Question

The parallel branches of a 2-wire transmission line are treminated in 100 $\Omega$ and 200 $\Omega$ resistor as shown in the figure. 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. $j\frac{5}{7}$
• B. $\frac{5}{7}$
• C. $\frac{-5}{7}$
• D. $-j\frac{7}{5}$

Answer 1

The correct option is B $\frac{5}{7}$

Ans : (d)


$Z_{in}=\frac{Z_0^2}{Z_L};ifl=\frac{\lambda }{4}$

$R_{1}dueto100\Omega =\frac{{50}^2}{100}=25$

$R_{2}dueto200\Omega =\frac{{50}^2}{200}=\frac{25}{2}$

$\Rightarrow R_1\left|\right|R_2=25\left|\right|\frac{25}{2}=\frac{25}{3}$

$Z_S=\frac{(50{)}^2}{25/3}=300\Omega$

$\Rightarrow \Gamma =\frac{Z_s-Z_0}{Z_s+Z_0}=\frac{300-50}{300+50}=\frac{5}{7}$