Roy Lewallen wrote:

Yet in my example, |rho|^2 *is* greater than one.

If so, |rho|^2 is NOT the power reflection coefficient. The conservation
of energy principle will not allow the power reflection coefficient to
be greater than 1.0.

If you calculate a forward Poynting vector and a reflected Poynting vector
at a passive load, you will find that the forward Poynting vector always has
a larger magnitude than the reflected Poynting vector. Thus,
if Pz-/Pz+ = |rho|^2, as asserted in Ramo & Whinnery,
|rho| cannot be greater than 1.0. I suspect you have stumbled upon a
single-port case where rho and s11 are not equal.

You have apparently calculated an s11 reflection coefficient and called
it "rho" under conditions where s11 doesn't have to equal rho.

Also, in the past, you and others have defined the "forward power" to be
the power calculated from the forward voltage and current waves, namely
Re(fE * fIconj) or |fE| * |fI| * cos(phiE - phiI). This is what you've
consistently been calling the "power of the forward wave" or some such.

ONLY for lossless lines. I never said or implied that it would work for
lossy lines. I have carefully avoided making any assertions about lossy
lines. The only assertion that I will make about lossy lines is that
they obey the conservation of energy principle.

Likewise for "reverse power". This is the definition I used for the
substitution for fP and rP in the equation for total average power.

Well, that's apparently a boo-boo for lossy lines. Apparently, Vfwd*Ifwd*
cos(theta) equals forward power only for lossless lines.

And the result is that the total power *isn't* equal to fP - rP.
What you're doing now is lumping the extra power into fP or rP, now
making those terms mean something else.

Yes, for lossy lines, they apparently do mean something else. It reminds
me of the s-parameter equations for power. Like your calculations, there
are four powers, not just two. They are |s11|^2, |s22|^2, |s21|^2, |s12|^2.
It looks as if you have set fP = |s22|^2 and rP = |s11|^2 and your other
two power components are |s12|^2 and |s21|^2. But in real life, these last
two powers are forced to join either the forward wave or the reflected wave.

The additional power term has
two components, one arising from the product of forward current and
reverse voltage, and the other from the product of forward voltage and
reverse current. (I combined the two cosine functions with a trig
identitity into a product of two sine functions, but you should go back
a step or two in the analysis to get a clear idea of their derivation.)
I believe you've chosen to assign each of these, or the sine product, to
either "forward power" or "reverse power", depending on its sign, even
though they're a function of both forward and reverse voltage and
current waves. I can't imagine the justification for doing this, ...

The justification is two, and only two directions, in a transmission line.
All coherent components are forced to superpose into Total Forward Power
or Total Reflected Power depending on the direction (sign).
--
73, Cecil http://www.qsl.net/w5dxp



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