“Classical” Amplitude Modulation

• A signal flow diagram describing amplitude modulation (AM) with sinusoidal oscillators is shown in Fig. 1.

  Figure 1: A signal flow diagram for amplitude modulation.

  

• The carrier oscillator has frequency $f_c$ and the modulating oscillator frequency is specified by $f_m$.

• A modulation index, $m$, is used to control the modulating oscillator amplitude in proportion to the unmodulated carrier oscillator amplitude $A$.

• That is, when $m = 0$, no modulation takes place. When $m = 1$, the amplitude of the modulating oscillator is equal to the unmodulated carrier amplitude, which represents 100% modulation.

• Using sinusoidal waveforms for both the carrier and modulator, the resulting AM spectrum (with $m > 0$) contains three frequencies as shown in Fig. 2: the carrier frequency ($f_c$) and two sidebands at $f_c \pm f_m$.

  Figure 2: The resulting AM spectrum using sinusoidal carrier and modulating waveforms.

  

• The modulation index controls the amplitude of each of the sideband frequencies by a factor $m/2$, but does not affect the carrier frequency amplitude.

• The perception of AM is dependent on the modulation frequency ($f_m$):
  • For $f_m$ less than about 10 Hz, the amplitude envelope variations are clearly heard.
  • For $f_m >$ 10 Hz but small enough that the sidebands fall within the same critical band, the loudness of the resulting sound is proportional to the average amplitude of the modulating waveform.
  • For an $f_m$ that exceeds one-half the critical bandwidth, the sidebands are perceived individually.