David Robbins wrote:
"Peter O. Brackett" wrote in message
link.net...



yes, i still hold that they are different. they are from completely
different realms of electromagnetics. in the transmission line reflection
coefficient you are working with a distributed system that is modeled with
wave equations. there are delays, waves travel and reflections return after
a finite delay. in your example you have coerced the voltage and current
waves to be the same in the transmission line, but that is not the same as
modeling the line itself.

In simulation programs, transmission lines are
solved for their two-port
parameters, and are then treated as lumped
circuits in the actual
simulation, just like any lumped-element circuit.
Which is a good way
to do it.

I notice that in the ARRL Antenna Book, 19th
edition , on page 24-7, it is stated with definite
finality that the reflection coefficient formula
uses the complex conjugate of Zo in the numerator.
I also understand that this has been established
by a "well-trusted authority".

I have used Mathcad to calculate rho and VSWR for
Reg's example, for many values of X0 (imaginary
part of Z0) from -0 to -250 ohms.

The data follows:

Note: |rho1*| is conjugated rho1, SWR1 is for
|rho1*|, |rho2| is not conjugated and SWR2 applies
to |rho2|

X0.......|rho1*|..SWR1.....|rho2|..SWR2
-250..... 0.935...30.0.....1.865...-3.30
-200..... 0.937...30.8.....1.705...-3.80
-150..... 0.942...33.3.....1.517...-4.87
-100..... 0.948...37.5.....1.320...-7.25
-050..... 0.955...43.3.....1.131...-16.3
-020..... 0.959...47.6.....1.030...-76.5
-015..... 0.960...48.4.....1.010...-204
-012..... 0.960...48.9.....0.997....+/- infinity
-010..... 0.960...49.2.....0.990....+305
-004..... 0.961...76.3.....0.974....+76.3
0000..... 0.961...50.9.....0.961....+50.9

The numbers for not-conjugate rho are all over the
place and lead to ridiculous numbers for SWR. It
is also obvious that for a low-loss line it
doesn't matter much. But values of rho greater
than 1.0, on a Smith chart correspond to negative
values of resistance (see the data).

Something is wrong here that we are overlooking.

The use of conjugate rho is so much better behaved
that I have some real doubts about some of our
conclusions on this matter.

What about it folks? How can we get to the bottom
of this?

Bill W0IYH