Hello,


Actually, my first posting:

Reflection Coefficient =(Zload-Zo)/(Zload+Zo)

was right all along, if Zo is always purely real. No argument there.



However, from Les Besser's Applied RF Techniques:

"For passive circuits, 0=[rho]=1,

And strictly speaking:

Reflection Coefficient =(Zload-Zo*)/(Zload+Zo)
Where * indicates conjugate.

But MOST of the literature assumes that Zo is real, therefore
Zo*=Zo."

This is why most of you know the "normal" equation.


And then i looked at the trusty ARRL handbook, 1993, page 16-2,
and lo and behold, the reflection coefficient equation doesn't have a
term for line reactance, so both this book and Pozar have indeed
assumed that the Zo will be purely real.


Here's a website that describes the general conjugate equation:


http://www.zzmatch.com/lcn.html



Additionally, the Kurokawa paper ("Power Waves and the
Scattering Matrix") describes the voltage reflection coefficient
as the same conjugate formula, but he rather foolishly calls it a
"power wave R. C.", which when the magnitude is squared, becomes the
power R. C.

Email me for the paper.



As Reg points out about the "normal" equation:


"Dear Dr Slick, it's very easy.

Take a real, long telephone line with Zo = 300 - j250 ohms at 1000 Hz.

(then use ZL=10+j250)

Magnitude of Reflection Coefficient of the load, ZL, relative to line
impedance

= ( ZL - Zo ) / ( ZL + Zo ) = 1.865 which exceeds unity,

and has an angle of -59.9 degrees.

The resulting standing waves may also be calculated.

Are you happy now ?"
---
Reg, G4FGQ



Well, I was certainly NOT happy at this revelation, and researched
it until i understood why the normal equation could incorrectly give
a R.C.1 for a passive network (impossible).

If you try the calculations again with the conjugate formula, you
will see that you can never have a [rho] (magnitude of R.C.)
greater than 1 for a passive network. You need to use the conjugate
formula if Zo is complex and not purely real.

How could you get more power reflected than what you put into
a passive network(do you believe in conservation of energy, or do
you think you can make energy out of nothing)? If you guys can tell
us, we could fix our power problems in CA!

Thanks to Reg for NOT trusting my post, and this is a subtle detail
that is good to know.


Slick