How Does Amplitude Modulation Work?

Using modulation in radio communications is unavoidable. If, e.g., audio would be transmitted directly as a radio signal, then a single transmission would occupy the complete band, since all audio signals occupy about the same frequency range. Hence, nobody else would be able to transmit at the same time. Modulation moves the signal to (much) higher frequencies, and makes it possible to assign a different frequency to each transmitter. There is also the additional benefit that the size of an antenna is proportional to the wavelength of the signal, so that modulation enables the use of much smaller antennas.

Carrier and Message

The simplest modulation technique is Amplitude Modulation (AM), where the amplitude of a carrier is varied according to the message (e.g., a radio broadcast) that is to be transmitted. A carrier is a simple sinusoidal wave, as illustrated in Figure 1.

Figure 1. Carrier wave.Figure 1. Carrier wave.

In practice, a carrier such as this one would have a frequency of around 1 MHz for broadcast radio. How to transmit the following message signal by modulating the amplitude of the carrier wave?

Figure 2. Message.Figure 2. Message.

Amplitude Modulation

Mathematically, the modulation amounts to multiplying the carrier wave with the message. The carrier wave is defined as

\[c(t) = A\cos(2 \pi f_ct),\]

with \(A\) the amplitude of the wave and \(f_c\) the frequency. If the message is \(m(t)\), with \(|m(t)|\leq1\), then the AM-modulated carrier is given by

\[c_\mathrm{AM}(t) = (1+m(t))\,A\cos(2 \pi f_ct).\]

Adding \(1\) to the message brings it to the range \([0,2]\), so that the carrier just vanishes at the smallest message values. The result is shown in Figure 3. The original message is the envelope of the modulated carrier.

Figure 3. AM-modulated carrier.Figure 3. AM-modulated carrier.

In practice, the ratio between the frequency of the carrier and the frequencies that are present in the message is typically much larger than shown in this illustration. For broadcast radio, the frequency of the carrier is around 1 MHz, as mentioned before, while the frequencies in the audio signal are limited to about 10 kHz.

Although AM has been almost completely replaced by FM for radio broadcasting (there is a follow-up post on frequency modulation), it is still in use. It also has the added benefit of being the easiest of all modulation schemes to explain…

Submitted by Tom Roelandts on 2 November 2014

Comments

Nice notes

very good and understandable description of AM thank you

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