A transmission line of characteristic impedance 50 $$\Omega $$ is terminated by a 50 $$\Omega $$ load. When excited by a sinusoidal voltage source at 10 GHz, the phase difference between two points spaced 2 mm apart on the line is found to be $$\pi /4$$ radians. The phase velocity of the wave along the line is

If the scattering matrix [S] of a two port network is $$$\left[ S \right] = \left[ {\matrix{ {0.2\,\angle \,\,{0^ \circ }} & {0.9\,\,\angle \,\,{{90}^ \circ }} \cr {0.9\,\angle \,\,{{90}^ \circ }} & {0.1\,\angle \,{{90}^ \circ }} \cr } } \right]$$$ then the network is

A transmission line has a characteristic impedance of 50 $$\Omega $$ and a resistance of 0.1 $$\Omega $$/m. If the line is distortionless, the attenuation constant (in Np/m) is

Many circles are drawn in a Smith chart used for transmission line calculations. The circles shown in Fig. represent