*Question E9E06:
Which of these transmission line impedances would be suitable for constructing a quarter-wave Q-section for matching a 100-ohm feed point impedance to a 50-ohm transmission line?*  

*Correct Answer is  C: 75 ohms*  

### AI Response: (may contain errors)  

To solve this problem, we need to use the concept of a quarter-wave transformer, also known as a Q-section, which is used to match two different impedances. The formula for the characteristic impedance ($Z_0$) of the quarter-wave transformer is:

$$
Z_0 = \sqrt{Z_1 \times Z_2}
$$

where:
- $Z_1$ is the impedance of the load (100 ohms in this case).
- $Z_2$ is the impedance of the transmission line (50 ohms in this case).

Let's calculate the suitable impedance for the Q-section:

$$
Z_0 = \sqrt{100 \, \text{ohms} \times 50 \, \text{ohms}} = \sqrt{5000} \approx 70.71 \, \text{ohms}
$$

The closest standard transmission line impedance to 70.71 ohms is 75 ohms, which makes choice C the correct answer.

### Explanation of Choices:
- **A: 50 ohms**  
  This is the impedance of the transmission line, not suitable for the Q-section as it does not match the calculated impedance of approximately 70.71 ohms.

- **B: 62 ohms**  
  This is not close enough to the calculated impedance of 70.71 ohms to be effective for matching.

- **C: 75 ohms**  
  This is the closest standard impedance to the calculated 70.71 ohms, making it the best choice for the Q-section.

- **D: 90 ohms**  
  This is too far from the calculated impedance of 70.71 ohms to be effective for matching.

By using a 75-ohm transmission line for the Q-section, you can effectively match a 100-ohm feed point to a 50-ohm transmission line.