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’s explore amplitude modulation formulas and definitions which can be used for the calculation of total power, carrier power, and sideband power for different AM modulation indices.

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<sub>Total</sub> = P<sub>Carrier</sub> + P<sub>Sidebands</sub>

Carrier Power (P_Carrier)

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

P<sub>Carrier</sub> = (A<sub>c</sub>)<sup>2</sup> * (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<sub>Sidebands</sub> = (A<sub>m</sub>)<sup>2</sup> * (1/4)

Where:

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

Modulation Index (m)

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<sub>m</sub> / A<sub>c</sub>

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, P<sub>Total</sub> ≈ P<sub>Carrier</sub>
• Critical Modulation (m = 1): The modulation index is equal to 1. The carrier and sidebands have equal power. Hence, P<sub>Total</sub> = P<sub>Carrier</sub> = P<sub>Sidebands</sub>
• 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, P<sub>Total</sub> ≈ P<sub>Sidebands</sub>

Amplitude Modulation Calculator

Here are two amplitude modulation calculators to help you find carrier power, sideband power, and total AM modulated signal power.

Calculator 1: Total Power and Modulation Index to Carrier and Sideband Power

Inputs:

• Total AM modulated signal power (Watt)
• Modulation Index (in %)

Outputs:

• Carrier Power (Watts)
• One Sideband Power (Watt)

Example:

• Inputs: Total AM signal power = 48 Watts, Modulation Index = 45%
• Outputs: Carrier signal power = 43.59 Watts, Sideband power = 2.205 Watts

Calculator 2: Carrier Power and Modulation Index to Total and Sideband Power

Inputs:

• Carrier Power (Watts)
• Modulation Index (in %)

Outputs:

• Total AM modulated signal power (Watt)
• One Sideband Power (Watt)

Example:

• Inputs: Carrier Power = 25 Watts, Modulation Index = 80%
• Outputs: Total AM power = 33 Watts, One Sideband power = 4 Watts

Amplitude Modulation Formula Summary

The following equations show the relationship between the total power of an AM modulated waveform, carrier signal power, and sideband signal power. These formulas are very useful for converting one parameter to another.

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.

Questions and Examples

How to calculate amplitude modulation parameters?

Questions on amplitude modulation numeric calculations are often asked in competitive exams such as IES, IAS, and GATE.

Example Question:

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

(a) the total power (b) the power in one sideband.