AM — Concept & Math
In FM, the message rides in the frequency of the carrier. Amplitude Modulation (AM) takes a simpler approach: the message controls the amplitude — the height — of the carrier wave. First used commercially in the 1920s, it powered the golden age of radio.
Ride the Envelope
Take a high-frequency carrier wave and scale its amplitude up and down in proportion to the message signal. The message is literally encoded in the outline — the envelope — of the transmitted waveform. A simple diode can recover it.
AM Signal
For a single-tone message x(t) = Am cos(2πfmt), the AM signal is:
Modulation Index m
The modulation index m = Am / Ac sets the depth of modulation. It controls how much the amplitude swings relative to the carrier.
Over- Modulation
When m > 1, the envelope goes negative — the carrier phase flips. This creates envelope distortion: a simple envelope detector produces a distorted, garbled output. The envelope is no longer a faithful replica of the message. m ≤ 1 is a hard constraint in standard AM.
Three Spectral Lines
Expand the AM equation and you get three frequency components: the carrier, and two sidebands offset by ±fm.
AM is Narrow
AM bandwidth is just twice the highest message frequency. For voice (3.4 kHz), BW = 6.8 kHz. This is why hundreds of AM stations can share the medium-wave band (535–1705 kHz) — each needs only a 10 kHz channel.
The Power Problem
Most transmitted power sits in the carrier — which carries no information. The total AM signal power is Ptotal = Pc(1 + m²/2). Even at 100% modulation (m = 1), only 1/3 of transmitted power is in the sidebands. The rest is wasted carrier energy.
DSB, SSB, and DSB-SC
- AM (DSB-FC) — carrier + both sidebands; simple to detect, power-inefficient
- DSB-SC — suppress the carrier; double sideband, no wasted carrier power
- SSB — transmit only one sideband; half bandwidth, best power efficiency
- VSB — vestigial sideband; compromise used in analog TV
The Envelope Detector
AM's greatest advantage: demodulation requires only a diode, capacitor, and resistor. The diode rectifies the signal, the RC network smooths it, and the envelope emerges — the recovered message. This is why cheap crystal radios work and why AM dominated for decades before transistors.
Key Takeaways
- AM encodes the message in the amplitude (envelope) of the carrier
- AM signal: s(t) = Ac[1 + m cos(2πfmt)]cos(2πfct)
- Modulation index m must stay ≤ 1 to avoid envelope distortion
- Spectrum: carrier + upper sideband + lower sideband; BW = 2fm
- Power-inefficient: 2/3 of power is in the carrier at m = 1
- SSB and DSB-SC improve efficiency by suppressing redundant components
M3-L3: AM Demodulation
We know AM is easy to demodulate — but how exactly does an envelope detector work? And how does coherent detection handle DSB-SC and SSB? Next lesson dives into the circuits and mathematics of AM recovery.