RadioBanter - View Single Post - Rho = (Zload-Zo*)/(Zload+Zo), for complex Zo

September 7th 03, 11:38 AM

(David or Jo Anne Ryeburn) wrote in message .. .

You mean i can't use Zo=50 + j200 with

Rho = (Zload-Zo*)/(Zload+Zo), for complex Zo?

Only up to Zo=50 + j50?

If Z_0 is supposed to be the surge impedance of a transmission line, then
yes, you *can't* use Z_0 = 50 + 200j, because God doesn't make
transmission lines of such an impedance. If Z_0 is supposed to mean
something else, then I'm not talking about whatever your Z_0 is, except to
say that you shouldn't talk about the voltage standing wave ratio and
expect others to understand your English, if there isn't any transmission
line.

Ok, well use Zo=50 + j50, and Zload = 50 - j50 and
the conjugate formula is correct again.

Ok, well, the conjugate formula still makes more sense to
me.

And never mind that it gives measurably *wrong* answers when used to
determine the voltage standing wave ratio on transmission lines?

Where is it wrong? It's the "normal" equation that is wrong when
Zo is complex! Nobody has explained how a rho1 will NOT lead to a
power RC that is also greater than one, thus violating conservation of
energy.

It says exactly what the formula says. Translating mathematics into some
other language is dangerous.

Is
Besser and Kurokawa and the ARRL incorrect?

It depends upon what they expect to be able to do with their formula for
rho. If they expect to be able to use the conjugate formula for rho to
determine the voltage standing wave ratio, by using VSWR = (1 + |rho|)/|1
- |rho||, then yes, they're incorrect -- demonstrably, *measurably*,
incorrect.

Where and when and how did you do a measurement? When you get a rho
greater than 1, the VSWR = (1 + |rho|)/(1 - |rho|) gives ridiculous
NEGATIVE SWRs. And rho WILL give you the SWR, assuming your tranmission
isn't extremely lossy. This is why people say that the SWR meter has to
be at the antenna, instead of at the end of 100' of RG-58.

The conjugate formula simply gives wrong answers (wrong in the
sense of disagreeing with measurements) while the non-conjugate formula
gives right answers. It also conflicts, mathematically, with the usual
formula for which you have seen a proof (based upon the two Kirkhoff laws
and Ohm's law). So there are theoretical as well as experimental reasons
for rejecting the conjugate formula. It's hard to argue against success or
for failure.

I saw the derivation, but i don't totally agree with it, yet.

Again, what actual bench measurement did you make?

What test setup, circuit did you use?

Did you actually get more reflected power that incident?
I'd really like to see THAT!

If you're not too sure
and you don't wanna say, i wouldn't blame you.

I'm more sure of this than I am of many things. If I had any doubts, then,
logically, I would also have to have doubts about at least two of the
following: (a) the Kirkhoff voltage law; (b) the Kirkhoff current law; (c)
Ohm's law; (d) many empirical measurments that have confirmed the
predictions that can be made using the non-conjugate version of the
formula for rho. It would be logically inconsistent to have confidence in
all four of these four things and, at the same time, doubt that the model
in question describes reality accurately.

David, ex-W8EZE

Please! No Straw man! I never debated a-c.

For (d), certainly, assuming Zo is purely real.

Slick