Post comments on this article and find any associated files and/or downloads at
www.nutsvolts.com/index.php?/magazine/article/january2016_HamWorkbench_SWR.
a small diameter straw
such as for mixed
drinks. Blow a short
puff of air through
each and feel the
resistance from the
straw at the rising
edge of the pulse. The
larger straw allows
more air to flow due
to its lower
impedance which you
experience as back
pressure resisting air
flow. This analogy isn’t
exact but illustrates
the general idea. If a
short pulse of voltage is
applied to a high Z0 cable
such as 300Ω twin-lead,
the resulting current surge
in the cable will be lower
than for a low Z0 cable
such as 50Ω coax.
Characteristic
impedance is important
because of how energy
gets into and out of a
transmission line. As an EM
wave travels — in space,
along a wire, in a
transmission line — any
change in Z0 causes some
of the energy in the wave
to be reflected in the
opposite direction to the
wave’s travel. The bigger
the difference in Z0, the more energy
is reflected. Whether the new Z0 is
higher or lower determines the phase
of the electric and magnetic fields of
the reflected wave with respect to
the forward wave.
Reading between the lines, so to
speak, if an antenna or circuit or
other load is attached to the line and
has an impedance equal to Z0, all of
the power traveling down the line will
be transferred to whatever is
attached. That’s exactly what you
want if you’re transmitting a radio
signal — for all of the transmitter’s
output to be transferred to the
antenna where it is radiated away
into space. Similarly, you want Z0 to
match in the receiving direction so
that all of that extremely weak signal
picked up by the antenna is
transferred to the line and thus
carried to the receiver. (Transmission
lines connected to antennas are
usually just called “feed lines.”)
Reflections on
Standing Wave Ratio
(SWR)
The condition in which the
impedance of whatever is attached to
the feed line equals Z0 of the line is
called matched. If the impedances
are not equal, that’s a mismatch. In
most cases, Z0 is not exactly
matched and so there
are EM waves traveling
up and down the
cable, bouncing back
and forth between the
terminations at each
end of the line. The
device that applies
power to the line is
called the generator,
and the device that
takes power from the
line is the load.
Forward refers to the
direction from the
generator to the load,
and reflected refers to
the opposite direction.
These waves set up an
interference pattern that is
stationary within the cable
called standing waves. If all
of the power is reflected at
one end of the line, the
pattern will include points
at which the electric fields
of the forward and
reflected waves are out of
phase and completely
cancel — resulting in zero
voltage. One-half
wavelength away, the
waves are in phase and
add, thus doubling the
voltage. Figure 2 shows a
calculated example of
standing waves in which
the load impedance is four times
higher than the line’s, reflecting a
portion of the forward wave. You can
see a neat flame-based visualization
of standing pressure waves in the
YouTube video at
www.youtube.com/watch?v=6jfU74e
nV_w. Think pressure = voltage and
you’ve got it!
The ratio of the maximum and
minimum voltages is the SWR. (If the
SWR is calculated from the voltage, it
is VSWR, and it can also be
calculated from the standing waves of
current as ISWR. The usual
convention is to assume that
references to SWR mean VSWR.)
SWR is always equal to or greater
16 January 2016
FIGURE 3. SWR as a function of forward and reflected power.
(Graphic courtesy of the American Radio Relay League.)
FIGURE 2. Standing waves on a transmission line, with the resulting
voltages (VNET) shown in different colors during one complete cycle of
the applied voltage. The generated wave with an amplitude of 1 travels
from left to right and is partially reflected by the load at right.
SWR = VMAX / VMIN = 1.6 / 0.4 = 4.0.
(Graphic created by Wikipedia contributor, Interferometrist and is used under the
Creative Commons Attribution-Share Alike 4.0 International license.)
