Question

The standing wave ratio on a 50$\Omega$ lossless transmission line terminated in an unknown load impedance is found to be 3. The distance between successive voltage minima is 20cm and the first minimum located at 5cm from the load. The magnitude of load impedance (in $\Omega$) is _______

Answer 1

$\text{The distance between successive voltage minima is}$$\frac{\lambda }{2}=0.2m\Rightarrow \lambda =0.2\times 2=0.4m$

So phase constant $\beta =\frac{2\pi }{\lambda }=\frac{2\pi }{0.4}=5\pi rad/m$

The angle of reflection, $\varphi =2\beta y_{min}-\pi =2\times 5\pi \times 0.05-\pi =-0.5\pi rad$

$\Gamma =|\Gamma |e^{j0}=0.5e^{-j05\pi }=-j0.5$

load impedance, $Z_L=Z_o\frac{1+\Gamma }{1-\Gamma }=50\left(\frac{1+j0.5}{1-j0.5}\right)=30+j40\Omega$

$\left|Z_L\right|=\sqrt{{\left(30\right)}^2+{\left(40\right)}^2}=50\Omega$