# Amplitude modulation formula and calculator

Amplitude Modulation (AM) is a modulation technique used in communication systems to transmit information by varying the amplitude of a carrier signal in accordance with the message signal (usually a lower-frequency signal). Let us explore amplitude modulation formula and definitions which can be used for calculation of total power, carrier power and sideband power for different AM modulation index.

Total Power (P_{Total}) :

The total power in an AM signal is the sum of the power in the carrier and the power in the sidebands.
It can be calculated using the following total power formula.

➨P_{Total} = P_{Carrier} + P_{Sidebands}

Carrier Power (P_{Carrier}):

The power of the carrier signal is the power at the carrier frequency.
It can be calculated using following carrier power formula .

➨P_{Carrier} = (A_c)^2 * (1/2)

Where:

A_c is the amplitude of the carrier signal.

Sideband Power (P_{Sidebands}):

The power in the sidebands consists of the power in both the upper and lower sidebands.
It can be calculated using the following sideband power formula.

➨P_{Sidebands} = (A_m)^2 * (1/4)

Where:

A_m is the amplitude of the message (modulating) signal.

The modulation index (m) is defined as the ratio of the amplitude of the message signal (A_m) to the amplitude of the carrier signal (A_c):

➨m = A_m / A_c

The modulation index determines the extent of modulation applied to the carrier signal.
Based on different modulation indices, we can categorize AM into three main types:

Undermodulation (m < 1): In this case, the modulation index is less than 1. The sidebands are smaller than the carrier.
Most of the power is in the carrier.

Hence, PTotal ≈ PCarrier

Critical Modulation (m = 1): The modulation index is equal to 1. The carrier and sidebands have equal power.

Hence, PTotal = PCarrier = PSidebands

Overmodulation (m > 1): Here, the modulation index is greater than 1. The sidebands are larger than the carrier.
Most of the power is in the sidebands.

Hence, PTotal ≈ PSidebands

## Amplitude modulation calculator | sideband and carrier power

Following are the inputs and outputs for this AM calculator:

Inputs: Total AM modulated signal power (Watt) , Modulation Index (in %)

Outputs: Carrier Power (Watts) , one sideband power (Watt)

Amplitude modulation calculator example #1:

INPUTS:
Total AM signal power (in Watts) = 48 ; Modulation Index (in percentage) = 45 %

OUTPUTS:
Carrier signal power = 43.59 Watt;
Sideband power = 2.205 Watt

## Amplitude modulation calculator | Total power, Sideband power

Inputs: Carrier Power (Watts), Modulation Index (in %)

Outputs: Total AM modulated signal power (Watt), one sideband power (Watt)

Amplitude modulation calculator example #2:

INPUTS:
Carrier Power (in Watts) = 25 ; Modulation Index (in percentage) = 80 %

OUTPUTS:
Total AM power = 33 Watt;
One Sideband power = 4 Watt

## Amplitude modulation formula

Following equation mentions relation between total power of AM modulated waveform, carrier signal power and sideband signal power. These formulas are very useful for conversion of one parameter to the other and so on. For example, calculator #1 converts total power and modulation index to carrier power and sideband power while calculator #2 converts carrier power and modulation index to total power and sideband power.

Equation-1 and Equation-2 are used for these AM modulation calculators.

**Conclusion** : It's important to note that in practice, AM signals are often expressed in terms of their power, and these formulas can be
used to analyze or design AM systems with different modulation indices. Adjusting the modulation index allows engineers to control
the trade-off between power in the carrier and power in the sidebands, depending on the specific requirements of a communication system.

## Question : How to calculate amplitude modulation parameters

The question on amplitude modulation numeric calculations have often been asked in competitive exams such as IES, IAS and GATE.

Question: An AM transmitter has carrier power of 25 W. The percentage of modulation is 80 percent. Calculate following:

(a) the total power

(b) the power in one sideband.

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