Page 377 - Engineering Electromagnetics, 8th Edition

CHAPTER 10 Transmission Lines 359

10.3 The characteristic impedance of a certain lossless transmission line is 72 .
If L = 0.5 µH/m, find (a) C;(b) ν p ;(c) β if f = 80 MHz. (d) The line is
terminated with a load of 60 . Find and s.
10.4 A sinusoidal voltage wave of amplitude V 0 , frequency ω, and phase
constant β propagates in the forward z direction toward the open load end in
a lossless transmission line of characteristic impedance Z 0 .At the end, the
wave totally reflects with zero phase shift, and the reflected wave now
interferes with the incident wave to yield a standing wave pattern over the
line length (as per Example 10.1). Determine the standing wave pattern for
the current in the line. Express the result in real instantaneous form and
simplify.
10.5 Two characteristics of a certain lossless transmission line are Z 0 = 50
and γ = 0 + j0.2π m −1 at f = 60 MHz (a) find L and C for the line. (b)A
load Z L = 60 + j80 is located at z = 0. What is the shortest distance
from the load to a point at which Z in = R in + j0?

10.6 A 50- load is attached to a 50-m section of the transmission line of
Problem 10.1, and a 100-W signal is fed to the input end of the line. (a)
Evaluate the distributed line loss in dB/m. (b)Evaluate the reflection
coefficient at the load. (c)Evaluate the power that is dissipated by the load
resistor. (d) What power drop in dB does the dissipated power in the load
represent when compared to the original input power? (e)On partial
reflection from the load, how much power returns to the input and what dB
drop does this represent when compared to the original 100-W input
power?
10.7 A transmitter and receiver are connected using a cascaded pair of
transmission lines. At the operating frequency, line 1 has a measured loss of
0.1 dB/m, and line 2 is rated at 0.2 dB/m. The link is composed of 40 m of
line 1 joined to 25 m of line 2. At the joint, a splice loss of 2 dB is
measured. If the transmitted power is 100 mW, what is the received power?
10.8 An absolute measure of power is the dBm scale, in which power is specified
in decibels relative to one milliwatt. Specifically,
P(dBm) = 10 log [P(mW)/1 mW]. Suppose that a receiver is rated as
10
having a sensitivity of −20 dBm, indicating the mimimum power that it
must receive in order to adequately interpret the transmitted electronic data.
Suppose this receiver is at the load end of a 50- transmission line having
100-m length and loss rating of 0.09 dB/m. The receiver impedance is 75 ,
and so is not matched to the line. What is the minimum required input
power to the line in (a) dBm, (b) mW?
10.9 A sinusoidal voltage source drives the series combination of an impedance,
Z g = 50 − j50 , and a lossless transmission line of length L, shorted at
the load end. The line characteristic impedance is 50 , and wavelength λ is
measured on the line. (a) Determine, in terms of wavelength, the shortest
line length that will result in the voltage source driving a total impedance of