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I think it might be useful to say a little more about standing waves.
Imagine a single lossless transmission line with a sine wave source at one end and a load at the other. Begin with a load equal to the line's Z0. Make a graph of the magnitude of the current or voltage as a function of distance from the source. With the Z0 load, the magnitude will be the same all along the line so your graph will be a straight line. This is a "flat" line, with no standing wave. A probe sitting at one spot would show the instantaneous voltage or current amplitude going up and down in a sinusoidal manner. A probe a bit farther down the line would look the same, but delayed; there's a phase difference between the voltages or currents at the two points. The phase difference is equal to the line's physical length in degrees divided by the velocity factor. Now change the load so the line is slightly mismatched. A standing wave will appear -- the graph of amplitude vs distance won't be flat any longer, but will have a ripple added to its previous constant value. (The VSWR is, by definition, the ratio of the highest to the lowest values of the voltage envelope on a line long enough to have a full maximum and minimum. The current SWR is the same.) The maxima and minima of the ripple don't move, hence the name "standing wave". If we look at the instantaneous voltage or current at a single point, it will go up and down in step with the source as before. If we also look at the second point, it'll also go up and down as before, and there will be a phase angle between the two. But there are two interesting differences from the flat line: One is that the amplitudes at the two points are now unequal unless they're an integral number of half electrical wavelengths apart (or a few other special cases). The other is that the phase shift isn't the same as before. There's still a phase shift between the two points, but it's no longer equal to the electrical length of the line between the points. We'll find that either the voltage has shifted more and the current less, or vice versa depending on the load and which points we've chosen. But at every point the current and voltage still have phase angles which change with position along the line. That is to say, the voltage or current at one point is delayed compared to the voltage or current at the other. As the mismatch gets more extreme (i.e., the SWR increases), the magnitudes at the two points get more different, and the phase deviates farther from the electrical length of line between them. (This is why you can't expect phased array "delay lines" to provide a delay equal to the lines' electrical lengths when they're not terminated with Z0.) At the most extreme case of mismatch -- an open, short, or purely reactive load, resulting in an infinite SWR -- the amplitude of the standing wave along the line goes from zero to twice the value it had when the line was flat. And a really interesting thing happens to the phase of the voltages and currents on the line. Remember how as the mismatch got worse, the voltage and current phase difference between two points got farther and farther away from the electrical line length between them? Well, when the SWR is infinite, it's gotten to the point where the voltage or current phase remains the same for a distance of a half electrical wavelength, then abruptly changes 180 degrees, repeating every half electrical wavelength. Some antennas behave in some (and only some) ways like transmission lines, and you'll find that modeling programs report just this behavior of the phase of the current along a straight wire antenna. The standing wave and all the characteristics of the voltage and current (e.g., how their magnitude and phase varies with position along the line) follow directly from an analysis of forward and reflected traveling waves on the line. The voltage or current at any point is simply the sum of the two waves at that point, and they have the properties I've just described. I hope this helps in clarifying the meanings of traveling and standing waves, voltage and current along a transmission line. I'm sure there are lots of good graphical illustrations available -- but some bad ones too. Hopefully keeping this explanation in mind when you look at the nice graphics displays will help you sort the bad ones from the good. Roy Lewallen, W7EL |
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