"David Robbins" wrote in message ...


yeah, verily...

note some interesting things about the case you present...

first, to get it out of the way. as i have stated elsewhere in this thread
today the VSWR calculation from rho is really only applicable to lossless
lines because of the simplifications needed to calculate it from
|Vmax|/|Vmin| which is its real definition. and since Vmax and Vmin are not
the same in any two points on a lossy line it really doesn't have much
physical significance either.



Zo and Zl can be the impedances at a connector, with NO
TRANSMISSION LINE.

Zo can be the impedance at the END of a transmission line.

VSWR = ([rho]+1)/([rho]-1) only works for 0=[rho]=1

or situations of return LOSS, not return GAIN (active networks)!



the actual value of rho for this case is -.9372-1.60477i (which mathcad
gives me as 1.8585/_120.283 but i started from R,G,L,C values and only got
it down to Zo=301.5-250.3i which is close enough for this discussion i
think)

now, how can this be real... the important case is to look at the voltages
at the line/load junction. at this point Vf+Vr=Vl according to the
derrivation of rho. so what do we get with a rho like this???

for Vf=1.0v
Vr=rho*Vf = -.9372+1.60477i
and then
Vl=.06279+1.60477i

so there is a small real voltage across the 10+250i load, and a large
reactive voltage... the reactive voltage is equal to a reactive voltage on
the transmission line side of the junction.... can i believe this? I am
still working on that, in some ways it makes sense because you no longer
have a purely resistive cable characteristic, though i haven't come to grips
with the physical meaning of it yet. i do believe that it has a
relationship to circulating currents and reactive power in power
distribution circuits where you can get very odd looking voltages and
currents when you have a reactive load. in looking at this you have a very
capacitive looking line feeding a very inductive load, with a bit of
resistance thrown in on each side... essentially it looks like a current
pumping a resonant circuit which can result in very high voltages and
currents.



But you will never get a Reflected voltage that is greater than
the
incident in a passive network. Sure, you may have an inductor
charging up a capacitor somewhere in a resonant circuit (like parallel
resonance, with
a "fly-wheel" effect). But this voltage will not be reflected.



on the other side, the rho calculated with the conjugate in the numerator
gives: -.9358-.001688i or .9358/_-179.9


Which makes WAY more sense than the "normal" equation result.

Consider: Zo=300-j250 and Zl=10+j250

Essentially, the two reactances should cancel, and it will be
identical to Zo=300 and Zl=10.

Now, this should be fairly close to a short (Zl=0), which it
really is, in the sense that almost all the voltage is reflected
and the phase shift is almost -180 (-179.9), as it should be for
a near-short.

The "Normal" equation's results of: RC = 1.8585/_120.283 is
absolutely
incorrect. You can't use the normal equation for complex Zo!

You folks can believe what you want, but you are convincing me
more that Besser and Kurokawa and the ARRL are all correct on this
one.

I won't hesistate to admit that i'm wrong, but nothing has been
presented to convince me of that.




btw, for whom ever has it... i am still waiting to see the derivation of the

conjugate rho formula. i published one on here for the 'classical' version,
where is the other one???


I'll send you the paper...

I'd like to see the derivation too, as Kurokawa seems to skip it
or just copied it from another paper! haha...

Anyways, it's the correct formula for complex Zo, you've
convinced me of that with this post.

Thank you for your time and effort David.


Slick (Garvin)