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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.

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  • \$\begingroup\$ What length of t-line? \$\endgroup\$
    – Andy aka
    Commented Jul 8, 2022 at 8:10

1 Answer 1

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  1. s11=0
  2. s11=0
  3. Y.
    . N

If the other end cannot be accessed then only s11 is relevant.

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