# S21 & S12 of a mismatched transmission line

I am trying to solve this problem:

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?

• 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? Commented Oct 9, 2022 at 19:04
• 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.
– Zzz
Commented Oct 10, 2022 at 19:18