It's often noted in texts that SWR is really a meaningless measure when
applied to lossy lines. So I wouldn't unduly worry about strange SWR
numbers for very lossy lines. Take a look at the analysis I just posted
on another thread, which gives voltages, currents, impedances, and
powers for an example case, and see if you can find anything wrong with
it. The calculation used for reflection coefficient is based on its
definition, namely reflected voltage divided by forward voltage. That
agrees with all the transmission line and electromagnetics texts I have,
which is getting to be quite a number now.

Roy Lewallen, W7EL

William E. Sabin wrote:

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