0195136047.pdf

15.1 WAVES, TRANSMISSION LINES, WAVEGUIDES, AND ANTENNA FUNDAMENTALS 679

L=LtLtaLchLraLr (15.1.22)

Srwould then be given by

Sr=

PtGtAre

4 πR^2 L

(15.1.23)

Using Equation (15.1.17) withGrrepresenting the receiving antenna gain, Equation (15.1.23)

becomes

Sr=

PtGtGrλ^2

( 4 π)^2 R^2 L

(15.1.24)

Quite often, for simplicity, in the case of LOS radio transmission illustrated in Figure 15.1.6,

the transmission loss for a path of lengthRis given by

LTR=

Pin

Pout

=

1

GtGr

(

4 πR

λ

) 2

(15.1.25)

which justifies the statements following Equation (15.1.16).

EXAMPLE 15.1.4

Let a LOS radio system and a transmission-line system both haveL= 60 dB when the distance

Rbetween transmitter and receiver is 15 km. Compute the loss of each when the distance is

increased to 30 km.

Solution

Ris doubled.LdBfor the transmission line is proportional to the distance, as per Equation

(15.1.13). Hence,LdBfor the new transmission line= 2 × 60 =120 dB.

LTRfor the LOS radio system is proportional toR^2 , as per Equation (15.1.25). Noting that

LdB=10 logLandL=KR^2 , whereKis a constant, it follows that

LdB=20 logKR

WhenRis doubled,

LdB new=20 log(K 2 R)= 20 (logKR+log 2)

=20 logKR+20 log 2=LdB old+ 6

Hence,LdBfor the new LOS radio system= 60 + 6 =66 dB.

R

Pin Pout

Power gain

Gt

Power gain

Gr

Figure 15.1.6Illustration of LOS radio trans-

mission.