AM / FM Modulation

Amplitude and frequency modulation — carrier, message and modulated waveforms with live spectrum

Message Signal m(t) = cos(2π·f_m·t)

Carrier Signal c(t) = A_c·cos(2π·f_c·t)

AM Output s(t) = A_c(1+m·msg)·cos(ω_ct)

Frequency Spectrum |S(f)| — sidebands

Mode

Message

Carrier

Modulated

Parameters

Carrier freq f_c200 Hz

Message freq f_m20 Hz

Mod. index m0.80

Live Metrics

200

f_c (Hz)

f_m (Hz)

—

Bandwidth

0.80

Mod. index

Formula

AM: s(t) = A_c[1 + m·cos(ω_mt)] · cos(ω_ct)
Sidebands at f_c±f_m, amplitude m/2.
Bandwidth = 2·f_m

About AM/FM Modulation

What It Demonstrates

In AM (Amplitude Modulation) the carrier's amplitude varies in proportion to the message signal — the classic technique used in medium-wave radio broadcasting. In FM (Frequency Modulation) the carrier's instantaneous frequency swings above and below f_c by an amount proportional to the message, giving better noise immunity and the richer audio of FM radio (88–108 MHz).

How to Use

Switch between AM and FM with the mode buttons. Drag the carrier and message frequency sliders to separate or overlap the waveforms. The modulation index slider controls depth: in AM, m > 1 causes over-modulation (distortion); in FM, larger β produces more sidebands. Watch the frequency spectrum update — sidebands appear at f_c ± n·f_m.

Did You Know?

Edwin Armstrong invented FM radio in 1933, patenting it against fierce opposition from RCA. FM's bandwidth is 200 kHz per channel — 100× wider than AM — yet it rejects static almost completely, because noise adds amplitude (AM-like) not frequency. The BBC switched its national networks to FM in the 1970s; AM transmitters are still used today for long-distance coverage via ionospheric sky-wave propagation.