Complex Z0 [Corrected]
-
Maybe it has already been noticed,
but anyway,
it seems [this time] that,
given a uniform transmission line with
complex characteristic impedance,
the magnitude of the reflection coefficient
for any passive terminal load
is lower or equal than
-
Sqrt([1 + Sin(Abs[t0])]/[1 - Sin(Abs[t0])]),
-
where t0 is the argument of Z0.
-
Sincerely,
-
pez,SV7BAX
&
yin,SV7DMC

Complex Z0 [Corrected]
-
Maybe it has already been noticed,
but anyway,
it seems [this time] that,
given a uniform transmission line with
complex characteristic impedance,
the magnitude of the reflection coefficient
for any passive terminal load
is lower or equal than
-
Sqrt([1 + Sin(Abs[t0])]/[1 - Sin(Abs[t0])]),
-
where t0 is the argument of Z0.
-
===============================

It is true the formula gives the greatest possible
magnitude of the reflection corfficient, Rho, for
any given value of the angle of Zo.

As t0 approaches -45 degrees, Rho approaches
1+Sqrt(2) = 2.414

As you must know, the formula is obtained by
differentiating Rho with respect to the angle of
Zo and then equating to zero.

It provides proof that values of Rho greater than
unity do exist. But a worship of mathematical logic
is not part of any religion on this newsgroup.
---
Reg, G4FGQ