Amplitude Modulation (AM): Working, Formula, Bandwidth & Power Calculations

Amplitude Modulation (AM) is one of the earliest and most widely used methods of modulation in communication systems. It is mainly used in radio broadcasting, aviation communication, and various signal transmission applications. In amplitude modulation, the amplitude of a high-frequency carrier signal is varied in proportion to the instantaneous amplitude of the message (or baseband) signal that contains information.

In simple terms, the message signal carries the information we want to transmit, while the carrier signal helps the message travel over long distances.

What is Amplitude Modulation?

Amplitude Modulation (AM) is a method where the amplitude of the carrier wave changes according to the amplitude of the message signal. The frequency and phase of the carrier remain unchanged. Only the height of the carrier wave varies to carry the information.

The message signal (or baseband signal) is the original signal that contains information such as voice, speech, or music.

The carrier signal is a high-frequency signal that does not contain any information by itself. It is used to transmit the message signal over long distances.

When the message signal modulates the carrier, the resulting wave shows the shape of the message signal around the carrier frequency. This outer shape is called the envelope, and it resembles the original message signal.

Amplitude Modulated Waveform

The following figure shows the waveform of an amplitude modulated signal.

Equation of Amplitude Modulation Wave

Let the message signal be:

m_(t)=A_mcos⁡(2πf_mt)

Let the carrier signal be:

c_(t)=A_ccos⁡(2πf_ct)

Where:

A_m – Amplitude of the message signal
A_c – Amplitude of the carrier signal
f_m – Frequency of the message signal
f_c – Frequency of the carrier signal

Equation of AM Wave

Modulation Index

When a carrier wave is modulated by a message signal, the extent to which its amplitude changes is known as the Modulation Index or Modulation Depth. It indicates how strongly the message signal influences the carrier wave.

Starting from the AM expression:

We can rewrite this as:

Here, μ (mu) is the modulation index, defined as:

This formula is used when the amplitudes of the carrier wave and the message signal are known.

Another way to find the modulation index is by using the maximum and minimum values of the modulated wave. Let:

• A_max = Maximum amplitude of the AM wave
• A_min = Minimum amplitude of the AM wave

When the message signal is at its peak, we get:

A_max=A_c+A_m

When the message signal is at its lowest point:

A_min=A_c−A_m

Adding and subtracting these gives:

So the modulation index becomes:

This is useful when analyzing a waveform directly from an oscilloscope.

The modulation index determines the nature of the AM wave:

• If μ < 1, the wave is under-modulated, meaning the carrier is not fully utilized.
• If μ = 1, the modulation is ideal, and the information is transmitted efficiently.
• If μ > 1, the wave is over-modulated, causing distortion, extra sidebands, and interference, which cannot be corrected.

In practice, maintaining a modulation index close to 1 (100%) ensures good signal quality without distortion.

Types of Modulation Based on μ

Bandwidth of AM Wave

The bandwidth of an AM signal represents the range of frequencies it occupies during transmission. In general, bandwidth is defined as the difference between the highest and lowest frequency components present in the signal.

Starting with the AM equation:

Expanding this, we get:

This shows that an AM signal consists of three main frequency components:

• The carrier frequency f_c
• The upper sideband frequency f_c+f_m
• The lower sideband frequency f_c−f_m

Since the highest frequency component is f_c+f_m and the lowest is f_c−f_m, the bandwidth becomes:

Therefore, the bandwidth required for amplitude modulation is twice the frequency of the modulating signal.

Power in AM Wave

To determine the power of amplitude modulated wave, we start with the expression for the AM signal:

This shows that the AM wave consists of three components:
the carrier frequency, the upper sideband, and the lower sideband.
Therefore, the total transmitted power is the sum of the power in each component:

To calculate power, we use the standard formula for the power of a cosine wave:

Here, v_m is the peak amplitude and v_rms is the RMS value of the signal.

Carrier Power:

Upper Sideband Power:

Lower Sideband Power:

Now adding all three power components:

This formula tells us that the total power in an AM signal increases with the modulation index μ.

If the modulation index is μ=1=1 (100% modulation), then:

P_t=1.5P_c

This means the transmitter must supply 1.5 times the carrier power during perfect modulation.

Types of Amplitude Modulation

There are three main types of amplitude modulation used in communication systems:

1. Double Sideband-Suppressed Carrier (DSB-SC):
   In DSB-SC, both upper and lower sidebands carry the information, but the carrier is suppressed to save power. It provides better efficiency compared to standard AM.
2. Single Sideband (SSB):
   SSB transmits only one sideband, either upper or lower, while eliminating the carrier and the other sideband. This reduces bandwidth usage and improves signal quality.
3. Vestigial Sideband (VSB):
   VSB transmits one full sideband and a small part of the other. It balances bandwidth efficiency and signal clarity, commonly used in TV broadcasts.

AM Communication Systems

An AM communication system uses amplitude modulation to send and receive information over long distances. In this system, the message signal alters the amplitude of a high-frequency carrier wave, while its frequency remains constant.

The World Radiocommunication Conference (WRC) establishes global standards for how electromagnetic signals are transmitted. These guidelines include how much information can be carried within a given frequency band.

For instance, if a carrier wave has a frequency of 100 MHz with a peak-to-peak voltage of 1 volt, any variation beyond this range would prevent accurate signal transmission. To transmit additional information, the amplitude of the carrier must be intentionally varied, which is the basis of AM.

Metasurfaces and Amplitude Wave Modulation

Metasurfaces are engineered surfaces designed to precisely control how electromagnetic waves behave. By manipulating properties such as amplitude, phase, and polarization, metasurfaces enable more efficient wave shaping compared to traditional materials.

When placed on antennas, they can guide or filter signals to improve performance. For instance, applying a metasurface layer can significantly reduce interference or noise levels. In practical terms, this can achieve up to a 20 dB reduction, meaning the interference becomes nearly ten times weaker.

Relation Between Amplitude Modulation and Antenna Height

In amplitude modulation (AM), the height of the antenna is an important factor for efficient signal transmission. The antenna height is related to the wavelength of the carrier signal and is usually taken as one-fourth of the wavelength, h=λ/4 .

Since AM signals use low carrier frequencies, they have large wavelengths, which require taller antennas—often hundreds of meters high. A taller antenna improves the coverage area and signal strength, making AM suitable for long-distance broadcasting. However, the large size of antennas makes AM less practical for compact or portable communication systems.

Amplitude Modulation vs Frequency Modulation

Here is the difference between Amplitude Modulation (AM) and Frequency Modulation (FM) in a clear table form:

Read detailed article: Difference Between Amplitude Modulation and Frequency Modulation

Advantages of Amplitude Modulation

• Simple to implement and easy to modulate and demodulate.
• Low-cost transmitters and receivers.
• Suitable for long-distance and medium-wave broadcasting.
• Wide coverage area, useful in rural and remote communications.

Disadvantages of Amplitude Modulation

• Poor noise resistance because noise affects amplitude.
• Inefficient power usage (majority of power is wasted in the carrier).
• Requires larger bandwidth compared to unmodulated signals.
• Not suitable for high-quality audio applications.

Applications of Amplitude Modulation

Conclusion

Amplitude Modulation is a fundamental technique in communication systems where the amplitude of a carrier signal is varied according to the message signal. Although modern systems now use advanced modulation techniques, AM remains the backbone of broadcasting and aviation communication due to its simplicity and long-range capabilities. Understanding modulation index, bandwidth, and power distribution is essential for anyone studying communication engineering.

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