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I am trying to solve this problem:

enter image description here

Since it is asking for a reference impedance of 50 Ω there will be a mismatch, and hence reflections at the Port 1 for calculation of S12.

I already know S11 and S22 to be 0.6, since the electrical length is a quarter-wave transformer, hence it is straightforward to compute Zin which turns out to be 200 Ω, and hence the input reflection coefficient γ to be 0.6.

Now, I need to write V1 and V2 in terms of {V1+, V1-} and {V2+, V2-} respectively, but I am completely lost. Any direction that I should take will be greatly appreciated.

Here is my wrong solution. Can someone guide me in the right direction? Is the derivations of V1+, V1-, V2+ and V2- correct?

enter image description here

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    \$\begingroup\$ Where's V1 and where's V2 located? Best to be explicit. Why are you trying to rewrite them? What are you aiming to achieve? \$\endgroup\$
    – Andy aka
    Commented Oct 9, 2022 at 19:04
  • \$\begingroup\$ Well, I was trying to derive the S12 parameter of the network. I have attached my solution, it's not right! The correct answer should be 0.8. \$\endgroup\$
    – Zzz
    Commented Oct 10, 2022 at 19:18

1 Answer 1

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Since the network is lossless the sum of the transmission coefficient squared and the reflection coefficient squared has to be equal to 1. With this, you get S12 and S21 equal to 0.8.

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