Explain modulation index for AM and peak frequency deviation for FM.

• A. For AM, m equals modulation frequency; for FM, Δf is the constant carrier deviation.
• B. For AM, m equals carrier amplitude; for FM, Δf is unrelated to modulating signal.
• C. For AM, m equals amplitude of modulating signal divided by carrier amplitude; for FM, Δf is the maximum carrier frequency deviation proportional to the modulating signal.
• D. For AM, m equals modulating frequency divided by carrier frequency; for FM, Δf is constant.

Answer: (C)

In amplitude modulation, the modulation index is the ratio of how strong the modulating signal is to the carrier signal itself. If the modulating signal has a peak amplitude Vm and the carrier has a peak amplitude Ac, then the modulation index is m = Vm / Ac. This appears in the common AM form s(t) = Ac [1 + m cos(ωm t)] cos(ωc t), where the envelope varies between Ac(1 − m) and Ac(1 + m). When m < 1 you have standard modulation without envelope distortion; if m > 1 you get over-modulation and envelope inversion.

In frequency modulation, the instantaneous frequency moves away from the carrier frequency by an amount that follows the modulating signal. The deviation from the carrier, Δf(t), is proportional to vm(t): Δf(t) = kf vm(t), where kf is the frequency sensitivity. The peak frequency deviation is Δf_peak = kf Vm for a sinusoidal modulating signal vm(t) = Vm cos(ωm t). So the frequency can swing by that maximum amount, not stay constant.

This matches the statement that AM modulation index equals Vm over Ac, and FM’s peak deviation is proportional to the modulating signal’s amplitude.