How it works
The AM signal is s(t) = A_c[1 + m_a·cos(2πf_m·t)]cos(2πf_c·t), which expands to a carrier plus two sidebands: s(t) = A_c·cos(ωct) + (m_a·A_c/2)cos((ωc+ωm)t) + (m_a·A_c/2)cos((ωc−ωm)t). Total power P_total = (A_c²/2)(1 + m_a²/2). Carrier power P_c = A_c²/2; sideband power P_sb = m_a²·A_c²/4 for both sidebands combined. Power efficiency η = P_sb/P_total = m_a²/(2 + m_a²) — at m_a = 1, efficiency is only 33.3%.
Key points to remember
Modulation index m_a = A_m/A_c; overmodulation (m_a > 1) causes envelope distortion and spectral splatter. For DSB-FC (conventional AM), bandwidth = 2f_m. For a single audio channel with f_m = 4 kHz, AM bandwidth = 8 kHz. DSB-SC eliminates the carrier (saving 67% of power at m_a = 1) but requires synchronous demodulation. SSB-SC further halves bandwidth to f_m by transmitting only one sideband. Envelope detection works for AM if m_a ≤ 1; it is simpler to implement than coherent detection but fails for DSB-SC. Figure of merit (SNR_o/SNR_i) for AM envelope detection is m_a²/(2+m_a²) at baseband.
Exam tip
Every Anna University paper asks you to find the power in each spectral component and power efficiency for a given AM signal — always split P_total into carrier and sideband components using the formula and express efficiency as a percentage.