Wave Propagation along a Transmission Line
General Instructions
This spectral simulation is an interactive Java applet. You can
change parameters by clicking on the vertical arrow keys. The five
control buttons at the lower right are used to start (triangle)
and pause (square) the simulation, to skip forward or back one section
at a time (double triangles), and to change speed (+ and -).
After the simulation is complete, the start button takes you back
to the beginning of the simulation. You may experience a delay at
this point.
Wave Propagation along a Transmission Line
When a sine wave from an RF signal generator is placed on a transmission
line, the signal propagates toward the load. This signal, shown
here in yellow, appears as a set of rotating vectors, one at each
point on the transmission line.
In our example, the transmission line has a characteristic impedance
of 50 ohms. If we choose a load of 50 ohms, then the amplitude of
the signal will not vary with position along the line. Only the
phase will vary along the line, as shown by the rotating vectors
in yellow.
If the load impedance does not perfectly match the characteristic
impedance of the line, there will be a reflected signal that propagates
toward the source. At any point along the transmission line, that
signal also appears to be a constant voltage whose phase is dependent
upon physical position along the line.
The voltage seen at one particular point on the line will be the
vector sum of the transmitted and reflected sinusoids. We can demonstrate
this by looking at two examples.
Example 1: Perfect Match: 50 Ohms
Set the terminating resistor to 50 ohms by using the "down arrow"
dialog box. Notice there is no reflection. We have a perfect match.
Each rotating vector has a normalized amplitude of 1. If we were to
observe the waveform at any point with a perfect measuring instrument,
we would see equal sine wave amplitudes anywhere along the transmission
line. The signal amplitudes are indicated by the green line.
Example 2: Mismatched Load: 200 Ohms
Now let's intentionally create a mismatched load. Set the terminating
resistor to 200 ohms by using the down arrow. Hit the PLAY button
and notice the change in the reflected waveform. If it were possible
to measure just the reflected wave, we would see that its amplitude
does not vary with position along the line. The only difference between
the reflected (blue) signal, say at point "z6" and point "z4", is
the phase.
But the amplitude of the resultant waveform, indicated by the
standing wave (green), is not constant along the entire line because
the transmitted and reflected signals (yellow and blue) combine.
Since the phase between the transmitted and reflected signals varies
with position along the line, the vector sums will be different,
creating what's called a "standing wave".
With the load impedance at 200 ohms, a measuring device placed
at point z6 would show a sine wave of constant amplitude. The sine
wave at point z4 would also be of constant amplitude, but its amplitude
would differ from that of the signal at point z6. And the two would
be out of phase with each other. Again, the difference is shown
by the green line, which indicates the amplitude at that point on
the transmission line.
The impedance along the line also changes, as shown by the points
labeled z1 through z7.
VSWR
The VSWR, or Voltage Standing Wave Ratio, is the ratio of the highest
amplitude signal to the lowest amplitude signal, as measured along
the transmission line. A "perfect" VSWR is 1. |
