*Question E8B01:
What is the modulation index of an FM signal?*  

*Correct Answer is  A: The ratio of frequency deviation to modulating signal frequency*  

### AI Response: (may contain errors)  

The modulation index of a Frequency Modulation (FM) signal is a key concept in understanding how FM works. 

### Correct Answer Explanation:
- **Correct Answer: A** - The modulation index ($\beta$) is defined as the ratio of frequency deviation ($\Delta f$) to the modulating signal frequency ($f_m$). This can be expressed mathematically as:
  
  $$
  \beta = \frac{\Delta f}{f_m}
  $$

  Here:
  - $\Delta f$ = frequency deviation (the maximum shift from the carrier frequency)
  - $f_m$ = frequency of the modulating signal

  This ratio indicates how much the carrier frequency varies in response to the modulating signal, which affects the bandwidth and quality of the transmitted signal.

### Incorrect Answer Explanations:
- **Choice B**: The ratio of modulating signal amplitude to frequency deviation.
  - This is incorrect because the modulation index does not involve the amplitude of the modulating signal; it strictly relates to frequency deviation and modulating frequency.

- **Choice C**: The modulating signal frequency divided by the bandwidth of the transmitted signal.
  - This is incorrect as it does not represent the modulation index. The modulation index is not defined in terms of bandwidth but rather in terms of frequency deviation and modulating frequency.

- **Choice D**: The bandwidth of the transmitted signal divided by the modulating signal frequency.
  - This is also incorrect. While bandwidth is related to the modulation index, the modulation index itself is not defined this way. The bandwidth of an FM signal can be estimated using Carson's Rule, which states that the bandwidth is approximately $2(\Delta f + f_m)$, but this does not define the modulation index.

### Summary:
- The modulation index is crucial for understanding FM signals, as it determines the extent of frequency deviation relative to the modulating frequency. 
- Remember the formula for modulation index: 

  $$
  \beta = \frac{\Delta f}{f_m}
  $$ 

This will help you in both understanding FM concepts and answering related exam questions.