I did not intend this to be difficult, or incomplete. I think it is
solveable without recourse to knowledge or speculation about source
impedance, or changing the problem by inserting additional lines, or
injecting photons, or whatever.

My answers are inline:

Owen Duffy wrote in
:

Breaking out of the previous thread to explore the "power explanation"
in a steady state situation:

The scenario for discussion is a transmitter connected to a half wave
of 600 ohm lossless transmission line connected to an antenna with a
feedpoint impedance of 70+j0.

The transmitter is rated for 100W output, 100W is developed in the 70
ohm load, the VSWR on the transmission line is 8.6, the "forward
power" (meaning Vf^2/Zo) on the transmission line is 267W, the
"reflected power" (meaning Vr^2/Zo) on the transmission line is 167W,
the DC input power to the transmitter is 200W.

The questions a

Is there any internal inconsistency in the scenario characterisation,
if so, identify / explain?

No, I cannot see any.


What is the heat dissipated in the transmitter (and why)?

Approximately 100W. It is reasonable to assume that all DC power into the
transmitter is converted to RF power output and heat. The heat then is
approximately DC power input minus the RF output power. Since the power
in the load is stated to be 100W, and the line is stated to be lossless,
the power out of the transmitter must be 100W, and given the stated DC
input power of 200W, the transmitter heat dissipation is approximately
100W.


What part of the "reflected power" of 167W is dissipated in the
transmitter (and why)?

None. The notion of the "reflected power" is part of describing the field
setup / energy storage / energy flow on the transmission line. It follows
from trying to reconcile the restriction the Vf/If=Zo, and Vr/Ir=Zo with
the V/I ratio of the circuit attached to the transmission line.

The problem defined the standing wave effects on the line. The
transmitter sees a load of 70+j0 due to the antenna and half wave
lossless line, and must be delivering 100W to that apparent load so as to
achieve the stated antenna load power.

Any notion that reflected power *must* flow back to the source and is
dissipated as heat will not lead to the correct solution of this problem.

As an exercise, think of a generator that has a Thevenin equivalent of
some voltage V and a series impedance of R+j0, connected to a half wave
of lossless transmission line where Zo=R. To give a numerical example,
lets make V=100 and R=50, so Vr=50 and "reflected power"=50. How much of
the "reflected power" is dissipated in the generator. In this case, the
generator dissipates less heat than were it terminated in 50 ohms.

When I said that the reflected power explanation is not a good
explanation, I did not say it was necessarily invalid, but it is my
opinion that it provides an incomplete explanation that folk with limited
knowledge and supported by ham radio folklore like to use to explain
things that are not necessarily explained by that explanation (if you are
still with me), for example why a transmitter (sometimes or necessarily)
gets hotter when the antenna VSWR is high.

Owen