Amplitude Modulation

Amplitude Modulation and its Applications

Amplitude modulation is a simple method to transmit a signal for example sound, from one end to other. The sound is a form of energy or vibrations. It travels in the air as waves. The nature of this wave is transverse. A wave has two important components amplitude and frequency. In amplitude modulation amplitude of the carrier wave is changed in accordance with the intensity of the signal.

Amplitude

Amplitude of a wave is defined as the maximum displacement of the vibrating particles in a given medium from the equilibrium position. Amplitude determines the energy of a wave. Higher amplitude waves have higher energy whereas lower amplitude waves possess lower energy. In the case of a sound wave, amplitude represents the loudness. For higher pitch sound amplitude will be more and lower pitch sound amplitude will be less.

What is modulation?

The music or speech generated in a broadcasting station has to be sent over a larger distance to a receiver. For sending these signals, first it is converted into audio signals using a microphone. The frequency range of these audio signals will be 20 – 20000 Hz. The energy of these signals is too low and they cannot travel over a long distance. If a signal has to transmit from one station to other, the signal should have a frequency above 20 kHz. The advantage of choosing high frequency is that it can transmit over a long distance with minimum power. So, in order to convert the low-frequency audio signal to a high frequency, audio signals will superimpose on a high-frequency electrical wave. This high-frequency wave is known as the carrier wave or carrier signal. The resultant wave after superimposing is known as the modulated wave and the process is called as modulation. From the radio stations, the modulated signal such as music or speech is transmitted through antennas. In the receiving stations, the audio signal and carrier signal are separated. This process is known as demodulation. With the help of a loudspeaker, the audio signals can be amplified and reproduced.

Modulation factor

Modulation factor is the ratio of change in amplitude of the carrier wave after modulation to the amplitude of the carrier wave before modulation. The strength and quality of a transmitting signal are decided by the modulation factor. It is denoted by the letter ‘m’.
If the modulation factor is greater than unity, the variation of the carrier amplitude is small. Hence the signal will be weak. If the modulation factor is greater than unity, the signal that has to be transmitted gets distorted and as a result, the signal wave cannot be reproduced properly. For a successful modulation, the degree of modulation should not exceed 100 %.

Amplitude modulation procedure and mathematical representation

In amplitude modulation, the amplitude of carrier wave is changed with respect to the intensity of the signal. A carrier wave has a positive half cycle and a negative half cycle. According to the audio signal, both half cycles are changed.
Mathematically, a carrier wave is written as
ec = Ec cos ωct ............... (i)
Here, ec is the voltage, Ec is the amplitude and ωc is the angular frequency of the carrier signal
In amplitude modulation, Ec (amplitude) of the carrier wave is changed.
Resultant modulating signal can be written as
es = Es cosωst ................ (ii)
Here, es is the voltage, Es is the amplitude and ωs represents the angular frequency of the signal that has to be transmitted.
To get the amplitude modulated wave amplitude of the carrier has to change according to the signal.
From eqn (i)
e= (Ec + Es cosωst ) cosωct
e = Ec cosωct = Ec[1+m cos ωst] cosωct
  = m, modulation factor
On simplification we get,
e = Eccos ωct + mEccos ωct . cosωst …………… (iii)
= Ec cos ωct + ]
= Ec cos ωct + [cos (+) t+cos (-)t]
e=Ec cos ωct + cos (+) t + cos (-) t …………… (iv)
Equation (iv) is the mathematical representation for amplitude modulated wave
We can see three components in this equation.
First component Ec cos ωct is the carrier wave
Second component, cos (+) t is called the upper sideband (USB) because its frequency is higher than the carrier wave.
Third component, cos (-) t is known as lower sideband (LSB) since its frequency is lower than the carrier wave.

Analysis of frequency spectrum and bandwidth

If the frequency spectrum of the amplitude modulated signal is drawn, it can be observed that the location of the carrier signal is in the middle. The upper sideband and the lower sideband of the wave is located on either side of the carrier with frequency interval of. If the modulation factor m=1, then the amplitude of the upper sideband and the lower sideband will be half of the amplitude of the carrier wave.
Bandwidth of an amplitude modulated wave ranges from (ωc – ωs) to (ωc + ωs). Upper sideband of the wave consists of sum components and carrier frequency. Similarly, lower sideband consists of different components of the signal as well as the carrier frequency.

Advantages of amplitude modulation

  • 1. Transmission and reception of amplitude modulated signal is comparatively easy

  • 2. The components used in building the AM transmitter and AM receiver are very cheap

  • 3. The circuit used in this is very simple

  • Disadvantages of amplitude modulation

  • 1. In the transmission of amplitude modulated signal two sidebands and carrier signal has to be sent. So it requires a high range of bandwidth and more power

  • 2. Since the efficiency of amplitude modulation is very low, the messages cannot be transmitted over a particular distance.

  • 3. In the absence of the carrier signal, it is difficult to tune.

  • 4. Transmission and reception of amplitude modulated wave is very noisy.

  • How to overcome these limitations?

    Limitations in the transmission of amplitude modulation can be overcome by adopting some methods

  • 1. DSBSC (Double Sideband Suppresses Carrier)

  • In this method of transmission, the carrier is suppressed and is sent along both the sidebands (upper sideband and lower sideband). By doing so, it is possible to reduce the power wastage in the carrier

  • 2. SSBSC (Single Sideband Suppressed Carrier)

  • In this method of transmission, one of the sidebands (either upper sideband or lower sideband) is sent. Carrier and the other sideband are suppressed to reduce the power wastage.

  • 3. Vestigial sideband

  • In this mode of transmission, one complete sideband of the signal and half of the remaining sideband is sent together. This method is a compromise between DSBSC and SSBSC.