In amplitude modulation, how is peak envelope power (PEP) related to carrier power and modulation index?

In amplitude modulation, how is peak envelope power (PEP) related to carrier power and modulation index?

• A. PEP = Pc(1 - m)^2
• B. PEP = Pc(1 + m)^2
• C. PEP = Pc(1 + m)
• D. PEP = Pc(1 - m^2)

Answer: (B)

Peak envelope power comes from the maximum possible amplitude of the AM signal’s envelope and the fact that power is proportional to the square of the amplitude. For a standard AM signal s(t) = Ac [1 + m cos ωm t] cos ωc t, the envelope is |Ac [1 + m cos ωm t]|. The largest envelope occurs when cos ωm t = +1, giving Emax = Ac (1 + m). Since instantaneous power is proportional to the envelope squared, PEP = (Emax^2)/(2R) = Pc (1 + m)^2, where Pc = (Ac^2)/(2R) is the carrier power. So the peak envelope power scales with (1 + m) squared. For example, if m = 0, PEP = Pc; if m = 1, PEP = 4 Pc.

Peak envelope power comes from the maximum possible amplitude of the AM signal’s envelope and the fact that power is proportional to the square of the amplitude. For a standard AM signal s(t) = Ac [1 + m cos ωm t] cos ωc t, the envelope is |Ac [1 + m cos ωm t]|. The largest envelope occurs when cos ωm t = +1, giving Emax = Ac (1 + m). Since instantaneous power is proportional to the envelope squared, PEP = (Emax^2)/(2R) = Pc (1 + m)^2, where Pc = (Ac^2)/(2R) is the carrier power. So the peak envelope power scales with (1 + m) squared. For example, if m = 0, PEP = Pc; if m = 1, PEP = 4 Pc.