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Define AM and FM with waveforms

Short answer

Amplitude modulation varies carrier amplitude according to the message signal, keeping frequency constant, with envelope shape of the message. Frequency modulation varies carrier frequency according to the message, keeping amplitude constant; the carrier cycles are dense at positive message peaks and sparse at negative peaks.

Define amplitude modulation and frequency modulation and draw the necessary waveforms.

Amplitude modulation

In amplitude modulation, the amplitude of the carrier changes according to the instantaneous value of the message signal, while its frequency stays constant.

vAM = Vc [1 + m sin ωm t] sin ωc t, with m = Vm/Vc.

Frequency modulation

In frequency modulation, the frequency of the carrier changes according to the instantaneous value of the message signal, while its amplitude stays constant.

vFM = Vc sin[ωc t + mf sin ωm t], with mf = Δf/fm, where Δf is the frequency deviation.

Waveforms

 Message (modulating):
   /\    /\    /\
  /  \  /  \  /  \
 /    \/    \/    \

 Carrier:
 /\/\/\/\/\/\/\/\/\/\/\

 AM (amplitude varies, frequency fixed):
    /\            /\
 /\/  \/\/\    /\/  \/\
 \/\  /\/\/  \/\/  \  /
    \/            \/
 (envelope follows message)

 FM (frequency varies, amplitude fixed):
 |||| | |  |   |  | | ||||
 dense when message high,
 sparse when message low

In the AM wave, the envelope has the shape of the message. In the FM wave, the carrier peaks stay at the same height, and the carrier cycles become closer together when the message is at its positive peak and spread out when it is at the negative peak.

✓ Answer checked by Claude Opus 5.5 (high effort)

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