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# Amplitude modulation

Amplitude modulation (AM) is a method used to modulate 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. This should be compared to frequency modulation (FM), which modulates the frequency rather than the amplitude.

Amplitude modulation typically produces a modulated output signal that has twice the bandwidth of the modulating signal, with a significant power component at the original carrier frequency. Single sideband modulation is a technique that improves this, at the cost of extra complexity.

Network schematic of an AM receiver.

The working principles of AM radio is as follows: 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. The receiver uses a diode to remove either the positive or negative part of the electrical signal, leaving a signal which when filtered and amplified produces 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.

One of the attractions of amplitude modulation 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. It was one of the most popular methods for sending voice and music over radio during the 20th century.

## Example

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

c(t) = Csin(Ωt)

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

m(t) = Msin(ωt + P)

Amplitude modulation is simply adding m(t) to C, the amplitude modulated signal is then

y(t) = (C + Msin(ωt + P))sin(Ωt)

The formula for y(t) above may be written

$y(t) = C \sin(\Omega t) + M \frac{\cos(P - (\omega - \Omega) t)}{2} - M \frac{\cos(P + (\omega + \Omega) t)}{2}$

So the broadcast signal consists of the carrier wave plus two sinusoidal waves each with a frequency slightly different from Ω. These are known as sidebands. In general a signal of frequency ω broadcast with a carrier wave frequency Ω will produce waves of frequency Ω +/- ω 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.

## SSB, VSB and reduced-carrier signals

In practice one of the sidebands is superfluous and is often wholly or partially filtered out before broadcast in order to reduce congestion of the airwaves (see single sideband modulation for a detailed treatment).

An alternative technique used for signal power reduction is to remove the remaining carrier signal from the AM signal; the signal produced is a double-sideband suppressed carrier (DSSC) signal. If the carrier signal is not completely removed, the signal is called a double-sideband reduced carrier (DSRC) signal. DSSC and DSRC signals need the carrier to be regenerated before they can be demodulated like ordinary AM signals, or they may be treated like SSB/VSB signals.