Why Is Instantaneous Value Used in Amplitude Modulation?

In summary, the amplitude modulation equation shows the value of the signal, V, at all times, taking into account the carrier frequency and the modulating signal. The maximum amplitude is Ec + Ei and the shape of the envelope is determined by the cosinusoidal modulating signal. To avoid distortion, the value of the modulating signal, Ei, should not exceed the value of the carrier signal, Ec.
  • #1
rahuld.exe
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In the amplitude modulation equation,
V=(Ec+Ei*coswt)coswt

I don't understand why the instantaneous value of information signal is used. Shouldnt it be peak value as that would give the maximum value (amplitude)?
 
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  • #2
rahuld.exe said:
In the amplitude modulation equation,
V=(Ec+Ei*coswt)coswt

I don't understand why the instantaneous value of information signal is used. Shouldnt it be peak value as that would give the maximum value (amplitude)?

There is an error here. There are two frequencies (ω) involved. ωc and ωi, where the suffices correspond to Carrier and Input (?) / Modulating signal (the same as the E suffices).
The equation tells you the value (in volts) of the signal, V at all times. It's what you will see on an oscilloscope. The maximum amplitude, for your equation, would be Ec + Ei and doesn't involve any Cos functions.
"Ei*coswt" is the shape of the envelope (the cosinusoidal modulating signal). If you want undistorted AM, Ei must be no greater than Ec. If it gets bigger then the phase of the carrier undergoes an abrupt change and this will involve a 'splash' which generates a large number of sidebands both in and out of band. (Not to be recommended)
 

Related to Why Is Instantaneous Value Used in Amplitude Modulation?

1. What is the equation for amplitude modulation?

The equation for amplitude modulation is given by:
S(t) = Ac[1 + m(t)] cos(2πfct)
where S(t) is the modulated signal, Ac is the carrier amplitude, m(t) is the modulating signal, and fc is the carrier frequency.

2. How do you calculate the modulation index for an amplitude modulated signal?

The modulation index is calculated by dividing the peak amplitude of the modulating signal by the peak amplitude of the carrier signal. This can be represented as:
μ = Am/Ac
where Am is the peak amplitude of the modulating signal, and Ac is the peak amplitude of the carrier signal.

3. What is the purpose of amplitude modulation in communication systems?

The purpose of amplitude modulation is to combine a low-frequency signal, such as an audio signal, with a high-frequency carrier signal in order to transmit information through a medium, such as radio waves. This allows for efficient use of bandwidth and the ability to transmit multiple signals simultaneously.

4. How does changing the modulation index affect the amplitude modulated signal?

Changing the modulation index can affect the amplitude modulated signal in several ways. If the index is increased, the amplitude of the modulated signal will also increase, which can result in distortion and potential interference with other signals. If the index is decreased, the amplitude of the modulated signal will decrease, potentially resulting in a weaker signal that is more susceptible to noise.

5. What are some practical applications of amplitude modulation?

Amplitude modulation has many practical applications, such as in radio broadcasting, television broadcasting, and voice communication systems. It is also used in radar systems for detecting and tracking objects, and in instrumentation for measuring and analyzing signals. Additionally, it is used in some types of digital communication, such as amplitude-shift keying (ASK) and quadrature amplitude modulation (QAM).

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