Modulation Index Calculator

Modulation Index Formula:

\[ \beta = \frac{\Delta f}{f_m} \]

Modulation Index (β):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Modulation Index?

The modulation index (β) is a measure of how much the carrier signal is varied by the modulating signal in frequency modulation (FM). It represents the ratio of frequency deviation to the modulating frequency.

2. How Does the Calculator Work?

The calculator uses the modulation index formula:

\[ \beta = \frac{\Delta f}{f_m} \]

Where:

\( \beta \) — Modulation index (dimensionless)
\( \Delta f \) — Frequency deviation (Hz)
\( f_m \) — Modulating frequency (Hz)

Explanation: The modulation index determines the bandwidth and quality of the FM signal. Higher β values result in more sidebands and wider bandwidth.

3. Importance of Modulation Index

Details: The modulation index is crucial in FM system design as it affects signal quality, bandwidth requirements, and noise immunity. Different applications require different β values.

4. Using the Calculator

Tips: Enter frequency deviation (Δf) and modulating frequency (f_m) in Hz. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a typical modulation index range?
A: For narrowband FM, β is typically 0.2-1.0. For wideband FM, β is usually 1.0-5.0 or higher.

Q2: How does modulation index affect bandwidth?
A: Bandwidth ≈ 2(Δf + f_m) = 2f_m(1 + β). Higher β means more sidebands and wider bandwidth.

Q3: What's the difference between β and modulation percentage?
A: Modulation percentage is (Δf/max allowed Δf) × 100%, while β is the ratio of Δf to f_m.

Q4: When is a high modulation index desirable?
A: High β provides better signal-to-noise ratio but requires more bandwidth. Used in high-quality audio broadcasts.

Q5: What happens when β < 0.2?
A: The FM signal becomes similar to AM with only two significant sidebands, called narrowband FM.