Question

A transmission line with characteristic impedance of $300\Omega$ is terminated in a purely resistive load. It is found by measurement that the minimum line voltage upon it is 5 m V and maximum 7.5 m V. If the voltage maxima occurs at the load, then the value of load impedance is

• A. $300\Omega$
• B. $200\Omega$
• C. $450\Omega$
• D. $367.5\Omega$

Answer 1

The correct option is C $450\Omega$

$V_{max}=V_0(1+|\Gamma |)$

$V_{min}=V_0(1-|\Gamma |)$

The voltage maxima occurs at x=0

$2\beta x_{max}=2n\pi +\Theta$

$n=0,\theta =0^0$

$\therefore \Gamma =|\Gamma |\angle \Theta =|\Gamma |\angle 0^o=|\Gamma |$

$\therefore \frac{V_{max}}{V_{min}}=\frac{1+\Gamma }{1-\Gamma }=\frac{1+\frac{Z_L-Z_0}{Z_L+Z_0}}{1-\frac{Z_L-Z_0}{Z_L+Z_0}}$

$\frac{V_{max}}{V_{min}}=\frac{Z_L}{Z_0}$

$\frac{7.5}{5}=\frac{Z_L}{300}$

or $Z_L=\frac{7.5}{5}\times 300=450\Omega$