Amplitude Modulation Derivation

Amplitude modulation is considered to be a process in which the wave signals are transmitted by modulating the amplitude of the signal. The amplitude modulation is often called AM. This technique was established in the 20^th century by Landell de Moura and Reginald Fessenden when they were conducting experiments using a radiotelephone. It is commonly used in the transmission of information through a radio carrier wave. It is mostly used in the form of electronic communication.

The amplitude modulation technique is used in different areas of communication. Some such areas of communication are portable two-way radios, citizens band radio, VHF aircraft radio. Also, in the modems of the computers Amplitude modulation is also used in mentioning the medium wave AM radio broadcasting. 

Amplitude Modulation Equation Derivation

Here, one will get a clear knowledge of how to derive an expression for amplitude modulation. 

The mathematical representation of amplitude-modulated waves in the time domain is as follows.

m(t) = Am cos (2πfmt)  (modulating signal)

m(t) = Ac cos (2πfct) (carrier signal)

s(t) = [ Ac  + Am cos (2πfmt) ] cos (2πfct) (equation of amplitude modulated wave)

Where,

Am: Amplitude of modulating signal

Ac: Amplitude of carrier signal

fm: Frequency of modulating signal

fc: Frequency of carrier signal

From the above information, a student can learn how to derive an expression for amplitude modulated waves.

Modulation Index Derivation

The modulation index is also considered as modulation depth. It is defined for the carrier wave in order to describe the modulated variable of the carrier signal, which is showing some variation with respect to its unmodulated level. The modulation index can be given as:

\[\mu =\frac{A_{m}}{A_{c}}\]

Consider the maximum and minimum wave amplitudes as Amax and Amin. 

Considering the equation cos (2πfmt), the following two equations are derived, which are having the maximum and minimum amplitude of the modulated waves.

Amax = Ac + Am

Amax = Ac - Am

Amax + Amin =  Ac + Am + Ac - Am =  2 Ac ⇒ \[A_{c}=\frac{A_{max}+A_{min}}{2}\]

 Amax - Amin = Ac + Am - (Ac - Am) = 2 Am ⇒ \[A_{m}=\frac{A_{max}-A_{min}}{2}\]

\[\mu =\frac{A_{m}}{A_{c}}\]

From this above information, students can learn about the concept of modulation index derivation.

Types of Amplitude Modulation

From the above information, students have gained a clear knowledge of what amplitude modulation is and how to derive an expression for amplitude modulated wave. Now, they will have a clear knowledge of the types of amplitude modulation from the below-given information.

There are three types of amplitude modulation, and they are discussed as follows.

Double Sideband-suppressed carrier (DSB - SC) Modulation

In this type of amplitude modulation, the transmitted wave only has two sidebands, which are the upper sideband and the lower sideband. The channel bandwidth requirement here is the same as before.

Single Sideband (SSB) Modulation

In this type of amplitude modulation, the transmission wave consists of only one sideband, either it can be the upper band or the lower band. It is required for translating the spectrum of the modulating signal into a new location that is present in the frequency domain.

Vestigial Sideband (VSB) Modulation

In this type of amplitude modulation, one sideband has almost passed through the transmission wave, and just a trace of the other sideband is retained. Here, the requirement of channel bandwidth is slightly more than the message bandwidth by an amount which is the same as the vestigial sideband's width.

Advantages and Disadvantages of Amplitude Modulation

Advantages

The advantages of amplitude modulation are as follows. 

• Amplitude modulation is considered to be economical and is easily obtainable.

• The implementation of amplitude modulation is simple and easy. 

• It can be demodulated easily just by using a circuit with a smaller number of components.

• The receivers of amplitude modulation are cheap and inexpensive as it does not require any specialized components for continuing the process.

Disadvantages

The disadvantages of amplitude modulation are as follows. 

• Amplitude modulation uses a lot of energy, which in turn reduces its efficiency.

• Amplitude frequency is used several times in this process for modulating the signal by a carrier signal.

• The original signal quality is poor in the receiving end, thus causing various troubles.

• They generate a lot of noise, which can turn out to be irritating.

• This application is limited to VHF and radios only.

• It is possible only in one-to-one communication, which is a major drawback.

The process by which a wave signal is transmitted by modulating the amplitude of the signal. Called AM, it is commonly used in transmitting a piece of information through a radio carrier wave. It is mostly used in the form of electronic communication.

Established in the 20th century by Landell de Moura and Reginald Fessenden when they were conducting experiments using a radiotelephone, the technique of  Amplitude modulation technique is used in various areas of communication like portable two-way radios; citizens band radio, and modems for computers. It is also used in medium wave AM radio broadcasting.

Derivation of Amplitude Modulation

m(t) = A_m cos (2πf_mt)  (modulating signal)

m(t) = A_c cos (2πf_ct) (carrier signal)

s(t) = [ A_c  + A_m cos (2πf_mt) ] cos (2πf_ct) (equation of amplitude modulated wave)

Where, 

A_m: Denotes the amplitude of a modulating signal

A_c: Denotes the  amplitude of a carrier signal 

f_m: Denotes the frequency level of the modulating signal

Lf_c: Denotes the frequency level of the carrier signal.

This helps to learn how to derive an expression for the amplitude modulated waves.