A transmission line terminates in two branches, each of length $$\lambda /4$$, as shown.The branches are terminated by 50 $$\Omega $$ loads. The lines are lossless and have the characteristic impedances shown. Determine the impedance $${Z_i}$$ as seen by the source.

One end of loss-less transmission line having the characteristic impedance of 75 $$\Omega $$ and length of 1 cm is short-ciruited. At 3 GHz, the input impedance at the other end of the transmission line is

The parallel branches of a 2-wire transmission line are terminated in 100 $$\Omega $$ and 200 $$\Omega $$ resistors as shown in the Fig. The characteristic impedance of the line is $$Z_0$$ = 50 $$\Omega $$ and each section has a length of $$\lambda /4$$. The voltage reflection coefficient $$\Gamma $$ at the input is:

A load of 50 $$\Omega $$ is connected in shunt in a 2-wire transmission line of $$Z_0$$ = 50 $$\Omega $$ as shown in the Fig. The 2-port scattering parameter matrix (S-matrix) of the shunt element is