> I created a simple plot consisting of two waves representing an AM
> signal. The amplitude of the carrier, Sin(10x) is modulated with a
> message signal, Sin(x) + 2.
>
> Picture attached.
>

Good plot! Looking at the expression, you're multiplying a sine wave (the
carrier) by another sine wave plus a constant. This is standard AM with
carrier. If you make the constant zero, you have double sideband
suppressed carrier. You can use the distributive property from algebra to
distribute the sin(10x) over the two terms in the sum. You get
sin(10x)*sin(1x) + 2*sin(10x). The first product is the sidebands (using
trig identities, you can expand it out to the sum or sins (I think it's
actually going to be the sum of cosines, but close enough!). The
2*sin(10x) is the carrier.

There's some real interesting stuff that can be done with AM. If you take
this AM signal and multiply it again by the carrier, you'll get a DC
component plus the original modulation plus a two times carrier component.
You can filter out everything but the original modulation to get the
original signal. This is often called a "product detector" or "synhronous
AM detector." Remove the carrier from the original AM signal (don't add
the 2 to the modulation in the original expression), and the DC output
goes away. This is the DSBSC signal used to carry L-R in FM stereo.

Now, at the receiver, rotate the signal you're multiplying the DSBSC or AM
signal by by 90 degrees. You still get the two times carrier output, but
no DC (for AM with carrier) or no modulation. You can transmit two
independent signals at the same frequency by using carriers that are 90
degrees apart. Receive them separately with two product detectors, each
driven by an RF signal 90 degrees from the other. This is QAM or
quadrature amplitude modulation. It's used for the chrominance signal on
analog color TV, used for data transmission on cable TV and modems, and
lots of other stuff.

When you add two sine waves (the outputs of the two balanced modulators
that are driven by RF in quadrature and two modulating signals) that are
90 degrees out of phase and with varying amplitudes, you get ANOTHER sine
wave. The amplitude of the sine wave is the square root of the sum of the
squares of the two sine waves. The phase is the arctangent of the ratio of
the two sine wave amplitudes. So, you can look at QAM as either the sum of
two DSBSC signals summed together or as a single signal that is being
phase and amplitude modulated. This phase and amplitude look is shown on a
vectorscope. For color TV, a linear QAM signal, the phase on the
vectorscope is the hue of the color, while the amplitude (how far from the
center of the display) is the saturation of the color. Digital QAM signals
show up as an array of dots. Ideally they are in fixed positions. Channel
impairments (noise, phase nonlinearities, etc.) cause the dots to wander a
bit. If they wander outside their region and into the region of another
dot, you just got a bit error.

Amazing stuff!

Harold








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