Re: rat race coupler
I have been looking at a similar question for a T junction. Pozar, "Microwave Engineering" notes that it is not possible to match all ports in a three port splitter (chapter eight). I have used the √2 used for rat races with good results. I was rushed and did not question why.
My current suspicion is that this choice reduces s22 and s33 at the expense of s11. I intend to look at the isolation and insertion loss interactions in more detail to see how they are effected by the input and output impedances. I am currently interested in an equal power split.