734 COMMUNICATION SYSTEMS
(a) Now consider a typical open-wire transmis-
sion line with parameters ofR= 14 /mi,
L=4.6 mH/mi,C=0.01μF/mi, andG=
0. 3 × 10 −^6 S/mi. If the line operates at 1 kHz,
find the characteristic impedanceZ ̄ 0 and the
propagation constantγ ̄.
(b) Then consider a 100-mi open-wire flat tele-
phone line with the same parameters as those
given in part (a). The matched transmission
line is shown in Figure P15.1.18(b). If the
frequency of the generator is 1 kHz, determine
the following:
(i) Sending-end currentI ̄S.
(ii) Sending-end voltageE ̄S.
(iii) Sending-end powerPS.
(iv) Receiving-end currentI ̄R.
(v) Receiving-end voltageE ̄R.
(vi) Receiving-end powerPR.
(vii) Power loss in dB, which is given by 10
log (PS/PR).
(c) Find the wavelength(λ= 2 π/β)of the signal
on the line in part (b) and the length of the
line in terms of wavelengths. Also, find the
transmission loss in nepers and decibels of the
transmission line in part (b). (1 neper=8.686
dB.)
(d) For alosslessline (withR=G=0) in which
the velocity of energy propagation is given by
vp=ω/β= 1 /√
LC, find expressions for
αandβ. Consider the line in part (b) to be
lossless, and calculate the correspondingα,
β, andvp.*15.1.19Describe the following phasor equations repre-
sented in the time domain:
(a)E ̄=K 1 e− ̄γz (b)E ̄=K 2 eγz ̄
wherezis the space coordinate,K 1 andK 2 are
constants, andγ ̄=α+jβ.
15.1.20Consider a transmission system as shown in Figure
P15.1.20. Determine the individual gains andG=
G 1 G 2 G 3.
15.1.21Consider a transmission system as shown in Figure
P15.1.21. TakingG 1 as large as possible, find the
needed gainsG 1 andG 2.
15.1.22In the transmission system of Figure 15.1.4, letG 1
=23 dB;α 1 =α 2 = 2 .5 dB/km,l 1 +l 2 =30 km,
Pin=1 mW; andPout=50 mW. Determinel 1 ,l 2 ,
G 2 , andG 3 such that the signal power equals 20
μW at the input toG 2 andG 3.
15.1.23A signal with bandwidth of 100 MHz is to be
transmitted 40 km by LOS radio transmission.
TakingB/fc=1/30, and using a circular-aperture
parabolic dish with 50-cm radius at each end,
compute the transmission loss.
*15.1.24Consider the LOS radio system of Figure 15.1.6,
with dipole antennas. LetPin=10 W,R=20 km,
Gt=Gr=2 dB, andfc=500 MHz. ComputePout.
15.1.25A satellite radio transmitter hasPin=3 W and
Gt=30 dB. The receiving antenna has a circular
aperture with radiusrat the ground station 30,000
km away. Findrin meters ifPout=30 pW.
15.1.26A microwave relay system uses two identical horn
antennas mounted on towers spaced 40 km apart.
Iffc=6 GHz, and each relay hop hasL=60 dB,
calculate the antenna aperture areaAein square
meters.5 mW 200 mW 200 mWPreamplifierG (^1) α L^1
1 = 1.5 dB/km
l 1
20 km
200 mW
Repeater
G 2
Receiving
amplifier
α L^2 G^3
2 = 1.5 dB/km
l 2
18 km
Figure P15.1.20
Pin = 2 mW
Preamplifier
G (^1) α = 0.6 dB/kmL^1
50 km
Pout = 0.4 W
Cable with 1-W power limitation
Output amplifier
G 2
Figure P15.1.21