Return loss ($RL$) is a measure of how much power is reflected back in a transmission line due to impedance mismatches. It is calculated using the following formula:

$RL = 20 \log_{10} \left| \frac{Z_L - Z_0}{Z_L + Z_0} \right|$

Where:

• $Z_L$ is the load impedance (600 ohms in this case)
• $Z_0$ is the characteristic impedance of the line (300 ohms in this case)

Step 1: Calculate the reflection coefficient

The reflection coefficient $\Gamma$ is:

$\Gamma = \left| \frac{Z_L - Z_0}{Z_L + Z_0} \right| = \left| \frac{600 - 300}{600 + 300} \right| = \left| \frac{300}{900} \right| = \frac{1}{3}$

Step 2: Calculate the return loss

Now, we can calculate the return loss using the reflection coefficient:

$RL = 20 \log_{10} \left( \frac{1}{3} \right)$

$RL = 20 \times \log_{10}(0.3333) = 20 \times (-0.4771) = -9.54 \, \text{dB}$

Since return loss is expressed as a positive value, the result is:

$RL = 9.54 \, \text{dB}$

Final Answer:

The return loss is $9.54 \, \text{dB}$, which corresponds to option D.

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Would you like more details or have any questions?

Here are some related questions you might consider:

1. How does return loss relate to signal reflection in a transmission line?
2. What happens if the load impedance and characteristic impedance are perfectly matched?
3. How does return loss affect signal quality in a communication system?
4. What is the significance of a negative return loss value?
5. Can return loss ever reach zero in practical applications?

Tip: Always aim for impedance matching in transmission lines to minimize power loss and reflections.