Problem 2 A directional coupler has the scattering matrix given below. Find the return loss,
coupling factor, directivity, and insertion loss. Assume that the ports are terminated in matched
loads.
[S]=[[(0.1)/(_(40))\deg ,(0.944)/(_(90))\deg ,(0.178)/(_(180))\deg ,(0.0056)/(_(90))\deg ],[(0.944)/(_(90))\deg ,(0.1)/(_(40))\deg ,(0.0056)/(_(90))\deg ,(0.178)/(_(180))\deg ],[(0.178)/(_(180))\deg ,(0.0056)/(_(90))\deg ,(0.1)/(_(40))\deg ,(0.944)/(_(90))\deg ],[(0.0056)/(_(90))\deg ,(0.178)/(_(180))\deg ,(0.944)/(_(90))\deg ,(0.1)/(_(40))\deg ]]