Amplitude Modulation: Types, Formulas and Applications

Amplitude modulation (AM) is a modulation technology used for communication purposes, mainly for radio wave transmission. 

• Amplitude modulation includes changing the amplitude of the wave (signal intensity) in accordance with the message signal, such as an audio signal. 
• This technology is different from angle modulation, in which either the frequency of the carrier wave is changed (frequency modulation), or its phase (phase modulation) in accordance with the message signal. 
• The first audio modulation technique used in radio broadcasting was AM. Roberto Landell de Moura and Reginald Fessenden developed it in 1900 with their radiotelephone experiments. 
• The original form of AM is sometimes referred to as double-sideband amplitude modulation (DSBAM).

Key Terms: Modulation, Bandwidth, Waves, Modulation index, Demodulation, Amplitude modulation, Frequency, Phase, Amplitude, Need of modulation

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Modulation

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The process of mounting or superimposing a very low-frequency signal over a high-frequency signal or carrier wave is known as modulation.

Different types of modulation are

• Amplitude Modulation: It is a type of modulation in which the frequency and phase of the carrier wave are constant but the amplitude of the carrier wave varies in accordance with the amplitude of the very low-frequency signal.
• Frequency Modulation: It is a type of modulation in which the amplitude and phase of the carrier wave are constant but the frequency of the carrier wave varies in accordance with the frequency of the very low-frequency signal.
• Phase Modulation: It is a type of modulation in which the frequency and amplitude of the carrier wave are constant but the phase of the carrier wave varies in accordance with the phase of the very low-frequency signal.

Types of modulation

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Amplitude Modulation

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Amplitude modulation or simply AM is generally defined as a type of modulation in which the magnitude of the carrier wave changes in accordance with the modulating data or signal. 

• One of the first modulation techniques used for radio communication is amplitude modulation. 
• This method was developed in the 20th century when Landell de Moura and Reginald Fessenden were performing tests with a radiotelephone in the 1900s. 
• The modulation technique was created and employed in electronic communication after several successful efforts. 
• In this process the voltage and the power level of the information to be sent change the amplitude of the carrier wave.

Amplitude modulation

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Types of Amplitude Modulation

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There are mainly three types of amplitude modulation

• Double Sideband-suppressed Carrier Modulation (DSB-SC): Double Sideband Full Carrier is a modulation technique used for the transmission of a signal that consists of a carrier along with two sidebands.
• Single Sideband Modulation (SSB): It is an amplitude modulation technique in which only a single sideband is transmitted through the channel. It is also known as Single Sideband Suppressed Carrier (SSB-SC).
• Vestigial Sideband Modulation (VSB): This technique of amplitude modulation involves modulating one sideband and the vestige portion of the signal.

Designations by ITU

In 1982, the International Telecommunication Union (ITU) categorized many amplitude modulation methods. These are

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Expression for Amplitude Modulated Wave

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The carrier wave can be represented by

e_c = E_c sin ω_ct

Where

• e_c is the instantaneous voltage
• ω_c is the angular frequency

The modulating signal can be represented by

e_m = E_m sin ω_mt

Thus, the amplitude-modulated (AM) wave is represented by

e = (E_c + e_m) sin ω_ct

⇒ e = (E_c + E_m sin ω_mt) sin ω_ct

⇒ e = E_c [1+ E_m/E_c sin ω_mt] sin ω_ct

⇒ e = E_c [1+ ma sin ω_mt] sin ω_ct

⇒ e = E_c sin ω_ct + E_c ma sin ω_mt sin ω_ct

Where ma = E_m/E_c is the modulation index

Using sin A + sin B = 1/2[cos (B - A) - cos (B + A)], we get

e = E_c sin ω_ct + (maE_c)/2 cos (ω_c - ω_m)t - (maE_c)/2 cos (ω_c + ω_m)t

Here (ω_c - ω_m) and (ω_c + ω_m) are respectively called lower side and upper side frequencies.

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Frequencies of Amplitude-Modulated Wave

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The amplitude-modulated wave contains three frequencies f₁, f₂, and f₃ corresponding to ω_c, (ω_c - ω_m), and (ω_c + ω_m). Where

• ω_c corresponds to f₁ known as carrier wave frequency.
• (ω_c - ω_m) corresponds to f₂ known as lower sideband frequency.
• (ω_c +ω_m) corresponds to f₃ known as upper sideband frequency.

The frequency spectrum of AM wave is shown in the figure

The frequency spectrum of AM wave

Bandwidth

The difference between the highest and lowest frequencies of the amplitude-modulated signal is known as its bandwidth.

Bandwidth, BW = Upper sideband frequency (f_max) - Lower sideband frequency (f_min)

⇒ BW = (f_c + f_m) - (f_c - f_m) = 2f_m

Hence, the bandwidth of the amplitude-modulated signal is twice the frequency of the modulating signal.

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Modulation Index

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The modulation index determines the quality of the modulated wave. It is given by the ratio of the amplitude of the modulating signal (A_m) to the amplitude of the carrier wave (A_c).

Modulation index, ma = A_m / A_c = (E_max - E_min) / (E_max + E_min)

• If ma = 0, then there is no modulation.
• If ma = 1/2, then E_max is three times the E_min
• If ma = 1, then E_min becomes zero
• If ma > 1, then there is over-modulation, in this case, the negative portion of AM wave is absent and hence the information contained will be distorted.

Read More:

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Why Do We Need Modulation?

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Low-frequency signals cannot travel large distances. The other factors responsible for not allowing the transmission of baseband signals from one place to another are:

• Height of the antenna
• Effective power radiated by an antenna
• Mixing up of signals from different transmitters

Height of the antenna

The height of the transmitting antenna must be of the order of wavelength λ of the transmitting signal. The minimum height of the transmitting antenna for transmitting the voice frequency signal is λ/4.

If a 15 kHz signal is to be transmitted, then the wavelength corresponding to this signal is given by

λ = c/f = (3 x 10⁸) / (15 x 10³) = 2 x 10⁴ m = 20 km

Hence the minimum height of the antenna = λ/4 = 20/4 = 5 km

It is impossible to erect such a tall antenna.

On the other hand if a 10⁶ Hz (1 MHz) signal is to be transmitted, then the wavelength corresponding to this signal is given by

λ = c/f = (3 x 10⁸) / (1 x 10⁶) = 300 m

Hence the minimum height of the antenna = 300/4 = 75 m

The antenna of such height is practicable.

Thus, we conclude that a signal of low frequency can be transmitted easily through a transmitting antenna if we manage to use high-frequency waves for transporting the signal.

Effective Power Radiated by Antenna

Power radiated by a dish antenna is given by

P = 6(D/λ)²

Where

• D is the diameter of the disc
• λ is the wavelength of the radiation

Similarly power radiated by the linear antenna is proportional to P ∝ 1/λ²

This indicated that power radiated is more for shorter wavelength i.e. for high-frequency waves.

For covering more area, power radiated should be more which is possible with high-frequency transmission.

Mixing up of signals from different transmitters

Another problem of transmitting very low-frequency signals directly is that various voice frequency signals from different transmitters get mixed up and it is difficult to distinguish these signals at receiving station. 

For differentiating signals, a particular portion of the frequency spectrum has to be assigned to a particular signal so that only the desired signal is selected at the receiving station and the remaining signals are rejected.

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Detection of an Amplitude-Modulated Wave

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The process of extracting the audio signals from the modulated waves is known as Demodulation. The device used for demodulating the signal is known as a demodulator.

The process of demodulation is

• A receiving antenna receives the AM signal.
• This high-frequency signal is amplified and then fed to the intermediate frequency stage to change it to a low-frequency signal before sending it to the demodulator.
• The demodulator extracts the audio frequency signal from the high-frequency carrier wave.
• Ans then the audio frequency wave is amplified by an amplifier.
• The amplified audio frequency signal is the required output of the receiver.

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Applications of Amplitude Modulation

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The following are the applications of amplitude modulation

• Broadcasting transmissions using AM are made using short, medium, and long wavebands. Amplitude modulation radio receivers are consequently simpler and more affordable to produce since AM is simple to demodulate.
• Many airborne applications, such as ground-to-air radio communications or two-way radio connections for ground staff workers, utilize AM in VHF broadcasts.
• Single side-band amplitude modulation is used for point-to-point or HF radio communication. AM makes better use of the transmitted power and has a smaller bandwidth.
• Data can be transmitted using quadrature amplitude modulation through short-range wireless networks like Wi-Fi to cellular telephones, among other methods.

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Advantages of Amplitude Modulation

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The advantages of amplitude modulation are

• Amplitude modulation is inexpensive.
• Amplitude-modulated signals are reflected by the earth from the ionosphere layer, allowing them to travel further and cover a larger region.
• The required carrier frequency is minimal.
• It requires the use of a basic transmitter and receiver.
• As a result, audio signal transmission and reception are simplified.
• The use of a circuit with minimal components makes amplitude-modulated signal demonstration less difficult.

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Disadvantages of Amplitude Modulation

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The disadvantages of amplitude modulation are

• Amplitude-modulated communications are extremely vulnerable to background noise.
• It is difficult for receivers of these signals to differentiate between signals and noise.
• As a result, the audio signal's quality is low.
• If the amplitude-modulated signal is weak, a complex configuration is required for the receiver.
• In terms of bandwidth utilization, amplitude modulation is less efficient.
• The modulated signal's bandwidth is twice the frequency of the signal wave.
• Amplitude modulation is similarly inefficient in terms of power consumption.
• Only the sideband power is used.

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Things to Remember

• Modulation is the process of superimposing a very low-frequency signal over a high-frequency signal.
• Amplitude modulation is a type of modulation in which the frequency and phase of the carrier wave remain unchanged but the amplitude of the carrier wave varies in accordance with the amplitude of the very low-frequency signal.
• The three types of amplitude modulation are Double Sideband-suppressed Carrier Modulation, Single Sideband Modulation, and Vestigial Sideband Modulation.
• The amplitude-modulated wave is represented by

e = E_c sin ω_ct +(maE_c)/2 cos (ω_c - ω_m)t - (maE_c)/2 cos (ω_c + ω_m)t

• The bandwidth of the amplitude-modulated signal is twice the frequency of the modulating signal.
• The modulation index is given by the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave.

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