Microwave Circuit: Quadrature Coupler

[sandy.bridge]

Homework Statement

Assume that the transmission lines are lossless (hence all characteristic impedances are real).

I am told that there is 6 dB coupling at port 3 from port 1. We are supposed to design the coupler to be matched at port 1.

Is port 4 still isolated from port 1?
Would this not depend on the values that I chose to use for the characteristic impedances? Normally when this type of problem is being analyzed it is assumed that port 4 is isolated and that b4=0. However, the way that it is being asked here leads me to believe that this cannot be assumed in this problem, which makes confuses me as to the analysis.

We are to assume arbitrary power division a=P2/P3.

I am a little confused by this problem.

 

[sandy.bridge]

I figured it out. Thanks