Question

A 75ohm coaxial transmission line has a length of 2cm and is terminated with a load impedance of (37.5 + j75) ohm. If the dielectric constant of the line is 2.56 and the frequency is 3GHz , find the input impedance of the line, the reflection coeffecient at the
lood, the reflection coeffecient at the input and the swr on the line​

Answer 1

Given that,

Impedance = 75 ohm

Length = 2 cm

Load impedance = 37.5 +j 75 ohm

Dielectric constant = 2.56

Frequency = 3 GHz

We need to calculate the wavelength

Using formula of wavelength

$\lambda=\dfrac{c}{f\sqrt{\epsilon_{r}}}$

Put the value into the formula

$\lambda=\dfrac{3\times10^{8}}{3\times10^{9}\sqrt{2.56}}$

$\lambda = 0.0625$

We need to calculate the value of β

Using formula of β

$\beta=\dfrac{2\pi}{\lambda}$

$\beta=\dfrac{2\pi}{0.0625}$

$\beta=100.53$

We need to calculate the input impedance

Using formula of input impedance

$Z_{in}=Z_{0}\dfrac{Z_{L}+jZ_{0}\tan(\beta l)}{Z_{0}+jZ_{L}\tan(\beta l)}$

Put the value into the formula

$Z_{in}=(75)\times{(37.5+j75)+j(75)\tan(100.531(0.02))}{75+j(37.5+j75)\tan(100.531(0.02))}$

$Z_{in}=18.9855-j20.5464$

We need to calculate the reflection coefficient at the load

Using formula of reflection coefficient

$\Gamma_{L}= \dfrac{Z_{L}-Z_{0}}{Z_{L}-Z_{0}}$

Put the value into the formula

$\Gamma_{L}=\dfrac{(37.5+j75)-75}{(37.5+j75)+75}$

$\Gamma_{L}=0.07692+j0.61538$

We need to calculate the reflection coefficient at the input

Using formula of reflection coefficient

$\Gamma_{in}=\dfrac{Z_{in}-Z_{0}}{Z_{in}+Z_{0}}$

Put the value into the formula

$\Gamma_{i}=\dfrac{(18.9855-j20.5464)-75}{(18.9855-j20.5464)+75}$

$\Gamma_{i}=-0.523195-j0332989$

We need to calculate the standing wave ratio

Using formula of standing wave

$SWR=\dfrac{1+|\Gamma|}{1-|\Gamma|}$

Put the value into the formula

$SWR=\dfrac{1+0.62017}{1-0.62017}$

$SWR=4.2655$

Hence, The standing wave ratio is 4.2655.

Answer 2

Answer:

hi how Zin is find out without taking conjugate