On Sun, 16 Oct 2005 21:49:38 -0400, Tom Rauch wrote:
>You received good answers, I just wanted to point out the
>problem with making measurements of resonance at the shack
>end of a feedline that has standing waves.
The analysis that helped me the most in understanding transmission
line behavior is the Smith Chart. The center of the chart is a
pure resistance equal to the Zo of the transmission line. At one
end of the line, you "enter the chart" at ZL/Zo. The distance
between this point and the center of the chart tells you the VSWR.
The impedance will then vary along the line as it follows a circle
whose radius is equal to the VSWR. Halfway around the chart is a
quarter wave, a full circle is a half wave.
For any real line (that is, one that has loss), the radius of that
circle will gradually decrease as you go along the line, which
means that the VSWR approaches unity. As you move along the line,
the Z at any point will be some R+jX (or R-jX) value depending on
the VSWR and where you are on the line. At resonance, you will
have j0 at the antenna, and at every half wave repetition of that
point, and at every quarter wave inverse of that point, but at
every point in between you'll see some R and some X.
The Smith Chart is a really powerful tool in understanding (or at
least visualizing) what a transmission line does, and how we
measure what's going on. I can't point to a specific place to
learn it -- I learned it in EE school 40+ years ago -- but I
recall seeing it in ARRL books on antennas. When I learned it, it
was all on paper. Now you can do it with computer software, and
many instruments generate Smith Chart displays of their data.
You can, for example, take complex data for the Z at the
transmitter end of a line, put it on a Smith Chart, and rotate
around the chart for a distance equal to the line length to find
the actual antenna impedance. I've done this using the AEA
analyzer, to good effect. Better analyzers can do it even better
(and probably faster, especially if they have a built-in Smith
Chart).
Jim Brown K9YC
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