I've been told that this discussion continues in Letters
to the Editor in QEX magazine, to which I don't subscribe
any more. Without knowing the context of those present
discussions, I composed a letter to the QEX editors.
Here it is:

“Where Does the Power Go?” was answered in my magazine article,
“An Energy Analysis at an Impedance Discontinuity in a Transmission
Line”, published by Worldradio magazine and available on my web
page at:

http://www.w5dxp.com/energy.htm

Here is a thought experiment that should lay the subject to rest.
Assume a one-second long lossless 50 ohm open-circuit transmission
line being driven by a 141.4 volt, 50 ohm Thevenin source. At time,
t = 0, source power is supplied to the transmission line. After one
second, 100 joules will have been delivered to the line’s forward
wave and the forward wave will have just reached the open-circuit at
the other end of the transmission line. What happens next simply
follows the laws of physics.

The conservation of energy principle tells us that the 100 joules
in the forward wave must be conserved. The conservation of momentum
principle tells us that the momentum in the forward wave must be
conserved. The open-circuit prohibits the forward wave from continuing
in the forward direction and the forward wave ceases to exist beyond
the open-circuit point. The forward wave ceases to exist so what
happens to the energy and momentum in the forward wave? Physically,
there is only one possibility.

The energy and momentum in the forward electromagnetic wave is moving
at the speed of light and is indeed conserved by transferring its
energy and momentum to the reflected wave at the open-circuit point
in accordance with the rules of the distributed-network/wave-reflection
model. This starts to happen at t = 1 second at which time 100 joules
of electromagnetic energy exists in the forward wave in the transmission
line. (One can actually calculate the force being exerted on the open-
circuit by the forward wave. It is akin to the pressure of sunlight.)

The transfer of energy and momentum from the forward wave to the
reflected wave continues throughout the t =1 to t = 2 second time
frame. At the end of two seconds, the forward wave contains 100
joules and the reflected wave contains 100 joules. Thus 200 joules
are "stored" in the transmission line during the first two seconds.
After two seconds, steady-state has been reached and the Thevenin
source ceases to supply any energy. No additional energy is needed
since the system is lossless. But please note that 200 joules exist
in the transmission line all during steady-state, exactly enough
energy to support the 100 joules/second forward watts and the 100
joules/second reflected watts.

Any theory of where the energy goes must account for the 200 joules
of energy in the transmission line. Those 200 joules cannot be
destroyed by sweeping them under the steady-state rug. An ideal
(lossless) directional wattmeter will tell us that forward
watts = 100 watts and that reflected watts = 100 watts. 200 joules
is required to support that number of forward and reflected watts.
Is it just a coincidence that the 200 joules existing in the
transmission line during steady-state is *exactly* the magnitude
of energy required to support 100 watts forward and 100 watts
reflected?

The number of joules in a transmission line is *always* exactly the
number required to support the forward watts and reflected watts.
Since EM waves cannot stand still, it seems logical to leave the
energy right where it is at the beginning of steady-state - 200 joules
per second being exchanged between the forward wave and the reflected
wave. The energy exchanges at the two ends of the transmission line
are balanced and equal so one might argue that there is no net energy
exchange between the forward and reflected waves during steady-state.
But since the two energy transfers are occurring thousands of miles
apart, that would seem to be a moot point.

The transmission line is charged with this energy during the power
on transient phase before steady-state is reached. The transmission
line is discharged (energy dissipated) during the power down transient
phase after steady-state. It is simply conservation of energy at work.
It is interesting to note that if the transmission is discharged
through a 50 ohm resistor at the far open-end, it will be discharged
at a rate of 100 watts for two seconds.
--
73, Cecil http://www.w5dxp.com