CM · Modulation basics

Amplitude Modulation

AM loads the message onto the carrier's amplitude, so the envelope that joins the peaks of the waveform is the message itself. This unit covers what it takes for the envelope to follow the message faithfully, and why the modulation index m must not exceed 1.

Does the envelope follow the message?

The blue trace is the rapidly oscillating carrier, and the dashed gold curves hugging it above and below are the envelope. Lowering and raising the modulation index m changes how deeply the envelope swings with the message. The moment m passes 1, the envelope folds below 0, and that stretch turns into a solid red line.

Modulation index mm = 1.30

m = 1 is the boundary. The starting value is above it, an overmodulated state, so part of the envelope shows red.

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 oscillation that carries the message along. Swell and shrink its amplitude in step with the message, and the curve joining the peaks of that fast oscillation, the envelope, draws the shape of the slow message. A receiver only has to pick off the envelope to recover the message, and a simple envelope detector built around a single diode does the job.

The modulation index m sets the depth of the swing

In s(t) = [1 + m cos(ωm t)] cos(ωc t), m tells how deeply the amplitude swings. With a small m the envelope barely moves and the message rides along weakly; as m approaches 1 the amplitude dips almost to 0 and then climbs to twice its resting value. Working backward, measure the envelope's peak height Amax and trough height Amin in the plot, and m = (Amax − Amin)/(Amax + Amin) gives the index.

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

The message rides on the envelope.

Choosem = (Amax − Amin) / (?)

The modulation index is measured from the envelope's peaks and troughs.

Overmodulation and bandwidth

Once m passes 1, 1 + m cos(ωm t) goes negative over part of each cycle. There the envelope punches through 0 and folds over to the other side, flipping top and bottom; that is the stretch drawn as a solid red line. An envelope detector cannot tell the flipped shape apart, so it reads a distorted message, and this is called overmodulation. Meanwhile, the multiplication places one copy of the message spectrum on each side of the carrier, creating two sidebands, so the bandwidth of AM is twice the message bandwidth, B = 2 fm.

Fill inm ? 1

For the envelope not to fold, m ≤ 1 must hold.

On your ownB = ?

Two sidebands → bandwidth is twice the message's.

Back to the first screen

As you raised the index, the envelope swung deeper and drew the message more clearly, and once m passed 1 the envelope punched through 0, folded, and that stretch turned red. Between 0.45 and 1 the envelope followed the message faithfully, and the meter pointed to gold. One thing to remember from AM: the message lives in the amplitude envelope, and that envelope has the message's shape only when m ≤ 1.

Amplitude modulation (AM) loads the message onto the carrier's amplitude, producing s(t) = [1 + m cos(ωm t)] cos(ωc t). The waveform's envelope is the message, and only when the modulation index satisfies m ≤ 1 does the envelope stay above 0 and hold the message intact. m > 1 is overmodulation, where the envelope folds and distorts. With two sidebands, the bandwidth is B = 2 fm.

In the next unit

Because AM puts the message in the amplitude, it is vulnerable to noise: any noise that shakes the amplitude dirties the envelope at once. The next unit, FM, loads the message onto the carrier's instantaneous frequency instead, trading extra bandwidth for strong resistance to noise.