# Modulation Index Formula and Calculator

In this post we present modulation index formula and calculators for three different modulation formats: AM, FM and FSK.

## Amplitude Modulation Index

Modulation index is a measure of the variation of the carrier signal by the modulating signal.

### Formula

m = Am / Ac

Where,

• m is the modulation index
• Am is the modulation amplitude
• Ac is the carrier amplitude

### Calculator

Enter Am and Ac in volt.

### Example

The picture below shows the message or modulating waveform and the carrier.

The three different pictures represent m=0.5, 1.0 and 1.5.

## Frequency Modulation

The modulation index of a FM signal is a measure of how much the carrier frequency deviates as a result of the modulating frequency.

### Formula

h = fd / fm

Where,

• fm is the highest frequency component present in the modulating signal
• fd is the maximum deviation of the instantaneous frequency from the carrier frequency

### Examples

An audio signal has a maximum frequency fm of 20 kHz. If the FM system used to broadcast this information has a maximum deviation fd of Â±75 kHz, then the modulation index h is 3.75.

## Frequency Shift Keying

FSK is the digital form of FM. As such the modulation index of an FSK signal is defined as the ratio of the frequency deviation of the modulated signal to the bandwidth of the modulating signal (or the message).

### Formula

h = 2 * fdT / (M-1)

Where,

• h is the modulation index
• T is the symbol period
• fd is the peak frequency deviation
• M is the order of the modulation

### Example

For a 4-FSK signal with a peak frequency deviation of 1 MHz and symbol period of 2 micro-seconds, the modulation index is 1.33.