Roy Lewallen wrote:
Let's run a quick calculation as Tom has suggested several times.

Consider a transmission line with Z0 = 50 - j10 ohms connected to a 50 +
j0 ohm load. As I hope will be evident, it doesn't matter what's
connected to the source end of the line or how long it is. We'll look at
the voltage V and current I at a point within the cable, but very, very
close to the load end. Conditions are steady state. When numerical V or
I is required, assume it's RMS.

I hope we can agree of the following. If not, it's a waste of time to
read the rest of the analysis.

1. Vf / If = Z0, where Vf and If are the forward voltage and current
respectively.

2. Vr / -Ir = Z0, where Vr and Ir are the reverse voltage and current
respectively. The minus sign is due to my using the common definition of
positive Ir being toward the load. (If this is too troublesome to
anyone, let me know, and I'll rewrite the equations with positive Ir
toward the source.)

3. Gv = Vr / Vf, where Gv is the voltage reflection coefficient. This is
the usual definition. Likewise,

4. Gi = Ir / If

5. V = Vf + Vr

6. I = If + Ir

Ok so far?


I am looking at W.C. Johnson, pages 15 and 16,
Equations 1.22 through 1.25, where he shows, very
concisely and elegantly, that the reflection
coefficient is zero only when the complex
terminating impedance is identically equal to the
the complex value of Z0.

And not the complex conjugate of Z0.

In other words (read carefully), the complex
terminating impedance whose value is Z0 is
equivalent to an *infinite extension* of the coax
whose complex value is Z0. This is the "clincher".

Observe also the the reflection coefficient for
current is the negative of the reflection
coefficient for voltage.

Bill W0IYH