In message , Jeff writes

If the ATU is adjusted so that the Tx sees a 1:1 match then no power
is reflected to the transmitter. A 1:1 match means that there is no
power reflected to the Tx by definition (and can be proved by
measurement).

By conservation of energy then all of the power must be radiated or
lost as heat, (mostly in the coax).

When the ATU gives a conjugate match, (ie the Tx sees a 1:1 vswr) the
phase of the re-reflected wave at the antenna is 0, ie it is in-phase
with the original forward wave and so any power that is not
re-re-reflected again adds to the power supplied to the antenna.

If the coax were lossless, and there were no losses in-the ATU, then
ALL of the power that was supplied by the tx would be radiated
regardless of the mismatch at coax to antenna interface.
However, in reality even small coax losses add up to a significant
loss when the mismatch at the coax to antenna interface is high due to
the number of times that the power bounces up & down the coax
suffering loss on each trip..


A concise explanation.

What is the easiest way of calculating the power loss (say, assuming
it's all in coax, and none in the ATU)? Is it simply a case of adding up
a large number of diminishing losses as the signal repeatedly rattles up
and down the coax (until it becomes so small that the losses can be
ignored), or are there some more-elegant (and accurate) methods?

The easiest way is to make an Excel spreadsheet.
Convert the VSWR to return loss and convert to a ratio.
Take the Tx power subtract the line loss and multiply the RL ratio to
get the reflected power. Subtract that power from the incident power to
find the power transmitted.
Take the reflected power and subtract twice the line loss, then
multiply that incident power by the RL ratio and continue as above,
adding the proportion that goes to that antenna to the transmitted
power. Also add the 2x line loss the the original line loss to get the
power dissipated in the coax.
Repeat above until the reflected power becomes insignificant; probably
at least six ox seven time if the vswr is very high.

Ah yes! Thanks. It's a while since I honed my skills in driving an Excel
spreadsheet! I'll certainly give it a go.


--
Ian