The Rest of the Story
Roger Sparks wrote:
. . .
If we remove the transmission line from the circuit, we have an open circuit with no current. Without current, there can be no power. How can power arrive at Rs if there is no power coming through the transmission line?
. . .
I regret that I haven't been able to take the time to contribute to or
even follow this very interesting thread. So please pardon me if the
following comment isn't relevant.
The quoted statement reminded me of an earlier thread where Keith asked
a similar question, and proposed some interesting alternative
explanations. The point in question was a current node in a lossless
line which had infinite SWR, e.g., an open circuited line. A look at the
energy flow in the vicinity of the node reveals a plausible explanation.
It turns out that energy is being stored at the node, in the line's
capacitance, to the tune of C*V^2/2. For half the cycle, energy is
flowing into the node equally from both directions, so the power
measured at that node is zero. During the other half of the cycle,
energy is flowing out of the node equally in both directions. So the
power remains zero at the node for the entire cycle. This is, of course,
consistent with the zero current at the node. The node's energy
increases to a maximum and down to zero periodically in step with the
square of the node voltage.
Now, I don't know of any way to assign "ownership" to bundles of energy.
But let's suppose that the energy which flows into the node from the
left side during the "inhalation" part of the cycle is the energy which
flows out to the right during the "exhalation" part of the cycle, and
the energy flowing into the node from the right exits on the left. So
now we've managed to get energy past the node going in both directions
while maintaining zero power and current at the node and conserving
energy as we must.
This can be seen graphically with the little TLVis1 program I made up a
while back -- see the thread of that name for more info. The phenomenon
I'm describing can be seen in demo 4, one cycle from the output (right)
end of the line.
Roy Lewallen, W7EL
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