I seem to remember that the shorted- vs open-transmission line reflection is out of phase by 180-degrees. I'm new to the mathematics behind transmission line theory and I'm trying to figure out how that phase shift is represented in the scattering matrix.
I couldn't find a reference for this, hence this question, so please correct me if I'm wrong: I am guessing the S-parameters for an ideal open-circuit and ideal transmission line are as follows. The values are in dB format, so "0" means no loss:
Ideal Transmission Line
S11: -INF+0j S12: 0+0j S21: 0+0j S22: -INF+0j
Ideal Open Transmission Line (ie, its been cut but is not shorted)
S11: 0+0j S12: -INF+0j S21: -INF+0j S22: 0+0j
- What are the S-parameters for an ideal transmission line that is:
- Shorted at one end?
- Open at one end?
- Are #1 and #2 represented purely as S11? It doesn't sound like S21 would play a part here.
- Does \$Z_0\$ play any part in the "ideal" case?
I would be interested to understand how the math for how this trivial circuit is represented to calculate the resulting S-parameter matrix. If you know the details then a bit of help understanding the math to create the resulting matrix would be appreciated.