Amplitude Modulation

Amplitude Modulation

Amplitude modulation (AM) is depicted. Mathematically, the process
can be expressed as



component that prevents loss of information, as explained subsequently. This
scheme is also known as double sideband transmitted carrier (DSBTC).

From Equation (6.11) and Figure 6.10, it can be seen that AM involves the
multiplication of the input signal by the carrier. The envelope of the resulting signal
is [1 + nax(t)] and, as long as na < 1, the envelope is an exact reproduction of the
original signaL If na > 1, the envelope will cross the time axis and information is lost.


It is instructive to look at the spectrum of the AM signal. An example is
shown in Figure 6.12. The spectrum cOI).sists of the original carrier plus the spectrum
of the input signal translated to te. The portion of the spectrum for Ifl > Itel
is the upper sideband, and the portion of the spectrum for Ifl < Itel is lower sideband.
Both the upper and lower sidebands are replicas of the original spectrum
M(f), with the lower sideband being frequency reversed. As an example, consider
a voice signal with a bandwidth that extends from 300 to 3000 Hz being modulated
on a 60-kHz carrier. The resulting signal contains an upper sideband of 60.3 to
63 kHz, a lower sideband of 57 to 59.7 kHz, and the 60-kHz carrier. An important
relationship is


where Pt is the total transmitted power in set) and Pe is the transmitted power in the
carrier.We would like na as large as possible so that most of the signal power is used
to carry information. However, na must remain below 1.
It should be clear that set) contains unnecessary components, because each of
the sidebands contains the complete spectrum of met). A popular variant of AM,
known as single sideband (SSB), takes advantage of this fact by sending only one of
the sidebands, eliminating the other sideband and the carrier. The principal advantages
of this approach are
• Only half the bandwidth is required, that is, BT = B, where B is the bandwidth
of the original signal. For DSBTC, BT = 2B.