[AMPS] Conjugate Matching and Efficiency

[Ian White, G3SEK]

Steve Thompson wrote:
>In my mind, I can't see how you can have or measure forward and 
>reflected power without a transmission line somewhere. Doesn't reflected 
>power only happen when the termination on a transmission line doesn't 
>equal Zo. I'm wide open to correction here.
>>

I don't think it's a matter for "correction", but of several equivalent
viewpoints. Since they are all analysing the same reality, all of these
viewpoints MUST agree. Any one of them can be used to check the others.

One viewpoint includes the transmission line with a lumped R-X load at
the far end, replacing the antenna. Analysing from this viewpoint
involves transmission-line wave mechanics which can be complex in all
senses of the word.

The alternative viewpoint is to reduce the problem to the same
transmitter feeding the equivalent lumped R-X load, connected directly
to the transmitter output [1]. In this viewpoint the words "forward" and
"reflected" are banned - the transmitter simply delivers whatever power
it can, into the resistive part of that load. If that is less than the
power that could be delivered into a design load of (50 + j0), this can
only be because the "missing" power was never generated in the first
place.

Both of these analyses MUST give the same results. If they don't, then
one of them is incorrect (or maybe both).

A third viewpoint is to analyse the lumped-load system with no
transmission line, using the normal mathematical relationships between
load impedance and SWR. In other words, you're analysing a system with
no transmission line *as if* there was a whole number of electrical
half-wavelengths in there. That doesn't matter - you MUST still get the
same results as the other two viewpoints. If you don't, then at least
one of your analyses has to be incorrect.

Even a half-baked analysis can be made to look good on its own home
territory. That's the easy part. But one of the key scientific tests for
any idea is to make it work in hostile territory - in this case, the
viewpoints that you normally *don't* like to use. 

Nobody has yet done this in a totally convincing way for the transmitter
conjugate matching problem - because if they had, the debate would be
finished.




[1] All these viewpoints are only equivalent after the system has
reached a steady state, which involves multiple reflections when a
transmission line is present. When the steady state has been reached,
the transmitter has no way how knowing how the load impedance connected
to its output terminals has been created. Summing multiple re-re-re-
reflections towards a steady state is one of the things that makes the
transmission line viewpoint so difficult to analyse with conclusive
proof of having done it correctly.

73 from Ian G3SEK          Editor, 'The VHF/UHF DX Book'
                          'In Practice' columnist for RadCom (RSGB)
                           http://www.ifwtech.com/g3sek

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