Richard Fry wrote:
"Roy Lewallen" wrote:

All the power produced by the transmitter arrives at the antenna
less whatever is lost as heat in the transmission line. There are no
waves of average power bouncing back and forth on a
transmission line. Mathematically separating the power moving
down the line into "forward" and "reverse" components doesn't mean
that waves of average power actually exist.
____________

Roy, I have been involved with the evaluation and repair of FM and TV
broadcast antenna systems where the initial problem was a failure in the
antenna, which then produced a high mismatch between it and the main
transmission line.

The allegedly non-existent nodes along the transmission line for this
condition did a fine job of melting holes in the inner conductor and
Teflon insulators of 3-1/8" OD (and larger) rigid transmission line, at
1/2-wavelength intervals over a considerable length of that line.

What other phenomenon do you believe caused such a result?

Let's suppose for a moment that the holes were melted by reflecting
waves of average power. Why do they repeat every half wavelength? Do the
waves of average power have a phase angle such that they reinforce
periodically? As an engineer, you of course know that the average of a
periodic function is the integral of that function taken over one
period, divided by the period. How then can average power have a phase
angle? Or do the waves not have a phase angle but rather change
amplitude as they travel? If so, what is the mechanism by which they do?
Can you write the equations showing the power at each point along the
line and how it can be greater at half wavelength intervals?

In contrast, the existence of traveling and standing waves of voltage
and current have long been established. You can find a rigorous analysis
of their behavior in a vast number of textbooks. Given the load and
transmission line impedances, you can very quickly calculate, even by
hand and without the use of a computer, the current and voltage at any
point along the line. Unless the line is perfectly matched, there will
be repeating points of high current and of high voltage. Depending on
the nature of the conductor and insulator, either or both of these can
cause localized heating. In the example you gave, the damage is almost
certainly caused by high current rather than high voltage. If you'll
provide me with the impedance of the load and the impedance and velocity
factor of the cable, I'll show that the high current points fall at the
points where the damage occurred. If you tell me the transmitter power
output, I'll also tell you what the current was at those points. Can you
do the same for your theory of power nodes resulting from bouncing waves
of average power? Anyone else having a basic understanding of
transmission line operation can explain your cable damage without any
necessity to imagine bouncing waves of average power.

If you insist on believing that the damage was caused by traveling waves
of average power, please provide an explanation of how these waves
interact to create more power at some points than others. Because power
is the rate of transfer or dissipation of energy, the power into any
point has to equal the sum of the power dissipated at that point and the
power leaving that point, unless that point contains some mechanism to
store energy. Your analysis has to be consistent with this in order to
avoid violating the law of conservation of energy.

I can provide a detailed mathematical quantitative analysis of the
nature of traveling voltage and current waves which explain the
phenomenon you cite. I'm looking forward to your corresponding
mathematical explanation of the phenomenon using traveling average power
waves.

Roy Lewallen, W7EL