[SI-LIST] Re: Transmission lines reflections again
- From: "Andrew Ingraham" <a.ingraham@xxxxxxxx>
- To: <si-list@xxxxxxxxxxxxx>
- Date: Thu, 20 Oct 2005 11:36:59 -0400
Leonard,
I'm not sure if this is what you're looking for precisely ... but don't
forget that current continues to flow from the battery out through all the
inductors in series, until (and for some time after) the signal reaches the
last capacitor. Current out of the battery keeps flowing, essentially
unchanged at the battery end, until two times the time it took for the
signal to reach the last capacitor.
While the last inductor's current is starting to collapse as you've
described, and the voltage on the last capacitor is doubling, the current
through the next-to-last inductor (and all previous inductors) is still
flowing.
After the last inductor's current collapses, the current through the
next-to-last inductor then starts to collapse too, and the next-to-last
capacitor's voltage doubles. And so on, all the way back to the battery.
The way I look at it, what's really happening on a transmission line is
governed by Maxwell's equations, and you could use them to explain why the
voltage doubles. But Maxwell's equations are hard to visualize, so we've
come up with various shortcuts and visual aids that help us understand it
... including the concepts of characteristic impedance, impedance matching
and mismatch, forward- and backward-traveling waves, standing waves, and so
on. All of these things are convenient ways to visualize what's happening,
but at its heart it's really Maxwell's equations (or perhaps something even
more basic than that), that dictate what's going on. Any point in space
(and any atom or electron) doesn't know anything about forward-traveling
waves and impedance mismatch and voltage doubling and so on; but Maxwell's
equations do apply at that point. All it "knows" about is Maxwell, if you
will. Those other things are just concepts that happen to work really well
to help us understand what's happening.
Each of us has something that makes the most sense to him or her. For some,
it's visualizing waves on a rope, or on water. For others, it's something
else. You seem to like the L-C-L-C analog. Because we are all different,
there isn't going to be one teaching method that works for everyone.
Regards,
Andy
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