Modulation index in FM signal

Options

A. varies inversely as the frequency deviation
B. varies directly as the modulating frequency
C. varies directly as the frequency deviation
D. varies inversely as the square of the modulating frequency.

Answer

To determine the modulation index in an FM (Frequency Modulation) signal, we can follow these steps:

### Step 1: Understand the Definition of Modulation Index
The modulation index (β) in FM is defined as the ratio of the frequency deviation (Δf) to the modulating frequency (fm). Mathematically, it can be expressed as:
\[ \beta = \frac{\Delta f}{f_m} \]

### Step 2: Analyze the Relationship
From the definition, we can see that:
- The modulation index is directly proportional to the frequency deviation (Δf).
- The modulation index is inversely proportional to the modulating frequency (fm).

### Step 3: Identify the Correct Option
Given the options:
1. Varies inversely as the frequency deviation
2. Varies directly as the modulating frequency
3. Varies directly as frequency deviation
4. Varies inversely as the square of modulating frequency

From our analysis, we conclude that the modulation index varies directly as the frequency deviation (Δf). Therefore, the correct answer is:
**Option 3: Varies directly as frequency deviation.**

### Step 4: Conclusion
The modulation index in an FM signal is an important parameter that helps in understanding how much the carrier frequency is varied in response to the modulating signal.

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