It's not a trivial problem. The Z12 & Z21 parameters in particular require some careful algebraic manipulation.

I made use of delta-wye transformation for Z11 & Z22 analysis.

Good luck.

It looks like the OP has either solved the problem, or given up.

I think it's probably ok at this point to publish a solution.

So, t_n_k, I'd like to see your solution. If you have a pdf of your work, would you please post it?

 

\(Z_{11}=Z{22}=\frac { 60 \omega^3 + 87 \omega +j \( 25 \omega^4 + 23 \omega^2 -18\)}{ 25 \omega^3 + 36 \omega }\)


\(Z_{12}=Z{21}=\frac { 40 \omega^3 + 57 \omega +j \( 25 \omega^4 + 24 \omega^2 -18\)}{ 25 \omega^3 + 36 \omega }\)


Only posting results as I am away from my desktop & scanner. Not 100% sure of Z12 Z21.

 

I was about to point out a tiny numerical error in your results, but I see you corrected it just before I posted!

The red numbers are the ones where you had the tiny error!

Here's what I get:

 

I'm not surprised the OP gave it up. A lot of points at which the algebra can go awry. I did it all by hand with pen & paper. Required several attempts before getting consistent result using different approaches.

 

I'm not surprised the OP gave it up. A lot of points at which the algebra can go awry. I did it all by hand with pen & paper. Required several attempts before getting consistent result using different approaches.

And this was for a circuit with 5 nodes. Imagine if there were even one more node. It would probably be next to impossible to solve without the assistance of an algebra software.

 

I did it few days ago. I will post my solution.

 

z11= z22 = -(w*5*i - (17*i)/w - 3/w^2 + 18)/((6*i)/w - 5);

z21 = z12 = ((((6*i)/w - 4)/(w*15*i - (51*i)/w - 9/w^2 + 54) + ((24*i)/w - 20)/(w*15*i - (51*i)/w - 9/w^2 + 54) + (w*((6*i)/w - 5)*i)/(w*5*i - (17*i)/w - 3/w^2 + 18) - (((3*i)/w - 2)*i)/(w^3*(w*5*i - (17*i)/w - 3/w^2 + 18)))*(w*5*i - (17*i)/w - 3/w^2 + 18))/((6*i)/w - 5);

I tested it using Multisim and it's good. Thank you all for help

 

Checking your results, I find that your result for Z11, Z22 is correct:

But I have a different result than you do for Z21, Z12:

If you transcribed your Z21 result into this forum by hand, rather than by copying and pasting, it's possible that your error is just a transcription error, but I copied and pasted your expression from the forum post into Mathematica, so there shouldn't be any transcription errors there.

 

I transcribed it by hand so I probably made mistake somewhere. Here is complete solution:

 

Yes, it appears the error is a transcription error. The final result for Z21 I see in your image is correct.