Page 341 - Engineering Electromagnetics, 8th Edition

CHAPTER 10 Transmission Lines 323

power (to line 1) is 100 mW. (a) Determine the total loss of the combination in dB.
(b) Determine the power transmitted to the output end of line 2.
Solution. (a) The dB loss of the joint is

1 1

L j (dB) = 10 log 10 = 10 log 10 = 0.41 dB
1 −| | 2 1 − 0.09
The total loss of the link in dB is now

L t (dB) = (0.20)(10) + 0.41 + (0.10)(15) = 3.91 dB

(b) The output power will be P out = 100 × 10 −0.391 = 41 mW.

10.10 VOLTAGE STANDING WAVE RATIO
In many instances, characteristics of transmission line performance are amenable to
measurement. Included in these are measurements of unknown load impedances, or
input impedances of lines that are terminated by known or unknown load impedances.
Such techniques rely on the ability to measure voltage amplitudes that occur as func-
tions of position within a line, usually designed for this purpose. A typical apparatus
consists of a slotted line, which is a lossless coaxial transmission line having a longitu-
dinal gap in the outer conductor along its entire length. The line is positioned between
the sinusoidal voltage source and the impedance that is to be measured. Through the
gap in the slotted line, a voltage probe may be inserted to measure the voltage ampli-
tude between the inner and outer conductors. As the probe is moved along the length
of the line, the maximum and minimum voltage amplitudes are noted, and their ratio,
known as the voltage standing wave ratio, or VSWR, is determined. The significance
of this measurement and its utility form the subject of this section.
To understand the meaning of the voltage measurements, we consider a few
special cases. First, if the slotted line is terminated by a matched impedance, then no
reflected wave occurs; the probe will indicate the same voltage amplitude at every
point. Of course, the instantaneous voltages that the probe samples will differ in phase
by β(z 2 − z 1 ) rad as the probe is moved from z = z 1 to z = z 2 ,but the system is
insensitive to the phase of the field. The equal-amplitude voltages are characteristic
of an unattenuated traveling wave.
Second, if the slotted line is terminated by an open or short circuit (or in general
a purely imaginary load impedance), the total voltage in the line is a standing wave
and, as was shown in Example 10.1, the voltage probe provides no output when it is
located at the nodes; these occur periodically with half-wavelength spacing. As the
probe position is changed, its output varies as |cos(βz + φ)|, where z is the distance
from the load, and where the phase, φ, depends on the load impedance. For example,