The 3port device as shown below is connected to a lossless t

The 3-port device as shown below is connected to a lossless transmission line with characteristic impedance Z_0=50ohm and electrical length beta1 = pi/8. The transmission line is terminated with a Short-Circuit. If port 3 is also connected to a Short-Circuit, determine the S_11 of the combined network.

Solution

S11 = I1/V2

= Zo * cos(22.5)

= 42.68 ohm