*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 an FM signal is a key concept in understanding frequency modulation. Let's break down the correct answer and why the other choices are incorrect.

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

The modulation index ($\beta$) for an FM signal is defined as:

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

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

This ratio indicates how much the carrier frequency varies in response to the modulating signal.

### Why the Other Choices are Incorrect:

- **Choice B: The ratio of modulating signal amplitude to frequency deviation**

  This choice is incorrect because the modulation index in FM is not related to the amplitude of the modulating signal. FM modulation is concerned with frequency changes, not amplitude changes.

- **Choice C: The modulating signal frequency divided by the bandwidth of the transmitted signal**

  This choice is incorrect because it describes a relationship that is not relevant to the modulation index. The bandwidth of an FM signal is typically calculated using Carson's Rule, which involves both the frequency deviation and the modulating frequency, but not in this ratio.

- **Choice D: The bandwidth of the transmitted signal divided by the modulating signal frequency**

  This choice is incorrect for similar reasons as Choice C. The modulation index is not defined by the bandwidth of the transmitted signal. Instead, the bandwidth is a result of the modulation index and the modulating frequency.

### Useful Formula:
- **Carson's Rule for Bandwidth**:  
  The bandwidth ($BW$) of an FM signal can be estimated using Carson's Rule:

  $$
  BW = 2(\Delta f + f_m)
  $$

  This formula shows how both the frequency deviation and the modulating frequency contribute to the overall bandwidth, but it does not define the modulation index.

Understanding these concepts will help you correctly identify the modulation index and its role in FM signal characteristics.