Wikipedia: Amplitude modulation

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Amplitude modulation (AM for short) is a method used to send a signal, typically using radio. In the case of an analog signal to be sent, the amplitude? of the radio wave is modulated to be directly proportional to the value of the analog signal at the time.

Suppose we wish to modulate a simple sine wave on a carrier wave. The equation for the carrier wave of frequency W is

  yc(t) = Ac * sin(W * t)

The equation for the simple sine wave of frequency w (the signal we wish to broadcast) is

  yt(t) = At * sin(w * t + P)

Amplitude modulation is simply adding yt to Ac, the amplitude modulated signal is than

  y(t) = (Ac + At * sin(w t + P)) * sin(W * t)

Someone could probably try some ascii art? Or maybe do a png drawing and send it to the maintainers for inclusion?

Example

The (high frequency) carrier wave Ac sin(W t):

The signal wave, At sin(w t + P):

The modulated wave y(t):

One of the attractions of AM is that decoding the signal at the receiver is very simple. This was significant for the early days of commercial radio when electronic components were still quite expensive. The decoding method consists of rectify?ing the radio frequency signal using some kind of diode, and then smoothing it a little to remove any remaining radio frequency signal.

AM was one of the most popular methods for sending voice and music over radio during the 20th century. Other competing methods included frequency modulation, [single sideband]?, and very late in the 20th century digital pulse methods became viable.

Can someone explain clearly what "modulation" means with respect to radio waves?

It is not radio waves that are modulated but rather the signal applied to the antenna whose amplitude is modulated. The carrier wave is a sine wave of appropriate frequency which is combined(modulated) with a signal. When another antenna recieves this modulated wave form, and is tuned approprately and has an attached detector(a diode in this case), the voltages measured at the detector will rise and fall in identical fashion as the original signal prior to modulation.

A Note on the Mathematics

The formula for y(t) above may be written

 y(t) = Ac sin(W t) + At 0.5 cos(P - (w-W) t) - At 0.5 cos(P + (w+W) t)

So the broadcast signal consists of the carrier wave plus two sinusoidal waves each with a frequency slightly different from W. These are known as "side bands". In general a signal of frequency w broadcast with a carrier wave frequency W will produce waves of frequency W +/- w and, as long as the broadcast (i.e. the carrier wave) frequencies are sufficiently spaced out so that these side bands do not overlap stations will not interfere with one another. In practice one of the sidebands is superfluous and is usually filtered out before broadcast in order to reduce congestion of the airwaves.

FIXME: Show how a diode/smoothing recovers the original signal

A carrier wave introduces an alternating positive and negative electrical voltage in the receiving antenna. Modulating the wave causes the amplitude of these electrical voltages to be greater or smaller but in equal and opposite amounts. Hence the diode is used to remove either the positive or negative part of the electrical signal, leaving a signal which when filtered and amplified will cause an audible sound. Because the carrier frequency is significantly greater than the modulating frequency it is possible to use a capacitor to smooth or filter the waveform to remove the carrier.