Page 338 - Engineering Electromagnetics, 8th Edition

320 ENGINEERING ELECTROMAGNETICS

are all end-to-end connected, the net loss in dB for the entire span is just the sum of
the dB losses of the individual elements.

D10.2. Two transmission lines are to be joined end to end. Line 1 is 30 m
long and is rated at 0.1 dB/m. Line 2 is 45 m long and is rated at 0.15 dB/m.
The joint is not done well and imparts a 3-dB loss. What percentage of the input
power reaches the output of the combination?

Ans. 5.3%

10.9 WAVE REFLECTION
AT DISCONTINUITIES
The concept of wave reflection was introduced in Section 10.1. As implied there,
the need for a reflected wave originates from the necessity to satisfy all voltage
and current boundary conditions at the ends of transmission lines and at locations
at which two dissimilar lines are connected to each other. The consequences of re-
flected waves are usually less than desirable, in that some of the power that was
intended to be transmitted to a load, for example, reflects and propagates back to
the source. Conditions for achieving no reflected waves are therefore important to
understand.
The basic reflection problem is illustrated in Figure 10.5. In it, a transmission line
of characteristic impedance Z 0 is terminated by a load having complex impedance,
Z L = R L + jX L .If the line is lossy, then we know that Z 0 will also be complex. For
convenience, we assign coordinates such that the load is at location z = 0. Therefore,
the line occupies the region z < 0. A voltage wave is presumed to be incident on the
load, and is expressed in phasor form for all z:

V i (z) = V 0i e −αz − jβz (70a)
e
When the wave reaches the load, a reflected wave is generated that back-propagates:

e
V r (z) = V 0r e +αz + jβz (70b)

V i
Z 0 Z = R + jX L
L
L
V r
z = 0

Figure 10.5 Voltage wave reflection from a complex load
impedance.