Expression for Amplitude Modulated Wave
Carrier wave will be generally a high frequency wave and similar to sine or cosine wave and can be represented as :
C(t)=Acsinωct ……..(1)
or
C(t)= Acsin( 2πfct)
where,
- Ac is the amplitude of carrier wave,
- sinωct is phase of carrier wave,
- fc is frequency of carrier wave
- C(t) is our carrier wave,
Modulating signal is also analogous to a sine or cosine wave and represented as:
m(t)= Amsinωmt ….. 2
or
m(t)= Amsin( 2πfmt)
where
- Am is the amplitude of modulating wave,
- sinωmt is phase of modulating wave,
- fm is frequency of modulating signal
- m(t) is our modulating or input signal.
We are now superimposing modulating signal into a carrier wave to interpret the data and speech information and thus also varying the amplitude of the carrier wave in accordance with the amplitude of the modulating signal, and hence the amplitude-modulated wave Cm(t) will be:
Cm(t) = (Ac + Am sin ωmt) sin ωct ………..(3)
This is the general form of an amplitude-modulated wave.
The degree of modulation is given by index of modulation.
From equation (3), we have,
Cm(t) = (Ac + Am sin ωmt) sin ωct
Taking Ac common in (3), we get
Cm(t)=Ac(1+(Am/Ac)sin(ωmt))sin(ωct ) …….. 4
where
Am/Ac= μ, which is known as modulation index also known as modulation factor, modulation coefficient or degree of modulation.
Thus modulation index is defined as the ratio of the amplitude of the modulating signal to the amplitude of the carrier wave.
Modulation Index
Modulation index (μ) is defined as ratio of the amplitude of the modulating signal to the amplitude of the carrier wave. Its mathematical expression and detailed explanation is discussed later in the article.
Amplitude Modulation – Definition, Types, Expression
Amplitude Modulation or AM, is a modulation technology mainly used for radio carrier wave-based message transmission which modifies the carrier wave’s amplitude (signal intensity) in accordance with the message signal, such as an audio signal, i.e., a modulating signal.
In this article, we will learn what amplitude modulation is, its definition, historical overview, equations to explain the process , its applications in telecommunication, and some related methodologies. We will also solve some numerical problems based on amplitude modulation and attempt to answer FAQs regarding this topic