4x4 s-parameter matrix for branchline coupler

Does anyone know how I would prove and solve for the 4x4 s-parameter matrix using even and odd mode decomposition. Assume length is a quarter of a wavelength.

And how where can i find the derivations for a multi-section branchline coupler.

Thanks.

Hi,

you can find these in the book Microwave Engineering by Pozar

flyhigh