AM / FM Modulation
Amplitude and frequency modulation — carrier, message and modulated waveforms with live spectrum
Mode
Parameters
Live Metrics
Formula
Sidebands at fc±fm, amplitude m/2.
Bandwidth = 2·fm
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 fc 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 fc ± n·fm.
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.
About AM/FM Modulation Simulator
This simulation models two fundamental techniques of analogue radio communication: Amplitude Modulation (AM) and Frequency Modulation (FM). In AM, the carrier wave's amplitude is varied in proportion to the message signal, while in FM the carrier's instantaneous frequency deviates above and below its centre frequency. Users can observe the carrier, message and modulated waveforms simultaneously alongside a live frequency-domain spectrum showing sidebands.
AM broadcasting dates to the early 1900s and still covers long distances via ionospheric sky-wave propagation. FM, patented by Edwin Armstrong in 1933, trades bandwidth for dramatically better noise immunity and is the basis of modern FM radio, stereo hi-fi, and many wireless data links.
Frequently Asked Questions
What is amplitude modulation (AM)?
Amplitude modulation is a technique in which the amplitude of a high-frequency carrier wave is varied in proportion to a lower-frequency message signal. The carrier frequency remains constant while its peak amplitude rises and falls, encoding the message as an envelope around the carrier. The modulated signal can be expressed as s(t) = Ac[1 + m·cos(2πfmt)]·cos(2πfct), where m is the modulation index.
What is frequency modulation (FM) and how does it differ from AM?
Frequency modulation varies the instantaneous frequency of the carrier rather than its amplitude; the carrier's amplitude stays constant throughout. The FM signal is expressed as s(t) = Ac·cos(2πfct + β·sin(2πfmt)), where β is the modulation index (ratio of frequency deviation to message frequency). This makes FM far more resistant to amplitude-based noise such as electrical interference, at the cost of occupying a wider bandwidth than AM.
How do I use this simulation to see AM and FM sidebands?
Select AM or FM using the mode buttons at the top of the controls panel. Adjust the carrier frequency fc and message frequency fm sliders to set the signal parameters, then watch the Frequency Spectrum canvas update in real time. In AM mode you will see one sideband pair at fc ± fm; raising the modulation index slider increases the sideband amplitude. In FM mode, increasing the modulation index β generates progressively more sideband pairs, each weighted by Bessel functions Jn(β).
What is the modulation index and why does it matter?
The modulation index m (AM) or β (FM) quantifies the depth or extent of modulation. In AM, m = 1 corresponds to 100% modulation — the amplitude just touches zero on negative message peaks — and values above 1 cause over-modulation, introducing distortion sidebands at fc ± 2fm, 3fm, etc. In FM, β = Δf / fm determines how many significant sidebands exist: at β = 0.5 only a few sidebands matter, but at β = 5 energy spreads across many pairs, each governed by the Bessel function Jn(β) — the FM spectrum becomes rich and wide.
How is FM broadcast radio bandwidth calculated?
Engineers use Carson's rule to estimate the 98%-power bandwidth of an FM signal: BW ≈ 2(β + 1)fm. Broadcast FM stations use a maximum frequency deviation of Δf = 75 kHz and audio up to fm = 15 kHz, giving β = 5 and BW ≈ 2×6×15 kHz = 180 kHz per channel. Stations are spaced 200 kHz apart in most regions (100 kHz in the US), keeping adjacent channels from overlapping. This simulator computes the same formula live as you drag the sliders.
Why is FM less noisy than AM?
Most natural and electrical noise acts by randomly altering signal amplitude, which is exactly what AM uses to encode information; the receiver cannot distinguish noise from the intended message. FM encodes information in frequency, so any amplitude variations introduced by noise are simply stripped away by a limiter stage in the FM receiver before demodulation. This noise rejection property, called the FM capture effect, is why FM audio sounds cleaner than AM even at the same transmitter power, though it only applies once the signal exceeds a threshold above the noise floor.
Who invented FM radio and when?
Edwin Howard Armstrong, an American electrical engineer, invented wideband FM radio and filed his key patent in 1933. He built the first experimental FM station (W2XMN in Alpine, New Jersey) in 1939 and demonstrated dramatically superior audio quality compared to AM. His work faced fierce opposition from RCA, whose AM broadcasting empire would be threatened, and from David Sarnoff, despite Armstrong's earlier collaboration with him. Armstrong died in 1954 without seeing FM radio achieve its commercial dominance; FM surpassed AM in US radio listenership during the 1970s-1980s.
What are sidebands and why do they appear in modulated signals?
Sidebands are additional frequency components created whenever two sinusoids interact through modulation. Mathematically, multiplying the carrier cos(2πfct) by the message cos(2πfmt) produces sum and difference frequencies at fc+fm and fc-fm via the product-to-sum identity. FM generates infinitely many sidebands in principle, but only those with Bessel coefficient |Jn(β)| > 0.01 carry significant power. Sidebands are both the mechanism by which a receiver extracts the original message and the reason modulated signals occupy more bandwidth than a pure carrier.
How is AM/FM modulation used in engineering today?
AM remains in use for medium-wave and short-wave broadcasting because sky-wave propagation enables continent-spanning coverage from a single transmitter, and because simple envelope-detector receivers require minimal circuitry. FM is used for high-fidelity audio broadcasting (88–108 MHz), two-way radio communications, analogue TV audio subcarriers, and as the basis of many wireless sensor and telemetry links. FM principles also underpin frequency-shift keying (FSK) and Gaussian minimum-shift keying (GMSK), which transmit digital data in Bluetooth, GSM, and RFID systems.
What advanced modulation schemes are built on AM and FM concepts?
Modern digital communications extend these classic techniques into schemes such as quadrature amplitude modulation (QAM), which simultaneously varies both amplitude and phase to encode multiple bits per symbol, achieving high spectral efficiency in Wi-Fi (802.11ax uses 1024-QAM) and 5G NR. OFDM (Orthogonal Frequency Division Multiplexing) combines hundreds of narrow AM subcarriers to handle multipath fading. Direct digital synthesis (DDS) chips generate software-defined AM or FM signals with programmable parameters, enabling the software-defined radio (SDR) platforms used in research, satellite communications, and spectrum monitoring today.