My, it sure didn't take long to get the discussion diverted from the
voltages, currents, and powers in the analysis. I'm sorry to say I
expected that.

Cecil Moore wrote:
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?


I'll leave the philosophical question to you of when a transmission line
is an n-port network and when it isn't, and which s parameter I
inadvertently calculated. Was I unclear about what I did calculate? What
part of it don't you understand?

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.


I don't know, and don't really care, where you're trying to go with your
S parameter analysis. But when you're all done, please translate all
that wonderful stuff to voltages, currents, and powers, using a finite
length transmission line, and present your analysis.

Are you having difficulty understanding what I've done simply with
voltages, currents, and powers?

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.

So, you mean that the term containing the product of two sine functions
is part of Pfwd when the angles are such that the sine functions return
a positive value, and part of Pref when they return a negative value?

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.

No, I did not derive an s parameter analysis. I derived voltages,
currents, and powers. Interpretation of this in terms of s parameters is
strictly your own doing, and it provides wonderful opportunities to
obscure and misinterpret what's really happening. If you're unable to
understand voltages, currents, and powers and want to argue instead
about s parameters (which indeed do represent voltages and powers, but
not necessarily in a one-to-one correspondence to those in the circuit I
analyzed), how many ports the circuit has, and the meaning of the power
reflection coefficient, have at it. But I won't participate. I'll simply
wait until you're done with your philosophising, calculations,
translation back and forth, and post your analysis with V, I, and P as
the variables.

Roy Lewallen, W7EL