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AM numerical: 20 sin2π500t on 60 sin2π10⁶t

Short answer

μ = Am/Ac = 20/60 = 0.333. Sidebands: 1,000,500 Hz and 999,500 Hz. Bandwidth = 2×500 = 1000 Hz. Carrier power Pc = 60²/(2×75) = 24 W. Total power Pt = 24×(1+0.333²/2) ≈ 25.33 W.

An audio frequency signal 20sin2π·500t is used for AM with a carrier of 60sin2π·10⁶t. Calculate: (a) modulation index (b) Sideband frequencies, (c) Bandwidth requirements, (d) Total power delivered with a load of 75 Ohm.

Message: Am = 20 V, fm = 500 Hz. Carrier: Ac = 60 V, fc = 10⁶ Hz = 1 MHz. R = 75 Ω.

a) Modulation index

μ = Am/Ac = 20/60 = 0.333 (33.3%)

b) Sideband frequencies

  • Upper sideband: fc + fm = 1,000,000 + 500 = 1,000,500 Hz
  • Lower sideband: fc - fm = 1,000,000 - 500 = 999,500 Hz

c) Bandwidth

BW = 2fm = 2 × 500 = 1000 Hz

d) Total power

Pc = Ac²/(2R) = 3600/150 = 24 W

Pt = Pc (1 + μ²/2) = 24 × (1 + 0.1111/2) = 24 × 1.0556 = 25.33 W

(Sideband power = 1.33 W.)

✓ Answer checked by Claude Sonnet 5.5

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