0195136047.pdf

688 COMMUNICATION SYSTEMS

USB LSB LSB USB

Spectral impulse

due to carrier

Spectral impulse

due to carrier

Lower sideband (LSB)

Amplitude spectrum

Amplitude spectrum

Upper sideband (USB)

0 ω

0

1

2

−ωc ωc ω

1

(a)

(b)

Figure 15.2.2Spectral behavior.(a)Informa-

tion-signal spectrum.(b)Corresponding AM

signal spectrum.

Ac cos 2πfct

Nonlinear

device

such as a

P–N diode

Bandpass

filter tuned

to fc

x(t)

Message signal Conventional

+ DSB AM signal

Figure 15.2.3Block diagram of power-law modulation.

LetsAM(t) of Equation (15.2.3) be a voltage representing the wave that excites the transmitting

station’s antenna, which is assumed to represent a resistive impedanceR 0 to the transmitter that

feeds it. The power insAM(t) is found by

PAM=

sAM^2 (t)

R 0

=Pc+Pf=

1

2 R 0

[

A^2 c+f^2 (t)

]

(15.2.5)

in which the overbar represents the time average, andf(t) is assumed to have no dc component,

as is the usual case.Pc=A^2 c/ 2 R 0 is the power in the carrier, andPf=f^2 (t)/ 2 R 0 is the added

power caused by modulation.Pfis called the useful power, since only this power caused by the

message contributes toward message quality.Pc, the carrier power, is not useful power in the

sense that it carries no information. However, it is important to the receiver’s ability to recover

the message with low-cost circuitry.Modulation efficiencyηAMof the transmitted signal is defined

as the ratio of the useful power to the total power,

ηAM=

Pf

Pc+Pf

=

f^2 (t)

A^2 c+f^2 (t)

(15.2.6)

Whenf(t) is a square wave of peak amplitudeAc, the largest possible value ofηAMequal to 0.5,

or 50%, occurs. Whenf(t) is a sinusoid,ηAM≤ 1 /3, as shown in Example 15.2.1. For practical

audio (voice and music) messages, efficiency could be less than^1 / 3.