*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 match a 100-ohm feed point impedance to a 50-ohm transmission line using a quarter-wave transformer (Q-section), we can use the following formula for the impedance of the transformer:

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

where:
- $Z_T$ = impedance of the transformer (Q-section)
- $Z_1$ = load impedance (100 ohms)
- $Z_2$ = transmission line impedance (50 ohms)

### 1. Why the correct answer is correct:
Using the formula, we can calculate the required transformer impedance:

$$
Z_T = \sqrt{100 \, \Omega \times 50 \, \Omega} = \sqrt{5000} \approx 70.71 \, \Omega
$$

The closest standard impedance value to 70.71 ohms is 75 ohms. Therefore, a 75-ohm Q-section is suitable for matching a 100-ohm feed point to a 50-ohm transmission line.

### 2. Why the other choices are incorrect:
- **A: 50 ohms**  
  This impedance would not provide a proper match since it is lower than the load impedance (100 ohms) and would not transform the impedance correctly.

- **B: 62 ohms**  
  While this value is closer than 50 ohms, it is still not optimal for matching 100 ohms to 50 ohms. It does not provide the necessary transformation.

- **D: 90 ohms**  
  This impedance is also too high for effective matching. It would not provide the correct transformation from 100 ohms to 50 ohms.

### 3. Useful formulas or rules of thumb:
- The quarter-wave transformer is a common method for impedance matching in RF applications.
- Always calculate the required transformer impedance using the square root formula to find the best match.
- Remember that the closer the calculated impedance is to standard values (like 75 ohms), the easier it is to find components for your design.

In summary, the correct choice of 75 ohms allows for effective impedance transformation, while the other options do not meet the requirements for proper matching.