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Short note: Amplitude modulation

Short answer

Amplitude modulation (AM) varies carrier amplitude proportional to message signal, with modulation index m=Vm/Vc≤1 to avoid distortion. The modulated wave contains carrier and sidebands (fc±fm), bandwidth 2fm. It is simple and cheap but power-inefficient and noise-prone, used in AM broadcasting.

Write a short note on Amplitude Modulation (AM).

Amplitude modulation (AM) is a modulation method where the amplitude of a high-frequency carrier is varied according to the instantaneous amplitude of the low-frequency message signal. The carrier frequency and phase remain constant.

Equations

Carrier vc = Vc sin ωc t, message vm = Vm sin ωm t.

vAM = Vc (1 + m sin ωm t) sin ωc t

Modulation index: m = Vm/Vc. For no distortion m ≤ 1 (100 % at m = 1). Overmodulation (m > 1) distorts the envelope.

Expanding:

vAM = Vc sin ωc t + (mVc/2) cos(ωc − ωm)t − (mVc/2) cos(ωc + ωm)t

so the AM wave contains the carrier, the lower sideband (fc − fm) and the upper sideband (fc + fm).

Waveform and spectrum

        /\          /\
     /\/  \/\    /\/  \/\
     \/\  /\/    \/\  /\/
        \/          \/

 amplitude
   |        |  carrier
   |    |   |   |
   |____|___|___|____ f
     fc-fm fc fc+fm

Features

  • Bandwidth = 2 fm (for 5 kHz audio, 10 kHz).
  • Power: Pt = Pc (1 + m²/2). Only m²/4 of Pc is in each sideband, which carry the information, so it is inefficient (at m = 1, only 33 % of the power is in the sidebands).
  • Advantages: simple, cheap transmitters and receivers (an envelope detector); long range.
  • Disadvantages: low efficiency, noise-prone, limited fidelity.
  • Applications: medium-wave and short-wave broadcasting, aircraft communication.

✓ Answer checked by Claude Opus 5.5 (high effort)

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