Tom, to save everybody a lot of trouble -

The greatest theoretical value of the magnitude of the
reflection coefficient occurs when the angle of Zo is
-45 degrees, and the terminating impedance is a pure
inductive reactance of |Zo| ohms.

Do you think I should have mentioned this when I
began this and other threads by saying a reflection
coefficient greater than unity can occur?

The riot police can now return to barracks.
----
Reg, G4FGQ.

====================================
---
"Tom Bruhns" wrote
"Reg Edwards" wrote
By the way, you've told us only half the story.
What's the value of the
load impedance which maximises the reflection
coefficient?
====================================
Hey, Reg, it's just a simple high-school (well,
maybe first-year
college) differential calculus problem. Just let
Garvin work through
it for us. Hey, good Dr., could you do that for
us? Just write an
expression for |Vr/Vf| = |(Zl-Zo)/(Zl+Zo)| in terms
of Rl and Xl and
find the partial derivatives with respect to those
two variables, and
set both equal to zero, while letting Ro=Xo. It's
mostly just a bunch
of bookkeeping. You should come up with values of
Rl and Zl in terms
of Ro, and you can check to be sure that's actually
a maximum and not
a minimum or saddle point. You should see a
symmetry for Ro=-Xo, the
more usual limiting case.

(Of course, that's not quite right, as I'm sure the
good Dr. and Reg
both know. Since we're talking passive here, you
need to insure that
Rl stays positive, so you just may need to check
along the boundary
where Rl=0. And you should convince yourself that
the most reactive
possible line really does yield the largest possible
|Vr/Vf|. So it
becomes a task of finding the maximum value of a
function f(Rl, Xl,
Xo) with Ro fixed positive non-zero, under the
constraints that Rl=0
and |Xo|=Ro.)