CM · Modulation basics

Amplitude Modulation

Ride the message on the carrier’s amplitude and the waveform’s envelope becomes the message itself. Learn the condition for a faithful envelope — why the modulation index m must not exceed 1.

Does the envelope track the message?

Sweep the modulation index m. The envelope (gold dashed) traces the message faithfully — until m passes 1, where it folds through zero and distorts.

Modulation index mm = 1.30

Sweep the index with the slider. m = 1 is the boundary.

Envelope at the present index

s(t) = [1 + m cos(ωm t)] cos(ωc t)

Overmodulated · distorted

The message rides the amplitude

The carrier cos(ωc t) is a fast-oscillating courier. Swell its amplitude up and down with the message, and the curve tracing the tops of the fast oscillation — the envelope — draws the slow message exactly. A receiver recovers the message simply by extracting this envelope.

The index m sets the depth

In s(t) = [1 + m cos(ωm t)] cos(ωc t), m is how deeply the amplitude swings. Small m makes the envelope ripple only slightly, carrying a faint message; m near 1 lets the amplitude dip almost to zero and rise to double. Measured from the peak Amax and trough Amin, m = (Amax − Amin)/(Amax + Amin).

Observes(t) = [1 + m cos(ωm t)] cos(ωc t)

The message rides in the envelope.

Choosem = (Amax − Amin) / (?)

The index is read from peak and trough.

Overmodulation and bandwidth

When m exceeds 1, there are stretches where 1 + m cos(ωm t) goes negative. The envelope folds through zero and flips top-for-bottom, so a simple envelope detector misreads the message. This is overmodulation. Meanwhile the multiplication shifts the message to both sides of ωc, making two sidebands, so AM’s bandwidth is twice the message bandwidth, B = 2 fm.

Fill inm ? 1

No fold requires m ≤ 1.

On your ownB = ?

Two sidebands → bandwidth is twice the message.

Back to the first screen

As you raised the index the envelope swung ever deeper and drew the message clearly, and the instant m passed 1 the envelope punched through zero, folded, and distorted in red. Between 0.45 and 1 it tracked the message faithfully and turned gold. The one thing to hear in AM is this: the message lives in the amplitude’s envelope, and that envelope equals the message only while m ≤ 1.

Amplitude modulation (AM) rides the message on the carrier’s amplitude, forming s(t) = [1 + m cos(ωm t)] cos(ωc t). The waveform’s envelope is the message, and only when the modulation index m ≤ 1 does the envelope stay above zero and hold the message faithfully. m > 1 is overmodulation, where the envelope folds and distorts. The bandwidth, from two sidebands, is B = 2 fm.

In the next unit

AM puts the message in the amplitude, which makes it fragile to noise — noise jostles the amplitude and the envelope is immediately fouled. Next, FM rides the message on the carrier’s instantaneous frequency instead, trading more bandwidth for resistance to noise.