# RF Wireless World

## What is Modulation Index Formula for AM and FM ?

AM (Amplitude Modulation) and FM (Frequency Modulation) are two common methods of modulating analog signals for communication purposes. The modulation index, also known as modulation depth or modulation ratio, is a key parameter in both AM and FM modulation schemes. It quantifies how much the carrier signal is altered by the modulating signal. Let's discuss the formulas and calculators which calculates modulation index values in both AM and FM.

### AM Modulation Index (m)

In AM, the amplitude of the carrier signal is varied in proportion to the amplitude of the modulating signal. The modulation index (m) is defined as the ratio of the peak amplitude of the modulating signal (Am) to the peak amplitude of the carrier signal (Ac).
Following is the AM modulation index formula.
➨ m = Am/Ac
Where,
m = Modulation index
Am = Peak amplitude of modulating signal
Ac = Peak amplitude of carrier signal

Modulation index is unitless and it ranges from 0 to 1 in standard AM modulation. m = 0 indicates that there is no modulation (i.e. unmodulated carrier)
When m = 1, the carrier signal's amplitude varies between zero and its maximum value due to full modulation.

### FM Modulation Index (β)

In FM, the frequency of the carrier signal is varied in proportion to the amplitude of the modulating signal. The modulation index (β) is defined as the maximum frequency deviation (Δf) divided by the frequency of the modulating signal (fm). Following is the FM modulation index formula.
➨ β = Δf/fm
Where,
β = Modulation Index
Δf = Maximum frequency deviation, it is the maximum amount by which the carrier frequency is shifted from its center frequency due to modulation.
fm = Frequency of modulating signal

The modulation index β quantifies how much the carrier frequency changes in response to changes in the modulating signal. Larger values of β correspond to greater frequency deviations and thus stronger frequency modulation.

It's worth noting that both AM and FM modulation can have different forms and variations, and these formulas provide a basic understanding of the modulation indices in their simplest forms. In practice, the modulation indices can vary based on the specific modulation scheme and application requirements.

### AM modulation index calculator

#### INPUTS

Modulating Signal Voltage (input1) :

Carrier Signal Voltage (input2) :

#### OUTPUT

AM Modulation Index (Output1):

Example: Amplitude modulation index calculator:
INPUTS: Modulating signal voltage = 0.5, Carrier Signal Voltage = 1.25
OUTPUT: AM Modulation Index = 0.4

### FM Modulation Index Calculator

#### INPUTS

Frequency Deviation, Fd (input1) :

Modulating Frequency, Fm (input2) :

#### OUTPUT

FM Modulation Index (Output1):

Example: Frequency modulation index calculation :
INPUTS: Fd = +/- 25KHz, Fm = 10 KHz
OUTPUT : Fm Modulation Index = 2.5

### AM FM Modulation Index Formula

Following formula are used in AM and FM analog modulation types. Conclusion : In this comprehensive guide, we've explored the essential concepts of AM and FM Modulation Index, delving into their respective formulas and showcasing the practical utility of our modulation index calculator. By understanding the intricacies of modulation depth, we have learnt how these indices profoundly influence signal transmission and quality.