K7ITM wrote:
So, for example, if I send 50 watts of a sinusoid down a 50 ohm line,
and there's a transition to a 291.4 ohm line that's half a wave long
at the sinusoid's frequency, terminated in 50 ohms, there's no
reflected power on the 50 ohm line. Cool. I knew that.

Make that no *NET* reflected power. Two reflected waves had
to engage in wave cancellation for there to be no net
reflected power. RF waves respond to real-world physical
impedance discontinuities.

In re-
reading what Roy wrote, I see NO disagreement with that. But in the
291.4 ohm line, there's 100 watts forward and 50 watts reverse. At
the interface between the two lines, there's a total of 100 watts
coming in: 50 from the 50 ohm line and 50 from the 291 ohm line. And
wonder of wonder, there's 100 watts going out; it happens to all be in
the 291 ohm line.

Let's analyze that example:

50W--50 ohm line--+--1/2WL 291.4 ohm line---50 ohm load
Pfor1=50w-- Pfor2=100w--
--Pref1=0 --Pref2=50w

The physical power reflection coefficient is 0.5. So Pfor1
splits into two parts, P1=25w being transmitted and P3=25w
being reflected. Pref2 likewise sees a power reflection
coefficient of 0.5 and splits into two parts, P2=25w re-
reflected and P4=25w not re-reflected.

Since Pref1=0, total destructive interference exists toward
the source.

Pref1 = P3 + P4 - 2*SQRT(P3*P4)

Pref1 = 25w + 25w - 2*SQRT(25w*25w) = 0

The associated S-Parameter equation is:

b1 = s11(a2) + s12(a2) = 0

P3 and P4 are the reflected wave components associated with
wave cancellation.

On the constructive interference side toward the load:

Pfor2 = P1 + P2 + 2*SQRT(P1*P2)

Pfor2 = 25w + 25w + 2*SQRT(25w*25w) = 100w

The associated S-Parameter equation is:

b2 = s21(a1) + s22(a2) where |b2|^2 = 100w

Everything is perfectly consistent. Where is an error?

If you go back to Roy's posting in this thread and look at the WHOLE
paragraph where he issued the challenge (if you want to call it a
challenge), you'll see that you have to come up with an example where
there's a node with different power coming out than going in, to be
disagreein' with him.

Well, if Roy is asking for proof of violation of the
conservation of energy principle, his concept of
"sloshing" energy comes pretty close.
--
73, Cecil http://www.w5dxp.com