On 6/26/23 06:32, Jim Lux wrote:
On 6/26/23 2:22 AM, Fran?ois wrote:
Hello
In the attached formula (ROS.png), as long as Zo is real, even if Zl is complex, everything is fine and S11 remains in a circle of radius 1. and the ROS is between 1 and infinity.
If Zo is complex, this is no longer the case.
While writing C# code looking for a (complex) adaptation by dichotomy, I was looking for a ROS of 1. It doesn't work. I had to use the modulus of the difference between my target and the current value.
double optimiseur = Complex.Subtract(Zouth_, Application.Zcibleh).Magnitude;
Is it legitimate to talk about S11 when Zo is complex?
73
Sure it is: S11 is just a representation of the reflection coefficient on port 1 of the UUT.? Generally people use just the log magnitude in dB, but it has a phase, too.
Nothing prevents the Z0 being complex.
Definitely so. When working with telephone cable pairs at voice frequencies, Zo is always complex, generally with a phase angle approaching -45 degrees. Various graphical aids were published by the Bell System for solving transmission line problems with complex Zo, but today it's more common to simply solve the appropriate expressions using complex math in software.
Various schemes were developed for "loading" cable pairs for voice transmission, the most common being the addition of inductors at intervals of a few thousand feet. The most common loading scheme in the Bell System added 88 mH every 6000 feet, but there were quite a few other loading schemes in use. Loading a pair made it's Zo close to, but not exactly, real across the frequency span of the load scheme, reduced the loss of the pair within that frequency span, and acted as a sharp cutoff low-pass filter, reducing significantly transmission at frequencies above the cutoff frequency.
73,
Maynard
W6PAP
