0195136047.pdf

15.2 ANALOG COMMUNICATION SYSTEMS 687

whereas the sinusoidal carrier waveform is given by

c(t)=Accos(ωct+φc)=Accos( 2 πfct+φc)

Sometimes the standard AM signal is expressed in the form of

xc(t)=sAM(t)=[Ac+f(t)] cos(ωct+φc) (15.2.3)

in which the total amplitude of the carrier [Ac+f(t)] is a linear function of the message. Figure
15.2.1 illustrates the AM waveforms.
If the maximum amplitude off(t) in Equation (15.2.3) exceedsAc,overmodulationis said
to occur. In order to prevent excessive distortion in the receiver, overmodulation is avoided in
standard AM by requiring

|f(t)|max≤Ac (15.2.4)

such that the envelope ofsAM(t)orxc(t) will never go negative and may at most become zero.
The spectral behavior is depicted in Figure 15.2.2, assumingφ 0 =0 for simplicity. The spectral
impulses are due to the carrier and will always be present, even if the message were to disappear.
The effect of AM is to shift half-amplitude replicas of the signal spectrum out to angular
frequenciesωcand−ωc. The band of frequencies aboveωcor below−ωcis called theupper
sideband(USB). The one on the opposing side is known as thelower sideband(LSB). Since AM
transmits both USB and LSB, it is known as double-sideband modulation. If the maximum circular
(radian) frequency extent off(t)isWfrad/s, the frequency extent of the standard AM waveform
is 2Wf. Thus, the low-pass signal is translated in frequency to the passband of the channel so that
the spectrum of the transmitted bandpass signal will match the passband characteristics of the
channel.
There are several different methods for generating amplitude-modulated signals. Since the
process of modulation involves the generation of new frequency components, modulators are
generally characterized as nonlinear and/or time-variant systems, because a linear or a time-
invariant system cannot create new frequencies other than those contained in its input signal.
Figure 15.2.3 shows a block diagram ofpower-law modulationthat is nonlinear. Let the voltage
input to such a device be the sum of the message signal and the carrier, as illustrated in
Figure 15.2.3. The nonlinear device (that has an input–output characteristic of the form of
a square law) will generate a product of the messagex(t) with the carrier, plus additional
terms. The desired modulated signal can be filtered out by passing the output of the nonlinear
device through a bandpass filter. The signal generated by this method is a conventional DSB
AM signal.

t

x(t)

xc(t) Envelope |A(t)|

(a)

(b)

−Ac

Ac

t

Figure 15.2.1AM waveforms.(a)Information (message or

modulating) signal.(b)Modulated wave (corresponding stan-

dard AM signal).