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Modulation; AM and FM modulated waves

Short answer

Modulation is the process of varying a carrier's amplitude, frequency, or phase in accordance with a message signal. AM varies amplitude: v=Vc(1+m sin ωmt) sin ωct, bandwidth 2fm. FM varies frequency: v=Vc sin(ωct+mf sin ωmt), with mf=Δf/fm, constant amplitude, Carson's rule bandwidth, higher noise immunity.

What is modulation? Explain AM and FM modulated wave.

Modulation is the process of changing a property (amplitude, frequency or phase) of a high-frequency carrier wave in accordance with the instantaneous value of a low-frequency message signal.

It is needed for practical antenna size (antenna length is about λ/4, so a 1 kHz signal would need 75 km), for multiplexing many signals, for reducing noise and interference, and for longer range.

AM modulated wave

The amplitude of the carrier varies according to the message; the carrier frequency is constant.

v = Vc (1 + m sin ωm t) sin ωc t, m = Vm/Vc (modulation index, m ≤ 1 to avoid distortion).

  • Frequencies: fc, fc + fm, fc − fm. Bandwidth = 2 fm.
  • Simple and cheap, but noise affects amplitude and power efficiency is low.
  • Used in medium-wave broadcasting (535 to 1605 kHz).
   /\            /\
 /\/  \/\      /\/  \/\    <- envelope follows
 \/\  /\/      \/\  /\/       message
   \/            \/

FM modulated wave

The frequency of the carrier varies according to the message; the amplitude is constant.

v = Vc sin(ωc t + mf sin ωm t), mf = Δf/fm.

  • Bandwidth by Carson's rule: BW = 2 (Δf + fm).
  • High noise immunity because noise mainly changes amplitude, and the receiver limits amplitude. Better sound quality, but needs larger bandwidth.
  • Used in FM broadcasting (88 to 108 MHz) and TV sound.
 |||| | |  |   |  | | ||||   <- constant height,
 closer when message high        spacing varies

✓ Answer checked by Claude Opus 5.5 (high effort)

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