*Question G5C07:
What transformer turns ratio matches an antenna’s 600-ohm feed point impedance to a 50-ohm coaxial cable?*  

*Correct Answer is  A: 3.5 to 1*  

### AI Response: (may contain errors)  

To match an antenna's 600-ohm feed point impedance to a 50-ohm coaxial cable, we use a transformer to adjust the impedance. The key is to find the correct turns ratio of the transformer that will match these impedances.

### Explanation:

1. **Transformer Turns Ratio Formula:**

   The impedance transformation ratio is the square of the turns ratio. The formula is:

   $$ \frac{Z_1}{Z_2} = \left(\frac{N_1}{N_2}\right)^2 $$

   where:
   - $Z_1$ is the impedance of the antenna (600 ohms).
   - $Z_2$ is the impedance of the coaxial cable (50 ohms).
   - $N_1/N_2$ is the turns ratio of the transformer.

2. **Solving for the Turns Ratio:**

   Rearrange the formula to solve for the turns ratio:

   $$ \frac{N_1}{N_2} = \sqrt{\frac{Z_1}{Z_2}} $$

   Substitute the given values:

   $$ \frac{N_1}{N_2} = \sqrt{\frac{600}{50}} = \sqrt{12} \approx 3.5 $$

   Therefore, the correct turns ratio is approximately 3.5 to 1.

### Why the Correct Answer is Correct:

- **Choice A: 3.5 to 1** is correct because it matches the calculated turns ratio needed to transform 600 ohms to 50 ohms.

### Why the Other Choices are Incorrect:

- **Choice B: 12 to 1** is incorrect because it would imply an impedance transformation of $12^2 = 144$, which is not the required ratio.
- **Choice C: 24 to 1** is incorrect because it would imply an impedance transformation of $24^2 = 576$, which is far too high.
- **Choice D: 144 to 1** is incorrect because it would imply an impedance transformation of $144^2 = 20736$, which is extremely excessive.

By using the formula and understanding the relationship between turns ratio and impedance transformation, we can determine that a 3.5 to 1 turns ratio is needed to match a 600-ohm antenna to a 50-ohm coaxial cable.