This is the method used in medium-wave and short-wave radio broadcasting. Figure 1.3 shows what happens when we apply amplitude modulation to a sinusoidal carrier wave.

Fig. 1.3 Amplitude modulation waveforms: (a) modulating wave; (b) carrier wave; (c) modulated wave

Figure 1.3(a) shows the modulating wave on its own.6 Figure 1.3(b) shows the carrier wave on its own. Figure 1.3(c) shows the resultant wave. The resultant wave shape is due to the fact that at times the modulating wave and the carrier wave are adding (in phase) and at other times, the two waves are opposing each other (out of phase).

Amplitude modulation can also be easily analysed mathematically. Let the sinusoidal modulating wave be described as

vm = Vm cos (ωmt ) (1.2)
vm = instantaneous modulating amplitude (volts)
Vm = modulating amplitude (peak volts)
ωm = angular frequency in radians and ωm = 2πfm where
fm = modulating frequency (hertz)

When the amplitude of the carrier is made to vary about Vc by the message signal vm, the modulated signal amplitude becomes
[Vc + Vm cos (ωmt )] (1.3)

The resulting envelope AM signal is then described by substituting Equation 1.3 into Equation 1.1 which yields
[Vc + Vm cos (ωmt )] cos (ωct + φc) (1.4)

It can be shown that when this equation is expanded, there are three frequencies, namely (f c – fm), f c and (f c + fm). Frequencies (f c – fm) and (f c + fm) are called sideband frequencies. These are shown pictorially in Figure 1.4.

Frequency spectrum of an AM wave

The modulating information is contained in one of the sideband frequencies which must be present to extract the original message. The bandwidth (bw) is defined as the highest frequency minus the lowest frequency. In this case, it is (f c + fm) – (f c – fm) = 2fm where f m is the highest modulation frequency. Hence, a radio receiver must be able to accommodate the bandwidth of a signal.

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