W5DXP wrote:

Roy Lewallen wrote:
Magid has the most rigorous derivation of power and energy flow on
transmission lines I've seen, as well as other extensive transmission
line information. One conclusion that pricked my ears was that on a line
with a pure standing wave (e.g., a lossless line terminated with an open
or short circuit), ". . . power (and therefore, energy) is completely
trapped within each [lambda]/4 section of this lossless line, never able
to cross the zero-power points and thus constrained forever to rattle to
and fro within each quarter-wave section of this line."

He's obviously talking about net energy.

Not obvious at all.

There is no impedance discontinuity
in a continuous piece of transmission line so there is nothing to cause
reflections at the zero-power points.

A mechanical analogue may help. Consider that executive toy: five steel
balls attached by string to a frame. Pull back the ball on one side and
let it go, when it strikes the second ball, the fifth ball swings up.
Reduce this toy to just two balls.

Pull one back, when it strikes the second, it swings out, then swings
back striking the first which then swings out. It is clear that there
is energy transfer between the balls.

Redo the experiment by pulling both balls back and letting them go at
the same time. After colliding, both balls bounce back. Were you to
place a very thin sheet of steel between the balls at the collision
point it would not move. Since Work is Force x Distance and the Distance
is zero there is no Work being done on the sheet so no energy can be
crossing it.

In the shorted or open transmission line (from Magid, above), the
analogue is two clumps of charge rushing towards each other and meeting
at a voltage maximum (current zero). No charge crosses this point
(obvious because the current is zero), but the charge coming from each
direction builds to a voltage maximum and bounces away again (since
like charge repels).

Net energy doesn't cross the zero-
power points but equal forward energy and reflected energy must cross the
zero-power points.

Not possible since NO energy crosses the zero voltage and zero current
points (unless you want to reject Pinst = Vist x Iinst).

That is easy to prove by observing ghosting on a TV set
being fed by 1000 feet of ladder-line. If energy is completely trapped
within each 1/4WL section, ghosting would be impossible.

This ghosting argument appears quite powerful along with the somewhat
similar observation that information can be sent in both directions
simultaneously on a phone line.

The difficulty I encountered, while trying to understand, is that
simultaneously holding the views that:
1) ghosting is caused by reflected energy flowing back along the line;
and
2) Pinst = Vinst x Iinst
required too much double think.

Item 2) seemed to be too universally applicable to let go, so a better
understanding of 1) was required.

Although it seems unrelated, it is worthwhile to consider how to send
information along a line without sending energy in the same direction.

For simplicity, consider an ideal transmission line of useful length
with
a matched Thevenin DC source on the left and a matched load connected
through a switch on the right. Initially, the switch is open and the
line is charged to V: the voltage of the voltage source. Observe that
there is no current flowing anywhere, hence no energy flowing and
therefore no power. This is entirely consistent with 2), above.

Close the switch. Charge starts flowing from the line through the load.
A negative voltage step begins to propagate backwards along
the line at the velocity of the line. When this voltage step reaches
the source, the line has entered a new energy state with constant
voltage V/2 across its length, a current of V/2/R flowing and
energy is flowing from the left to the right at V**2/R/4 Watts. This
power is dissipated in the load at the right.

Opening the switch will cause a positive voltage step to propagate to
the left and when it reaches the source, the line will have been
restored to its initial conditions with no energy flowing.

A detector at the source (monitoring voltage or current) can determine
if the switch is open or closed (after the voltage steps have finished
propagating), thus information can be transferred from right to left
while energy only flows from left to right.

This information is transferred by doing something that changes the
energy state on the line and waiting for the new energy state to
propagate along the line. It is important to note that the
propagation of the change in energy state is not the same as the
propagation of energy. They can, and often do, occur in different
directions at the same time.

And to return to the original question, this is the cause of ghosting;
it is the propagation of the change in energy state on the line that
results in ghosting. If the source was matched, then the line settles
to its final state in one round trip and no ghosting is observed.
When the source is not matched, it takes several round trips for the
line to settle and ghosting is what you see.

By the way, this is not quite Magid's situation since he was saying
the energy completely bounced back and forth only when the line was
open or shorted. In other situations with standing waves, some of the
energy is bouncing within the 1/4 wave sections, while other energy
is flowing forward.

....Keith