This module covers the idea of voltage standing wave ratio (VSWR).
A standing wave pattern
In making
this plot ,
we have made use of the fact that the propagation constant
can also be expressed as
, and so for the independent variable, instead of
showing
in meters or whatever,
we normalize the distance away from the load to the wavelengthof the excitation signal, and hence show distance in
wavelengths. What we are showing here is called a
standing
wave . There are places along the line where the magnitude
of the voltage
has a maximum value. This is where
and
are adding up in phase with one another, and places
where there is a voltage minimum, where
and
add up out of phase. Since
, the maximum value of the standing wave pattern is
times
and the minimum is
times
. Note that anywhere on the line, the voltage is
still oscillating at
, and so it is not a constant, it is just that the
magnitude of the oscillating signal changes as we
move down the line. If we were to put an oscilloscope across theline, we would see an AC signal, oscillating at a frequency
.
A number of considerable interest is the ratio of
the maximum voltage amplitude to the minimum voltage amplitude,called the
voltage standing wave ratio , or VSWR for
short. It is easy to see that:
Note that because
,
.
Although
looks like the
standing wave pattern is more or less sinusoidal, if we increase
to 0.8, we see that it most definitely is not. There
is also a temptation to say that the spacing between minima (ormaxima) of the standing wave pattern is
, the wavelength of the
signal, but a closer inspection of either
or
, shows that in fact the spacing between
features is only
half a wavelength, or
. Why is this? Well,
goes as
and
, and so every time
increases by
,
decreases by
and we have come one full cycle on the way
behaves.
Standing wave pattern with a larger reflection coefficient
Now let's go back to the
Crank Diagram . At the position shown,
we are at a voltage maximum, and
just equals the VSWR.
Note also that at this particular point, that the voltage and
current phasors are in phase with one another (lined up in thesame direction) and hence the impedance must be
real or resistive.
We can move further down the line, and now the
phasor starts shrinking, and the
phasor starts to get bigger
.
Moving further down the line
Moving further down the line from a
If we move even further down the line, we get to a point wherethe current phasor is now at a maximum value, and the voltage
phasor is at a minimum value
. We are now
at a voltage minimum, the impedance is again real (the voltageand current phasors are lined up with one another, so they must
be in phase) and
Moving even further down the line
Crank diagram at a
The only problem we have here is that except at a voltage
minimum or maximum, finding
from the crank diagram is not very straightforward,
since the voltage and current are out of phase, and dividing thetwo vectors becomes somewhat tedious.
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