On May 26, 8:53*pm, Keith Dysart wrote:
It was my understanding that in a sequence of connected linear
networks, if any connection exhibited a conjugate match, then they
all were conjugately matched. Is this not correct?

The theorem requires linear *lossless* networks which do not exist in
reality, i.e. networks containing only reactances. Therefore an
*ideal* system-wide conjugate match cannot exist in reality just as a
lossless transmission line cannot exist in reality. In low-loss
systems, we can only achieve a system-wide near-conjugate match with
an ideal conjugate match existing at one point, e.g. the Z0-match
point where reflected energy flowing toward the source is eliminated.

Are you saying that if a conjugate match is present between the line
and the antenna, it might not be present between the transmitter and
the line?

Yes, speaking for me, in the real world, it is easy to prove that the
system-wide impedance looking in one direction is not always exactly
the conjugate of the impedance looking in the other direction. Thus
the "maximum power transfer" assertion has to be modified to "maximum
*available power* transfer". In the real world, ohmic and dielectric
losses reduce the power available to be delivered to the load.

It's easy to see. Let's say we have a completely flat 50 ohm system;
50 ohm source, 50 ohm coaxial feedline, and 50 ohm antenna. Now assume
we install an antenna tuner between the source and the feedline that
exhibits some series impedance and we adjust the tuner such that the
source sees 50 ohms. At the output of the tuner looking toward the
antenna, we will see 50 ohms. Looking back through the tuner toward
the source, we will see the tuner impedance in series with 50 ohms.
That proves it is not an *ideal* (lossless) conjugate match although
it may be considered to be a near-conjugate match, as close as we can
come in the real world.

What I don't know is how close a real-world conjugate match has to be
to an ideal lossless conjugate to be called a "conjugate match". A
purist might argue that an ideal conjugate match cannot exist in
reality. A realist might argue that if we are within 10% of an ideal
conjugate match, then it is a real-world conjugate match, by
definition.

Note that I am not speaking for Walt here, just for myself.
--
73, Cecil, w5dxp.com