Question

A line of characteristic impedance $Z_0\Omega$ and phase velocity $v_p=2\times {10}^{8}m/s$ and length $l=2m$ is terminated by load impedance $Z_L\Omega$. Reflection coefficient at the input end and load end are respectively ${\Gamma }_i\text{and}{\Gamma }_R.\text{Then}\frac{{\Gamma }_i}{{\Gamma }_R}$ for the frequency of 50 MHz will be

• A. 1
• B. 0
• C. -1
• D. $\sqrt{-1}$

Answer 1

The correct option is A 1

$\lambda =\frac{v_p}{f}\Rightarrow \lambda =\frac{2\times {10}^8}{50\times {10}^5}=4m$
$\frac{\lambda }{l}=\frac{4}{2}=2\Rightarrow l=\frac{\lambda }{2}$
For $l=\frac{\lambda }{2}$
$Z_{i/p}=Z_0\frac{Z_L+j{Z}_{0}tan\frac{2\pi }{\lambda }.\frac{\lambda }{2}}{Z_0+j{Z}_{L}tan\frac{2\pi }{\lambda }.\frac{\lambda }{2}}$

$=Z_0.\frac{Z_L}{Z_0}$
So at any point on the line input impedance is $Z_L$
Reflection coefficient $\Gamma =\frac{Z_{i/p}-Z_0}{Z_{i/p}+Z_0}$
So Reflection coefficient is also same on every point of line.
${\Gamma }_{i/p}=\frac{Z_L-Z_0}{Z_L+Z_0}={\Gamma }_{load}$
$\frac{{\Gamma }_{i/p}}{{\Gamma }_{load}}=1$