Your Question:

A transmission line with a characteristic impedance of 300 ohm is terminated in a purely resistive load. It is found by measurement that the minimum voltage of the resultant standing wave is 5mV and the maximum voltage is 7.5mV.  The value of the load resistance must be _____ & ______

Step By Step Answers with Explanation

Step-by-step explanation of how to calculate the load resistance of a transmission line with a characteristic impedance of 300 ohms terminated in a purely resistive load, given that the minimum voltage of the resultant standing wave is 5mV and the maximum voltage is 7.5mV:

1. Calculate the reflection coefficient:

• Vmin is the minimum voltage of the standing wave

Substituting the given values into the formula, we get:

where:

• ZL is the load resistance

Therefore, the load resistance must be 450 ohms.

Explanation of the formulas used:

• rho is the reflection coefficient

• Vreflected is the reflected voltage

ZL = (Vmax + Vmin) / (Imax - Imin)

where:

• Imin is the minimum current of the standing wave

The load resistance can also be calculated using the following formula, which is based on the reflection coefficient:

• rho is the reflection coefficient

The second formula is more commonly used to calculate the load resistance, as it is easier to measure the reflection coefficient than the voltage and current of the standing wave.