Question

A $75\Omega$ transmission line is terminated by a load impedance $Z_L-j50\Omega .$ If the line is $\frac{5\lambda }{8}$ long, then input impedance $Z_{in}$ is given by

Answer 1

$Z_{in}=Z_0\frac{Z_L+j{Z}_{0}tan\beta l}{Z_0+j{Z}_{L}tan\beta l}$

$\beta l=\frac{2\pi }{\lambda }.\frac{5\lambda }{8}=\frac{5\pi }{4}$

$tan\beta l=tan\frac{5\pi }{4}=1$

$Z_{in}=75\frac{j50+j75}{75-50}=75\times j5$

$=375|\underset{–}{{90}^o}\Omega$