# What would be the S-parameters for an "ideal" shorted transmission line?

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


Questions:

• What are the S-parameters for an ideal transmission line that is:
1. Shorted at one end?
2. Open at one end?
3. 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.

• What length of t-line? Jul 8, 2022 at 8:10