In AM, why are there two symmetric sidebands, and how does modulation index affect their amplitude distribution?

In AM, why are there two symmetric sidebands, and how does modulation index affect their amplitude distribution?

• A. Each sideband carries identical information; amplitudes scale with m; total sideband power increases with m
• B. Sidebands carry different information; amplitudes independent of m
• C. Only one sideband carries information; sidebands cancel with high m
• D. Sidebands are not related to modulation index

Answer: (A)

In AM, the carrier is multiplied by a term that contains the modulation, so the carrier’s amplitude varies with the modulating signal. For a single-tone modulating signal, the transmitted signal is Ac[1 + m cos ωm t] cos ωc t. Expanding this gives two extra frequency components: (Ac m/2) cos(ωc+ωm)t and (Ac m/2) cos(ωc−ωm)t, in addition to the original carrier term Ac cos ωc t. These are the upper and lower sidebands, and they are symmetric around the carrier. Both sidebands carry the same information because they arise from the same baseband modulation of the carrier; they are essentially two copies of the modulating signal shifted to ±ωm around the carrier. The amplitudes of these sidebands are proportional to the modulation index m, so increasing m increases each sideband’s amplitude linearly. Since power is proportional to the square of the amplitude, the total sideband power grows with m^2 (while the carrier power stays tied to the carrier term). This is why the statement that each sideband carries identical information, their amplitudes scale with m, and the total sideband power increases with m is the correct description.

In AM, the carrier is multiplied by a term that contains the modulation, so the carrier’s amplitude varies with the modulating signal. For a single-tone modulating signal, the transmitted signal is Ac[1 + m cos ωm t] cos ωc t. Expanding this gives two extra frequency components: (Ac m/2) cos(ωc+ωm)t and (Ac m/2) cos(ωc−ωm)t, in addition to the original carrier term Ac cos ωc t. These are the upper and lower sidebands, and they are symmetric around the carrier.

Both sidebands carry the same information because they arise from the same baseband modulation of the carrier; they are essentially two copies of the modulating signal shifted to ±ωm around the carrier. The amplitudes of these sidebands are proportional to the modulation index m, so increasing m increases each sideband’s amplitude linearly. Since power is proportional to the square of the amplitude, the total sideband power grows with m^2 (while the carrier power stays tied to the carrier term). This is why the statement that each sideband carries identical information, their amplitudes scale with m, and the total sideband power increases with m is the correct description.