Question

Consider the transmission line with resistive load of $50\Omega$. The characteristic impedance of the line is $100\Omega$. The line is very long, then the minimum and maximum impedance on line is

• A. $75\Omega ,300\Omega$
• B. $100\Omega ,200\Omega$
• C. $100\Omega ,100\Omega$
• D. $50\Omega ,200\Omega$

Answer 1

The correct option is D $50\Omega ,200\Omega$

${\Gamma }_L=\frac{Z_L-Z_0}{Z_L+Z_0}=\frac{50-100}{50+100}=-\frac{1}{3}=\frac{1}{3}{e}^{-jx}$
$SWR\left(\rho \right)=\frac{1+|{\Gamma }_L|}{1-|{\Gamma }_L|}=\frac{3+1}{3-1}=2$
$Z_{min}=\frac{Z_0}{\rho }=\frac{100}{2}=50\Omega$
$Z_{max}=Z_0\rho =100\times 2=200\Omega$