Radar System Engineering

392 RF COMPONENTS [SEC.11.1
line, such as might be introduced by a change in dimension of one of the
conductors, or any change in geometry introduced by a sharp bend, or
by a dent or an obstacle in the line, will produce a reflection. The
reflected energy travels back toward the source. This results in standing
waves in the line. These can be observed by sliding a small probe along
a slot in the line after the manner shown for a concentric line in Fig. 11.1.
Only a negligible fraction of the
power is abstracted by the probe,
but, fed into a suitable indicator,
this M sufficient to regw,ter the voltw~o*~
age;ariati;nsalong~heline. In
~~. 11”1.—slot~d VWfi~ ~ne “~ general there will be voltage maxima
probe for observing utandmgwaves (cutaway
view). spaced at half-wavelength intervals
with minima halfway bet ween them.
Only if the line is perfectly matched will the voltage reading be constant as
the probe moves along. The ratio of the maximum to the minimum voltage
is called the “voltage standing-wave ratio” (VSWR) and is the usual
criterion of how well a line is matched. Complete reflection at the end
of the line, such as would be expected from an open circuit or a short
circuit, results in zero voltage at half-wave intervals and a VSWR of
infinity. The mismatch may also be expressed as a power ratio (PSWR),
or in decibels. The relations between these three measures are
PSWR = (VSWR)Z
SWR, db = 10 log,, (PSWR).
Quarter-wave and Half-wave Lines.—It can be shown that when a lossless
transmission line of characteristic impedance Z, a quarter wavelength
long is terminated in an impedance 2,, the input impedance is
Zi = Z~/Zl. (1)
This property is widely used. For example, two transmission lines of
differing impedance can be matched to each other by joining them through
a quarter-wave line whose characteristic impedance is the geometric
mean of that of the two lines. This is called a matching transformer.
Or, if a quarter-wave line is terminated by a short circuit, the input
impedance is infinite, i.e., equivalent to an open circuit. Conversely,
an open-circuited quarter-wave line appears at the input terminal to be
a short circuit. For a lossless line half a wavelength long
2, = 2,, (2)
irrespective of the characteristic impedance of the line. This principle
has many uses also, particularly in duplexers (Sec. 11.5) and mixers
(Sec. 118).