the L - R channel, from 38 - 53 kHz is the upper side band for
the L - R channel, 57 - 72 kHz is the upper sideband for the store/business
background muzak channel.  The 38 kHz subcarrier for the L - R signal is not
transmitted, but it is reconstructed in-phase in the reciever by doubling the
19 kHz stereo pilot signal (via full wave rectification followed by narrow
passband filtering).  This reconstituted subcarrier is then added to the
L - R sidebands and the resulting L - R AM signal is demodulated to extract
the  L - R channel which is then algebraically combined with the mono L + R
signal to give both the L and the R stereo channels.  If the subscription
muzak channel is to be demodulated then the 19 kHz pilot signal has its
frequency tripled and amplified. An intense version of this 57 kHz subcarrier
is combined with the muzak channel's upper sideband and then the result is
demodulated.  (Echoing Donald here I also don't know if the muzak channel is
used anymore either.)  If the "muzak" channel is used then the full
multiplexed audio signal occupies 0 - 72 kHz of bandwidth, otherwise the 
multiplexed signal occupies 0 - 53 kHz of bandwidth, and this signal is used
to shift the rf carrier frequency by up to +- 75 kHz from the nominal rf 
frequency as it is modulated.

As far as TV MTS stereo sound and the third SAP channel go I don't know how
they are encoded on a NTSC TV signal.  As far as closed captioning is
concerned, it is digitally encoded on the video signal only during the
vertical retrace time when the screen is temporarily blank and the electron
beam returns to the top of the screen after a field has just been traced out.
Such signals if they are present can bee seen "raw" by intentionally mis-
adjusting the vertical hold on the set and looking at the vertical blanking
bar which separates the top of the picture from the bottom.  If close
captioning is present this bar will have flickering light flashes on it.

> Subcarriers on an FM signal are often amplitude modulated. Sometimes phase
> modulated. Too bad these textbooks which have a "technology" orientation
> seldom cover this very interesting technolgy which touches all of us, for
> better or worse.

Hear, Hear.

> Find a ham radio operator in your area to bring you up to date on the
> latest technology. This post is off the top of my head, and someone surely
> can improve on it. The Radio Amateur's Handbook has lots of good info on
> this, but my copy is at the office, and I am at home.

My post is also off the top of my head so what I have said here may also not
be 100% correct (but I think I'm closer to the truth than Donald is here.) :-)

BTW, I don't know know how a high speed modem works.  How does one get a
200 - 2500 Hz bandwidth telephone channel to carry 28.8, 33.6, or 57.6 kbps 
without violating Shannon's theorem?  Does anyone want to tackle this
question?

David Bowman
dbowman@gtc.georgetown.ky.us