Amplitude Modulation

Amplitude modulation is a type of modulation where the amplitude (signal strength) of the carrier signal is varied in accordance with the amplitude (signal strength) of the message signal.

or

Amplitude modulation is a type of modulation where the information (message signal) is transmitted over a carrier wave by varying its amplitude in accordance with the amplitude of the message signal.

or

Amplitude modulation is a type of modulation where the height of the carrier signal is changed in accordance with the height of the message signal.

In amplitude modulation, only the amplitude of the carrier wave is changed while the frequency and phase of the carrier wave remain constant.

The above figures show the amplitude modulation.

The first figure shows the modulating signal or message signal which contains information, the second figure shows the high frequency carrier signal which contains no information and the last figure shows the resultant amplitude modulated signal.

The third figure shows that the amplitude of both the positive and negative half cycles of the carrier wave is varied in accordance with the instant amplitude of the message signal. It can be observed that the positive and negative peaks of the amplitude modulated (AM) wave are interconnected with an imaginary line. This imaginary line on the AM wave is called envelope. The shape of the envelope of AM wave looks same as the message signal. Therefore, this envelope helps in recreating the exact shape of the message signal.

The carrier signal does not contain any information so even if we change the amplitude of the carrier signal, no information loss will occur. However, if we change the characteristics (amplitude, frequency, or phase) of the message signal, information loss will occur because the message signal contains the information. So the characteristics of the message signal should not be changed.

Amplitude modulation was the earliest modulation technique used to transmit voice signals by radio signals. Amplitude modulation is still used in many forms of communication; for example, it is used in portable two-way radios, citizens band radio, VHF aircraft radio, and in computer modems in the form of QAM (Quadrature Amplitude Modulation).

In amplitude modulation, the message signal is an audio signal which represents sound, (or) a video signal which represents the image. The carrier wave which has a much higher frequency than the message signal carries the information. At the receiving station, the message signal is extracted from the amplitude modulated wave by demodulation technique.

Mathematical Expression

Consider a sinusoidal modulating signal or message signal  (a_m) of frequency (ω_m) and amplitude (A_m) given by:

                     a_m = A_m sin ω_mt   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  (1)

and carrier wave (a_c) of frequency (ω_c) and amplitude (A_c) given by:

                     a_c = A_c sin ω_ct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

Where,

a_m is the modulating signal or message signal

a_c is the carrier signal

A_m is the maximum amplitude of the message signal

A_c is the maximum amplitude of the carrier signal

ω_m is the frequency of the message signal

ω_c is the frequency of the carrier signal

Using the above mathematical expressions for message signal and the carrier signal, we can create a new mathematical expression for the complete modulated wave.

The amplitude modulated wave (A) is given as:

                   A = A_c + a_m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  (3)

Put a_m value from equation (1) into equation (3), then we get

                   A = A_c + A_m sin ω_mt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4)

The instantaneous value of the amplitude modulated wave (a) can be given as:

                 a = A sin θ

                  a = A sin ω_ct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (5)

Put A value from equation (4) into equation (5), then we get

                 a = (A_c + A_m sin ω_mt) sin ω_ct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  (6)

This is an equation of amplitude modulated (AM) wave.

Modulation index of amplitude modulation

Modulation index or modulation depth describes how the amplitude, frequency or phase of the carrier signal and message signal affects the amplitude, frequency or phase of the modulated signal.

Amplitude modulation index describes how the amplitude of the carrier signal and message signal affects the amplitude of the amplitude modulated (AM) signal.

or

Amplitude modulation index is defined as the ratio of the maximum amplitude of message signal to the maximum amplitude of carrier signal. I.e.,

Where,

A_m is the maximum amplitude of the message signal

A_c is the maximum amplitude of the carrier signal

The maximum amplitude of the message signal must be less than the maximum amplitude of the carrier signal to avoid any distortion in the modulated signal. For example, if the carrier signal amplitude is 5 volts then the message signal amplitude must be less than 5 volts. The maximum value of the modulation index will be equal to one when  A_m = A_c. The minimum value of the modulation index will be zero. If modulation index is higher than 1, then it is called overmodulation. In overmodulation, the data loss will occur. When modulation index is expressed in percentage, it is also called percentage modulation.

Calculation of Modulation Index from Amplitude Modulated (AM) waveform

The below figure shows the amplitude modulated (AM) waveform through which we can calculate the modulation index.

It is clear from the below figure that the modulating signal rides above the carrier signal.

From the above figure, we can write,

The above equation (I.e. eq 5 ) gives the technique of calculating modulation index from amplitude modulated (AM) wave.

Modulation Index or Modulation Depth Examples

The maximum amplitude of the message signal must be less than (or equal to)  the maximum amplitude of the carrier signal to avoid any distortion in the modulated signal. For example, if the carrier signal amplitude is 5 volts then the message signal amplitude must be less than (or equal to) 5 volts. Hence, the maximum value of the modulation index will be less than one or equal to one (M_i<=1) when  A_m <= A_c. The minimum value of the modulation index will be zero.

Based on this, there are three types of modulation:

1. Perfect-Modulation

2. Under-Modulation

3. Over-Modulation

Perfect-Modulation:

Perfect-modulation occurs when the maximum amplitude of the message signal or modulating signal is exactly equal to the maximum amplitude of the carrier signal (A_m = A_c).

The modulation index is the ratio of the maximum amplitude of the message signal to the maximum amplitude of carrier signal. For example, if the message signal maximum amplitude is 4 volts and carrier signal maximum amplitude is also 4 volts, then the ratio of modulating signal amplitude (4 volts) to the carrier signal amplitude (4 volts) is equal to 1. Therefore, the modulation index in perfect-modulation is equal to one (M_i = 1)_.

The modulation index is also known as the modulation depth. The perfect-modulation has a modulation depth of 100%. In perfect-modulation, the carrier level falls to zero. Perfect-modulation causes no distortion.

Under-Modulation:

Under-modulation occurs when the maximum amplitude of the message signal or modulating signal is less than the maximum amplitude of the carrier signal (A_m < A_c).

The modulation index is the ratio of the maximum amplitude of the message signal to the maximum amplitude of carrier signal. For example, if the message signal maximum amplitude is 2 volts and carrier signal maximum amplitude is 4 volts, then the ratio of modulating signal amplitude (2 volts) to the carrier signal amplitude (4 volts) is equal to 0.5. Therefore, the modulation index in under-modulation is less than one (M_i < 1). The under-modulation has a modulation depth of less than 100%. In under-modulation, the carrier level falls above zero. Under-modulation causes no distortion.

Over-Modulation:

Over-modulation occurs when the maximum amplitude of the message signal or modulating signal is greater than the maximum amplitude of the carrier signal (A_m > A_c).

The modulation index is the ratio of the maximum amplitude of the message signal to the maximum amplitude of carrier signal. For example, if the message signal maximum amplitude is 6 volts and carrier signal maximum amplitude is 4 volts, then the ratio of modulating signal amplitude (6 volts) to the carrier signal amplitude (4 volts) is equal to 1.5. Therefore, the modulation index in over-modulation is greater than one (M_i > 1). The over-modulation has a modulation depth of greater than 100%. In over-modulation, the carrier wave experiences 180° phase reversals where the carrier level falls below the zero point.

Over-modulation causes severe distortion of the waveform of the message signal which results in data loss. Over-modulation is one of the reasons why amplitude modulation is no longer used to transmit high-quality sound signals. At the transmitter, limiters are included which prevent more than 100% modulation.

Frequency Spectrum of Amplitude Modulation

The carrier is an un-modulated sinewave which has a single value of frequency (eg: 3 MHz) and carries no useful information. When such a carrier is modulated with a message signal, other frequencies can be detected in it. These new frequencies that are caused by modulation are called sidebands. These sidebands are created above and below the carrier frequency.

The sidebands that are created above the carrier frequency are called upper sidebands and the sidebands that are created below the carrier frequency are called lower sidebands.

I.e. f_USB = f_c + f_m   and   f_LSB = f_c – f_m

Where, f_c is the carrier frequency

f_m is the message signal frequency

f_LSB is lower sideband frequency

f_USB is upper sideband frequency

To see how it works, take the example of a carrier of 800 kHz frequency which is modulated by a message signal (audio signal) of 10 kHz frequency. The process of modulating a carrier signal with message signal is same as mixing two signals together. As a result of modulation, two sideband frequencies are produced.

One sideband frequencies are created above the carrier frequency. These sidebands are known as upper sidebands or sum frequencies. The upper sidebands are created due to the addition of carrier signal frequency (800 kHz) with the message signal frequency (10 kHz) I.e. 800 kHz + 10 kHz = 810 kHz.

Another sideband frequencies are created below the carrier frequency. These sidebands are known as lower sidebands or difference frequencies. The lower sidebands are created due to the subtraction of message signal frequency (10kHz) with the carrier signal frequency (800 kHz) I.e. 800 kHz – 10 kHz = 790 kHz.

I.e. 10 kHz frequency is produced above and below the carrier.

Consider the expression of AM (amplitude modulated) wave given by equation (6)

 a = (A_c + A_m sin ω_mt) sin ω_ct  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)

We know that M_i = A_m / A_c. Hence we have A_m = M_i A_c.

Putting this value of A_m in above equation (1) we get,

a = (A_c + M_i A_c sin ω_mt) sin ω_ct 

= A_c (1 + M_i sin ω_mt) sin ω_ct 

= A_c sin ω_ct + A_c M_i sin ω_mt sin ω_ct . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

In the above equation, the first term represents unmodulated carrier, the second term represents lower sideband and the last term represents upper sideband.

Note that ω_c = 2πf_c and ω_m = 2πf_m. Hence, the above equation (3) can also be written as

From these above equations (4) and  (5), we can prepare the frequency spectrum of AM wave as shown in the below figure.

This contains the full carrier and both the sidebands. Hence, it is also called Double Sideband Full Carrier (DSBFC) system. 

Bandwidth of Amplitude Modulation

The bandwidth of the signal can be obtained by taking the difference between the highest and lowest frequencies of the signal. From the above figure, we can obtain the bandwidth of AM wave as, 

BW = f_USB – f_LSB 

       = (f_c + f_m) – (f_c – f_m)

 BW = 2 f_m

Advantages of Amplitude Modulation

1. Few components needed: At the receiver side, the original signal is extracted (demodulated) using a circuit consisting of very few components.

2. Low cost: The components used in amplitude modulation is very cheap. So the AM transmitter and AM receiver build at low cost.

3. It is simple to implement.

4. Long distance communication: Amplitude modulated waves can travel a longer distance.

Disadvantages of Amplitude Modulation

1. Amplitude modulation is inefficient in terms of its power usage: As we know that the message signal contains information whereas the carrier signal does not contain any information. In amplitude modulation, most of the power is concentrated in the carrier signal which contains no information. At the receiver side, the power consumed by the carrier wave is wasted.

2. It requires high bandwidth: The amplitude modulation is not efficient in terms of its use of bandwidth. It requires a bandwidth equal to twice that of the highest audio signal frequency.

3. This type of transmission can be easily affected by the external radiation.

4. This type of transmission is also affected by the man-made noises or radiations like waves from other antennas or channels.

5. Amplitude modulation (AM) cannot be used for transmitting music as done by frequency modulation (FM).

6. Amplitude modulation cannot be used for transmission of sensitive information like in the army, where interpretation or loss or disruption during transmission is not an option.

Applications of Amplitude Modulation

1. Air band radio: The amplitude modulation is extensively used in aerospace industry. The VHF (Very High Frequency) transmissions made by the airborne equipment still use amplitude modulation. The radio contact between ground to ground and also ground to air use amplitude modulated (AM) signals.

2. Broadcast transmission: Amplitude modulation (AM) is still widely used for broadcasting either short or medium or long wave bands.

3. Quadrature amplitude modulation: Amplitude modulation is used in the transmission of data of almost everything, from short-range transmission such as wifi to cellular communications. Quadrature amplitude modulation is formed by mixing two carriers that are out of phase by 90°.

4. Single sideband: The amplitude modulation (AM) in the form of single sideband is still used for HF (High Frequency) radio links.