# Modulation Calculator

Created by AbdulRafay Moeen
Reviewed by Steven Wooding
Last updated: Jun 05, 2023

Using our modulation calculator, you can obtain the ratio of the modulation signal against the amplitude of the carrier signal, known as the modulation index.

The following article will discuss phase, frequency, and amplitude modulation and share how we calculate the modulation index by formula.

## Overview of modulation

Modulation is converting data into radio waves by adding information from a low-frequency signal to a high-frequency electronic or optical carrier signal.

This carrier signal is a pure wave of constant frequency that can travel long distances but doesn't carry any useful information. Thus, we include information by imposing our high-frequency input signal wave on this carrier wave.

💡 To learn about the relationship between frequency and waves, check out our frequency to wavelength calculator.

The shape of the carrier wave changes with modulation, i.e., after we encode the sound waves or data information from the input signal to the carrier signal. The base of these changes are the following wave parameters:

1. Amplitude – The peak of the wave;
2. Frequency – Number of waves crossing a point in a given second; and
3. Phase – The offset of a wave from a given point.

Based on these wave parameters, there are three types of modulation techniques for analog carriers, all of which vary according to the unmodulated levels of the message signal:

1. Amplitude Modulation – Varying amplitude of the carrier signal;
2. Frequency Modulation – Varying frequency of the carrier signal; and
3. Phase Modulation – Varying phase shift of the carrier signal.

🔎 Phase and frequency modulations have many commonalities. So we collectively refer to them as angle modulation, where the angle is the modification of the quantity passed to a sine or cosine function.

## What is modulation index?

Calculating the modulation ratio from the message signal to the carrier signal, this numerically expressed degree of modulation is the modulation index.

## How to calculate modulation index by formula

We use the following modulation index equations to find the variation between the message and the carrier signals:

• Amplitude modulation index
The definition of AM modulation index is the amplitude ratio of the message signal to the carrier signal:

$\mu_a = A_m / A_c$

• Frequency modulation index
It is the ratio of frequency deviation of the message signal to the sinusoidal message signal frequency:

$\mu_f = \Delta f / f_m$

• Phase modulation index
It is the maximum phase change corresponding to the maximum message signal amplitude:

$\mu_p = \Delta \theta$

where:

• $\mu_a, \mu_f, \mu_p$ – Modulation indexes for amplitude, frequency, and phase, respectively, also known as modulation factors;
• $A_m$ – Amplitude of the message signal;
• $A_c$ – Amplitude of the carrier signal;
• $\Delta f$ – Peak frequency deviation in the message signal;
• $f_m$ – Highest frequency in the message signal; and
• $\Delta \theta$ – The peak phase deviation.

## How to use the modulation calculator

Below you will find out how simple it is to use the modulation calculator.

Select the wave parameter for calculating its modulation index. For example, by selecting amplitude, we get the following three fields:

1. Message signal amplitude (Aₘ)
Here you may enter the amplitude of the message signal, e.g., 40 volts.

2. Carrier signal amplitude (A꜀)
And here, you may enter the respective amplitude of the carrier signal, e.g., 50 volts.

3. Modulation index (μa)
You'll then get how much the modulated variable varies around its unmodulated levels, i.e., 0.8.

Similarly, if we select frequency as our wave parameter, we have the following fields for calculating the frequency modulation index:

1. Max frequency deviation (Δf)
Here you enter the peak frequency-deviation of your message signal.

2. Message signal frequency (fₘ)
And here, you may enter the highest frequency of the message signal.

🙋 At a constant modulating frequency, phase modulation is indistinguishable from frequency modulation. Thus, the frequency modulation index in such an instance equals the phase deviation.

You might be interested in checking out our sound absorption coefficient calculator. It would help understand the quality of sound in various situations.

## Modulation index example

Let's take an FM broadcast station for a modulation index example:

A station has a maximum frequency deviation of 75 kHz, with the highest message signal frequency at 15 kHz. What is its modulation index?

We know that the equation of modulation index for frequency is:

$\mu = \Delta f / f_m$

Placing the values in the formula, we get:

$\mu = 75 / 15$

or:

$\mu = 5$

Thus, the frequency modulation index of our station is 5.

If you want to learn more about the role of modulation in other fields, make sure to check out our baud rate calculator.

## FAQ

### How do I calculate modulation index?

Divide the message signal amplitude (Aₘ) by the carrier signal amplitude (A꜀) to obtain the amplitude modulation index (μa). Mathematically, its representation is:

• μa = Aₘ / A꜀

Or divide the max frequency deviation (Δf) by the message signal frequency (fₘ) to obtain the frequency modulation index (μf). Mathematically, we represent that as:

• μf = Δf / fₘ

### Amplitude modulation vs frequency modulation

Amplitude modulation

• The modulation index is between 0 and 1.
• To send data, the carrier wave's amplitude is modified.
• Requires low bandwidth.
• Sound quality is poor.

Frequency modulation

• The modulation index is always greater than 1.
• To send data, the carrier wave's frequency is modified.
• Requires high bandwidth.
• Sound quality is better than AM.

### What is the modulation index when the message signal is 20 V at 100 V carrier?

0.2 is the modulation index when the message signal is 20 V with a 100 V carrier.

We obtain this modulation index by dividing the message signal by the carrier signal:

Modulation index = message signal / carrier signal

### What is amplitude modulation?

Altering the amplitude of the carrier signal by combining it with a message signal to transmit information is known as amplitude modulation. It generally requires low bandwidth and is used for broadcasting audio signals.

AbdulRafay Moeen
Calculate modulation index of
amplitude
Message signal amplitude (Aₘ)
V
Carrier signal amplitude (A꜀)
V
Amplitude modulation index (μₐ)
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