Calculating S parameter of the sub network

Given the following 2 port network:

Port 1 (Z0) Transmission Line1->Sub Network->Transmission Line 2->Port 2 (Z0)
Line1 = has impedance of Z0 and electrical length of θ1
Line1 = has impedance of Z0 and electrical length of θ2
Sub Network has S parameter of S11', S12', S21' and S22'


The whole network together (port 1, 2) has S parameter of S11, S12, S21 and S22.

Can any one give me the direction of how to express S11', S12', S21' and S22' interms of S11, S12, S21 and S22?

Thanks

You can convert the S-parameters to ABCD parameters and then cascading the blocks is easy.
Have a look here at the "Cascade connection" section: Two-port network - Wikipedia, the free encyclopedia

I stumbled on this, didn't try it but it looks nice:
Calabazas Creek Research, Inc. | CASCADE - Scattering Matrix Code