Answer to Question #180855 in Electricity and Magnetism for passout

Question

Derive the expression for impedance which varies along the transmission line. A 30-m-long lossless transmission line with Zo = 50  operating at 2 MHz is terminated with a load ZL =70+j30. Find the reflection coefficient and standing wave ratio.

Answer 1

Answer

Zo = 50 

ZL =70+j30

So reflection coefficient

$\tau=\frac{Z_L-Z_0}{Z_L+Z_0}\\=\frac{ 20+j30 }{ 120+j30 }$

And also

Standing wave ratio

$SWR=\frac{\tau+1}{\tau-1}\\=\frac{(\frac{ 20+j30 }{ 120+j30 }+1)}{(\frac{ 20+j30 }{ 120+j30 }-1)}\\$

$=\frac{20+j30+120+j30}{20+j30-120-j30}$

$\\= \frac{140+j60}{-100}$