On Jan 31, 11:52 pm, "camelot" wrote:
Hi Tom,
as far as I am concerned, your observations are rights only if we are
talking about real quantities. If you have a load that is complex then
you obtain perfect matching (there is no reflection) only if Z0 is not
equal to Zin but it is the conjugate of Zin. If you remember, this is
the same condition valid for the maximum power transferring when the
load in complex. Do you agree with these considerations?

Regards,

Camelot

OK, it is easy to see that a perfect match is NOT the conjugate, but
an impedance equal to the line's Z0. Consider an "infinitely long"
line. You know that the input impedance equals Z0 for all time, and
there can be no reflection. Whatever you send out just keeps going.

Now think about that line as two pieces, connected together. The
first piece is, say, 100 meters long, connected on one end to the
signal generator, and on the other end to the remaining piece of line,
still infinitely long. Now you have connected a load of Z0 (the
infinitely long piece) to a 100 meter section of line with
characteristic impedance Z0, and clearly there are no reflections
where the lines are connected together.

It should be clear that you can just as well replace the infinite
section of line with a load equal to Z0 (NOT equal to the conjugate of
Z0, if Z0 has a reactive part), and there will be no change in the
conditions in the 100 meter section between the Z0 load and the signal
generator.

You can arrive at EXACTLY the same conclusion if you consider the
current and voltage in a "forward" wave (including their phase
relationship) and the current and voltage in a load equal to Z0, and
the current and voltage in a load equal to the complex conjugate of
Z0. You will see that for a line of impedance Z0, only a load equal
to Z0 will have the correct voltage and current at its terminals to
match only a forward wave on the line, and thus allow for zero
reflected wave.

It is a separate, but related, issue to discuss exactly what the
matching should be to get the most power from a generator to a load
through a section of such line. But it should be clear that to have
zero reflection, zero S11, the load must equal Z0 and in general not
Z0* (though of course Z0=Z0* if Z0 is purely resistive).

Cheers,
Tom