## What is Modulation Index?

This page describes modulation index equations.It explains basics of modulation index in AM and FM.

As we know, in order to have proper amplitude modulation, modulating signal voltage Vm should be less than carrier voltage Vc.
Hence the relationship between amplitudes of these two signals is very important.
This relationship is expressed in terms of **modulation index** 'm'.
The term modulation index is also known by other terms such as modulating factor, modulation coefficient or degree of modulation.

Before we understand modulation index, let us understand AM and FM. AM is the short form of Amplitude Modulation and FM is the short form of Frequency Modulation. In AM, carrier amplitude is varied in accordance to modulating signal amplitude. In FM, carrier frequency is varied in accordance to modulating signal frequency. Refer AM vs FM vs PM and modulation basics for more information.

### Modulation Index in AM

The modulation index is ratio of modulating signal voltage(Vm) to the carrier voltage(Vc).
The modulation index equation is as follows.

m = Vm/Vc

The modulation index should be a number between 0 and 1.
When m is greater than 1, severe distortion results into the modulated waveform.
This condition results when Vm is greater than Vc and it is also known as over modulation.

The ideal condition is when Vm is equal to Vc and m is equal to 1. In this situation, greater output is generated at the receiver with no or minimal distortion.

Modulation index can be calculated by knowing modulating voltage and carrier voltage. But it is very common to measure the modulation index from the modulated waveform. The same can be viewed in the CRO(i.e. Oscilloscope).

After the modulated envelope is displayed in the Oscilloscope,
Vmax and Vmin is noted down. Using this Vm and Vc is derived using following formulas or equations.

Vm = (Vmax-Vmin)/2 .....Equation-1

Vc = (Vmax+Vmin)/2 .....Equation-2

Now modulation index is calculated either taking ratio of Vm by Vc as mentioned in equation-3 below or directly using equation-4.

m = Vm/Vc .....Equation-3

m = (Vmax-Vmin)/(Vmax+Vmin) .....Equation-4

When modulation index is multiplied by 100, the degree of modulation is expressed as a percentage. This is known as percentage of modulation.

### Modulation Index in FM

In FM, modulation index is the ratio of frequency deviation(Fd) to the modulating frequency(Fm).
It is expressed as follows.

m = Fd/Fm

Example:

Max. frequency deviation of carrier = +/- 25KHz

Max. modulating frequency = 10 KHz

modulation index = 25/10 = 2.5

It is known as deviation ratio when both Fd and Fm are used with maximum value in the calculation.

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