Skip to main content

AM numerical: 10 sin1000πt on 50 sin 2π×10⁵t

Short answer

From message 10sin1000πt and carrier 50sin2π×10⁵t, Am=10 V, Ac=50 V, fm=500 Hz. Modulation index μ=Am/Ac=0.2. Bandwidth=2fm=1 kHz. Carrier power Pc=Ac²/(2×60Ω)=20.83 W; total power Pt=Pc(1+μ²/2)=21.25 W.

An audio frequency signal 10 sin1000πt is used for single tone amplitude modulation with a carrier of 50 sin2π×10⁵t. Calculate: (i) Modulation index (ii) Bandwidth requirement (iii) Total power delivered if load = 60 Ω

Compare with the standard forms: message m(t) = Am sin(ωmt), carrier c(t) = Ac sin(ωct).

  • Am = 10 V, ωm = 1000π, so fm = 1000π/2π = 500 Hz
  • Ac = 50 V, ωc = 2π×10⁵, so fc = 100 kHz
  • R = 60 Ω

(i) Modulation index

μ = Am/Ac = 10/50 = 0.2 (20%)

(ii) Bandwidth

BW = 2fm = 2 × 500 = 1000 Hz = 1 kHz (the sidebands are at 99.5 kHz and 100.5 kHz)

(iii) Total power

Carrier power Pc = Ac²/(2R) = 2500/120 = 20.83 W

Pt = Pc (1 + μ²/2) = 20.83 × (1 + 0.04/2) = 20.83 × 1.02 = 21.25 W

(Sideband power = 0.417 W.)

✓ Answer checked by Claude Sonnet 5.5

Related questions

All Data Communication chapter 5 questions →