I believe that "Mother Nature's" voltage reflection coefficient is the well
known classical one, i.e.

rho = (Z - Zo)/(Z + Zo) is "Mother Nature's" reflection coefficient.

I believe this simply because it corresponds to the "image match"!

i.e. rho will be null when Z = Zo [NOT conj(Zo)], and is the condition for
there to be no reflected voltage wave.

Note: this is *NOT* the condition for a "conjugate match" i.e. maximum
power transfer does not result in a null voltage refelection coefficient in
the case of a general complex surge impedance Zo.

As a "thought experiment" to support my contention that

rho = (Z - Zo)/(Z + Zo)

Is "natural", consider the case of an infinitely long transmission line of
surge
impedance [characteristic impedance] Zo, where in general Zo may be complex
and not necessarily a real constant e.g. [Zo is not 50 Ohms resistive or
some other
such simple case.] i.e.

Zo = Zo(p) = sqrt((R + pL)/(G + pC))

Where, R, L, G and C are the primary parameters of the line and p is the
complex
frequency p = s + jw and the value of Zo is complex in general and may vary
with frequency p.

In this thought experiment consider that you are standing in the "center" of
this
infinitely long line of surge impedance Zo and that you cut said line with a
pair of
pliers.

Looking in one direction down the semi-infinite line you see a
driving point impedance equal to the surge impedance Zo of that
semi-infinite
line. Looking in the other direction you will also see a driving point
impedance equal to the surge impedance Zo of a semi-infinite line.

And so...

at the cut you have made, there is an "image match". i.e. at the
cut two equal driving point impedances Zo are facing each
other.

This is a Zo match, or "image match", it is not a conjugate match! In
a conjugate match Zo would be facing conj(Zo).

Now solder the cut back together and then consider a "wave" launched from
one end of this infinite line in one direction. If you have trouble
picturing this
situation just imagine it is Douglas Adams sitting on the patio of the
Restaurant
at the End of the Universe with his handy wave generator who launches the
wave!

Such a wave will move in one direction only on down that Zo line forever and
will never be reflected because there are no discontinuities over that
infinite
distance.

Now as the wave is passing the "cut" that you made in the center of that
infinite
line, quickly insert a reflectometer with internal reference impedance R =
Zo,
the characteristic surge impedance of the line.

This reflectometer will read a rho of:

rho = (Z - Zo)/(Z + Zo)

Where, since one sees Zo in both directions at the cut and so Z = Zo and
rho = 0, as it should of course indicate zero reflected voltage since there
are no
"reflections" on this infinite line with a wave travelling in only one
direction.

This is a very natural situation...

And so I maintain that "Mother Nature" favors the *definition*

rho = (Z - Zo)/(Z + Zo)

or as I like to write it rho = (Z - R)/(Z + R) since I like to use R
representing the
[R]eference impedance i.e. R = Zo because R is the [R]eference impedance
used
inside the reflectometer and whichmay or may not be equal to Zo as
appropriate for the
intended use.

I have no problem whatsoever with this definition of rho not being null
when there is a conjugate match.

In the general case for "Mother Nature's" reflection coefficient rho will
not be
zero when there is maximum power transfer.

In fact there may well be considerable reflected VAR's in that case...
VAR's being Volt Amperes Reactive, i.e. reactive power reflected at the
conjugate match point.

On the other hand, I have no argument with those who choose to define rho
as:

rho = (Z - conj(Zo))/(Z + conj(Zo))

just as long as they are consistent in it's use and the conclusions they
draw from
it. Here they will get a null rho for a conjugate match, and they will not
get a null
rho for an image match.

I can see situations in which such a defintion of rho using conj(Zo) might
be useful,
not necessary mind you, but perhaps more convenient for solving some
problems.

But I still maintain that defining rho in terms of the conjugate of Zo is
"unatural" and
that "Mother Nature" naturally likes the classical...

rho = (Z - Zo)/(Z + Zo)

because that is what she uses herself when she supports the natural
propagation of waves
on transmission lines.

Thoughts, comments?

--
Peter K1PO
Indialantic By-the-Sea, FL.

--
Peter K1PO
Indialantic By-the-Sea, FL.