Amplitude Modulation (AM)

General
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Amplitude Modulation (AM)

Amplitude Modulation (AM) is a technique where the amplitude of a high-frequency carrier signal is varied according to the amplitude of a low-frequency message signal.

1. Carrier Signal

A carrier signal is a high-frequency sinusoidal wave used to carry the message signal over long distances. It does not contain any useful information on its own.

Mathematical Representation:

c(t) = Ac * cos(2π fc t)

Where:

  • c(t) = Carrier signal
  • Ac = Carrier amplitude
  • fc = Carrier frequency
  • t = Time

Example:

  • In AM radio, a carrier frequency of 1 MHz is commonly used.
  • It helps transmit signals efficiently over large distances.

2. Message Signal (Modulating Signal)

A message signal, also called a modulating signal, is the actual information that needs to be transmitted. It is usually a low-frequency signal such as voice, music, or data.

Mathematical Representation:

m(t) = Am * cos(2π fm t)

Where:

  • m(t) = Message signal
  • Am = Message amplitude
  • fm = Message frequency

Example:

  • Human speech typically ranges from 300 Hz to 3 kHz.

3. Modulated Signal (AM Wave)

The modulated signal is the result of combining the message signal with the carrier signal. This forms the AM waveform, where the carrier’s amplitude varies according to the message signal.

Mathematical Representation:

s(t) = [Ac + Am * cos(2π fm t)] * cos(2π fc t)

Where:

  • s(t) = AM modulated signal
  • Ac = Carrier amplitude
  • Am = Message amplitude
  • fc = Carrier frequency
  • fm = Message frequency

Key Properties:

  • The frequency of the modulated wave remains the same as the carrier frequency.

  • The envelope of the AM signal follows the shape of the message signal.

  • The modulation index (m) is defined as:

    m = Am / Ac

    If m > 1, it causes overmodulation, leading to distortion.

Graphical Representation in DCAClab

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  1. Carrier Signal: A high-frequency sine wave.
  2. Message Signal: A low-frequency wave (speech/music).
  3. Modulated Signal: The amplitude of the carrier changes according to the message signal.

Thanks
DCAClab Community Forum Organizer
Md. Anisur Rahman