0195136047.pdf

676 COMMUNICATION SYSTEMS

Pin Pout

G 1

Preamplifier

L 1

α 1

1

G 2 G 3

Repeater Receiving

amplifier

L 2

α 2

2

Figure 15.1.4Transmission system with preamplifier, repeater, and receiving amplifier.

(an additional amplifier) at some intermediate point in the line. All amplifiers will of course be

impedance-matched for maximum power transfer. The final output powerPoutin Figure 15.1.4 is

then given by

Pout

Pin

=

G 1 G 2 G 3

L 1 L 2

(15.1.15)

where theGs are the power gains of the amplifiers, and theLs are the transmission losses of the

two parts of the line. Equation (15.1.15) reveals that we can compensate for the line loss and get

Pout≥PinifG 1 G 2 G 3 ≥L 1 L 2. Noise considerations often call for a preamplifier to boost the signal

level before the noise becomes significant. As in the case of transcontinental telephone links,

several repeaters are generally required for long-distance transmission.

EXAMPLE 15.1.3

From a source withPin=2.4 mW, we want to getPout=60 mW at a distancel=20 km from

the source.αfor the transmission line is given to be 2.3 dB/km. The available amplifiers have

adjustable power gain, but are subject to two limitations: (i) the input signal power must be at

least 1μW to overcome internal noise, and (ii) the output signal power must not be greater than

1 W to avoid nonlinear distortion. Design an appropriate system.

Solution

αl= 2. 3 × 20 =46 dB

LdB= 46 or L= 1046 /^10 ∼=40,000

Hence, we need a total gain of

Gtotal=L(Pout/Pin)=40,000×( 60 / 2. 4 )= 106 ,or 60 dB

We cannot put all the amplification at the destination, because the signal power at the output

of the line would bePin/L= 2. 4 × 10 −^3 /( 40 × 103 )= 0. 06 μW, which falls below the amplifier

noise level. Nor can we put all amplification at the source, because the amplified source power

GPin= 106 × 2. 4 × 10 −^3 = 2 .4 kW would exceed the amplifier power rating. But we could

try a preamplifier withG 1 =400, so as to getG 1 Pin= 400 × 2. 4 × 10 −^3 = 0 .96 W at the

input of the line, andG 1 Pin/L= 24 μW at the output. The output amplifier should then have

G 2 =Pout/( 24 μW)= 60 × 10 −^3 /( 24 × 10 −^6 )=2500, and a repeater is not needed.

Antenna Fundamentals

We shall discuss here only the fundamental concepts needed to understand the role of an antenna as

a power-coupling element of a system. Figure 15.1.5 illustrates the elements of a communication