*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)  

The modulation index of a phase-modulated (PM) emission is defined as the ratio of the phase deviation to the modulation frequency. It is given by the formula:

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

where:
- $\Delta \phi$ = peak phase deviation in radians
- $f_m$ = modulation frequency in hertz

### Explanation of the Correct Answer (D)

- **Correct Answer: D - It does not depend on the RF carrier frequency.**
  
  The modulation index in phase modulation is determined by the amount of phase shift introduced by the modulating signal and the frequency of that modulating signal, not the RF carrier frequency. Therefore, regardless of how high or low the RF carrier frequency is, the modulation index remains constant as long as the phase deviation and modulation frequency are unchanged.

### Explanation of Incorrect Answers

- **A: It increases as the RF carrier frequency increases.**
  
  This is incorrect because the modulation index is not influenced by the RF carrier frequency. The carrier frequency affects the bandwidth and propagation characteristics but does not change the modulation index itself.

- **B: It decreases as the RF carrier frequency increases.**
  
  Similar to option A, this is incorrect. The modulation index remains constant regardless of the RF carrier frequency. The relationship between phase deviation and modulation frequency is what defines the modulation index.

- **C: It varies with the square root of the RF carrier frequency.**
  
  This is also incorrect. There is no relationship between the modulation index and the square root of the RF carrier frequency. The modulation index is solely dependent on the phase deviation and the modulation frequency.

### Summary

- The modulation index for phase modulation is independent of the RF carrier frequency.
- It is determined by the peak phase deviation and the modulation frequency.
- Understanding this concept is crucial for grasping how phase modulation works in amateur radio communications.