Amplitude Modulation: AM, DSB-SC and SSB

Amplitude modulation varies the amplitude of a high-frequency carrier with the message. It is simple, and appears in GATE as power, bandwidth and receiver questions.

Conventional AM (DSB-FC)

s(t) = A_c[1 + μ cos ω_m t] cos ω_c t

• Modulation index μ = A_m/A_c (must be ≤ 1 to avoid over-modulation). From the envelope: μ = (A_max − A_min)/(A_max + A_min).
• Spectrum: carrier at f_c and sidebands at f_c ± f_m. Bandwidth = 2f_m (2W for a message of bandwidth W).
• Total power P_t = P_c(1 + μ²/2); sideband power = P_c μ²/2.
• Power efficiency η = μ²/(2 + μ²): at most 33.3% (μ = 1).
• Multiple tones: μ_t = √(μ₁² + μ₂² + …).
• Envelope detector: simple; needs μ ≤ 1 and an RC time constant with 1/f_c ≪ RC ≪ 1/W.

DSB-SC

s(t) = m(t) cos ω_c t: no carrier power wasted, bandwidth 2W. Needs coherent (synchronous) detection: multiply by a local carrier and low-pass filter. A phase error φ scales the output by cos φ (zero at 90°). Carrier recovery by squaring loop or Costas loop.

SSB and VSB

• SSB: only one sideband, bandwidth W: saves bandwidth and power. Generated by filtering or the phase-shift (Hilbert transform) method.
• VSB: one sideband plus a vestige of the other; used for TV picture signals where the message has low-frequency content.

Superheterodyne receiver

All stations are converted to a fixed intermediate frequency (IF) (455 kHz for AM broadcast).

• Local oscillator f_LO = f_s + f_IF (usually above the signal).
• Image frequency f_image = f_s + 2f_IF; it must be rejected by the RF stage.
• Image rejection ratio α = √(1 + Q²ρ²), with ρ = f_image/f_s − f_s/f_image.

Worked example

A 100 W carrier is amplitude modulated with μ = 0.5.

• P_t = 100(1 + 0.125) = 112.5 W; sideband power 12.5 W; efficiency = 12.5/112.5 = 11.1%.

Practice