Coaxial Transmission Line with Discontinuities - Overall S-Matrix?

[mrjava241]

Hi,

I'm working on the following problem but I'm getting stuck, I wouldn't mind some ideas on how to proceed:
"A coaxial transmission line having two identical discontinuities as shown below. Calculate the overall scattering matrix seen at the reference plane shown at 4 GHz assuming that the scattering matrix of the discontinuity is:
S11=1/3+j2/3, S12=j2/3 S22=1/3- J2/3

Assume that the two ports are terminated as shown below. Explain how to calculate the resonant frequency of the resultant resonator"



I've attached a picture of the geometry of the coax transmission line.

So my ideas so far were to:
1) Figure out the ABCD matrix of the 6mm portion of the line.
2) Use symmetry to I only need to calculate the resultant ABCD matrix of 1/2 of the 3mm section.
3) Get a resultant ABCD matrix for the discontinuity and the coax line on the 3mm section (not sure how to do this at the moment...)
4) Subsequently get a resultant ABCD matrix for the entire line. Convert back to S-matrix.

I'm currently quite stuck though, any ideas on how to proceed?

Thanks!

 

[BigBoss]

Convert s matrix of each portion to ABCD and then convert those data of discontinuties to also ABCD matrix and then multiply these ABCD matrices in respect of the sequence then convert the result ABCD matrix to s matrix.( I believe you got the data W,L,er,H of TL portions to able to calculate respective s-parameters)