Amplitude Modulated Waves

An amplitude modulated wave is a carrier wave whose amplitude is changed by the parameters of the signal wave or the modulating signal. From the set of many modulation schemes available, amplitude modulation (AM) is an old and very simple modulation technique.

In this modulation technique, the information carried by a low frequency modulating signal is essentially superimposed on the carrier wave of high frequency by changing the amplitude of the carrier wave. Hence, the term amplitude modulation.

Amplitude Modulation Theory

Let us further understand how a signal’s amplitude is modulated.

Transmitting a message signal directly is very difficult as many factors are there that deteriorate the signal’s quality. If not properly taken care of, this results in a bad signal at the receiver’s end. Thus, modulation techniques that have been proven advantageous in such scenarios were introduced.

Amplitude modulation is a straightforward and simple way to modulate a signal. Here, only the amplitude is changed without changing the frequency and phase of the wave.

Types of Modulation

Different modulations exist depending on what carrier (characteristic of the signal) is being changed. It is based on the information signal that we want to transmit.

The carriers that can be changed are amplitude, phase, the frequency corresponding to amplitude modulation, phase modulation, and frequency modulation.

Types of Amplitude Modulation

Double sideband with a carrier is the most widely used amplitude modulation type. Most of the radio channels use this modulation.

Double Sideband Suppressed Carrier (DSBSC) is the kind of amplitude modulation that is like the Double Sideband but has no carrier.

Single Sideband (SSB) is the type where only half of the Double Sideband Suppressed Carrier signal is used.

Vestigial Sideband (VSB) is the type of modification of the SSB, which makes the generation and reception of the signal easier.

Expression for Amplitude Modulation

Consider a modulating signal m(t)  given by the expression,

m(t) = A_m Cos ω_mt

and a carrier signal c(t) given by the expression

c(t) = A_c Cos ω_ct

Now, according to the message signal, the amplitude of the carrier is changed and its amplitude is modulated, which is given by the equation:

y(t) = A_o Cos ω_ct

Here, A_o = A_c + m(t)

Thus, the modulated wave is given by,

y(t) = (A_c + A_m Cos ω_mt) Cos ω_ct   ——————— (1)

But what is the extent to which a carrier can be amplitude modulated?

This we get to know by finding out the modulation index.

The modulation index shows the amount by which a carrier signal can be amplitude modulated.

From equation (1)

y(t) = (A_c + A_m Cos ω_mt) Cos ω_ct

Taking Ac out of the above equation a common factor, we will have

y(t) = A_c (1 + (A_m/A_c) Cos ω_mt) Cos ω_ct ——————– (2)

Thus, the term:

A_m /A_c = μ = The modulation index.

The modulation index is thus the ratio of the amplitude of the messaging signal and the carrier signal.

Frequencies of Amplitude Modulated Wave

When it comes to the frequencies, there are 3 in an amplitude modulated wave, which corresponds to ω_c , ω_c + ω_m and ω_c – ω_m

They are:

F₁ corresponding to ω_c

F₂ corresponding to ω_c + ω_m

F₃ corresponding to ω_c – ω_m

F₂ represents the upper-side band frequency

F₃ represents the lower-side band frequency

Linear and Overmodulation

Consider the modulation index. It can either have a ratio greater than 1 or less than 1.

When the modulation index is less than unity, it is called an under-modulated wave.

And when the modulation index is greater than unity, it is called an overmodulated wave.

Remember that an overmodulated wave should be avoided as in many points the amplitude of the carrier wave is not changed in accordance with the messaging signal. This could lead to loss of information and signal distortion.

Transmission Efficiency

The ratio of the power required for the transmission of the message signal to the total power transmitted is called transmission efficiency.

Advantages of amplitude modulation

Amplitude modulation is the simplest and oldest modulation technique. Some advantages are as follows:

• It is simple to demodulate a modulated wave.
• The cost required is low.

Disadvantages of amplitude modulation

• The signal attenuation is relatively high due to the noise.
• The efficiency is low.

Conclusion

We must remember that amplitude modulation is done to transmit the signal. The modulated wave has to be demodulated again at the receiver’s end to get the original wave that is carrying the actual information.