*Question E8B02:
How does the modulation index of a phase-modulated emission vary with RF carrier frequency?*  

*Correct Answer is  D: It does not depend on the RF carrier frequency*  

### AI Response: (may contain errors)  

In phase modulation (PM), the modulation index is a measure of the extent of phase variation in the carrier signal. The modulation index in PM is defined as the ratio of the peak phase deviation to the modulating frequency:

$$ \text{Modulation Index} = \frac{\Delta \phi}{f_m} $$

where:
- $\Delta \phi$ = peak phase deviation (in radians)
- $f_m$ = modulating frequency

### Explanation:

1. **Correct Answer (D): It does not depend on the RF carrier frequency**

   - The modulation index in phase modulation is determined by the peak phase deviation and the modulating frequency, not the RF carrier frequency. Therefore, changes in the RF carrier frequency do not affect the modulation index.

2. **Why the Other Choices are Incorrect:**

   - **Choice A: It increases as the RF carrier frequency increases**
     - This is incorrect because the modulation index is independent of the RF carrier frequency. It is solely dependent on the peak phase deviation and the modulating frequency.

   - **Choice B: It decreases as the RF carrier frequency increases**
     - This is incorrect for the same reason as Choice A. The modulation index does not change with the RF carrier frequency.

   - **Choice C: It varies with the square root of the RF carrier frequency**
     - This is incorrect because there is no mathematical relationship between the modulation index and the square root of the RF carrier frequency. The modulation index is not influenced by the carrier frequency in any form.

### Key Point:

- The modulation index in phase modulation is independent of the RF carrier frequency. It is determined by the characteristics of the modulating signal and the peak phase deviation.