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.

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