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# Calculating Z parameter Z21?

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#### isend

##### Newbie level 3

Z11 is more intuitive to me than Z21. Here I have a bilateral setup I want to find the Z parameters for. By definition Z11=V1/I1 (I2=0), so I think Z11=Zin with Port 2 open. Therefore I just need to assume Zload=inf at Port 2, and then calculate the input impedance at the left end of the right transmission line, and then move step by step to the left, and the last step should be calculating Zin at Port 1 for the left transmission line.

But how do I calculate Z21=V2/I1 (I2=0)? Should Ia/Ib=R/Za? (where Ia+Ib=I1.) Then does V2=Ib*R-Ia*r? (I guess there is no voltage drop along a transmission line?)

Am I thinking correctly? Any suggestion would be very much appreciated!

Eventually I used transmission line Zo:
https://en.wikipedia.org/wiki/Transmission_line#Input_impedance_of_lossless_transmission_line
to calculate Zo in two conditions: ZL=inf and ZL=0 at Port 2.
Then I use the impedance relations
https://en.wikipedia.org/wiki/Impedance_parameters#Impedance_relations
to get Z11 and Z21. My calculation results are vary close to Sonnet simulation.

However I am still not sure how to calculate Z21 directly. I'll think about it later, and I welcome any hints from you. Thank you very much.

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