Roy Lewallen wrote:

Well, Cecil, you've redefined Pref and Pfwd.

Nope, I haven't, Roy. You have somehow arrived at the equations for
a four-port network while dealing with what appears to be a two-port
network. Inadvertently, you seem to have calculated |s11|^2, |s12|^2,
|s21|^2, and |s22|^2 for what appears to be a two-port network. Is a
two-port lossy line network with inductive load really a four-port
network in disguise? Does the delay in the inductor returning energy
to the system constitute an 'a2' term in the s-parameter analysis?

Pref used to be solely a
function of the forward voltage and current waves, and Pref a function
of the reverse voltage and current waves. But now you've chosen to add
an extra term to one or the other of those, or both -- a term which
contains components of both forward and reverse waves.

Roy, that is built right into the s-paramater analysis. For instance,
for a Z0 (image) matched system:

Forward Power = |s11|^2 + |s12|^2 + |s21|^2 + |s22|^2

For a matched system, Forward Power contains four power terms.
In fact, Forward Power can contain from one to four terms depending
on system configuration.

You might recall
from the analysis that I originally had two cosine terms, one arising
from the product of forward voltage and reverse current, and the other
arising from the reverse voltage and forward current. Which of these do
you assign to the "forward power" and which to "reverse power"?

You are talking about |s12|^2 and |s21|^2. The sign and phase of their
power flow vectors will indicate whether they are forward power or
reverse power.

When combined into a product of two sine functions as
I did in the analysis, do you assign this combined function to Pref or
Pfwd?

If the sign is positive, it is flowing toward the load, i.e. it will
superpose with the forward wave. If the sign is negative, it is flowing
toward the source, i.e. it will superpose with the reverse wave. The
conservation of energy principle will not allow the power in the reverse
wave to exceed the power in the forward wave for passive loads, no matter
what the value of rho.

So now when you say Pref and Pfwd, what do you mean?

What I have always meant. Pfwd is the total of all the coherent forward
components. Pref is the total of all the coherent reverse components.

If you were to stick with the definition you've always used in the past,
i.e., powers calculated from solely forward or reverse voltage and
current waves, the answer is yes. For evidence I offer my derivations.

All you have derived is the s-parameter analysis which is known to include
four power parameters. It is known that s11 doesn't always equal rho for
a four-ternimal network. You seem to have proven that to be true for what
appears to be a two-port network.
--
73, Cecil http://www.qsl.net/w5dxp



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